Mössbauer Spectroscopy on rare Earth-Based Oxides

Mössbauer Spectroscopy on rare Earth-Based Oxides

Chapter 3 Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides P.C.M. Gubbens1 Delft University of Technology, Delft, The Netherlands 1 Corresponding a...

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Chapter 3

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides P.C.M. Gubbens1 Delft University of Technology, Delft, The Netherlands 1 Corresponding author: E-mail: [email protected]

Chapter Outline 1. Introduction 2. Rare Earth Mo¨ssbauer Spectroscopy and Methodology 2.1 The Recoilless Fraction 2.2 Nuclear Energy Levels 2.2.1 Isomer Shift 2.2.2 Electric Quadrupole Interaction 2.2.3 Magnetic Hyperfine Interaction 2.2.4 Line Positions and Intensities 2.3 Methodology of Rare Earth Mo¨ssbauer Spectroscopy 3. Theoretical Aspects 3.1 Introduction 3.2 Crystal Fields 3.3 Magnetic Interaction

145

147 147 147 147 148 148 149 149 153 153 153 156

3.4 Relation to Mo¨ssbauer Parameters 3.5 Magnetic Relaxation 3.6 Analysis Procedure: Examples 3.6.1 TmBa2Cu3O7  x 3.6.2 Yb2Ti2O7 4. Overview of Rare Earth-Based Oxides 4.1 Introduction 4.2 R2O3 Compounds 4.3 RMO3 Compounds 4.4 RMO4 Compounds 4.5 RBa2Cu3O7 Compounds 4.6 R2BaMO5 Compounds 4.7 R2M2O7 Compounds 4.8 R3M5O12 Compounds 5. Conclusions, Justification, and Acknowledgment References

160 163 165 165 169 171 171 171 175 182 194 206 215 225 229 231

1. INTRODUCTION The Mo¨ssbauer effect, discovered in 1958 by R.L. Mo¨ssbauer, has become a powerful nuclear measuring technique in different branches of physics, chemistry, biology, geology, and materials science. He discovered that nuclei Handbook of Magnetic Materials, Vol. 25. http://dx.doi.org/10.1016/bs.hmm.2016.10.001 Copyright © 2016 Elsevier B.V. All rights reserved.

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146 Handbook of Magnetic Materials

imbedded in solids can show recoilless absorption and emission of radiation. The bond of the nuclei with the solid results in quantization of the recoil energy and therefore a part of the nuclei, the recoilless fraction, shows a zero recoil energy. This phenomenon made resonant absorption of nuclear radiation possible and small variations in the nuclear levels could be studied. Detailed descriptions of the technique are published in a lot of standard works (Frauenfelder, 1962; Goldanskii and Herber, 1968; May, 1971; Wegener, 1964; Wertheim, 1964). First rare earth studies were already performed in the sixties and seventies of the 20th century. The Mo¨ssbauer technique gives information about crystal field effects and magnetic ordering, indirectly, by measuring the electric quadrupole-splitting and the magnetic hyperfine field. The studies are relevant for magnetic materials, superconductors, minerals, and chemical rare earth complexes. This paper will survey the results of rare earth-based oxides studied with rare earth Mo¨ssbauer spectroscopy. The emphasis will be mainly on the nuclei 141 Pr, 155Gd, 161Dy, 166Er, 169Tm, and 170Yb. In this chapter of the Hand book of Magnetic Materials a survey of the different magnetic aspects of the rare earth insulator compounds will be given. Only in the case of Gd, Tm, and Yb Mo¨ssbauer spectroscopy a clear quadrupole-splitting above the magnetic ordering temperature is found. Below the magnetic ordering a clear quadrupole-splitting is also found in Dy and Er Mo¨ssbauer spectroscopy. An overview of all these Mo¨ssbauer nuclei will be given in Chapter 2. Mo¨ssbauer spectroscopy is a very sensitive tool and selective for crystallographically different rare earth atoms. If the total angular momentum of a rare earth is an integer, the ground state of the rare earth atom shows a larger variety in ground-state level than in the case of a half integer total angular momentum, which consists only of Kramers doublets. Then, below and above the magnetic ordering temperature crystal field levels consisting of singlets, doublets give a large variety of physical behavior. This depends mainly on the local symmetry of the rare earth atom. In general, one derives from the hyperfine field and the electric quadrupole-splitting the physical behavior of the ground state at low temperature. At higher temperatures the magnitude of the hyperfine field and the quadrupolesplitting are proportional to the Boltzman distribution over the energy levels of the crystal field. So far, more extended publications on this topic were published as invited papers by Gubbens et al. (1985a, 1985b, 1990), Stewart (1994), Gubbens and Mulders (1998) and Stewart (2010). An extended overview on rare earth Mo¨ssbauer spectroscopy on intermetallic rare earth compounds is published by Gubbens (2012). Two papers concerning a theoretical fundamental explanation and interpretation of 169Tm Mo¨ssbauer spectra in terms of crystal fields were published by Stewart (1985) and Stewart and Gubbens (1999).

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¨ SSBAUER SPECTROSCOPY AND 2. RARE EARTH MO METHODOLOGY 2.1 The Recoilless Fraction The Mo¨ssbauer effect is based on resonant absorption of gamma radiation by atomic nuclei. In the process of emission and absorption of gamma radiation, energy as well momentum conservation have to be obeyed. The line width G of the Mo¨ssbauer resonance is equal to G ¼ Z=s where s is the half-life of the excited nuclear level. s can take values from 1 to 100 ns, corresponding to G values between 0.01 and 1 meV. When a nucleus of a single atom initially at rest emits a photon, it will obtain the same momentum of opposite sign. Then there is a recoil energy ðR ¼ E02 =2mc2 Þ of the order of 102 eV, which is at least four orders of magnitude larger than an average line width of the nuclear energy levels involved. However, when the nucleus is embedded in a solid, the momentum to the solid is quantized via the phonon excitations. Phonon quantizations in solids can amount to 102 eV, comparable with the recoil energy. Therefore, for a certain fraction of photons, the emission and absorption will occur without energy loss due to the fact that the momentum is transferred to the whole crystal with a large mass and the recoil energy is zero.

2.2 Nuclear Energy Levels The hyperfine splitting of the energy levels of the nuclei is determined by the following Hamiltonian H hf ¼ H e þ H m of which H e represents the electrostatic interaction and H m the magnetic interaction of the nucleus. The electrostatic part of the Hamiltonian H e consists of a “dipole” and a “quadrupole” part giving rise to the Isomer Shift and to the Electric Quadrupole Interaction, respectively.

2.2.1 Isomer Shift The Isomer Shift (IS), the first parameter, is unique for Mo¨ssbauer spectroscopy and is sensitive to the electronic charge density around the nucleus, that is, it gives a value that is mainly proportional to the valency of the atom. The Isomer Shift is expressed in mm/s and it has the form:    2  D 2 E 2pcZe2  re  rg IS ¼ jA ð0Þ2   jS ð0Þ2  (1) 3Eg In Eq. (1), c is the speed of light, Ze the nuclear charge, Eg the energy of 2 i the averaged nuclear radii of the excited and the Mo¨ssbauer resonance, hre;g ground state, respectively, and ejjA,S(0)2j the electronic charge density at the nucleus of the absorber (A) and the source (S).

148 Handbook of Magnetic Materials

2.2.2 Electric Quadrupole Interaction The second contribution to the electrostatic part of the Hamiltonian is the electric quadrupole interaction, which is associated with the nonspherical charge distribution around the nucleus. For a level of nuclear spin I, the interaction between the quadrupole moment of the nucleus (Q) and the electric field gradient tensor (Vii with i ¼ x, y and z) is given by the Hamiltonian  i eQVzz h 2 H e;q ¼ (2) 3Iz IðI  1Þ þ h I2x  I2y 4Ið2I  1Þ   with the asymmetry parameter h ¼ Vxx  Vyy =Vzz. In this equation Vxx, Vyy and Vzz are the nonzero electric field gradient tensor elements expressed with respect to the principal x, y and z axes and h is the electric field gradient tensor asymmetry parameter (h ¼ 0 for axial asymmetry along the z axis). In the case of 169Tm Mo¨ssbauer spectroscopy, only the excited state I ¼ 3/2 level has a nonzero quadrupole moment. In the absence of a magnetic hyperfine field, this level is split into two levels resulting in a simple doublet spectrum.   1 1 2 1=2 (3) DEQ ¼ eQVzz 1 þ h 2 3

2.2.3 Magnetic Hyperfine Interaction The magnetic part of the Hamiltonian characterizes the magnetic hyperfine field at the nuclear site. The degeneracy of the nuclear levels is lifted by the so-called Zeeman splitting. The magnetic hyperfine field interaction is then given by Hm ¼ gN mN I$Heff

(4)

where gN is the nuclear g-factor, mN the nuclear magneton, and I the nuclear spin operator. For 169Tm the nuclear ground-state moment mg ¼ 0.231 mN and the moment ratio between excited and ground states me/mg ¼ 2.223 as found by Wit and Niesen (1976). For the ground nuclear spin operator, one has Ig ¼ 1/2 and for the excited nuclear spin operator Ie ¼ 3/2. The magnetic hyperfine field is composed of several contributions: Heff ¼ HJ þ HFC þ HD þ HTR þ Happ :

(5)

HJ is the total angular moment and by far the largest contribution, HFC is the Fermi contact interaction term, HD the dipolar field, HTR the transferred hyperfine field, and Happ the external field. HD and HTR are for rare earth very small and can be neglected.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

The 4f total angular magnetic moment gives rise to a field

1 HJ ¼ 2mB 3 hJi r

149

(6)

A much less important contribution is the Fermi contact interaction, which originates from the spin polarization of the electrons at the nuclear site: HFC ¼ 

8p m hSz i; 3 B

(7)

where mB is the Bohr magneton and hSzi the spin polarization around the nucleus. This spin polarization can be divided into two contributions originating from the core s-electrons and from the valence electrons. 2.2.4 Line Positions and Intensities By combining the electric quadrupolar and magnetic interactions of the hyperfine Hamiltonian H hf ¼ H e þ H m , one composes a total Mo¨ssbauer spectrum. H hf has specific eigenvalues and energy levels, which lead to a number of transitions between the nuclear levels and the transition probabilities between these levels, given by the ClebscheGordan coefficients. As shown in Tables 1 and 2, the multipolarity of the Mo¨ssbauer nucleus gives the rules for the allowed transitions. In the case of M1 and E1, it is DM or DE ¼ 0, 1. In the case of E2, it is DE ¼ 0, 1, 2.

2.3 Methodology of Rare Earth Mo¨ssbauer Spectroscopy In Tables 1 and 2, eight rare earth Mo¨ssbauer resonances are listed, which are amendable to material research. In Table 1 the sources are listed, which can be used at room temperature. The resonance energy is then low enough to have a recoilless fraction. A material under study with these sources can be measured at least up to room temperature, in the case of 169Tm due to its low energy even up to 2000K. The sources tabulated in Table 2 can only be used at low temperatures due to their high energy. In this case to achieve a recoilless fraction, both source and absorber have to be cooled down to helium temperatures. In the case of 166Er (80.56 keV), shown in Table 2, the highest temperature, where the nuclear resonance is observable, is about 100K. With exception of 149Sm, all the sources for these nuclei can be made in a reactor via neutron irradiation. The source (149Eu) for 149Sm has to be made with proton irradiation (150Sm þ pþ ¼ 149Eu þ 2n). The source for 151Eu, which has a very long halflife time of 87 year, is commercially available. As an example the energy spectrum of the 169ErAl9 as source of 169Tm is given in the overview paper of Gubbens (2012). The main applications of the Mo¨ssbauer effect in these nuclei is also given in Tables 1 and 2. In Fig. 1, a schematic representation is given of the pure electric quadrupole-splitting and this parameter as a perturbation on

Isotope

149

Ie and Ig

5/2 and 7/2

7/2 and 5/2

5/2 and 5/2

3/2 and 1/2

Multipolarity

M1

M1

E1

M1

Energy (keV)

22.49

21.53

25.66

8.40

Qe and Qg (barn)

0.51 and 0.058

1.48 and 1.14

2.35 and 2.35

1.20 and 0

me and mg (mN)

0.67 and 0.72

3.47 and 4.64

0.48 and 0.39

0.23 and 0.10

Parent activity

149

151

161

169

Half-life

106d

87y

6.9d

9.4d

Raw source material

150

150

160

Activation

(p,2n)

(n,g)

(n,g)

(n,g)

Natural line width (mm/s)

1.71

1.30

0.38

8.33

Application

IS and Heff

IS and Heff

IS, QS and Heff

QS and Heff

Sm

Eu

Sm2O3

151

Eu

Sm

SmF3

161

169

Dy

Tb

Gd162 0.5

Dy0.5F3

168

Tm

Er

ErAl3-Al

Ie and Ig are the nuclar spin operators of excited and ground states. Multipolarity indicates the character of the transitions between the nuclear levels. Qe and Qg are the quadrupole moments and me and mg are the magnetic moments of the excited and ground states.

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TABLE 1 Relevant Parameters of Rare Earth Nuclei With Mo¨ssbauer Effect Possible at Room Temperature

Isotope

141

Ie and Ig

7/2 and 5/2

5/2 and 3/2

2 and 0

2 and 0

Multipolarity

M1

E1

E2

E2

Energy (keV)

145.4

86.54

80.56

84.25

Qe and Qg (barn)

0.28? and 0.059

z01.30

1.59 and 0

2.14 and 0

Pr

155

Gd

166

Er

170

Yb

me and mg (mN)

2.80 and 4.28

0.515 and 0.254

0.63 and 0

0.67 and 0

Parent activity

141

155

166

170

Half-life

32.5d

1.81y

27h

130d

Raw source material

CeF3

154

HoPd3/(Ho,Y)H2

TmB12

Activation

(n,g)

(n,g)

(n,g)

(n,g)

Natural line width (mm/s)

1.02

0.5

1.89

2.03

Application

IS and Heff

IS, QS and Heff

QS and Heff

QS and Heff

Ce

Eu

SmPd3

Ho

Tm

Ie and Ig are the nuclear spin operators of excited and ground states. Multipolarity indicates the character of the transitions between the nuclear levels. Qe and Qg are the quadrupole moments and me and mg are the magnetic moments of the excited and ground states.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

TABLE 2 Relevant Parameters of Rare Earth Nuclei With Mo¨ssbauer Effect, for Which Helium Temperatures are Required

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FIGURE 1 Mo¨ssbauer spectra for the pure electric quadrupole interaction (lower spectrum of each pair) and for coaxial quadrupole and magnetic hyperfine interactions (upper spectrum of each pair). Unless indicated otherwise, the spectra are for the trivalent ions. They are based on values close to the free ion values. This figure has been taken from Stewart, G.A., 1994. Mater. Forum 18, 177.

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the hyperfine field. More details of this paragraph can be found in the publication of Gubbens (2012).

3. THEORETICAL ASPECTS 3.1 Introduction In the rare elements the incomplete 4f shell, which becomes more and more filled going from La to Lu, is responsible for their magnetic properties. Most rare earths have three conduction electrons. These electrons have either 5d or 6s character and are mainly delocalized. On the other hand, the 4f electrons remain localized deep in the electron shell and there is in general no overlap between the 4f wave functions of two neighboring atoms. The “normal” electronic configuration of rare earths in the metallic state is then4fn5d16s2. In Tm, n ¼ 12. Since 4f electrons are deeply embedded in the electron cloud, electrical fields are rather small and the spin orbit coupling is not broken up as in the case of the 3d metals. Spin, orbital, and total angular moments, present in rare earths, are determined by Hund’s rules. For trivalent rare pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi earths the magnetic moment is proportional to gJ mB JðJ þ 1Þ in the paramagnetic and to gJJmB in the magnetically ordered state. Tm has a 3H6 multiplet ground state. This means that S ¼ 1, L ¼ 5 and J ¼ 6. Since gJ ¼ 7/ 6, the free-ion value of the magnetic moment in the paramagnetic phase is 7.57 mB and in the magnetically ordered state 6 mB. The relevant parameters of the other rare earths are tabulated in Table 3. The dominant terms in the Hamiltonian, which describes the magnetic properties of rare earth atoms is usually presented as H ¼H

cf

þH

(8)

mag

where the term H cf represents the crystal field interaction and H scribes the magnetic exchange interaction.

mag

de-

3.2 Crystal Fields A rare earth atom in a crystal is situated in a potential field (electric field gradient). The crystalline field arises from the electric charges on the neighboring atoms. This potential partially lifts the (2J þ 1) degeneracy of the ground state multiplet levels of the 4f electrons of the rare earths. Since the 4f electrons are deeply embedded in the electron cloud, in general, the splittings due to the potential are much smaller than the multiplet separations. This means that there is no mixing of multiplets. The number of singlets and doublets is depending on the symmetry of the crystal field. Rare earths with a

154 Handbook of Magnetic Materials

TABLE 3 Selected Ionic Properties of Trivalent Rare Earth R

Ground Term

S

L

J

gJ

gJ[J(J þ 1)]1/2

gJ J

S0

0

0

0

e

0

0

F3/2

1/2

3

5/2

6/7

2.54

2.14

H4

1

5

4

4/5

3.58

3.20

I9/2

3/2

6

9/2

8/11

3.62

3.28

H5/2

5/2

5

5/2

2/7

0.84

0.72

F0

3

3

0

0

0

0

S7/2

7/2

0

7/2

2

7.94

7

F6

3

3

6

3/2

9.72

9

H15/2

5/2

5

15/2

4/3

10.63

10

I8

2

6

8

5/4

10.60

10

I15/2

3/2

6

15/2

6/5

9.59

9

H6

1

5

6

7/6

7.57

7

F7/2

1/2

3

7/2

8/7

4.54

4

S0

0

0

0

e

0

0

La

1

Ce

2

Pr

3

Nd

4

Sm

6

Eu

7

Gd

8

Tb

7

Dy

6

Ho

5

Er

4

Tm

3

Yb

2

Lu

1

For symbols refer to the text.

higher symmetry have more unsplit levels. Since the charges are distributed in a nonspherical way, there will be a preferential orientation of the 4f shell resulting in an electric field gradient at the 4f site. In this description of the socalled crystal field effects an interaction Hamitonian is introduced, describing the electric characteristics of the 4f shell by Stevens (1952). The crystal field Hamiltonian of a rare earth atom can be described by the Eq. (9) X X m m H cf ¼ Bm qn hr n iAm (9) n On ¼ n On m;n

where Om n erators Jz,

m;n

are operator equivalents (polynomials of the angular moment opn m J2, Jþ and J) and Bm n ¼ qn hr iAn . In this equation, qn represents the Stevens constants aJ, bJ and gJ for n ¼ 2, 4, and 6, respectively. The symbol hrni represents the nth power of the radial integrals of the 4f shell as calculated by Freeman and Desclaux (1979). Am n are the crystal field potentials. In Table 4, Stevens constants of all the rare earth are tabulated. The aJ is the most dominant Stevens constant. The sign and magnitude of aJ determines for

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TABLE 4 The Total Angular Momentum Parameters of Trivalent Rare Earth R

J

aJ hr 2 ið103 a20 Þ

bJ hr 4 ið104 a40 Þ

gJ hr 6 ið106 a60 Þ

Ce

5/2

74.8

þ251.7

0

Pr

4

25.54

24.95

þ1141.66

Nd

9/2

7.161

8.471

570.96

Sm

5/2

þ40.209

þ56.527

0

Gd

7/2

0

0

0

Tb

6

8.303

þ2.101

7.683

Dy

15/2

5.020

0.891

þ6.260

Ho

8

1.676

0.459

6.959

Er

15/2

þ1.831

þ0.564

þ9.969

Tm

6

þ6.976

þ1.916

24.33

Yb

7/2

þ21.04

18.857

581.94

The Stevens factors and its multiplication with the radial integrals of the 4f shell are given. The last 2 values were taken from Freeman and Desclaux (1979). Note that a2 ¼ 3:571  A , 4

6

6   a4 0 ¼ 12:751 A , and a0 ¼ 45:541 A Bnm and the crystal field potentials Am n.

0

. These values interconnect the crystal field parameters

the second order the shape of the potential of the 4f shell: for aJ > 0, it has a cigar shape and for aJ < 0, it has a disc shape. For Sm, Er, Tm, and Yb, aJ is positive, while for Pr, Nd, Tb, Dy, and Ho, it is negative. For Gd, aJ ¼ 0. If there is a center of inversion for the local symmetry, m and n are even. For rare earth atoms, there are no Bm n with m and n larger than 6. In the Hamiltonian for cubic symmetry with z chosen in the (001) direction:



(10) H cf ¼ B4 O04 þ 5O44 þ B6 O06  21O46 For hexagonal local point symmetry: H

cf

0 0 0 6 6 ¼ B02 O02 þ BO 4 O4 þ B6 O6 þ B6 O6

(11)

For trigonal local point symmetry: H

cf

¼ B02 O02 þ B04 O04 þ B34 O34 þ B06 O06 þ B36 O36 þ B66 O66

(12)

For tetragonal local point symmetry: H

cf

¼ B02 O02 þ B04 O04 þ B44 O44 þ B06 O06 þ B46 O46

(13)

In all these cases the asymmetry parameter of the Mo¨ssbauer effect h ¼ B22 =B02 ¼ 0, while the principal axis of the electric field gradient is parallel to the crystallographic c axis as main axis.

156 Handbook of Magnetic Materials

For orthorhombic symmetry: H

cf

¼ B02 O02 þ B22 O22 þ B04 O04 þ B24 O24 þ B44 O44 þ B06 O06 þ B26 O26 þ B46 O46 þ B66 O66

(14)

In this case the asymmetry parameter h s 0. The principal axes are orthogonal. They can potentially be relabeled. Also for lower symmetries like monoclinic and triclinic the asymmetry parameter h s 0, but the main crystallographic axes are not orthogonal. For a locally monoclinic symmetry the crystal field Hamiltonian has the form: H

cf

2 0 0 2 2 2 2 ¼ B02 O02 þ B22 O22 þ B2 2 O2 ðrank 2Þ þ B4 O4 þ B4 O4 þ B4 O4 4 0 0 2 2 2 2 4 4 þ B44 O44 þ B4 4 O4 ðrank 4Þ þ B6 O6 þ B6 O6 þ B6 O6 þ B6 O6 (15) 4 6 6 6 6 þ B4 6 O6 þ B6 O6 þ B6 O6 ðrank 6Þ

For the above shown Hamiltonian for monoclinic symmetry the large number of unknown rank 4 and rank 6 crystal field parameters for each site can 0 be reduced to just B04 and B06 by calculating within-rank ratios, rnm ¼ Bm n =Bm , using simple crystal field models. For the purpose of such computations, only the nearest-neighbor oxygen atoms can be considered here, an approximation which is expected to be reasonable for the shorter-range rank 4 and rank 6 crystal field components. The three alternative sets of ratios can be computed using the superposition model of Bradbury and Newman (1967) with the following different radial dependencies: (1) the ideal point charge model, (2) a model proposed by Nekvasil (1979), and (3) a model as derived theoretically by Garcia and Faucher (1984). For these compounds, all oxygens were assumed to have the same effective charge. In the case of triclinic symmetry the number of crystal field parameters is 27, which makes an interpretation very complex. In general, for rare earth insulators, no cubic or hexagonal compounds are found. The highest found symmetry is tetragonal. In general, the energy levels (eigenvalues) and the eigenfunctions are determined by diagonalization of the above shown Hamiltonians.

3.3 Magnetic Interaction When we include the interaction of the rare earth moments with the molecular field present at these sites, the Hamiltonian H becomes H ¼H

cf

 gJ mB HM $J

(16)

In this expression the quantity gJ is the Lande´ g-factor and HM is the molecular field. Alternatively, this equation is often written as H ¼H

cf

where Hex is the exchange field.

þ 2mB ðgJ  1ÞHex $J

(17)

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In this equation the relation between Hex and HM can be written as gJ Hex ¼ HM (18) 2gJ  1 In most of the models, the magnetic coupling energy between two localized moments is taken proportional to Si$Sj. In the case of rare earths the 4f electrons interact in an indirect way. Usually, results are explained with the RKKY interaction. In this case the magnetic interaction is in an indirect way, that is, the magnetic coupling proceeds via the spin polarization of the rare earth 6s conduction electrons. The essential form of indirect interaction between localized moments was introduced by Rudermann and Kittel (1954) to explain the magnetic interactions between nuclear moments. This model was applied by Kasuya (1956) and Yosida (1957) to the interaction of localized moments. Alternatively, Campbell (1972) proposed a coupling interaction based on an indirect interaction via the 5d electrons, which have a far less localized character than the 4f electrons. Roughly, the variation of the magnetic interaction between the 4f moments scale with the de Gennes factor is as G ¼ ðgJ  1Þ2 JðJ þ 1Þ

(19)

which is proportional to the magnetic ordering temperature. Especially for the heavy rare earth elements, this is true and regarded as a prove for the validity of the RKKY model. The spin polarization of the exchange interaction between the localized spin moments can be described by the Heisenberg Hamiltonian as X H ¼ Ji;j Si $Sj (20) i;j

where Ji,j is the exchange parameter between the localized spins residing on sites i and j. For rare earths, we use the spin operator SR ¼ (gJ  1)JR. Then the Hamitonian between the rare earths becomes X H ¼ JR;R ðgJ  1Þ2 JR $JR (21) R;R

with JRR the exchange parameter between the 4f spins SR. In a mean field approximation, one can replace all spins moments by their mean value hSRi. In this case the exchange field acting on the spin moment is 1 X Hex ¼ (22) JRR hSR i 2mB R;R where the summation runs over the surrounding spins. The molecular field and the corresponding exchange field Eq. (20) can be estimated from the magnetic ordering temperature with the equation Jz HM ¼ 3kB Tc;N (23) gJ mB JðJ þ 1Þ where Jz is the eigenvalue of the ground state level.

158 Handbook of Magnetic Materials

Alternatively, Noakes and Shenoy (1982) have developed a model by including the expectation value of the eigenfunctions due to the crystal fieldda model in which the maximum of the magnetic ordering temperature TM in the rare earth series moves from Gd toward Tb or Dy with equation   TM ¼ 2JRR ðgJ  1Þ2 Jz2 ðTM Þ cf (24) In this equation, hJz2 ðTM Þicf is the expectation value of Jz2 under influence of the Hcf alone, without any exchange term, evaluated at a certain temperature. In uniaxially symmetric materials the magnetocrystalline anisotropy energy can be defined as E ¼ K1 sin2 q þ K2 sin4 q

(25)

where K1 and K2 are the anisotropy constants and q is the angle between the easy magnetization direction and the c axis. The single ion contribution due to the rare earth atoms can be obtained from crystal field theory by means of the following expressions     3     K1 ¼  aJ r 2 A02 O02 þ 5bJ r 4 A04 O04 2

(26)

where hO02 i and hO04 i denote the Boltzman average of the corresponding O02 and O04 terms and K2 ¼ 

35  4  0  0  b r A4 O 4 8 J

(27)

If the temperature is not too low, one has only to consider the term 3     K1 ¼  aJ r 2 A02 O02 2

(28)

From this equation, it appears that the second-order term of the crystal field is the most important one and in most cases determines the easy axis of magnetization. We then can simplify the Hamiltonian of Eq. (9) to H ¼ aJ hr 2 iA02 Jð2J  1Þ  gJ mB HM $Jz for an easy axis of magnetization parallel to the c axis and to H ¼  ð1=2ÞaJ hr 2 iA02 Jð2J  1Þ  gJ mB HM $Jx for an easy axis of magnetization perpendicular to the c axis. After diagonalizing this Hamiltonian, one can determine the case with a minimal energy. For all the rare earths in the presence of a crystal field, one finds that the magnetic anisotropy is parallel to the c axis if (K1 > 0) A02 < 0 and aJ > 0, while the magnetic anisotropy is perpendicular to the c axis (K1 < 0) if A02 < 0 and aJ < 0. In the case of A02 > 0, the opposite behavior is obtained. Since higher order crystal field terms or the magnetic anisotropy contribution of the 3d sublattice may disturb this picture, it has to be regarded as a simplified one. The magnetic coupling of rare earth spins with 3d spins is antiparallel. For compounds in which the rare earth is a light one (J ¼ L  S), this implies that

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

159

the total rare earth moment (gJJmB) is coupled parallel to the 3d moment. By contrast, for the heavy rare earth (J ¼ L þ S) and the total rare earth, moment is coupled antiparallel to the 3d moment. In the case of light rare earth, one can expect gradually an increase of total magnetic moment from Tc down to 4.2K, whereas in the case of heavy rare earth compensation points (M ¼ 0) can be found due to the larger temperature dependence of the magnetic moment of the heavy rare earths compared to the smaller temperature-dependence of the 3d magnetic moments, to whom they are antiparallely coupled. In general, the 4fe3d coupling strength varies as (gJ  1)J throughout the rare earth series. This means that usually for the Gd compound in the rare earth series, a maximum in Tc has been found. The molecular field magnetic part in Eq. (15), as shown by Gubbens and Buschow (1982), can be written as HM ¼ 2ZRM JRM ðgJ  1ÞhSM ðTÞi=ðgJ mB Þ:

(29)

The mean number of M neighbors (M ¼ 3d metal) of the R atoms in RxMy compounds is represented by ZRM and the ReM coupling constant by JRM. Commonly, a mean field model as shown by Gubbens and Buschow (1982) has been used to describe the variation of Tc in a certain rare earth-3d transition intermetallic compound. In such a model Tc can be written as 3kTc ¼ aMM þ aRR þ ½ðaMM  aRR Þ2 þ 4aRM aMR 1=2

(30)

where axy represents the magnetic interaction between the x and y spins. These energies can be expressed in terms of the corresponding coupling constants JRR, JRM and JMM by means of the relations aRR ¼ ZRR JRR ðgJ  1Þ2 JðJ þ 1Þ

(31)

aMM ¼ ZMM JMM SM ðSM þ 1Þ

(32)

2 aRM aMR ¼ Z1 Z2 SM ðSM þ 1ÞðgJ  1Þ2 JðJ þ 1ÞJRM

(33)

where ZRR and ZMM represent the average number of similar neighbor atoms to an R atom and a 3d atom, respectively. The quantities Z1 and Z2 represent the number of 3d neighbors to an R atom and the number of R neighbors to a 3d atom, respectively. Since the RKKY exchange between the R atoms has a longrange character, it is not sufficient to consider only the nearest neighbors. However, the ReR magnetic interaction is relatively weak. For this reason the aRR term can be neglected in a rare earth-3d intermetallic. In that case, the variation of Tc can be written in a more simplified form

1=2 (34) 3kTc ¼ aMM þ a2MM þ 4aMR aRM

160 Handbook of Magnetic Materials

3.4 Relation to Mo¨ssbauer Parameters As we have shown earlier in Section 2 for rare earth Mo¨ssbauer spectroscopy the two measurable most important parameters are the magnetic hyperfine field (Heff) and the electric quadrupole-splitting (QS). The temperature dependence of the hyperfine field determined by the energy levels and the eigenfunctions of the crystal fields of the rare earth has the expression   4f  (35) Heff ðTÞ ¼ Heff hJz iav  J where hiav indicates a thermal average over the energy levels of the crystal 4f is the value of the hyperfine field for the free ion. In a rare field scheme. Heff earth (with exception of Gd) the orbital contribution is by far the largest contribution to the hyperfine field. The transferred hyperfine field due to the surrounding magnetic moments has only a minor influence, as shown for some 3de4f compounds. This means that one can simply calculate the magnetic moment of a Tm atom by means of the simple relation M ¼ gJ m B J

Heff ðTÞ 4f Heff

(36)

The temperature dependence of the quadrupole-splitting is given by the equation  2  3Jz JðJ þ 1Þ av 4f DEQ ðTÞ ¼ QS þ QSlatt (37) Jð2J  1Þ where hiav indicates a thermal average over the energy levels of the crystal field scheme. QSlatt is the lattice contribution of the electric quadrupolesplitting and QS4f is the free-ion value. A schematic representation is given in Fig. 2. Since in Gd the 4f electrons fill half of the shell, there is no orbital moment present (L ¼ 0). This means that the 4f-contribution of the electric quadrupolesplitting in 155Gd Mo¨ssbauer spectroscopy is zero and only the lattice contribution has to be considered. In this way the lattice contribution in Eq. (39) can be determined independently from a separate 155Gd Mo¨ssbauer spectroscopic investigation. When the symmetry is lower than cubic the lattice contribution of the quadrupole-splitting is QSlatt ¼ 1=2e2 Vzzlatt Q in the case of axial symmetry as shown by Eq. (3). Then

1 (38) 3cos2 q  1 þ hsin2 qcos 2f 2 where q is the angle between the easy axis of magnetization and the symmetry axis of the electric field gradient, f the angle of the projection of the magnetization in the plane and h ¼ A22 =A02 ¼ B22 =B02 . Alternatively, since the eVzzlatt ¼  4$C$A02 $

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

161

FIGURE 2 Schematic representation of the two crystal field contributions to the electric tensor at the rare earth nucleus: The lattice contribution due to the crystal field of the surrounding magnetic moments and the 4f-contribution due to the asymmetry of the 4f-charge cloud. This figure has been taken from Stewart, G.A., 1994. Mater. Forum 18, 177.

4f term in the quadrupole-splitting is averaging out at very high temperatures, the lattice contribution can be determined by measuring the 169Tm Mo¨ssbauer spectra at such high temperature as shown in Fig. 3 for TmNi2B2C. Traditionally, the constant C was taken to be equal to (1  gN)/(1  s) with gN the antishielding factor of Sternheimer (1966) and s the screening factor. Values of gN and s are calculated by Gupta and Sen (1973). For a long time such an interpretation is still valid for insulators as shown by Stewart (1985) and Stewart and Gubbens (1999). For metallic systems a more modern interpretation has been given on the basis of electronic band structure calculations on the GdM2Si2 compounds performed by Coehoorn et al. (1990). Eqs. (37) and (38) are very useful tools for determining the crystal field potential A02 . Since for rare earth-3d-rich intermetallic compounds the molecular field experienced by the rare earth ion (Eq. 30) is very large, the exchange splitting of the 2J þ 1 ground multiplet is much larger than the crystal field splitting. In that case Jz in Eq. (37) is equal to J and the 4f-contribution of the quadrupolesplitting is the free-ion value. The difference between the free-ion value and the measured quadrupole-splitting gives then the lattice contribution. From Eq. (38) one then can determine the A02 term as shown in Table 5. The constant C can also be determined experimentally. For instance, this value can be determined from a combined inelastic neutron experiment, which determines the eigenfunction of the ground state and a Mo¨ssbauer experiment, which gives

162 Handbook of Magnetic Materials

TmNi2B2C

sample A sample B

QSlatt

FIGURE 3 The quadrupole-splitting (QS ¼ 1/2eVzzQ) as observed by 169Tm Mo¨ssbauer spectroscopy in two samples of TmNi2B2C (A and B). In sample A, only a quadrupole-splitting is observed as shown by the empty dots. In sample B, the filled triangles are deduced from the corresponding subspectrum, which shows a moment of 4.3 mB at 0.3K and the filled dots are deduced from the other subspectrum. Note that the filled and empty dots are identical to each other within the experimental error. The solid curve is obtained from a tentative set of crystal field parameters and can be considered as a guide to the eye. At high temperatures the QSlatt determined by 169Tm and 155Gd Mo¨ssbauer spectroscopy coincide. The Gd result is taken from Mulder et al. (1995). For further explanation see ref. of Mulders et al. (1998).

latt , Used TABLE 5 Lattice Contributions to the Electric Field Gradient, Vzz C-Factors and Corresponding Values of the Crystal Field Potentials A02 for the Rare Earth Mo¨ssbauer Spectroscopy Measured RCo5 þ x Compounds

Compound

latt ð1017 V cm2 Þ Vzz

C

A02 ðK=a20 Þ

GdCo5

þ8.2

320

206

DyCo5.1

7.0  2.0

285

400  100

ErCo5.9

þ8.0  1.5

270  30

230  50

TmCo6.1

þ5.6  1.0

243  30

185  30

TmCo8.5

þ4.2  1.0

243  30

140  30

(Tm2Co17)

þ1.4  1.0

243  30

46  30

GdCo8.5

þ4.3

320

108

(Gd2Co17) It has to be noted that hexagonal Tm2Co17 has two different Tm sites and rhombohedral Gd2Co17 one-only Gd site. Furthermore, the C-factors were experimentally determined for Er and Tm. The others were estimated.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

163

the lattice contribution. For TmNi5 (Gubbens et al., 1985c) the C value amounts about 243. Using this value for the data of RCo5 þ x C-factors were determined by Gubbens et al. (1988a, 1988b, 1989). For the GdxCoy compounds the A02 values were determined directly and for the other rare earth from the difference of the free-ion value and the measured quadrupole-splitting in both cases using Eq. (38). They give a good impression about of the sensitivity of the different types of rare earth Mo¨ssbauer isotopes. It is clear that 155Gd is the most sensitive one, since no orbital and hence no 4f-contribution is present. For the other cases the sensitivity decreases in the sequence 169 Tm, 166Er and 161Dy as shown in Table 5. Recently, Bertin et al. (2012) has determined with inelastic neutron scattering measurements the crystal field parameters of Tb2Ti2O7. They found for the A02 parameter a value of 40:5  1:0 meV=a20 , which is equal to 470K=a20 . Results on Ho2Ti2O7 and rescaled Tb2Ti2O7 by Malkin et al. (2004) give approximately the same value. Moreover, results from Yb3þ ions diluted Y2Ti2O7 give also this value as found by Mirebeau et al. (2007) and Rosenkranz et al. (2000). This means that this A20 value is well established. Bonville et al. (2003) and Armon et al. (1973) have found from 155Gd Mo¨ssbauer spectroscopy a lattice contribution of 5.6 mm/s. In this structure the asymmetry parameter h ¼ 0. With Eq. (38) using a Sternheimer value of gN ¼ 61 and screening coefficient s2 ¼ 0.67 Bertin et al. (2012) has computed for A02 a value of 95 meV=a20 for Gd2Ti2O7, which gives after scaling 97 meV=a20 for Tb2Ti2O7. This is a factor 2.4 larger than the result from the inelastic neutron scattering on Tb2Ti2O7. Calculation of the Constant C in Eq. (38) gives a value of 385, which is 20% higher than the value used for the intermetallic compound GdCo5 in Table 5. This should mean that metals and insulators are probably not too different. However, this is only one result. Therefore, it is clear that a more extended study both experimental and theoretical is necessary to modernize the use of Mo¨ssbauer spectroscopy on rare earth (especially Gd) insulators for determination of the second order parameter of the crystal field. It might be that covalency effects have an important contribution to the value of C ¼ (1  gN)/(1  s).

3.5 Magnetic Relaxation In studies of rare earth compounds with Mo¨ssbauer spectroscopy, a broadening of the Mo¨ssbauer lines of the hyperfine field due to magnetic relaxation effects are observed. At low temperatures, in the slow relaxation limit (slower than 107 s), mostly no line broadening is observed. Usually, with increasing temperature, lines of hyperfine fields show an increasing line broadening, until at a certain temperature one reaches a relaxation time, which is close with the Larmor precession time of a certain Mo¨ssbauer nucleus, where the hyperfine field collapses and only a broadened quadrupole spitting is left. This last broadening will disappear at the fast relaxation limit. For instance, in the case

164 Handbook of Magnetic Materials

of 169Tm Mo¨ssbauer spectroscopy, one observes just below this fast relaxation limit the same asymmetric doublet as is described by Blume (1965) for 57Fe Mo¨ssbauer spectroscopy. Blume and Tjon (1968) have considered a model with stochastic fluctuating magnetic spins parallel and perpendicular to the electric field gradient. A more complex treatment is given by the model of Clauser and Blume (1971). As an example, DyPO4 (TN ¼ 3.39K), which has been studied by Forester and Ferrando (1976a), is shown in Fig. 4. This figure shows that above TN ¼ 3.39K the Mo¨ssbauer spectrum is fully split. Above 16K, increasing relaxation broadening of the spectrum is observed until at 73K the spectrum is completely collapsed and only a broadened single line is observed typically for a 161Dy Mo¨ssbauer spectrum above the magnetic ordering temperature. The crystal field of DyPO4 consists of eight Kramers doublets with an overall splitting of approximately 570K. At low temperature the hyperfine field is close to the free-ion value, which indicates that the ground state doublet is Seff ¼ 1/2. At low temperature, the Eigen functions of the almost purified Kramers doublets j15/2i and jþ15/2i by “local strong dynamic fields” are moving up and down parallel to the c axis as indicated by 161Dy Mo¨ssbauer spectroscopy. Although at higher temperatures more levels are becoming populated and principally the spin upespin down model is not valid any more,

FIGURE 4 Temperature dependence of the 161Dy Mo¨ssbauer spectra of DyPO4 below and above TN ¼ 3.39K. The term U/G indicates the value of the broadening of the Larmor precession frequency as indicated for the spectra at each temperature. This figure has been earlier published by Forester, D.W., Ferrando, W.A., 1976a. Phys. Rev. B 13, 3991.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

165

the 161Dy Mo¨ssbauer spectra are becoming more and more populated and the dynamic process is becoming much faster. In the literature, this slow relaxation behavior above the magnetic ordering temperature is called “ferromagnetic relaxation”. In these cases, there is no direct transition possible between these two low-lying energy levels of the Kramers doublet. The relaxation is dominated by an Orbach (1961) spin-lattice process over an intermediate level. In the case of DyPO4, this level is at an excited of about 100K above the ground state doublet as described by Forester and Ferrando (1976a). Further discussion will be given in Section 4.4. In the magnetic ordered region the magnetic relaxation is often mentioned “electronic relaxation”. In the slow magnetic relaxation limit, one observes in a Mo¨ssbauer spectrum the hyperfine fields, which are related to the eigenfunction of each of the populated energy levels. Each level has its own hyperfine field. In this case information over the distance between the crystal field levels at low temperature can be determined from the intensity of the subspectra in relation with the Boltzman distribution. In the fast relaxation limit, one observes only the average of the hyperfine fine fields belonging to these eigenfunctions. However, usually one observes broadened Mo¨ssbauer lines with a strong overlap near the Larmor precession time. If the crystal field diagram is not too complex, simulations of these spectra can be made with relaxation models as described by Blume and Tjon (1968) and Clauser and Blume (1971).

3.6 Analysis Procedure: Examples In this paragraph, two examples will be shown. The first example is a description of the determination of the crystal field with help of the temperature dependence of the 169Tm electric quadrupole-splitting of the superconductor TmBa2Cu3O7x using Eqs. (37) and (38). Furthermore, a second example will be shown about the temperature dependence of the 179Yb hyperfine field and the deduced behavior of the magnetic relaxation of the compound Yb2Ti2O7.

3.6.1 TmBa2Cu3O7  x Since the quadrupole-splitting in 169Tm Mo¨ssbauer spectroscopy through its crystal field is quite sensitive for small distortions as shown by Gubbens (2012), it was originally interesting to study the temperature dependence of the electric quadrupole-splitting of the high-temperature superconductor TmBa2Cu3O6.9 as initially shown by Gubbens et al. (1988a, 1988b). Fig. 5 shows the 169 Tm Mo¨ssbauer spectra of TmBa2Cu3O6.9 measured between T ¼ 4.2 and 680K as studied by Gubbens et al. (1988b). In Fig. 6 the values of the temperature dependence of the 169Tm quadrupole-splitting of TmBa2Cu3O6.9 and TmBa2Cu3O6.6 are shown. Near the superconducting (SC) transition Tc a broad minimum is observed in the temperature dependence of the quadrupole-splitting. This phenomenon might be attributed to a change in the orthorhombic symmetry of the crystal. On the

166 Handbook of Magnetic Materials

FIGURE 5 Temperature dependence of the 169Tm Mo¨ssbauer spectra of TmBa2Cu3O6.9. The drawn line is the best fit. This figure has been earlier published by Gubbens, P.C.M., van Loef, J.J., van der Kraan, A.M., de Leeuw, D.M., 1988b. J. Magn. Magn. Mater. 76 & 77, 615.

other hand, such a temperature behavior of the quadrupole-splitting can also be explained by temperature dependence of the crystal field. In a first approximation the higher order terms in Eq. (14) were neglected. From the results of the 155Gd Mo¨ssbauer spectroscopy measurements on GdBa2Cu3O6.9 by Smit et al. (1987) the lowest order crystal field terms B02 ¼ 1:9 and B22 ¼ 1:0K terms of Tm in TmBa2Cu3O6.9 were deduced. Then with Eqs. (14), (37) and (38) the temperature dependence of the electric quadrupole-splitting as shown in Fig. 6 was calculated (drawn curve). The 4fcontribution of the electric quadrupole-splitting is opposite in sign with the lattice contribution and negative. Therefore, the data are also negative as plotted in Fig. 6 (open dots). Due to the large discrepancy between the measured and calculated values higher order terms as shown in Eq. (14) are included. To analyze TmBa2Cu3O6.9 a tetragonal symmetry was used ignoring the orthorhombic distortion as shown by Nekvasil (1988). By using an iterative procedure of Eqs. (14), (37), and (38) with respect to the data points, the crystal field values shown in Table 6 on the first line were found. These Bm n values calculated are in good agreement with the values scaled from the inelastic neutron scattering measurements on HoBa2Cu3O6.9 by Fu¨rrer et al. (1988) as shown on the third line in Table 6. This result is given in Fig. 6 as the dashed curve. Hence the temperature dependence can be described with common crystal field parameters.

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FIGURE 6 Temperature dependence of the electric quadrupole-splitting of 169Tm Mo¨ssbauer spectra of TmBa2Cu3O6.9 and TmBa2Cu3O6.6. For the drawn dashed lines, see text. This figure has been earlier published by Gubbens, P.C.M., van Loef, J.J., van der Kraan, A.M., de Leeuw, D.M., 1988b. J. Magn. Magn. Mater. 76 & 77, 615.

In order to discriminate between the two possible explanations for the observed minimum in the quadrupole-splitting, the 169Tm spectra of TmBa2Cu3O6.6 has been measured with 169Tm Mo¨ssbauer spectroscopy on a compound with a lower oxygen content and hence a lower Tc as shown by Cava et al. (1987). From the measurements on TmBa2Cu3O6.6 with a Tc of 58K, it appears that the minimum in the temperature of the quadrupole-splitting is still found at a temperature of about 90K as shown in Fig. 6 (full dots). So it can be concluded that this minimum should be attributed to crystal field effects and not to a distortion at Tc Moreover from Fig. 6, it appears that oxygen removal in these high-Tc superconductors does not alter the crystal field parameters. Bergold et al. (1990) have repeated the measurement on the 169Tm Mo¨ssbauer spectra of TmBa2Cu3O6.9. Their spectra are slightly broadened with respect to spectra shown in Fig. 5. The temperature of the electric quadrupole-splitting shows qualitatively the same behavior as shown in Fig. 6. Results of 155Gd Mo¨ssbauer spectra of GdBa2Cu3O6.9 by Wortmann et al. (1988a, 1988b) were used to determine the crystal field terms B02 and B22 as shown on the second line in Table 6. They used the scaled higher order terms Fu¨rrer et al. (1988). The fit with these crystal terms (second line Table 6) is quite good, indicating that the higher order terms are quite well determined by the inelastic neutron scattering measurements by Fu¨rrer et al. (1988). Fritz and Dixon (1992) have restudied the 169Tm Mo¨ssbauer spectra of TmBa2Cu3O6.9 between T ¼ 0.06 and 92K. Their results could be well explained by the scaled crystal field parameters from Fu¨rrer et al. (1988). Rudowicz

Publication

B02 (K)

B22 (K)

B04 (mK)

Gubbens et al. (1988a, 1988b)

þ1.90

þ1.0

20

Bergold et al. (1990)

þ1.75

þ0.67

44.1

Fu¨rrer et al. (1988)

þ2.41

þ1.05

44.1

B24 (mK)

B44 (mK)

B06 (mK)

B26 (mK)

B46 (mK)

B66 mK

120

250

þ2.91

þ203

183

þ110

5.48

þ77.1

þ2.91

þ203

183

þ110

5.48

þ77.1

5.0

Results were taken from Gubbens et al. (1988a, 1988b), Bergold et al. (1990) and a scaled result from the inelastic neutron scattering measurement of HoBa2Cu3O6.9 by Fu¨rrer et al. (1988).

168 Handbook of Magnetic Materials

TABLE 6 Comparison of the Crystal Field Parameters Bm n for TmBa2Cu3O6.9

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

169

et al. (2009) have reanalyzed the crystal field parameters of TmBa2Cu3O6.9. Their results are roughly in agreement with the results shown in Table 6. From the description of all these results, it is clear that inelastic neutron scattering are additional and crucial to come to a full description of the electric crystal field in these type of compounds.

0.8 0.4 0.0 100

50

Yb2Ti2O 7

0 0.0 0.1 0.2 0.3 0.4

3+

mag. fract. (%)

1.2

moment (µ B / Yb )

3.6.2 Yb2Ti2O7 The pyrochlore structured compound Yb2Ti2O7 has been studied with 170Yb Mo¨ssbauer spectroscopy. Selected 170Yb Mo¨ssbauer absorption spectra are shown in the left panel of Fig. 7. At T ¼ 0.036K, a five-line spectrum is observed, indicating a “static” hyperfine field of 115T. In the present case, “static” means that the fluctuation frequency of the field is slower than the lowest observable relaxation limit of 15 MHz. Knowing that for Yb3þ the hyperfine field is proportional to the 4f shell magnetic moment, it was found that each of the Yb atoms carries a magnetic moment of 1.15 mB. In the absence of a significant quadrupole hyperfine interaction, the local direction of the Yb3þ magnetic moment cannot determined using Eqs. (37) and (38) with the principal axis of the electric field gradient along the [111] direction. Instead, for an anisotropic Kramers doublet, the size of the spontaneous magnetic moment is linked to the zero angle with the local [111] symmetry axis through the relation  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 MYb ¼ gt mB (39) cos q r 2 þ tan2 q 2

Temperature (K) 170

FIGURE 7 Left panel: Yb Mo¨ssbauer spectra of Yb2T2O7 above, within, and below the firstorder transition occurring near 0.24K. Right panel: thermal variation of the size of the Yb3þ magnetic moment obtained from the hyperfine field (top) and relative weight of the static magnetic fraction (bottom). The lines are eye guides. These figures have been earlier published by Hodges, J.A., Bonville, P., Forget, A., Yaouanc, A., Dalmas de Re´otier, P., Andre´, G., Rams, M., Kro´las, K., Ritter, C., Gubbens, P.C.M., Kaiser, C.T., King, P.J.C., Baines, C., 2002. Phys. Rev. Lett. 88, 077204.

170 Handbook of Magnetic Materials

where r is the anisotropy ratio gt/gz as shown by Bonville et al. (1978). With gt/gz y 2.5 q ¼ 44(5) was found. Thus each moment does not lie perpendicular to its local [111] axis as would be expected if the orientation were governed only by the crystal field anisotropy. With increasing temperature up to 0.24K, an additional single-line subspectrum appears. It is linked with the fraction of the Yb3þ whose moments fluctuate “rapidly” so that the magnetic hyperfine splitting becomes “motionally narrowed”. The two subspectra (see Fig. 7, left panel at 0.24K) are both present up to 0.26K, evidencing the coexistence of temperature regions with “static” and “rapidly fluctuating” moments. The right panel in Fig. 7 shows that, as the temperature increases, there is a progressive decrease in the relative weight of the static hyperfine field subspectrum. This behavior shows a clear evidence of a first-order transition. The single-line subspectrum progressively narrows as the temperature increases. Since magnetic correlations are still present above 0.24K, we attribute this change to the progressive increase in nM, the fluctuation rate of the hyperfine field (Heff) The relation between the dynamic line broadening, DGR, and nM is written DGR ¼ (mIHeff)2/nM, where mI is the 170Yb nuclear moment as given by Dattagupta (1981). As shown in Fig. 8 below, when the temperature is lowered from 1K to just above 0.24K, the rate decreases

Fluctuation rate (106 s−1)

100000

Yb2Ti2O7

10000 1000 ¨ Mossbauer lower limit

100 10

νμ νM

1 0.1

1 Temperature (K)

10

FIGURE 8 Estimate of the Yb3þ fluctuation rates as obtained from 170Yb Mo¨ssbauer (nM) and mSR (nM) measurements. The first-order transition in the fluctuation rates takes place at the L transition. Above w0.24K, the fluctuation rates deduced from mSR and Mo¨ssbauer spectroscopy match for a Yb3þ muon spin coupling of DHT/gm equal to x80 mT. This value agrees reasonably well with the value of 85.6 mT obtained by scaling from Tb2T2O7 as published by Gardner et al. (1999). Below w0.24K, the fluctuation rate is independent of temperature and has dropped below the lowest value, which is measurable with the Mo¨ssbauer method (dashed line). The solid line follows a thermal excitation law. This figure has been earlier published by Yaouanc, A., Dalmas de Re´otier, P., Bonville, P., Hodges, J.A., Gubbens, P.C.M., Kaiser, C.T., Sakarya, S., 2003. Physica B. 326, 456.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

171

from z15 to z2 GHz. This decrease is linked to the slowing down of the spin fluctuations. Below 0.24K, nM drops to a value, which is less than the lowest observable 170Yb Mo¨ssbauer relaxation value. In conclusion, magnetic fluctuations in materials can be followed with rare earth Mo¨ssbauer spectroscopy. Scientific descriptions can be made from the results in combinations with results of other measuring techniques like mSR, neutron diffraction, and specific heat. In Section 4.7 more results of R2M2O7 will be shown and discussed.

4. OVERVIEW OF RARE EARTH-BASED OXIDES 4.1 Introduction In the following paragraphs the rare earth Mo¨ssbauer effect measurements of the different rare earth-based oxides will be discussed and compared with measurements of other techniques.

4.2 R2O3 Compounds In this paragraph the Mo¨ssbauer results of rare earth oxides are discussed. With exception of Dy2O3 (Forester and Ferrando, 1976b) and PrO2 (Moolenaar et al., 1996) all other rare earth oxides, Gd2O3 (Cashion et al., 1973), Er2O3 (Cohen and Wernick, 1964), Tm2O3 (Barnes et al., 1964), and Yb2O3 (Meyer et al., 1995), studied with rare earth Mo¨ssbauer spectroscopy, are not magnetically ordered. From a physical point of view, Tm2O3 is very interesting for the determination of its crystal field. For Tm2O3 the temperature dependence of the electric quadrupole-splitting of both Tm sites (C3i and C2) have been measured and analyzed up to room temperature by Stewart et al. (1988) and Stewart (2010) as shown in the left side of Fig. 9. Moreover, on the right side, the temperature dependence of the unsplit quadrupole interaction for both sites is shown as measured by Barnes et al. (1964). The quadrupole-splitting at the monoclinic C2 site is about 5% smaller than that obtained with a single doublet analysis. The two sets of data converge above 150K. The quadrupole-splitting measured for the C3i site is consistently larger than that for the trigonal C2 site in the temperature range between T ¼ 0 and 300K. The relative intensity of the doublet of the two C2 and C3i Tm sites is 3:1. The crystal field Hamiltonians for the C3i and C2 are given by Eqs. (12) and (15). The solid curves in Fig. 9 represent theoretical fits to the data for each site using the respective sets of parameters of the crystal field Hamiltonians for the C3i and C2 as given by Eqs. (12) and (15). The used Bm n for the C2 Tm site were taken from Leavitt et al. (1982) and for the C3i Tm site from Gruber et al. (1985). Traditionally, QS4f is proportional to r1 ¼ Q(1  RQ)hr3i, where Q ¼ 1.5b is the quadrupole moment of the 169Tm nucleus (Olesen and Elbek, 1960), RQ ¼ 0.128 the antishielding factor (Gupta and Sen, 1973) and

172 Handbook of Magnetic Materials

FIGURE 9 Electric quadrupole-splitting DEQ versus temperature of Tm2O3: (A) Resolved data for the two Tm sites (C3i and C2): full symbols (Stewart et al., 1988). (B) Original unresolved data (Barnes et al., 1964). The solid curves (Stewart et al., 1988) representing the parameter fits of theory to the resolved data are included in both plots. 3 ¼ 12:105 au3 (Dunlap, 1971) for the 169Tm nucleus. The shielding r4f parameters as calculated by Stewart et al. (1988) fit very well for the 4fcontribution for Tm2O3 and thulium ethylsulfate (TmES) as determined by Barnes et al. (1964). Whereas the atomic shielding represented by r1 is consistent with theory, the lattice EFG shielding parameter, r2, is seen to be reduced considerably for both sites in Tm2O3. The found values for C by Stewart et al. (1988) are 94(4) and 45(13) for the C2 and the C3i of Tm2O3, respectively. Stewart et al. (1988) argues that (1  gN) in C ¼ (1  gN)/(1  s) will not vary significantly from one material to another. Therefore, this reduction is most likely due to the influence of the TmeO covalent bonding on the factor (1  s). Comparison with the calculated field gradients from the 155Gd Mo¨ssbauer measurements of Gd2O3 by Cashion et al. (1973) is good for the C2 site and bad for the C3i site. However, Stewart et al. (1988) regards the crystal field results of the C3i site less reliable. It is apparent that the extent of covalent bonding is similar for the two Tm3þ sites despite their differing symmetries. This is supported by the work of Ryzhkov et al. (1985) who performed numerical calculations for TmO9 6 clusters in Tm2O3 and concluded that the electronic structures of the two Tm3þ sites are practically the same. In general, this kind of behavior implies that covalency effects have influence on the value of C ¼ (1  gN)/(1  s) as has been shown earlier in the case of Yb2Ti2O7 in Section 3.4. An 161Dy Mo¨ssbauer spectrum obtained at T ¼ 7K for Dy2O3 is shown at the top of Fig. 10 as measured by Forester and Ferrando (1976b). In this figure

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the predominant spectral features are associated with ions at sites with C2 symmetry. However, a second, weaker and broadened spectrum is noted with an overall splitting greater than the C2 site spectrum, which can be ascribed to the C3i site. The solid line drawn through the data in Fig. 10 is the result of a least-squares computer analysis using an effective spin S ¼ 1=2, hyperfine interaction Hamiltonian for each of the C2 and C3i sites. The broadening of the spectrum of the C3i site was included in the analysis by a spin-upespin-down relaxation. The frequency at T ¼ 7K is 6  106 s1. Whereas the C2 site is reduced to the free-ion value, the C3i site has the same hyperfine field as shown for DyPO4 in Section 3.5, which has an almost pure j15/2i doublet ground state. Then, the 4f-contribution of the quadrupole-splitting has the free-ion value. Therefore, from the lattice contribution of the quadrupole-splitting the crystal field potential A02 ¼ 200K, which is much smaller than the value of 480K, used by Stewart et al. (1988) for his analysis of the crystal field in Tm2O3. Moolenaar et al. (1994, 1996) have studied with 141Pr Mo¨ssbauer spectroscopy the isomer shift of Pr2O3, Pr6O11 and PrO2 as a function of the valency. In Section 4.5, this subject will be further discussed in combination

FIGURE 10 161Dy Mo¨ssbauer spectrum taken at T ¼ 7K. The solid curve through the data points is a computer fit for both C3i and C2 site ions. The two solid curves at the bottom are calculated C3i and C2 spectra that make up this composite fit. This figure has been earlier published by Forester, D.W., Ferrando, W.A., 1976b. Phys. Rev. B 14, 4769.

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of the result of PrBa2Cu3O7. Since at ambient oxygen pressure only Pr6O11 is stable, it is, however, possible that PrO2 is oxygen-deficient (and Pr2O3 oxygen-redundant). Using 141Pr Mo¨ssbauer spectroscopy the magnetic order and the oxygen content of PrO2 could be checked. The spectrum splits below the Ne´el temperature of T ¼ 14K (Kern et al., 1984) into a magnetically split and a broad unsplit contribution as shown in Fig. 11. When the magnetically split part is ascribed to stoichiometric PrO2 and the unsplit part to oxygen deficient PrO2  x, assuming that the recoilless fractions are not too different, it was found that about 6% of PrO2 is oxygen deficient as shown in Fig. 11. The determined hyperfine fields amount 78, 71, and 30T at T ¼ 4, 8, and 12K, respectively. The result of PrO2 is in good agreement with those of Bent et al. (1971), Kapfhammer et al. (1971) and Groves et al. (1973), which were measured with a scattering method of 141Pr Mo¨ssbauer spectroscopy.

FIGURE 11 141Pr Mo¨ssbauer spectra PrO2 measured with a CeF3 source. The curves drawn give the fit to the data points. The spectrum at 4.2K has a second contribution, approximately indicated by the dotted curve. This figure has been earlier published by Moolenaar, A.A., Gubbens, P.C.M., van Loef, J.J., Menken, M.J.V., Menovsky, A.A., 1996. Physica C 267, 279.

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The high-pressure behavior of the cubic C-type Yb2O3 was investigated by 170Yb Mo¨ssbauer spectroscopy and up to a pressure of 20 GP at T ¼ 4.2K by Meyer et al. (1995). They confirm the occurrence of a pressure-induced phase transition from a cubic to a monoclinic structure. The monoclinic phase is retained after releasing the pressure. The Mo¨ssbauer quadrupole splitting values were evaluated in combination with the structural data in a coherent way.

4.3 RMO3 Compounds In this paragraph the magnetic properties of perovskite RMO3 compounds are discussed. These compounds are quite interesting and are well investigated because of their properties, which range from colossal magnetoresistance, charge ordering, and multiferroicity in hole-doped RMnO3. Recently, it was found that RMnO3 compounds with light rare earth, for example, Pr have a first-order transition near room temperature and can be used for magnetic cooling. The compound GdAlO3 has is an orthorhombically distorted perovskite with a c axis lying along one pseudocubic axis. The magnetic ordering direction in GdAlO3 is the orthorhombic a axis as determined by Cook and Cashion (1976, 1980) with a Ne´el temperature of 3.870K. At temperatures well below TN, GdAlO3 can be well described in terms of a molecular-field theory for a two-sublattice uniaxial antiferromagnet. At temperatures close to TN the exchange interaction is small and the magnetic sublattices are aligned close to the principal axis of crystal electric field and will cant to the a axis as the temperature is decreased. 155 Gd Mo¨ssbauer spectroscopy has been performed on single crystals of GdAlO3. The spectra were analyzed using Eqs. (37) and (38) for Gd. For the lowest temperatures, it was found that the values of the hyperfine fields vary linearly with T3. The hyperfine fields just below TN were proportional with d(1  T/TN)b. From a logarithmic plot the calculated critical exponents are d ¼ 1.24  0.05 and b ¼ 0.37  0.02. An estimate of the values of b and d has been made using the theoretical studies of Rushbrooke et al. (1974). The Heisenberg model for a ferromagnet predicts, for S ¼ 7/2, the value of b ¼ 0.368  0.033, which is in agreement with the value found for GdAlO3. For simple-cubic lattice structure the value of d has been extrapolated, using the Ising model, to be 1.32  0.02, which is larger than the value found for GdAlO3. Near the magnetic ordering temperature of 3.87K the electric field gradient makes a canting angle of 43  4 to the a axis. The sublattices rotate toward a axis very quickly with decreasing temperature below TN and remain nearly constant below 3.2K on a value of 7.2  1.5 . This behavior could well be described with an electronic Hamiltonian by Cook and Cashion (1980).

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The compounds DyCrO3 and DyFeO3 were studied with by 161Dy Mo¨ssbauer spectroscopy by Eibschu¨tz and Van Uitert (1969) and Nowik and Williams (1966), respectively. The Mo¨ssbauer spectra of DyCrO3 (orthorhombic symmetry) are below and above TN ¼ 2.16K well split and similar as in the case of DyVO4 (Section 3.5). Above T ¼ 20K the spectra are broadening and show typical paramagnetic relaxation behavior arising from the isolated and almost pure j15/2i Kramers-doublet ground. The magnetization axis is strongly anisotropic as shown from the g-tensor with gz ¼ 19.7 and gx ¼ gy ¼ 0. In DyFeO3 the Fe sublattice orders magnetically at 635K. Down to TN ¼ 4.5K the Dy sublattice in this compound stays paramagnetically until it orders antiferromagnetically. The Mo¨ssbauer spectra above TN show also typical paramagnetic relaxation behavior up to 300K. From the hyperfine splitting and the g-tensor (with only one component along the z axis), it appears also that the Kramers-doublet ground state is almost pure j15/2i. In this respect, DyFeO3 is comparable with DyCrO3 (above) and DyVO4 as described in Section 3.5. Spectra above 50K magnetic hyperfine fields of excited (Stark) levels. Apparently, the relaxation time is long enough to observe them due to the magnetic field of 0.29T caused by the magnetic Fe sublattice. In this respect the observation of the higher lying Kramers doublet levels above TN ¼ 4.5K in DyFeO3 is so far known as a unique observation. The distorted perovskite compound TmAlO3 is studied by Hodges et al. (1984). In the temperature range of 4.2e300K, the observed absorption was in the form of a symmetric quadrupole-splitting without any magnetic interaction. This is compatible with the expected nonmagnetic nature of the Tm3þ ion. The absolute value of temperature dependence of the quadrupole interaction could be used to calculate the crystal field parameters. However, this attempt was not successful. The distorted perovskite compound TmVO3 has a Ne´el temperature of 106K, associated with the ordering of the 3d lattice of Vanadium. This compound was studied with 169Tm Mo¨ssbauer spectroscopy by Hodges et al. (1984). Three temperature zones were defined. In the first one, down to TN ¼ 106K, the Tm3þ ion is nonmagnetic. From TN down to about 15K, the Tm3þ ion is weakly magnetic and then below about 15K, the spectra show more strongly magnetic behavior. At that temperature the hyperfine field increases rapidly with more than a factor five until it reaches a saturated Tm magnetic moment of 2.1 mB, which is still much lower than the free ion value of 7 mB. These three behaviors are represented by three different 169Tm Mo¨ssbauer absorption line shapes. To obtain adequate line shape fits below 7K, it was necessary to allow the widths of the individual absorption lines to be independent of each other; the intensities of the lines being imposed by the fitting procedure. The electric quadrupole-splitting shows changes at

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TN ¼ 106K and at 15K. At T ¼ 4.2K the 169Tm Mo¨ssbauer spectrum is clearly relaxation broadened. No clear explanation could be given. The distorted perovskite compound TmCrO3 has a Ne´el temperature of 124K, associated with the ordering of the 3d lattice of Chromium. This compound was studied with 169Tm Mo¨ssbauer spectroscopy by Hodges et al. (1984). The compound TmCrO3 has two excited Tm3þ singlet levels at 26 and 63K. The 169 Tm Mo¨ssbauer absorption spectra show a line shape of a symmetric quadrupole doublet down to TN and a magnetic splitting at lower temperatures. The electric quadrupole-splitting, the hyperfine field, and q (the angle between the electric field gradient and the magnetization direction) all vary with temperature. As the parameters DEQ and Heff are approximately the same size, this is a favorable case for determining the sign of DEQ and for accurately obtaining q. DEQ is found to be negative and the experimental accuracy of theta is estimated to vary from close to 90 at 1.4K, to close to 45 at 80K. Since the electric field gradient is not changing in direction, this behavior can ascribed to a direction change of the hyperfine field. This result could well be explained by a model of Bertaut et al. (1966). With this structural model and knowing the Tm3þ moment from the Mo¨ssbauer data, the canting angle of the Cr3þ lattice could be calculated. The most convenient temperature for the calculation is the compensation point near 28K, where the resultant ferromagnetic Cr3þ moment is equal and opposite to the Tm3þ moment as shown by Bertaut et al. (1966). At 28K, our value for the Tm3þ moment is 0.33  0.02 mB and the individual Cr3þ moment is 2.56 mB. This latter value is obtained by interpolating the data at 4.2 and 80K as given by Bertaut et al. (1966) using a Brillouin function B3/2. A comparison of the total spontaneous moment and the individual Tm3þ and Cr3þ moments at other temperatures between 4.2 and 80K leads to the same result. From the results, it is unclear whether the Tm3þ moment is magnetic by itself or induced by the Cr3þ moment. The 169Tm Mo¨ssbauer of h-TmMnO3 are studied by Salama and Stewart (2009). Representative spectra are presented in Fig. 12. There is evidence of magnetic splitting over a wide temperature range and all of the spectra were able to be fitted with the superposition of a magnetic sextet and a quadrupole split doublet in the intensity ratio of 2:1. This confirms that the MneTm exchange interaction acts only at the more prevalent Tme4b site. The magnetic moment induced on the Tm3þ 4b site and the associated hyperfine field, Bhf (which is Heff in our notation), acting at its 169Tm nucleus are expected to align with the c axis. This is because the triangular arrangements of Mn spins in the layers above and below combine to produce a molecular field acting along the c axis. Based on symmetry arguments, the c axis is also expected to be the principal of the total electric field-gradient tensor acting at the nucleus. Although the 4b site symmetry of 3 (C3) allows for a nonzero asymmetry parameter, the 2a site symmetry of 3m (C3v) does not. However, the two sites have very similar local environments so that we might expect the asymmetry

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FIGURE 12 Left panel: Representative 169Tm Mo¨ssbauer spectra for h-TmMnO3. The fitted theory curve is the sum of a magnetic sextet [red online] and an asymmetric doublet [green online] corresponding to the Tm-4b and 2a sites, respectively. Right panel: Temperature dependence of the 169 Tm hyperfine field, Bhf, at the 4b site of h-TmMnO3. The fitted theory curve is based on a simple two-singlet crystal field ground-state model (see text) with a ¼ 6, D ¼ 20K and a saturation MneTm molecular field of BM(MnTm) ¼ 1.27T. The temperature dependence of the quadrupole interaction, ð1=2ÞeQVZZ , is shown in the inset for both the 4b site (solid diamonds) and the 2a site (solid circles). These figures have been earlier published by Salama, H.A., Stewart, G.A., 2009. J. Phys. Condens. Matter 21, 386001.

parameter to be negligible for the 4b site. This approach was employed successfully with the analyses of magnetic 170Yb Mo¨ssbauer spectra of hYbMnO3 as published by Salama et al. (2008, 2009), discussed later in this paragraph. The analysis of the 4.2-K spectrum yielded a hyperfine field of 311.8  2T, which is less than half of the free ion value for insulators of 662.5T. This means that magnetic moment on the 4b site is 3.29  mB, which is approximately 47% of the maximum free ion moment of 7 mB and is indicative of significant crystal field quenching as shown in Fig. 12. The fitted quadrupole interaction parameters yielded 1/2DEQ ¼ 41.9  2 mm/s and 22.3  mm/s, respectively for the 4b and 2a sites. These values are significantly smaller than the free ion value of 58.6 mm/s, ignoring the lattice contribution. Again a strong reduction of the quadrupole interaction measured for the 4b site sextet, which is about twice that measured for the 2a site doublet as shown in Fig. 12. With increasing temperature the magnetic splitting of the 4b site collapses and eventually vanishes at 82e83K, which is in good agreement with the values of TNMn z81e84K reported. The fitted Bhf values are shown as a function of temperature in Fig. 12 and the fitted quadrupole interactions are shown in the figure’s inset. The quadrupole interactions appear to be temperature

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independent over the full range of temperature that is associated with the Mn magnetization. This behavior indicates two well-isolated singlets in the crystal field scheme. Using a set of recalculated parameters of h-YbMnO3 for the 4b site as assumed earlier by Divis et al. (2008), the crystal field of h-TmMnO3 was calculated by diagonalizing Eq. (12) for a trigonal symmetry. The most important result is a well-isolated two-singlet nonmagnetic ground state. Since the singlet states are nonmagnetic, the inducement of a net Tm3þ magnetic moment on the 4b site requires that the molecular field associated with the weak MneTm exchange interaction brings about a mixing of these levels. Under these circumstances, the induced magnetic moment is given by  0  2g2 m2 a2 BM D m ¼ J B0 tanh (40) D 2kB T where BM is the molecular field acting in the z direction (the crystallographic c axis), a ¼ h0jJzj1i is the Jz coupling parameter between the two singlets, and D0 ¼ ½D2 þ ð2gJ mB aBM Þ2 1=2 is the field enhanced energy separation of the two singlets (D is the energy separation in absence of a molecular field). In order to arrive at a theoretical estimate of the induced moment, it was assumed that the molecular field acting at the 4b site is proportional to the Mn moment. This problem was solved by using a temperature dependence described by an empirical formula by Lonkai et al. (2002). The theory curve (solid line) drawn through the experimental data in Fig. 12 corresponds to the values of BM(T ¼ 0K) ¼ 1.27  1 and the two-singlet state parameters D ¼ 20.2  2K and a ¼ 6.00  2K. Although the authors argue that the solution is not unique due to insufficient information about the crystal field, the form of the theory curve matches closely with the temperature dependence of the experimental data and is a nice example to describe such a two-singlet crystal field system. Salama et al. (2010) has studied with 169Tm Mo¨ssbauer spectroscopy the orthorhombic phase of o-TmMnO3. AC susceptibility and specific heat measurements confirm that the Mn sublattice of o-TmMnO3 orders magnetically at TNMn z41K with a weaker feature at Tc z 32K. From 169Tm Mo¨ssbauer spectra of o-TmMnO3 it appears, that down to 10K, there is no evidence of magnetic splitting and all of the spectra were fitted in terms of a single asymmetric, quadrupole split doublet. However, there is a more subtle effect of line broadening that increases with decreasing temperature. From the spectra the authors argue that the half-width of the absorption lines undergoes a sharp increase in the vicinity of Tc z 32K. Therefore, it is reasonable to assume that the transition of the Mn spin order from incommensurate to collinear antiferromagnetic results in a nonzero exchange field at the Tm site. Similar behavior was reported in an earlier 155Gd Mo¨ssbauer investigation of oGdMnO3 by Zukrowski et al. (2003), where the Mn sublattice orders at 40K, but the 155Gd hyperfine field is not observed until the lower temperature of 21K. As the temperature decreases, the quadrupole-splitting, DEQ, increases

180 Handbook of Magnetic Materials

from 1.1 cm/s at room temperature to 9.2 cm/s at 4.2K with abrupt increases close to both TNMn and Tc. Since the temperature-dependent 4f shell contribution to the electric field gradient involves a thermal average over the crystal field levels, it is unusual to observe such changes in DEQ. This aspect warrants further investigation to possible structural changes associated with the two transitions. Finally, there appears to be some additional structure in the 4.2-K spectrum, indicating the onset of a distinct magnetic hyperfine field. The distorted perovskite compound TmFeO3 has a Ne´el temperature of 630K, associated with the ordering of the 3d lattice of iron. This compound was studied with 169Tm Mo¨ssbauer spectroscopy by Hodges et al. (1984). As in the case of TmCrO3, TmFeO3 has first two excited states at 25 and 56K. Above 95K, the Fe sublattice of TmFeO3 has an antiferromagnetic component parallel to the a axis and a ferromagnetic component is parallel to the c axis. Below 80K, the antiferromagnetic component is parallel to the c axis and the ferromagnetic component is parallel to the a axis. The field inducing Tm3þ moment is parallel to the Fe3þ weak ferromagnetic component, so that the Tm3þ magnetic moment is expected to be parallel to the c axis above 95K and perpendicular to the c axis below 80K. These magnetic moments are a perturbation on the electric quadrupole-splitting. Since the authors argue that DEQ is negative, a correct interpretation can be made with the above found direction of the Tm3þ moment. For the higher temperature range above 95K the moment is increasing with decreasing temperature, until a Tm3þ moment is found of 8T (0.08 mB), and below 80K the moment increases again with decreasing temperature, until at 4.2K Tm3þ moment is found of 8.5T (0.085 mB). A possibility could be that induced hyperfine field on Tm is caused by a transferred field from the Cr sublattice to the Tm sublattice. However, that idea has not been taken into consideration. Mo¨ssbauer spectroscopy measurements have been carried out on 170Yb in some rare earth orthoaliminates (RAlO3) by Bonville et al. (1978). The relaxation behavior Yb3þ ions diluted in TmAlO3 and YAlO3 was studied. The parameters measured in the slow relaxation limit indicate an almost pure j7/2i Kramer’s doublet ground state. In this case, this diluted compound is highly anisotropic. The relaxation time in the spectra was fitted from the line shape using a simple stochastic model with diagonal hyperfine interactions by Gonzalez-Jimenez et al. (1974). The temperature dependence of the relaxation time could be fitted with a mixture of Raman and Orbach contributions between 40 and 70K. At lower temperatures just above 40K, the Orbach contribution is more dominant. In YbA1O3 a long range-ordering temperature has been found with a Ne´el temperature of 0.8K by Bonville et al. (1978). The value of the electric quadrupole-splitting 4.05 mm/s, which is the same value observed in YbAlO3, above TN. This indicates that the ground-state wave functions are consisting mainly of a j7/2i Kramer’s doublet, which is well separated from the j5/2i doublet, agreeing with a gz value of about 6.9. The hyperfine field increases as

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the temperature is lowered below TN ¼ 0.8K. Between 0.55 and 0.34K, no further increase in this field is observed, clearly showing that it has reached its maximum value. The data fit gives a maximum field of 263  5T, corresponding with a magnetic moment of 2.49  0.05 mB along a direction that is within a few degrees of the local z axis. In the spinespin-driven relaxation region, two temperature zones were observed, where the relaxation rate has, respectively, a conventional temperature-independent value and anomalous temperature-dependent values. For the third case, the YbxY1  x AlO3 compounds, the dependence of the relaxation rate on the Yb3þ concentration was studied. For YbAlO3 using a formalism based on the Fermi golden rule, the relaxation rates in the paramagnetic region arising from different types of interactions between the spins were calculated. The magnetic exchange between nearest neighbors in the ab plane is dominant for the relaxation mechanism. The origins of the moment lowering and short-range ordering observed in this system were also discussed in terms of the Yb concentration. With increasing Yb, a decreasing percentage of the relaxation of the Yb3þ is in the slow relaxation limit. For x ¼ 0.50, both groups of Yb ions show finite relaxation rates. 170 Yb Mo¨ssbauer spectroscopy measurements have been performed on hexagonal manganite h-YbMnO3 by Salama et al. (2008, 2009). Representative 170Yb Mo¨ssbauer spectra are presented in Fig. 13. The spectrum measured

170 FIGURE 13 Representative Yb Mo¨ssbauer spectra for h-YbMnO3. The fitted theory curve is the sum of relaxation subspectra for Ybe4b site [red] and the Ybe2a site [green], respectively. This figure has been earlier published by Salama, H.A., Voyer, C.J., Ryan, D.H., Stewart, G.A., 2009. J. Appl. Phys. 2010 (5), 07E110.

182 Handbook of Magnetic Materials

at the base temperature of 1.5K was able to be fitted in terms of two static, five-line, and magnetically split subspectra with intensities in the ratio of 2:1 as expected for the relative occurrence of the Yb 4b and 2a sites. Since the electric quadrupole interaction is small, it was not possible to determine the alignment of the magnetic direction with respect to the principal axis of electric field gradient. Therefore, a simple coaxial model was used. For both sites, both the hyperfine field and the electric quadrupole interaction are significantly smaller than the maximum possible Yb3þ free ion values of 412.5T and 55.77 mm/s, respectively, indicating a strong crystal field quenching. For the 4beYb site, this could be determined with the crystal field parameters as determined by Divis et al. (2008) with infra red. With increasing temperature the 2a site subspectrum collapses at 5K and presents a broad, motionally narrowed line above this temperature. However, a residual magnetic structure persists up to 20K for the 4b-site subspectrum. All of the 170Yb Mo¨ssbauer spectra could be analyzed in terms of a superposition of two relaxation broadened, magnetic subspectra with integrated intensities in the ratio of 2:1. The spectra were analyzed with the relaxation model of Wickman et al. (1966). In this model, the Kramers-doublets relaxation was described with effective spin Seff ¼ 1=2. At all temperatures, the linewidth, isomer shift, and quadrupole interaction strength were fixed at values obtained for the 1.5-K spectrum. Only the hyperfine field and the Kramers-doublets splitting were allowed to vary. The relaxation time for both sites is decreasing with increasing temperature. The 4beYb site has a longer relaxation time than the 2a site. This last shows a rapid decrease with increasing temperature below a Ne´el temperature of 5K. In Table 7 an overview has been given about the results of the rare earth Mo¨ssbauer spectroscopy of the perovskite compounds RMO3 with M ¼ Al, V, Cr, Mn and Fe and R ¼ Gd, Dy, Tm, and Yb. Whereas the rare earth sublattice orders magnetically below 5K, the 3d sublattice can have even a much higher transition up to 635K. Moreover, in the case of Tm and Yb compounds, the magnetic moments are strongly reduced with respect to the free ion magnetic moments of 7 (for Tm) and 4 (for Yb) mB above the rare-earth magnetic ordering temperature. This means that the ReM magnetic interaction is most likely the prevailing magnetic exchange in these compounds on the rare earth sites.

4.4 RMO4 Compounds The rare earth compounds of the general formula RMO4 oxides with R ¼ rare earth and M ¼ P, V, As, and Cr crystalize in two structural types depending on the size of the rare earth cation. The first member of the vanadates and chromates LaMO4 as well as the phosphate with R ¼ LaeTb and the arsenates with R ¼ LaeNd have the monazite-type structure. All the other rare earth compounds with M ¼ P, V, As, and Cr have the tetragonal zircon

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(ZrSiO4)-type crystal structure. This means that all the rare earth compounds studied with rare earth Mo¨ssbauer spectroscopy, which will be overviewed in this paragraph, have this tetragonal zircon (ZrSiO4) type of crystal structure. The slow relaxation above the magnetic ordering temperature of the compounds DyPO4 (TN ¼ 3.39K) and DyVO4 (TN ¼ 3.0K) were studied with 169 Dy Mo¨ssbauer spectroscopy. In Section 3.5 a study of DyPO4 by Forester and Ferrando (1976a) is shown as example of typical slow relaxation behavior above the magnetic ordering temperature. The slow magnetic relaxation of DyVO4 above TN has been studied by Gorobchenko et al. (1973). In Fig. 14 the inverse temperature dependence of the logarithm of the spin-lattice relaxation is shown. For DyPO4 and DyVO4 the data fall on a straight line between 36 and 16K and between 4 and 11K, respectively. The transition between the two levels of the ground-state Kramers doublet is thus an indirect scattering process, involving an excited electronic energy state at D above the ground state with U ¼ U0eD/T, known as an Orbach process (Orbach, 1961). From the slope of the straight line, it was obtained D ¼ 110K for the excited state in DyPO4 and D ¼ 40K in DyVO4, respectively.

TABLE 7 Tabulation of Magnetically Ordered Gd, Dy, Tm and Yb Compounds With a Perovskite Compounds RMO3 With M ¼ Al, V, Cr, Mn, and Fe Compound

Heff (T)

MR (mB)

TNRE ðKÞ

TNM ðKÞ

GdAlO3

29.1  0.2

6.1

3.87

e

DyCrO3

565  14

10

2.16

e

DyFeO3

582  14

10

4.5

635

TmVO3

210

2.0

15?

106

TmCrO3

82

0.8

?

124

h-TmMnO3 4b site

311.8  0.2

3.29  0.01

e

z100

o-TmMnO3

Very small

e

?

Tc ¼ 31, TN ¼ 41

TmFeO3

9

0.09

?

630

YbAlO3

263  5

2.49  0.05

0.8

e

h-YbMnO3 4b site

165.9  0.2

1.61

e

89

2a site

109.2  0.1

1.06

5

89

The hyperfine fields, the magnetic moments, and the magnetic ordering temperatures are shown for the rare earth sublattice and the magnetic ordering temperatures for the 3d sublattice.

184 Handbook of Magnetic Materials

FIGURE 14 Inverse temperature dependence of the logarithm of the spin-lattice relaxation frequencies determined from DyPO4 by Forester and Ferrando (1976a) and DyVO4 by Gorobchenko et al. (1973). This figure has been earlier published by Forester, D.W., Ferrando, W.A., 1976a. Phys. Rev. B 13, 3991.

169

Tm Mo¨ssbauer measurements were reported on TmVO4 by Triplett et al. (1974), TmPO4 by Hodges (1983), and TmAsO4 by Hodges et al. (1982). Furthermore, 170Yb Mo¨ssbauer measurements in TmMO4 and in YbMO4 (M ¼ P, V and As) were performed by Hodges (1983) and Hodges et al. (1982). The 170Yb Mo¨ssbauer experiments on the TmMO4 compounds were obtained from a source experiment on neutron-activated TmMO4 using an YbB6 absorber. The ytterbium is present as 170Yb (Ie ¼ 2, Ig ¼ 0, E ¼ 84.4 keV) at very low concentrations so that the bulk structural JahneTeller transition temperatures in TmAsO4 (TD ¼ 6.0K) and TmVO4 (TD ¼ 2.15K) are expected. The measured hyperfine parameters were used to provide information concerning the electronic properties of the rare earth ions. A set of crystalline electric field (CEF) parameters is obtained for Tm3þ in TmPO4 and in TmAsO4 in the tetragonal phase above the JahneTeller transition temperature (TD ¼ 6.0K) as shown in Fig. 15 by Hodges et al. (1982). Previously proposed CEF parameters for Tm3þ in TmVO4 (TD ¼ 2.15K) as determined by Knoll (1971) and later refined by Wortman et al. (1974) were discussed. TmAsO4 and TmVO4 have a doublet ground state with approximately the same ground-state wave functions. On the other hand, TmPO4 has a singlet ground state and consequently no JahneTeller transition. The measured ground-state properties of Yb3þ diluted into the two TmMO4 can be generated by sets of CEF parameters close to those obtained for Tm3þ in the corresponding matrix.

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FIGURE 15 Thermal variation of a ¼ DEQ, the electric quadrupole-splitting for Tm3þ in TmAsO4 from 10 to 295K (A) and from 1.4 to 24K (B). The solid curve is calculated for the tetragonal phase using the crystal field parameters given in Table 8. A clear difference exists between the extrapolation of these calculated values to low temperatures (dashed curve) and the measured values of the quadrupole-splitting in the orthorhombic phase. This figure has been earlier published by Hodges, J.A., Imbert, P., Je´hanno, G., 1982. J. Phys. 43, 1249.

Spinespin relaxation rates were measured in the paramagnetic state of the YbMO4 compounds and the origin of this relaxation rate in YbVO4 was discussed by Hodges et al. (1982). Magnetic ordering is observed in YbVO4 below about 0.15K and also in YbPO4 in a comparable temperature zone. The CEF parameters (in K) relevant to Tm3þ and Yb3þ in TmPO4, TmVO4 and TmAsO4 are given in Table 8. For Tm3þ the parameters concern the tetragonal phase (above the JahneTeller transition temperature, if it exists). For Yb3þ the tetragonal CEF parameters also account for the ground-state magnetic hyperfine parameters in the orthorhombic phase. It can be noticed that in TmAsO4 and TmVO4 Tm3þ has approximately the same ground-state wave function. However, the ground-state wave functions for Yb3þ are different in these two matrices. As mentioned by Hodges et al. (1982) this behavior is compatible with one common set of CEF parameters for both Tm3þ and Yb3þ in TmAsO4 and one common set for both Tm3þ and Yb3þ in TmVO4. Rare earth chromates belong to tetragonal compounds (I41/amd) with the general formula RMO4 with M ¼ V, P, As, and Cr, as shown by Buisson et al. (1964). These RCrO4 oxides allow us to study the effect of the magnetic interaction between the S ¼ 1/2 Cr5þ sublattice and the rare earth sublattice on the overall magnetic properties. The obtained results can be compared with

186 Handbook of Magnetic Materials

3þ n TABLE 8 The Crystal Field Parameters Am and n hr i in K Relevant to Tm 3þ Yb in TmMO4With M ¼ As, P, and V

Tm3þ in TmAsO4 Yb



A46 hr 6 i

53

22.6

980

60

86

5.9

924

63

15.6

60.7

1253

55.1

50.7

190

in TmPO4

Similar

in TmVO4

125.7

Tm Yb

A06 hr 6 i

in TmPO4





A44 hr 4 i

Similar

Tm Yb

A04 hr 4 i

in TmAsO4





A02 hr 2 i

in TmVO4

Similar with

A02 hr 2 i

¼ 208



Tm

Ground-State Wave Functions



in TmAsO4

þ0.88j5i0.44j1iþ0.19jH3i



in TmPO4

0.32jþ4iþ0.90j0i0.32j4i



in TmVO4

w0.89j5i0.42j1iþ0.19jH3i

Tm Tm

Tm

But probably slightly richer in j5i

Yb3þ

Ground-State g Values

Ground-State Wave Functions

Yb3þ in TmAsO4

gz ¼ 0.4 and gt ¼ 3.60

aj5/2i þbjH3/2i

Yb3þ in TmPO4

gz ¼ 1.2 and gt ¼ 3.19

Probably aj5/2iþbjH3/2i

Yb3þ in TmVO4

gz ¼ 6.45 and gt ¼ 0.6

aj7/2i þbjH1/2i

For Tm3þ the parameters concern the tetragonal phase above the JahneTeller transition temperature if it exists. The Tm3þ ground-state wave functions and the Yb3þ experimental ground-state g values and wave functions are shown in TmMO4. This table has been earlier published by Hodges, J.A., 1983. J. Phys. 44 833.

other RXO4 compounds, of which M is not magnetically ordered. We focus our study on the derivates where R ¼ Nd  Lu showing the same tetragonal structural type, so that only a different electronic constitution of the rare earth ion could produce a change in the properties of these oxides. Formerly, with neutron diffraction, it was found that ferromagnetic TbCrO4, as shown by Buisson et al. (1976) undergoes at T ¼ 48K a second-order phase transition from a tetragonal to an orthorhombic symmetry. Since only GdCrO4, TmCrO4, and YbCrO4 have been studied with rare earth Mo¨ssbauer spectroscopy, this paragraph will be restricted to these compounds, respectively published by Jimenez-Melero et al. (2006), Jimenez et al. (2004a, 2004b). The results on TmCrO4 by Jimenez et al. (2004b) are further supplied with later-performed measurements. Study of the crystal structure of GdCrO4 has been performed by the roomtemperature X-ray diffraction data. The derived structural parameters have

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been employed as initial values in the refinement of the neutron diffraction data between 2 and 300K. In this way, accurate oxygen coordinates have been obtained which, in turn, have yielded appropriate bond distances and angles for the coordination polyhedron of both Cr5þ and Gd3þ. Furthermore, bulk magnetic measurements indicated the presence of a ferromagnetic order in this compound below Tc ¼ 22K. The analysis of the neutron diffraction pattern at lower temperatures has allowed us to determine the established magnetic structure. The ordered magnetic moment of the ion is located along the crystallographic c axis, while that associated with the Gd3þ ion forms an angle of z 24 with the mentioned axis. Moreover, specific heat measurements reveal the presence of a second weaker magnetic transition at lower temperatures. Such a transition has been confirmed by subsequent 155Gd Mo¨ssbauer spectroscopy experiments as shown in Fig. 16. The Mo¨ssbauer spectra indicate that only 20% of Gd orders

1240000 1220000 1000000

Intensity (counts)

960000 840000

800000 480000 460000 1260000

1200000 -4

-2

0

2

4

FIGURE 16 155Gd Mo¨ssbauer spectra of GdCrO4 measured between 4.2 and 36K. Two subspectra were observed with an intensity ratio of 80% and 20%. The 80% subspectrum show magnetic order below 8K, whereas the 20% subspectrum show magnetic order below 22K. This figure has been earlier published by Jimenez-Melero, E., Gubbens, P.C.M., Steenvoorden, M.P., Sakarya, S., Goosens, A., Dalmas de Re´otier, P., Yaouanc, A., Rodrı´guez-Carvajal, J., Beuneu, B., Isasi, J., Sa´ez-Puche, R., Zimmermann, U., Martı´nez, J.L., 2006. J. Phys. Condens. Matter 18, 7893.

188 Handbook of Magnetic Materials

magnetically at 22K, while the remaining 80% do not show any magnetic order down to around 10K as shown for the hyperfine fields in Fig. 17. This 80% Gd site may be attributed to a low-temperature orthorhombic phase. The following mSR results indicate that the whole Cr5þ sublattice presents a magnetic order at the mentioned value of the Curie temperature. Besides that, short-range GdeCr magnetic correlations have been clearly observed in the paramagnetic state. Bearing all these facts in mind, we can conclude that the Cr5þ ion presents a ferromagnetic order at the temperature of 22K, and induces the magnetic order in the 20% Gd3þ sublattice via a relatively large GdeCr exchange field. Since the ordered moments of both sublattices are not fully collinear (as expected due to the isotropic nature of the Gd3þ ion), a small anisotropic contribution should be present in the GdeCr magnetic exchange interactions. The magnetic order of the remaining 80% Gd3þ sublattice, resulting from an orthorhombic distortion, takes place at a lower temperature of around 10K. However, further experimental evidence seems to be necessary to shed more light on the nature of this second magnetic transition. The experimental observation of the magnetic order in the rare earth sublattice being induced by the Cr5þ order can help us to better understand the magnetic properties in the remaining RCrO4. Since it was found that the Tm-ordered magnetic moment in TmCrO4 was axial, but uncommonly strongly reduced with respect to the free ion value of 7 mB, it is of interest to study TmCrO4 further with magnetization, specific heat, neutron diffraction, 169Tm Mo¨ssbauer spectroscopy, inelastic neutron 8

GdCrO4

7 6

Heff (T)

5 4 3 2 1 0 -1

0

5

10

15

20

T (K)

25

30

35

40

FIGURE 17 Temperature dependence of the magnetic hyperfine field of GdCrO4. Whereas the 20% subspectrum of the tetragonal phase 1 shows an hyperfine field over the whole temperature range below Tc ¼ 23K, no clear hyperfine field has been found for the 80% subspectrum of the orthorhombic phase 2 between 8 and 22K. This figure has been earlier published by JimenezMelero, E., Gubbens, P.C.M., Steenvoorden, M.P., Sakarya, S., Goosens, A., Dalmas de Re´otier, P., Yaouanc, A., Rodrı´guez-Carvajal, J., Beuneu, B., Isasi, J., Sa´ez-Puche, R., Zimmermann, U., Martı´nez, J.L., 2006. J. Phys. Condens. Matter 18, 7893.

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189

scattering, and muon spin relaxation (mSR) to understand the magnetic behavior of the Tm3þ and Cr5þ sublattices and their mutual magnetic interplay. Temperature dependence of the magnetization of TmCrO4, measured in external fields of 50 and 250 Gauss, shows clearly hysteresis in the magnetization below Tc ¼ 18.75K. The magnetic specific heat of TmCrO4 at zero field shows clearly quite a broad peak with a maximum at 15.3K. In fact the magnetic transition starts at around 20K. From T ¼ 20 to 15.3K, magnetic order starts to build up. The experimental change in the entropy due to the transition is 5.73 J/mol K. The theoretical value for Cr5þ (S ¼ 1/2) is 5.76 J/mol K, which confirms that the Cr5þ is fully ordered. However, there seems to be no contribution coming from the Tm3þ sublattice. It may be due to the fact that Tm3þ is not yet magnetically ordered in the sample around the transition. A study on the magnetic structure of TmCrO4 at T ¼ 2K determined with neutron diffraction shows two ferromagnetic Tm and Cr sublattices both parallel to the c axis with magnetic moments of 0.83  0.04 mB and 3.64  0.06 mB for the Cr5þ and Tm3þ, respectively. Moreover, the neutron diffraction measurements show that above z 40K the structure of the sample is tetragonal, whereas below z 40K, it is mainly orthorhombic (about 80%). This means that the Tm magnetic moment is relatively very small to the free ion value of 7 mB. The total angular momentum might partly quenched due to the competition with the Cr5þ sublattice. On the other hand, high-order crystal field terms might also influence the ground state, leading to such a smaller magnetic moment. In Fig. 18 the temperature dependence of some of the 169Tm Mo¨ssbauer spectra measured from 4.2 up to 300K are shown. The spectrum at T ¼ 4.2K consists of two magnetic sextets with a proportion of four to one and a nonmagnetic doublet. As shown, the spectrum at T ¼ 28K had to be clearly analyzed with two quadrupole doublets. This is also the case for the spectra up to 300K. Thus, the Mo¨ssbauer results do not confirm directly the picture found by neutron diffraction that above 40K the structure of the sample is only tetragonal, whereas below 40K, it is mainly orthorhombic (75%). In Fig. 19 the temperature dependences of the 169Tm hyperfine fields of the two structures are shown together with the percentage of magnetic ordering. This behavior indicates also the first-order character of the magnetic transition of the Tm sublattice. In Fig. 20 at 20K, some inelastic bumps were observed, which are not any more present at 70K. This behavior gives support for the interpretation that these bumps belong to the crystal field of the orthorhombic structure of TmCrO4 below 40K. In Fig. 21 the temperature dependence of the relaxation rate lZ is shown. Three different anomalies are shown. The first one below T ¼ 10K is indicative for the first-order magnetic transition of the Tm sublattice. The second one at Tc ¼ 18.75K represents the second-order magnetic transition of the Cr sublattice. Finally, the drop of lZ around 30e40K might be indicative either for the structure transition from orthorhombic to tetragonal and subsequently a crystal field change. This drop might also

190 Handbook of Magnetic Materials

1.000 0.985 1.000 0.986 1.000 0.986 1.000 0.993

-400

-200

0

200

400

FIGURE 18 Several 169Tm Mo¨ssbauer spectra measured in the magnetically ordered phase below T ¼ 17.5K (Tc ¼ 18.75K). As shown at T ¼ 4.2K the spectra consist of a nonmagnetic and a magnetic part. The last one is decreasing with increasing temperature. At T ¼ 4.2K the magnetic part of the Mo¨ssbauer spectrum has been analyzed with two subspectra in an intensity ratio of 75% and 25%. Since between 10 and 17.5K the two magnetic spectra are not discernable, only one averaged magnetic spectrum has been analyzed. As shown at T ¼ 18K, above 17.5K no magnetic splitting was observed. The nonmagnetic part of the Mo¨ssbauer spectra has been analyzed with two electric quadrupole doublets with intensity ratios of 75% and 25%. This figure was published by Jimenez E., Gubbens, P.C.M., Sakarya, S., Stewart, G.A., Dalmas de Re´otier, P., Yaouanc, A., Isasi, J., Sa´ez-Puche, R., Zimmermann, U., 2004b. J. Magn. Magn. Mater. 272e276, 568.

indicate the energy peak of about 30K, representing a crystal field transition, observed in the inelastic neutron scattering spectrum. One can conclude that from the magnetization, mSR and 169Tm Mo¨ssbauer measurements of TmCrO4 show that the Cr sublattice orders with a secondorder magnetic phase transition at Tc ¼ 18.75K and the Tm sublattice orders gradually at lower temperatures with a first-order magnetic phase transition, which agrees with the hysteresis observed in the bulk magnetization measurements. This means that in the Tm sublattice a first-order magnetic phase transition is observed and the magnetism is induced in the Tm sublattice by the TmeCr magnetic interaction. Therefore, one can expect that the crystal field scheme of Tm has a nonmagnetic singlet ground state. We estimate an eigenfunction aj4iþbj0icjþ4i with c ¼ a as shown in Table 9. Under an

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3 100

500

Hyperfine Field [T]

191

400 300 [%] 200 100 0

0 0

5

10

15

20

Counts [Arbitrary units]

FIGURE 19 Temperature dependence of the 169Tm hyperfine field below Tc ¼ 18.75K. At T ¼ 17.8 and 18.1, no hyperfine field splitting has been observed. Above T ¼ 10K, only an averaged hyperfine field is observed. The lines are drawn to guide the eyes. The crosses indicate the percentage of the intensity ratio of the nonmagnetic part of the Mo¨ssbauer spectrum. This figure is not yet published.

70 K

20 K

−10

−5

0

5

10

15

Energy Transfer [meV] FIGURE 20 Inelastic neutron scattering measurements of TmCrO4 taken at T ¼ 20 and 70K. It had to be noted that the bump at an energy of about 2e3 meV (z30K), observed at T ¼ 20K, is not present at T ¼ 70K. Therefore, these bumps have to be ascribed to the orthorhombic and not to the tetragonal structure. The higher points are an enlargement of the lower ones. This figure is not yet published.

192 Handbook of Magnetic Materials

( s )

TmCrO4

Z

zero-field

FIGURE 21 Temperature dependence of the relaxation rate lZ. At Tc ¼ 18.75K the asymmetry has a loss of 2/3 of its signal and the lZ a sharp maximum, indicating the magnetic ordering temperature of the Cr sublattice in TmCrO4. The anomaly below 10K is indicative for a first-order magnetic transition of the Tm sublattice in TmCrO4. The drop around T around 30e40K can be related with a structure transition from orthorhombic to tetragonal and subsequently a crystal field change. An alternative explanation is the coincidence with an energy of z30K in the inelastic neutron scattering spectrum, as shown in Fig. 20. This figure is not yet published.

influence of magnetic exchange, this eigenfunction will purify in the direction of a pure j4i, as shown above in Table 9. This provisional approach fits nicely for the orthorhombic structure (site I), but much less for the tetragonal structure (site II). Likely, higher energy inelastic neutron scattering is needed to determine a full crystal field diagram both in the tetragonal and orthorhombic phases than as shown in Fig. 20. In contrast with neutron diffraction

TABLE 9 The Values of the 169Tm Hyperfine Fields of TmCrO4 in Tesla, Their Corresponding Magnetic Moments in mB and the 4f-Contribution of the 169 Tm Electric Quadrupole-Splitting Measured at T ¼ 4.2K Site I (75%)

Site II (25%)

Free Ion Value

Pure j4iValue

Heff(T)

412

367

662.5

441.7

Magnetic moment (mB)

4.4

3.9

7.0

4.67

1 eQV 4f ðmm=sÞ zz 2

þ12.0

7.1

þ176

þ16

The values of the last parameter are determined by subtracting the lattice contribution (determined from 155Gd Mo¨ssbauer Spectroscopy on GdCrO4) from the total measured electric quadrupole4f is proportional to 3J 2 JðJ þ 1Þ, this value is easy to calculate for a pure splitting. Since ð1=2ÞeQVzz z j4i state.

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at high temperatures above 40K, TmCrO4 shows still two electric quadrupolesplittings. That would mean that there still two crystal structures are present. No explanation for this behavior has been yet given. In contrast with TmVO4 and TmAsO4, which show JahneTeller transitions due to doublets as ground states, TmPO4 and TmCrO4 do not show this effect due to a singlet ground state. On the other hand, the occurrence of two slightly different crystallographic Tm sites even at T ¼ 28K is indicative of a JahneTeller transition in TmCrO4. Since we found the same type of results in GdCrO4 compound in which Gd has no crystal field, one can argue that this JahneTeller behavior can be ascribed to the Cr5þ sublattice. The 170Yb Mo¨ssbauer spectra on YbCrO4 were measured between 4.2 and 30K by Jimenez et al. (2004a). Some selected spectra are represented in Fig. 22. An extra absorption has been detected near the center of the spectrum coming from an impurity phase, the Yb2O3 oxide, whose known spectrum has been included in Fig. 22 as a dashed line. Its substantially high Debye temperature, when compared with the one corresponding to the YbCrO4 compound, can probably be the cause for its seemingly large Mo¨ssbauer percentage, which amounts to 35%  10%. The YbCrO4 Mo¨ssbauer spectra comprise only a quadrupolar contribution between 25 and 30K, with a quadrupole-splitting of 1.75 mm/s. Below 25K, a mixed magneticequadrupolar hyperfine pattern is clearly present. In local tetragonal symmetry the principal axis of the electric field gradient tensor is along the fourfold symmetry axis. The spectrum at 4.2K has a hyperfine field of 55T, corresponding to a Yb magnetic moment of 0.55 mB, which is significantly reduced with respect to the free ion value of gJ ¼ 4 mB. Moreover, the hyperfine field is perpendicular to the c axis. In Yb compounds, an isolated Kramers is usually the ground state of Yb3þ ion. Such doublet can be described by an effective spin S ¼ 1=2 and a spectroscopic g-tensor, which, in the case of axial symmetry, has two components gz and gt. In local tetragonal symmetry, these crystal field eigenfunctions of the doublets are mixtures. From the measured values of the quadrupolesplitting and gt ¼ 1.1 at 4.2K, the approximate wave function for the ground state is 0.87j7/2iþ0.49j1/2i. This wave-function results in gz ¼ 5.8 These values are relatively close to those obtained for the Yb3þ ion in YbVO4: gz ¼ 6.46 and gt ¼ 0.77, and in YVO4: gz ¼ 6.08 and gt ¼ 0.85 as shown by Bowden (1998). Surprisingly, in the magnetically ordered state, the Yb moments do not lie along the easy c axis but in the ab plane, which is the hard magnetic plane. Therefore, the YbeCr exchange imposes the direction of the Yb magnetic moments with the Cr5þ ion having an isotropic g-tensor. The saturated moment of the Cr5þ ion is 2S ¼ 1 mB. The magnetic moment of the Yb3þ ion depends on the orientation of the magnetic field. For a polycrystalline sample, the saturated magnetization of an extremely anisotropic doublet (i.e., gt/gz  1) averaged over all orientations is ð1=4Þgz mB . From this result for Yb in YbCrO4 (gt/gz z 0.2), it is 1.45 mB. Then, the remanence

194 Handbook of Magnetic Materials FIGURE 22 170Yb Mo¨ssbauer spectra of the YbCrO4 oxide. The dashed line represents the spectrum of the impurity phase Yb2 O3. This figure is published by Jimenez E., Bonville, P., Hodges, J.A., Gubbens, P.C.M., Isasi, J., Sa´ez-Puche R., 2004a. J. Magn. Magn. Mater. 272e276, 571.

moment at 2K is of 0.55 mB per formula unit. This gives a ferrimagnetic structure with the YbeCr coupling being antiferromagnetic. In contrast with GdCrO4 and TmCrO4, no structure change behavior has been found in YbCrO4 as far as known. In this respect, YbCrO4 resembles ErCrO4.

4.5 RBa2Cu3O7 Compounds In this paragraph the magnetic influence of rare earth on the high-temperature orthorhombic SC compounds RBa2Cu3O7 (Tc ¼ 90K) as studied with rare earth Mo¨ssbauer spectroscopy will be discussed. A comparison will be made with the tetragonal nonsuperconducting (NSC) but magnetic compounds RBa2Cu3O6 (TN z 400K). Since the measuring technique of rare earth Mo¨ssbauer spectroscopy is not sensitive for superconductive parameters, only direct or indirect magnetic parameters of RBa2Cu3O7 compounds can be determined. The compound PrBa2Cu3O7  y has a rather special place in the yttrium and rare earth-substituted RBa2Cu3O7  y compounds, because this compound is not a superconductor as shown by Soderholm et al. (1987), but a semiconductor and the CueO planes order antiferromagnetically near 280K. This is in contrast to all other compounds of this stoichiometry, for which no such ordering is observed. Moreover, it has by far the highest transition temperature for the antiferromagnetic ordering of the rare earth sublattice (17K), much

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larger than the corresponding Gd compound. Originally, the suppression of the SC state in PrBa2Cu3O7  y was attributed to the filling of the SC holes due to a tetravalent or mixed valency of Pr as was shown by X-ray absorption spectroscopic studies by Dalichaouch et al. (1988). However, later studies excluded the presence of any Pr4þ in PrBa2Cu3O7  y. The hybridization of the Pr-4f levels with the CueO plane bands was instead postulated as a cause for the suppression of the SC state, but questions remained because some of these studies did show some features that could not be explained on the basis of solely trivalent Pr as argued by Lytle et al. (1990). Since the isomer shift and the hyperfine field in Mo¨ssbauer spectroscopy are the most direct ways of measuring the valency and the ground state magnetic moment of Pr in PrBa2Cu3O7  y, 141Pr Mo¨ssbauer spectra of PrBa2Cu3O7  y were measured at 4.2 and 25K. In addition, the formally tetravalent PrO2, the intermediate valent Pr6O11 and the trivalent Pr2O3 compounds were measured at 25K, as shown by Moolenaar et al. (1994, 1996). These spectra are shown in Fig. 23. In Fig. 24, the isomer shift is plotted against the valency. One can see that the isomer shift of PrBa2Cu3O7  y lies in between that of Pr2O3, Pr6O11, and PrO2. However, because of reasons of entropy and because of the fact that at ambient oxygen pressure only Pr6O11 is stable, it is almost inevitable that PrO2 is to some extent oxygen deficient as shown Section 4.2. Because, due to this oxygen deficiency, the isomer shift is presumably too low, we therefore compare the isomer shift of PrBa2Cu3O7y at 25K with that of Pr2O3 and Pr6O11. Assuming a linear relationship between the valency and the isomer shift, for PrBa2Cu3O7  y, a valency for the isomer shift was found of 3.4  0.1. However, the Mo¨ssbauer peak of PrBa2Cu3O7y is much broadened with respect to that of Pr2O3. Such a broadening can probably not be attributed to an electric field gradient, for its influence is negligible in 141 Pr Mo¨ssbauer spectroscopy. The broadening of the peak must then be ascribed to a distribution in isomer shifts. Furthermore, Fig. 23 reveals that the spectrum at 4.2K is magnetically split. Analysis of this spectrum gives a hyperfine field of 29(3)T. This is only 10% of the free-ion value of 326T and less than that of PrO2, indicating for this sample a small magnetic moment of 0.32  0.03 mB only, which is about half the value found by Li et al. (1989). However, the resonance absorption effect we observe at 4.2K is less than that at 25K, in sharp contrast to PrO2. The analysis furthermore required a rather large peak width. Therefore, we suggest that in Fig. 23 essentially the inner part of a relaxation spectrum is shown. This means that the moment of the Pr ion is fluctuating on the characteristic time scale of 141 Pr Mo¨ssbauer spectroscopy. Another explanation would be that the spectrum is composed of two subspectra, one from a tetravalent and magnetically ordered part, and one from a trivalent part which has only a small induced moment. The tetravalent part must then be hidden in the background. Then it can exclude the possibility of a single hyperfine field, that is, there must be a wide distribution in hyperfine fields. However, such a distribution is in

196 Handbook of Magnetic Materials

FIGURE 23 141Pr Mo¨ssbauer spectra of Pr2O3, Pr6O11 and PrO2 at 25K, and PrBa2Cu3O7  y at 4.2 and 25K. This figure is published by Moolenaar, A.A., Gubbens, P.C.M., van Loef, J.J., Menken, M.J.V., Menovsky, A.A., 1994. Hyperfine Interact. 93, 1717.

contradiction with the results of Li et al. (1989). Concluding, 141Pr Mo¨ssbauer spectroscopy on PrBa2Cu3O7  y shows clearly an intermediate valency and at low temperature (<17K) not a well-defined magnetic order. 151 Eu and 141Pr Mo¨ssbauer spectroscopy was used to study the effects of Pr substitution for Eu or Ba atoms in Eu1  x PrxBa22Cu3O7  d and EuBa2  x$xPrxCu3O7  d, respectively as published by Klencsar et al. (2000a, 2000b) and Kuzmann et al. (2000). It was found that there exists a correlation

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

197

FIGURE 24 Isomer shift values from the 141 Pr Mo¨ssbauer spectra of Pr2O3, Pr6O11, PrO2 and PrBa2Cu3O7  y measured as a function of the valency according to the number of the oxides. The valency of PrBa2Cu3O7  y[I] is obtained by linearly interpolating between the isomer shifts of Pr2O3, Pr6O11and PrO2. This figure is earlier published by Moolenaar, A.A., Gubbens, P.C.M., van Loef, J.J., Menken, M.J.V., Menovsky, A.A., 1996. Physica C 267, 279.

between the 151Eu isomer shift and the onset temperature of the SC transition, independent of the location of Pr. This shows that the extra electrons provided by the Pr increase the electronic density in the copper oxide planes and in the 4f orbitals of Eu3þ, simultaneously. The polycrystalline compound EuBa1.3Pr0.7Cu3O7  d has been investigated by 141Pr Mo¨ssbauer spectroscopy. The observed 141Pr isomer shift, of 0.10(15) mm/s relative to PrF3, reflects a valence state of 3þ for the Pr located at the Ba site in EuBa1.3Pr0.7Cu3O7  d, being in contrast to the valence state of 3.4þ found earlier for Pr, which was situated at the rare earth site as shown in Fig. 24. This means that the valence state of Pr substituted for Eu is different from that of Pr substituted for Ba. These results suggest that the suppression of superconductivity by Pr substituted for the rare earth atoms is a consequence of a hole-filling effect. 155 Gd Mo¨ssbauer studies of Pr0.925Gd0.075Ba2Cu3O7  d were measured in the tetragonal (d ¼ 0.9) and orthorhombic (d ¼ 0.1) phases by Wortmann and Felner (1990). Below 7.5K and 16.5K, the quadrupole doublets shown exhibit broadenings in their line widths, which are caused by magnetic hyperfine interactions as shown in Fig. 25. In the orthorhombic phase, such effects are expected below TN ¼ 17K as shown by Li et al. (1989) because of the magnetically ordered Pr neighbors. The temperature dependence and

198 Handbook of Magnetic Materials

FIGURE 25 Temperature dependence of the 155Gd resonance line width Wexp in both phases of Gd doped PrBa2Cu3O7  d Full (open) squares denote the fully (partly) oxidized orthorhombic sample, and full circles, the tetragonal sample. This figure is earlier published by Wortmann, G., Felner, I., 1990. Solid State Commun. 75, 981.

magnitude of the magnetic interactions are, however, quite different from the splittings observed in the GdBa2Cu3O6.9 systems below TN ¼ 2.3K. In addition, the resonance lines are strongly broadened, indicating either a distribution of magnetic hyperfine fields with random orientations or dynamic fluctuations of the Gd moment with respect to the ordered Pr sublattice, in which the Pr moments are also randomly ordered as shown above. Even at the lowest temperature (1.4K), far below the magnetic ordering temperature of the orthorhombic Pr system, the corresponding values in orthorhombic GdBa2Cu3O6.9 is Beff ¼ 290kG. This behavior was explained by the weak exchange mechanism between the hybridized 4f electrons of Pr and the localized 4f electrons of Gd3þ. For the tetragonal phase, it was clearly stated that the magnetic ordering of the Pr sublattice occurs at a considerably lower temperature, at TN ¼ 7.5(5)K as shown in Fig. 25. This ordering behavior as revealed by the increase of W, indicates, as in the orthorhombic case, a weak coupling of the Gd moment to the Pr sublattice. The magnetic nature of the ordering (probably antiferromagnetic) was not given by this study of Wortmann and Felner (1990). A comparable study has been performed on Pr1  xYxBa2Cu3O7 by Hodges et al. (1993). Therefore, 170Yb3þ Mo¨ssbauer spectroscopy was used on Yb3þ diluted in Pr1  xYxBa2Cu3O7 and PrBa2Cu3O6. The substitution of Pr3þ for Y3þ decreases the SC transition Tc, and for x > 0.6 the system is no longer SC. This behavior is probably due to the influence of hybridization between the Pr3þ orbitals and those of the Cu subsystem as shown above. Mo¨ssbauer

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spectra in the fully substituted (NSC) PrBa2Cu3O7 are shown in Fig. 26. They can be interpreted with a single spectrum at each temperature. The thermal variation of the derived parameters are also shown in Fig. 26. At all temperatures, the Yb3þ ion experiences a molecular field of 0.2T coming from the ordered Cu(2) sublattice (TN z 300K), and below 16K, they experience a molecular field coming from the ordered Pr3þ sublattice. This relaxation is driven by the coupling between the Yb3þ and the collective excitations of the Pr3þ sublattice. Below 16K, the Yb3þ relaxation rate drops sharply and it follows a thermal excitation law with a characteristic energy of 54K. This energy scale is linked to that of the separation between the lowest crystal field levels of the Pr3þ ion. At intermediate x levels, inhomogeneous local behavior is observed and is attributed to the influence of statistical variations in the Pr3þ/Y3þ occupancies. The results of this study agree with those shown above from the 141Pr Mo¨ssbauer spectroscopy on PrBa2Cu3O7  y. The temperature dependence of the isomer shift and the recoil-free fraction of the 21.6-keV Mo¨ssbauer resonance of 151Eu is studied in the high-Tc

FIGURE 26 Mo¨ssbauer absorption on 170Yb substituted into PrBa2Cu3O7 (left). The line shapes are governed by the size of the static molecular field acting on the Yb3þ and by the Yb3þ paramagnetic relaxation rate (right top). Below 16K, the relaxation rate follows an excitation law-dependence (right bottom). This figure is earlier published by Hodges, J.A., le Bras, G., Bonville, P., Imbert, P., Je´hanno, G., 1993. Physica C 218, 283.

200 Handbook of Magnetic Materials

superconductor EuBa2Cu3O7  x between 4.2 and 300K by Wortmann et al. (1988a, 1988b), Nagarajan et al. (1988), Eibschu¨tz et al. (1987), and Coey and Donnelly (1987). These four studies show the same results. For Eu, it was found that it has a stable 3þ ion value from its isomer shift. The Mo¨ssbauer Debye temperature is typical for an ionic oxygen surrounding and no anomaly near Tc was found. The electric field gradient tensor Vzz ¼ 3.1  5 1017 V/cm2 and the asymmetry parameter h s 0 have been determined by Wortmann et al. (1988a, 1988b). The magnetic ordering of the Gd sublattice in the orthorhombic and tetragonal structure of GdBa2Cu3O7  d have been studied by Mo¨ssbauer spectroscopy using the 86.5-keV gamma resonance of 155Gd by Wortmann et al. (1987), Smit et al. (1987) and Bornemann et al. (1987). Below the Ne´el temperature of TN ¼ 2.4K, the magnetic hyperfine field at the Gd nucleus reflects the increasing local sublattice magnetization extrapolating to a saturation value of Heff(T ¼ 0K) ¼ 31.5T (S ¼ 7/2). The effective magnetic hyperfine field is found to be parallel to the main axis of the electric field gradient tensor [Vzz ¼ (4.6  0.2)  1017 V/cm2] with an asymmetry parameter of h ¼ 0.40  0.05. The observed isomer shift and the value of Heff are typical for trivalent Gd. For both, the orthorhombic and tetragonal structures of GdBa2Cu3O7  d, the same type of values have been found by all three groups. The high-Tc superconductor DyBa2Cu3O7  x as shown Fig. 27 and its oxygen deficient tetragonal NSC counterpart have been studied by 161Dy Mo¨ssbauer spectroscopy down to 0.05K as shown by Hodges et al. (1988). Comparable spectra of DyBa2Cu3O7  x have been published by Wortmann et al. (1989). In Table 10 the results of the fit and the calculations of the parameters are given. The low temperature Dy3þ magnetic properties, which are similar in the two compounds, show the influence of crystal fields and the DyeDy magnetic correlations. The difference between the values of the 4f shell parameters in the SC and NSC samples is much smaller than the widths of the distributions in either sample. The observed Dy3þ sublattice magnetic ordering is chiefly attributed to superexchange with a smaller contribution coming from the dipoleedipole interaction. The ground states show only a modest anisotropy. The Dy3þ paramagnetic fluctuation rates also show the influence of these correlations. Magnetic ordering occurs within the Dy sublattices near 1K. The Dy3þ saturated magnetic moments show fairly large distributions around mean values of 7.0 (SC) and 7.3 mB (NSC). These distributions are attributed to crystal field inhomogeneities linked to the sample microstructure. Both the susceptibility and the Mo¨ssbauer paramagnetic relaxation rate measurements show that DyeDy magnetic correlations are present above the Dy3þ long-range magnetic ordering temperature. However, temperature dependence indicates an Orbach behavior further above the magnetic ordering temperature in agreement with a first excited state of 40K. In the same way as described in Section 3.6.1 for TmBa2Cu3O7  x, Bergold et al. (1990) have determined the crystal field parameters of the

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FIGURE 27 161Dy Mo¨ssbauer absorption in orthorhombic superconducting state DyBa2Cu3O7  x. At 0.05K in the magnetically saturated state, the line fits are obtained in terms of linearly correlated Gaussian distribution in the hyperfine field and in the electric field gradient taking into account the Boltzmann populations of the nuclear levels. At the three other temperatures, which are above the Dy3þ long-range ordering temperature, the line fits are obtained in terms of a paramagnetic relaxation model. This figure is earlier published by Hodges, J.A., Imbert, P., Marimom da Cunha, J.B., Hammann, J., Vincent, E., Sanchez, J.P., 1988. Physica C 156, 143.

tetragonal phase of DyBa2Cu3O7  x. Due to the magnetic character of the CF-split doublets of Dy3þ (Kramers ion with J ¼ 15/2), the spectra exhibit magnetic broadenings, which increase with decreasing temperature. Their 161 Dy Mo¨ssbauer spectra were analyzed in terms of an axial quadrupole interaction and the magnetic relaxation line broadening mechanism described by Wegener (1965). The electric field gradient values were derived as a function of temperature. Although an asymmetric electric field gradient is expected for the orthorhombic phase, inclusion of h as an additional parameter failed to improve the quality of their spectrum fits. Therefore, a crystal field analysis of the quadrupole-splitting was performed only for the data of the tetragonal phase. The results of tetragonal HoBa2Cu3O7  x of Allenspach et al. (1989a) have been used. The determined crystal field

202 Handbook of Magnetic Materials

TABLE 10 161Dy Mo¨ssbauer-Derived Hyperfine Parameters in the Dy3þ Magnetically Saturated Region for Superconducting (SC) and Nonsuperconducting (NSC) DyBa2Cu3O7  x Values Superconducting State

Values Nonsuperconducting State

Heff

415  40

430  25

hjJzjiT¼0

5.3  0.5

5.5  0.3

MT ¼ 0 (mB)

7.0  0.7

7.3  0.4

exp VZZ ð1021 V=m2 Þ

16.2  7.6

18.2  5.1

lat ð1021 V=m2 Þ VZZ

6.0

5.3

4f ð1021 V=m2 Þ Vzz

22.2  7.6

23.5  5.1

h3Jz2

JðJ þ 1ÞiT ¼0

45.6  15.6

48.5  10.5 exp VZZ

4f are obtained from the experimental values The VZZ after correcting for the lattice contribution lat estimated by extrapolating from isomorphous Gd3þ compounds. The Dy3þ 4f shell properties VZZ derived from these hyperfine parameters are also given as shown by Hodges et al. (1988).

parameters are included in Table 11 of where they are seen now to compare more favorably with their counterparts measured via inelastic neutron scattering for the orthorhombic DyBa2Cu3O6.9 phase as determined by Allenspach et al. (1989b). The results of both are roughly in the same range. 166 Er Mo¨ssbauer measurements, down to 0.05K, have been reported for the high-Tc superconductor ErBa2Cu3O7  x (SC) and for its oxygen deficient, tetragonal, NSC counterpart by Hodges et al. (1989). In Fig. 28 several of the 166 Er Mo¨ssbauer spectra in orthorhombic SC state ErBa2Cu3O7  x are shown. A rough estimate for the magnetic transition temperature for the SC and NSC samples is 0.6K. However, magnetic fluctuations are observed around this temperature. From the relaxation broadening (D) of the 166Er Mo¨ssbauer spectra the temperature dependence of the splitting of the ground state doublet around the magnetic ordering has been determined. For the SC compound a decreasing value of D with increasing temperature has been found. On the other hand, for the NSC sample D is roughly constant near the magnetic ordering temperature. No explanation for this behavior has been given. However, magnetic fluctuations are observed around this temperature. In Table 12 the found values for the hyperfine field and the electric quadrupolesplitting are given. Using the relation (Heff/m) y 850T/mB between the hyperfine field and the magnetic moment of the Er3þ ion saturated magnetic moments were found of 4.2  0.1 and 3.7  0.1 mB for the SC and NSC samples, respectively. In both materials the magnetic moments are strongly reduced compared to the free ion value of 9 mB owing to the influence of the

B02 (K)

B22 (K)

B02 (mK)

B24 (mK)

B44 (mK)

B06 (mK)

B26 (mK)

B46 (mK)

B66 (mK)

Tetragonal (NSC)

1.04

0

þ13.1

0

59.2

þ32.1

0

þ1.05

0

Orthorhombic (SC)

1.16

0.36

þ16.3

3.9

77.8

þ22.1

4.85

þ0.604

þ4.85

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

TABLE 11 Comparison of the Determined Crystal Field Parameters Bm n for Nonsuperconducting (NSC) Phase of Tetragonal DyBa2Cu3O7  x by Bergold et al. (1990) With the Parameters of the Superconducting Orthorhombic Phase of DyBa2 Cu3 O7  x as Determined With Inelastic Neutron Scattering by Allenspach et al. (1989b)

203

204 Handbook of Magnetic Materials

FIGURE 28 166Er Mo¨ssbauer spectra in orthorhombic superconducting state ErBa2Cu3O7  x. The line shape in the magnetically saturated Er3þ region at 0.05K was fitted with an effective hyperfine field model. The line shapes at the two other temperatures were fitted with a longitudinal relaxation model (see text). This figure is earlier published by Hodges, J.A., Imbert, P., Marimom da Cunha, Sanchez, J.P., 1989. Physica C 160, 49.

CEF. Inelastic neutron scattering experiments on tetragonal and orthorhombic ErBa2 Cu3O7  x seem to confirm the similarity of the leading CEF parameters in the two compounds as performed by Allenspach et al. (1989a). In addition to the 169Tm Mo¨ssbauer spectroscopy measurements on TmBa2Cu3O7  d as shown in Section 3.6.1, Stewart et al. (1998) performed new Mo¨ssbauer spectroscopy measurements of the temperature-dependent 169 Tm quadrupole-splitting for TmBa2Cu4O8 and an oxygen-depleted TmBa2Cu3O6.64 as a complement to earlier measurements for TmBa2Cu3O7

TABLE 12 Hyperfine Parameters in the Er3þ Magnetically Saturated Region for Superconducting (SC) and Nonsuperconducting (NSC) ErBa2Cu307  x Heff (T)

eVzz (mm/s)

SC

360  5

0.05  10

NSC

315  5

1.35  10

Heff is the Hyperfine field and eVzz the quadrupole interaction.

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and TmBa2Cu3O6 by Bergold et al. (1990). The 1-2-3 and 1-2-4 systems are members of a homologous series of compounds. In this series the rare earth layers are essentially unchanged. The measured curves reveal a smooth decrease in maximum DEQ with oxygen depletion of the 1-2-3 type compounds, with the TmBa2Cu4O8 value located approximately midway between the TmBa2Cu3O7 and TmBa2Cu3O6 extremes. In Table 13 the rank-2 parameters A02 and A22 are shown as determined by Stewart et al. (1998). In general A02 and subsequently the overall splitting is decreasing marginally with decreasing d value and is smallest for TmBa2Cu4O8. The 170Yb Mo¨ssbauer results on the YBa2Cu3O7 type of compounds described above can be divided into two groups. The first concerns the intrinsic properties of the Yb3þ ions, while the second concerns the use of the Yb3þ ion as a probe to follow the evolution of the local properties of YBa2Cu3O7 when its SC properties are weakened (or removed). The high critical temperature superconductor YbBa2Cu3O7 has been studied over the range 0.05e95K with 170 Yb Mo¨ssbauer spectroscopy by Hodges et al. (1987). Magnetic ordering is found at TN ¼ 0.35K. The saturated magnetic moments amount 1.7 mB. In YbBa2Cu3O7 above 0.35K, the Yb3þ paramagnetic relaxation rate is driven by the dipoleedipole and super-exchange interactions between the Yb3þ ions. The evolution of the local properties has been followed as the SC state in YBa2Cu3O7 is weakened (and eventually removed) by decreasing the oxygen content as studied by Hodges et al. (1994). When the oxygen level is lowered, the Yb paramagnetic relaxation rate remains low and the transition from the SC state to the state where the Cu(2) are magnetically ordered is accompanied by the appearance of a molecular field on the Yb3þ probe. From a study of this field, it was found that at the x ¼ 6.35 level, there is no well-defined magnetic ordering temperature as shown but rather the fluctuation rate of the correlated Cu(2) magnetic moments decreases progressively as the temperature decreases as shown in Fig. 29. In the SC samples with intermediate oxygen levels for which Tc is 60K and below, it was found that part of the sample continues to show fluctuating correlated magnetic moments.

TABLE 13 A Summary of Rank-2 Crystal Field Parameters of TmBa2Cu3O7  d and TmBa2Cu4O8 Obtained From Theory Fits to Experimental DEQ(169Tm) Data as Determined With the Help of Converted Ho INS Parameters d¼0

d ¼ 0.34

d¼1

TmBa2Cu4O8

A02 ðKÞ

89.6

66.3

27.3

41.8

A22 ðKÞ

60.9

29.3

0.0

96.1

206 Handbook of Magnetic Materials

FIGURE 29 170Yb Mo¨ssbauer absorption substituted into YBa2Cu3O6.35. The evolution is governed by the thermal dependence of the fluctuation rate of the Cu(2)derived molecular field. This figure is earlier published by Hodges, J.A., Bonville, P., Imbert, P., Je´hanno, G., 1994. Hyperfine Interact. 90, 187.

In Table 14 a summery is given of the antiferromagnetic ordering temperatures and magnetic moments of the R3þ ions in SC RBa2Cu3O7 and NSC RBa2Cu3O6 compounds. The PrBa2Cu3O7 compound is NSC due to hybridization of the Pr3þ ion.

4.6 R2BaMO5 Compounds Since the discovery of high-Tc superconductors of the type RBa2Cu3O7  d with R ¼ rare earth, the related R2BaCuO5 have been studied extensively in an effort to gain a better understanding of the magnetic exchange interaction between the Cu and R sublattices. For most R, the Cu sublattice orders antiferromagnetically in the higher temperature range of 15K  TN1  20K (the detection of this transition is often assisted by the induced magnetic behavior of the weakly coupled R sublattice) and the R sublattice orders at a lower temperature, TN2. The orthorhombic structure of R2BaCuO5 (space group Pnma) has two R sites, each with monoclinic point symmetry. A 155Gd Mo¨ssbauer spectroscopy study of Gd2BaCuO5 determines TN2 ¼ 11.75  5K for the Gd sublattice as studied by Strecker et al. (1998). In Fig. 30 and Table 15 the results of the 155Gd Mo¨ssbauer spectroscopy measurements on Gd2BaCuO5 are shown. It is clear that the Gd magnetic moments have a canted direction with angles as given in Table 15. The Beff values are rather close to the saturation value of z 32T at 1.5K. However, they differ

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TABLE 14 A Summary of the Magnetic Ordering Temperatures TN (K) and Magnetic Moments MmB of the Rare Earth in RBa2Cu3O7 and RBa2Cu3O6 Obtained From the Temperature Dependence of the Hyperfine Field Behavior as Determined From Rare Earth Mo¨ssbauer Spectroscopy RBa2Cu3O7

RBa2Cu3O6

R

TN (K)

M (mB)

TN (K)

M (mB)

Pr

16.5

0.32  3

7.7

?

Eu

0.0

0.0

?

?

Gd

2.3

7.0

?

?

Dy

z1.0

7.0

z1.0

7.3

Er

z0.6

4.2

z0.6

3.7

Tm

0.0

0.0

0.0

0.0

Yb

0.35

1.7

?

?

The symbol ? means not measured.

FIGURE 30 Temperature dependence of the magnetic hyperfine field, Beff, at the Gdl and Gd2 sites of Gd2BaCuO5 (insert defines angles a, b and c with respect to principal electric field gradient axes x, y, and z and the crystallographic axes a, b, and c). This figure is earlier published by Strecker, M., Hettkamp, P., Wortmann, G., Stewart, G.A., 1998. J. Magn. Magn. Mater. 177e181, 1095.

208 Handbook of Magnetic Materials

TABLE 15 Hyperfine Interaction Parameters for Gd2BaCuO5 Determined From the Measured 155Gd Mo¨ssbauer Spectra Site Gd1

Site Gd2

3.77  0.08

5.83  0.06

h

0.71  0.07

0.99  0.09

b (deg)

60  2

37  2

a (deg)

45  5

90  5

Beff (at 1.5K) (T)

26.9  0.03

22.3  0.03

21

Vzz (10

2

Vm )

The angles b and a are shown in Fig. 30.

clearly from each other. In contrast with the other R2BaCuO5 compounds no difference in magnetic ordering temperature between the Gd and Cu sublattice has been found. Therefore, Gd2BaCuO5 has been studied with 57Fe Mo¨ssbauer spectroscopy on a 57Fe (1/2%) doped sample and with muon spin relaxation on an undoped sample. CueCu and GdeGd magnetic orders are found to occur simultaneously at TN ¼ 11.8K. The Mo¨ssbauer results suggest a first-order magnetic transition for the Cu sublattice in Gd2BaCuO5 as studied by Stewart et al. (2003). The orthorhombic compounds Tm2BaCoO5 and Tm2BaNiO5 (Harker et al., 2000), Tm2BaCuO5 (Stewart and Gubbens, 1999), and also Tm2Cu2O5 (Stewart and Cadogan, 1993) were studied with 169Tm Mo¨ssbauer spectroscopy to determine the crystal field from the temperature dependence of the quadrupole-splitting. In Fig. 31 the temperature dependence of the measured 169 Tm Mo¨ssbauer spectra of Tm2BaCuO5 (TN ¼ 19K) are shown. Since this type of compounds have the space group Pnma (D2h16), the local symmetry of the two Tm sites is lower and have each a monoclinic point symmetry. This is also the case for Tm2BaCoO5 and Tm2BaNiO5. In Tm2Cu2O5 the point symmetry of the two Tm site stays orthorhombic. No difference has been found for the measured results of the hyperfine field and quadrupole-splitting between the two Tm sites in this compound. Then, the crystal Hamiltonian for the 3H6 ground term of Tm3þ takes the conventional form as shown Eq. (15) in this chapter, where the Om n are Stevens operator equivalents (Stevens, 1952) and the Bm are crystal field parameters. Further details are given in Section 3.2. n Since Gd (L ¼ 0) does not experience any crystal field effects the 155Gd Mo¨ssbauer results for isotructural Gd2BaCuO5 as shown above can be enlisted to describe the three-rank two-crystal field parameters for each site in terms of just one unknown parameter for that site following the same procedure as in Eq. (38) for this Hamiltonian in Eq. (15). For the case of Gd2BaCoO5 and Gd2BaNiO5 the electric field gradient values of the 155Gd Mo¨ssbauer results of

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FIGURE 31 Representative 169 Tm Mo¨ssbauer spectra of Tm2BaCuO5 (TN ¼ 19K) measured between T ¼ 0.3 and 300K. Note that the hyperfine field is a perturbation on the electric quadrupolesplitting. This figure is earlier published by Stewart, G.A., Gubbens, P.C.M., 1999. J. Magn. Magn. Mater. 206, 17.

Strecker et al. (1998) were used to calculate the second-order crystal field parameters in the same way as shown above. By a rotation transformation of the second Tm site over 104.6 about the b axis to place the oxygen atom in the same position as for the first Tm site, both Tm sites can be regarded as equal. This manipulation highlights the similarity of the two local environments and brings the calculated ratios for the two sites into closer agreement with respect to both sign and magnitude. As expected, the rank 6 ratios are more sensitive than the rank 4 ratios to the type of calculation employed. They are observed to decrease in magnitude as the radial dependence is varied over the three models, as mentioned above. Furthermore, experimental data published from optical spectroscopy and inelastic neutron scattering can be used to provide an estimate of the low-lying crystal field levels energy levels. In Fig. 32 the results of the calculations are shown. The insets show both crystal field energy diagrams of the two Tm ground-state multiplets. In Table 16 the results of the used crystal field parameters for the calculation of the temperature dependence of the quadrupolesplitting of the two Tm sites in Tm2BaMO5 (M ¼ Co, Ni and Cu) are shown, which were determined by Harker et al. (2000) and Stewart and Gubbens (1999). The low-lying singlet states of the Tm3þ ions in Tm2BaCuO5 (TN ¼ 19K) are nonmagnetic as shown by Stewart and Gubbens (1999). Hence, the

210 Handbook of Magnetic Materials

FIGURE 32 Quadrupole-splitting, DEQ, as function of the temperature in Tm2BaCuO5. The fitted theoretical curves correspond to the crystal field schemes for sites Tm1 (solid line) and Tm2 (broken line) as shown in the inset. This figure is earlier published by Stewart, G.A., Gubbens, P.C.M., 1999. J. Magn. Magn. Mater. 206, 17.

inducement of net magnetic moments by the magnetically ordered Cu sublattice requires that the molecular field associated with the weak CueTm exchange interaction brings a mixing of these levels. Full crystal field calculations show that at 4.2K only the lowest two levels of the various fitted crystal field schemes are significantly perturbed by a small molecular field. Magnetic moments are induced only along the main z axis of the crystal field (the crystallographic b axis). In other words, the crystal field analysis of the experiment predicts that all the induced Tm-site moments will be directed along the crystallographic b axis. In the absence of a precise knowledge of the crystal field schemes for the two Tm sites, it is useful to apply a two-singletinduced moment model. Then, the averaged moment induced at a Tm site is given by  0  2g2J m2B a2 BM D tanh (41) hmi ¼ D0 2kB T which is practically the same formula as Eq. (40). In this equation, BM is the molecular field acting in the z direction (the crystallographic b axis) proportional to the Cu sublattice magnetization, which follows a mean field Brillouin curve with S ¼ 1=2. Furthermore, a ¼ h0jJZj1i is the JZ coupling parameter between the two singlets and D0 ¼ ½D2 þ ð2gJ mB aBM Þ2 1=2 is the field enhanced energy separation of the two singlets (D is the energy separation in absence of a molecular field). In Fig. 33 curves have been calculated for the parameter combinations D ¼ 19K, a ¼ 5.3 (solid line) and D ¼ 29K, a ¼ 4.5 (dotted line) as derived for the two Tm sites from the CF analysis (Table 16).

TABLE 16 Crystal Field Parameters for the Two Tm Sites of the Pnma Phases of Tm2BaMO5 (M ¼ Co, Ni and Cu) and Orthorhombic Tm2Cu2O5 as Calculated by the Point Charge Model Using the Oxygen-Nearest Neighbors, Together With the Preferred Values for the B0n Parameters Obtained by Grid Searches Tm2BaCoO5

Tm2BaNiO5

Tm2BaCuO5

Tm2Cu2O5

Tm1

Tm2

Tm1

Tm2

Tm

B20 ðKÞ

1.356

0.44

3.846

0.12

1.038

1.869

2.23

r22

1.47

1.31

3.64

0.10

1.14

0.96

5.1

r22

0.28

0.59

1.82

1.82

0.70

0.33

e

B40 ðmKÞ

40.8

30.4

45.9

22.4

29.2

52.5

62.8

r42

2.34

3.19

2.28

3.77

2.62

3.95

0.454

r42

0.52

1.95

0.52

1.31

0.49

1.06

e

r44

3.82

1.66

4.04

4.07

4.63

5.14

4.54

r44

2.94

5.51

3.07

4.15

2.94

4.08

e

B60 ðmKÞ

26.2

59.8

47

49.4

50.9

70.3

266.5

r62

14.36

8.93

15.97

13.28

16.36

12.98

1.205

r62

4.22

6.65

4.71

5.38

3.46

4.19

e

r64

23.04

6.94

26.63

24.43

24.50

25.43

8.36

r64

21.45

35.55

22.45

31.88

21.9

27.9

e

r66

12.38

3.11

15.28

10.78

16.0

15.49

9.96

r66

17.43

19.22

22.85

16.18

16.5

14.1

e

These values were earlier published by Harker, S.J., Stewart, G.A., Gubbens, P.C.M., 2000. J. Alloy. Compd. 307, 70 and Stewart, G.A., Cadogan, J.M., 1993. J. Magn. Magn. Mater. 118, 322.

211

Tm2

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

Tm1

212 Handbook of Magnetic Materials

FIGURE 33 Induced magnetic moments in mB as a function of temperature for the two Tm sites of Tm2BaCuO5 (TN ¼ 19K). The theory curves are for the two-singlet-induced moment models with D ¼ 19K, a ¼ 5.3 (solid line) and D ¼ 29K, a ¼ 4.5 (broken line) and are labeled with the fitted values of the saturation molecular field, BM(sat). This figure is earlier published by Stewart, G.A., Gubbens, P.C.M., 1999. J. Magn. Magn. Mater. 206, 17.

Within the context of this simple model, the only remaining free parameter is BM(sat), the saturation value of BM at T / 0K. For each curve, this parameter was adjusted to give the observed low-temperature value of the local moment. The resultant values of BM(sat) are 0.09 or 0.18T for the site with the smaller moment and 0.19 or 0.40T for the site with the larger moment. These values are included with their corresponding curves in Fig. 33. For Tm2BaCuO5 the magnetic behavior of the two Tm sites are distinguishable with saturation moments of 0.503  0.006 mB and 0.23  0.01 mB along the b axis. This is in contrast with the result in Tm2Cu2O5, where the BM(sat) ¼ 1.65T for both Tm sites and the undistinguishable magnetic moment 3.90  0.08 mB. The antiferromagnetic ordering temperatures for Tm2BaCoO5 and Tm2BaNiO5 are 3.5 and 4.85K, respectively, the order being induced by the transition metal as found by Harker et al. (2000). For Tm2BaNiO5 an additional first-order transition is observed at T  1.4K, which is identified with the independent magnetic order of the Tm sublattice. The indirect coupling between NieOeNi chains of the Immm-phase nickelates for Gd2BaNiO5 and Tm2BaNiO5 results in an interesting magnetic behavior as studied by Harker et al. (1996). In this work, 155Gd Mo¨ssbauer spectroscopy data for Gd2BaNiO5 (TN ¼ 55K) are interpreted in terms of a constant electric field gradient tensor and a temperature-dependent magnetic hyperfine field with a saturation value of 24.5T. The sensitivity of the spectra to the projection of the hyperfine field enables a magnetic feature at T ¼ 24K to be identified with magnetic reorientation from the a axis to the b axis. Mo¨ssbauer spectroscopy measurements are presented for 169Tm nuclei in the

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Immm phase of Tm2BaNiO5 by Stewart et al. (2000). The temperaturedependent hyperfine interactions are consistent with a Tm moment induced by the antiferromagnetically ordered Ni sublattice, and a Ne´el temperature of TN ¼ 14.5K. A crystal field parameter determination of Tm2BaNiO5 with the 155 Gd Mo¨ssbauer results of Gd2BaNiO5 has been performed on the temperature dependence of the quadrupole-splitting of Tm2BaNiO5 using the method ascribed above by Stewart et al. (2000). The most favorable solution of crystal field parameters are B02 ¼ 3:38K, r2 þ 2 ¼ 0.4, B04 ¼ 24:2 mK and B06 ¼ 127 mK with D10 ¼ 23K and D20 ¼ 32.7K as distances from the ground state to the first- and second excited states, respectively. Moreover, Harker et al. (1996) has studied the temperature dependence below TN ¼ 14.5K as described in Eq. (41) using an S ¼ 1 Brillouin function. The results are D ¼ 18  1K, a ¼ 5.7  3 and BM(T ¼ 0K) ¼ 1.4  0.1K. In Fig. 34 170Yb Mo¨ssbauer spectra of Yb2BaCuO5 (TN ¼ 15K) measured at 2.35K and 0.05K by Hodges and Sanchez (1990) are shown. Since energy levels of the crystal field of Yb3þ consist of doublets, the ground-state doublet will be split by the magnetic molecular field of the Cu2þ sublattice below TN ¼ 15K. As shown in Table 17, two hyperfine fields of the two Yb sites are observed with magnetic moments of 2.2 and 1.1 mB. From the temperature dependence of the hyperfine field in the same way as in Eq. (41), the groundstate splitting D together with the molecular/dipole field of the doublets can be determined as shown in Table 17. 151 Eu Mo¨ssbauer measurements on Eu2BaNiO5, where the Ni2þ form well separated S ¼ 1 antiferromagnetic chains, were measured by Hodges and Bonville (2004). The appearance of magnetic moments in this compound evidences a crossed bootstrap polarization since neither the Eu3þ nor the Ni2þ are carrying the magnetic moments. However, it is confirmed that the Eu3þ ion carries a magnetic moment below 30K implying that Ni2þ (S ¼ 1) ordered moments also appear below this temperature. Both show distributions that can be linked to the role of defects in the nickel chains. The measurements also FIGURE 34 170Yb Mo¨ssbauer absorption in Yb2BaCuO5 at 2.35K (top) and 0.05K (bottom). The line fits are obtained in terms of two equally intense quadrupole plus magnetic hyperfine subspectra. This figure is earlier published by Hodges, J.A., Sanchez, J.P., 1990. J. Magn. Magn. Mater. 92, 201.

DEQ (mm/s)

h

Heff (T)

q (degrees)

m (mB)

D (K)

HCu  Yb (T)

Site 1

1.95  0.06

0.28  0.04

216  6

30  5

2.2  0.1

3.6  0.1

1.2  0.1

Site 2

1.33  0.04

0.78  0.10

113  4

75  5

1.1  0.1

3.2  0.1

The sizes of the derived 4f shell-saturated magnetic moments (m), the ground doublet splitting (D), and the molecular field acting on the Yb given.



2.2  0.1 CuYb

4f shell (H

) are also

214 Handbook of Magnetic Materials

TABLE 17 For Each of the Two Sites in Yb2BaCuO5: 170Yb3þ Mo¨ssbauer Values for the Electric Quadrupole Interaction Above 15K, the Values of the Low-Temperature Saturated Effective Hyperfine Field (Heff) and Its Polar Direction (q)

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provide the thermal dependence of the relative size of the Ni2þ moments. From the measurements, it appears the Eu magnetic moments are of the order of a fraction of a mB. The peak in the distribution of the exchange field acting on the Eu3þ occurs at 7.4T and the magnetic moment at 0.17 mB. In Table 18 the antiferromagnetic ordering temperatures and the magnetic moments are given for R2BaMO5 with R ¼ Gd, Tm and Yb and M ¼ Co, Ni and Cu for Pnma and Immm structures, and Tm2Cu2O5. Most of the compounds are magnetic induced systems from the Co, Ni, and Cu sublattice. Only in the Immm phase of Gd2BaNiO5 likely the Gd sublattice is magnetically ordered by itself. Moreover, for the Pnma phase of Tm2BaNiO5, it was found that the Tm sublattice orders magnetically below 1.4K.

4.7 R2M2O7 Compounds The pyrochlore lattice compounds R2M2O7 (space group Fd3m), where R is a rare earth and M is a transition or sp metal, are very interesting compounds. The main motivation is that the R ions form corner-sharing tetrahedra such that the interionic interactions are prone to geometrical frustration. A number of different situations have been found depending on the form, sign, size, and

TABLE 18 Magnetic Ordering Temperatures and Magnetic Moments of R2BaMO5 With R ¼ Gd, Tm, and Yb and M ¼ Co, Ni, and Cu for Pnma and Immm Structures, and Tm2Cu2O5 TN (K)

Magnetic Site 1

Moment mB Site 2

Origin of Rare Earth Magnetic Moment

Gd2BaCuO5

11.75

5.9

4.9

Induced?

Tm2BaCoO5

3.5

2.0

0.4

Induced

Tm2BaNiO5

4.85

1.18

0.28

Induced

1.4

3.8

0.8

Tm order

Tm2BaCuO5

19

0.50

0.23

Induced

Yb2BaCuO5

15

2.2

1.1

Induced

Gd2BaNiO5

55

5.4

Gd order

Tm2BaNiO5

14.5

3.6

Induced

Tm2Cu2O5

17.5

3.9

Induced

Pnma

Immm

Free ion

7.0

216 Handbook of Magnetic Materials

anisotropy of the various possible interionic interactions as reported by Gardner et al. (2010). The search for the spin liquid state, a ground state where the spins are strongly correlated, show no long-range order and are dynamical, has motivated important theoretical and experimental efforts. For instance, Ho2Ti2O7, which has a large axial anisotropy and a net ferromagnetic interaction, gives evidence for a magnetic frustration, which shows analogies with the positional fluctuations of the protons in ice. Such systems have been mentioned “spin ice”. Their behavior is essentially driven by dipolar interaction between the spins. Recently, the interest has focused on the quantum spin liquid model where exchange interactions determine the low-temperature behavior and the possibility has been raised that the pyrochlore Yb2Ti2O7 is a physical realization of this model as shown by Savary and Balents (2012). Other more newer models are now in progress of development and discussion. In this paragraph the description of the R2M2O7 will be mainly limited to the results of the rare earth Mo¨ssbauer spectroscopy. A comparison with muon spin relaxation (mSR) and rare earth Mo¨ssbauer results of R2M2O7 will be made. In Section 3.6.2, these combined results for Yb2Ti2O7 were already shown. First, some 155Gd Mo¨ssbauer data of Gd2M2O7 compounds with M ¼ Ti, Sn and Mo will be discussed. Second, the 161Dy Mo¨ssbauer results of the compound Dy2Ti2O7 will be shown. Furthermore, 170Yb Mo¨ssbauer results and mSR will be compared for the compounds Yb2M2O7 with M ¼ Ti, Sn, mixed GaSb and Mo. Bonville et al. (2003) have combined specific heat, 155Gd Mo¨ssbauer, magnetic susceptibility and magnetization measurements to examine Gd2Sn2O7 and Gd2Ti2O7. The specific heat measurements evidence a single, strongly first-order magnetic transition near 1.0K in Gd2Sn2O7 and confirm the existence of two transitions, near 1.0K and 0.75K, in Gd2Ti2O7 as earlier shown by Ramirez et al. (2002). In Gd2Sn2O7, it was shown previously by Bertin et al. (2002). that spin dynamics with frequencies below this value persists down to the very low temperature of 0.03K. In Fig. 35 155Gd Mo¨ssbauer spectra of Gd2Sn2O7 and Gd2Ti2O7 are shown in panels (A) and (B), respectively. For Gd2Sn2O7 down to 1.1K, only a quadrupole interaction is observed. The quadrupolar interaction (splitting) is 4.0 mm/s, with the sign obtained from the data below 1.0K. An additional magnetic hyperfine interaction appears between 1.10 and 1.05K. Below 1.05K the data analysis gives the size of the hyperfine field and its direction relative to the principal axis of the electric field gradient tensor, which is the local [111] axis. At each temperature, the Mo¨ssbauer line shape is well described by a unique hyperfine field that is oriented 90  5 to the principal axis of the electric field gradient. Since the Gd3þ spontaneous magnetic moment m(T) is proportional to the hyperfine field Heff(T), this shows that at each temperature the four moments of a tetrahedron have a common size and each is perpendicular to the local [111] axis. The magnetic moment is saturated at low temperature and the Gd3þ moment of 7 mB has the free ion value. The thermal variation of m(T) is given

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FIGURE 35 155Gd Mo¨ssbauer spectra of Gd2Sn2O7 [left-hand panel, (A)] and Gd2Ti2O7 [middle panel, (B)] as a function of temperature. Thermal variation of the Gd3þ magnetic moment in Gd2Sn2O7 (right-hand panel, top) and Gd2Ti2O7 (right-hand panel, bottom) obtained from the 155 Gd Mo¨ssbauer measurements. The dashed line marks the position of the maxima of the specific heat peaks (z1.05K) in the two compounds. The chain line marks the position of the second transition in Gd2Ti2O7 (z0.75K). Above this temperature, two different Gd3þ moments are evidenced (full and open triangles) (see text). This figure is earlier published by Bonville, P., Hodges, J.A., Ocio, M., Sanchez, J.P., Vulliet, P., Sosin, S., Braithwaite, D., 2003. J. Phys. Condens. Matter 15, 7777.

in the top part of the right-hand panel of Fig. 35. The moment shows a smooth decrease as the temperature is increasing from 0.03 to 1.065K. At 1.065K, it amounts to 75% of the saturated value and then drops abruptly to zero at 1.1K, indicating a possible strong first-order character in Gd2Sn22O7. The observed hyperfine fields (and the associated correlated magnetic moments) are “static” with a Larmor frequency scale of 120  106 s1 with magnetic moments directions that are perpendicular to each local [111] axis. 155 Gd Mo¨ssbauer spectra of Gd2Ti2O7 are shown in the middle panel (B) of Fig. 35. At 4.2K, an electric quadrupole-splitting is visible, with a value of 5.6 mm/s. As the temperature is decreased from 4.2 to 1.1K, which is just above that of the upper specific heat peak, each of the two absorption lines start to broaden considerably. This broadening is due to the slowing down of the fluctuations of the short range-correlated Gd3þ magnetic moments. No such comparable line broadening was found in Gd2Sn2O7. This line broadening masks the magnetic transition near 1.0K. Well below this temperature, the line shape evidences the characteristic structure associated with combined quadrupole and magnetic hyperfine interactions. Up to 0.6K, the spectra of Gd2Ti2O7 are very satisfactorily fitted with a single hyperfine field perpendicular to the principal axis of the electric field gradient, like in the case of Gd2Sn2O7. This means that the four Gd3þ ions of

218 Handbook of Magnetic Materials

the tetrahedron carry equal magnetic moments and each is perpendicular to the local [111] axis. The moments were obtained from the hyperfine field values using the scaling law (36), with a measured saturated hyperfine field Heff(0) ¼ 28.3T, which is slightly smaller than in Gd2Sn2O7. Their thermal variation is shown in the bottom part of the right-hand panel of Fig. 35. At low temperatures, the Gd3þ moment is essentially temperature-independent, whereas at 0.8K and above, it decreases with increasing temperature. At 0.8K and above, the Mo¨ssbauer analysis indicates that the four moments of a tetrahedron are no longer identical and no reliable values for the moments could be obtained above 0.9K due to the influence of the dynamical broadening of the Mo¨ssbauer lines. Attempts to fit the spectrum of Gd2Ti2O7 measured at T ¼ 0.8K with different models were not successful. It is clear that the transition of the two compounds near 1.0K has a very complex character. Its main feature is that it is strongly first order in Gd2Sn2O7 and there is some evidence of weak first-order behavior in Gd2Ti2O7. Although the pyrochlore lattice is capable of displaying a first-order magnetic transition, which does not involve long-range magnetic ordering, the transition at 1K in both compounds is associated with the onset of long-range order. The magnetic structure, however, is probably different in the two cases. The rare earth molybdates R2Mo2O7 are formed with the rare earths from Nd3þ to Lu3þ. For R from Nd to Gd, these compounds show metallic behavior, whereas for R from Dy to Lu (and with Y), they show semiconducting behavior with an activation energy of the order of 15 meV, as shown by Greedan et al. (1987). The change in behavior (metalesemiconductor crossover) has been related to variations in the MoeO bond lengths associated with the changing lattice parameter (lanthanide contraction) as explained by Katsufuji et al. (2000) and in the MoeOeMo bond angles as studied by Moritomo et al. (2001). The metalesemiconductor crossover leads to profound changes in the magnetic properties. In the R2Mo2O7, the dominant exchange interaction is that within the d-ion sublattice. The next most important interaction is the intersublattice exchange. The interaction within the f-ion sublattice is the weakest of the three. For the dion sublattice, the dominant exchange mechanism is different on either side of the metalesemiconductor crossover. In the semiconducting compounds, the antiferromagnetic superexchange prevails, whereas in the metallic compounds, the direct ferromagnetic coupling involving the Mo 4d-spin density at the Fermi level dominates, as shown by Kang et al. (2002). The 155Gd Mo¨ssbauer absorption measurements were performed over the temperature range between T ¼ 0.027 and 80K by Hodges et al. (2003a). At 80K, in the paramagnetic phase, the absorption takes the form of a nearly symmetric doublet. It corresponds to an electric quadrupole-splitting with a value of 5.1 mm/s, not much different from the other R2M2O7 compounds with M ¼ Sn and Ti as shown above. A hyperfine field, proportional to the Gd3þ magnetic moment, appears when the temperature is lower than 75K,

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which is the magnetic transition. In Gd2Mo2O7, the magnetic hyperfine interaction is much smaller than the quadrupole interaction, and acts only as a broadening on each of the two absorption lines. Therefore, the asymmetry h and subsequently the angle q are hardly to determine as discussed by Hodges et al. (2003a, 2003b). At 0.027K, the saturated hyperfine field is 19.8T, which is markedly smaller than that usually found in insulating Gd compounds (z30T). This reduced value in this metallic compound is probably linked to the exchange polarization of s-type conduction electrons, which contributes a hyperfine field opposite to that arising from the polarization of the core selectrons by the 4f shell moment. Fig. 36 shows the thermal variation of the Gd3þ magnetic moment, obtained from the hyperfine field value by scaling, using the relation that the measured saturated hyperfine field of 19.8T corresponds to a saturated Gd3þ moment of 7 mB. Then, the temperature dependence of the Gd3þ magnetic moment is calculated with a modified molecular field model including a Brillouin function for S ¼ 7/2 and a derived exchange field for Mo (Tc ¼ 75K) as described by Hodges et al. (2003a). The MoeGd exchange field amounts 5.5T. This is about 30% lower than found from specific heat analysis by Raju et al. (1992). Furthermore, in Gd2Mo2O7, it was observed that the steady-state Gd hyperfine populations at 0.027K are out of thermal equilibrium, indicating that Gd and Mo spin fluctuations persist at very low temperatures. Frustration is thus operative in this essentially isotropic pyrochlore where the dominant Mo intrasublattice interaction is ferromagnetic. A study on quadrupole interactions and relaxation phenomena of Dy2Ti2O7 with increasing temperature up to 750K have been performed using the 161Dy Mo¨ssbauer effect by Almog et al. (1973). 161Tb in 160Gd2Ti2O7 at 150K was used as source in order to emit a very narrow line. Quadrupole interaction

FIGURE 36 Temperature dependence of the Gd3þ 4f shell magnetic moment in Gd2Mo2O7 obtained from the 155Gd Mo¨ssbauer measurements. The solid line is a fit with the molecular field model. This figure is earlier published by Hodges, J.A., Bonville, P., Forget, A., Sanchez, J.P., Vulliet, P., Rams, M., Kro´las, 2003a, Eur. Phys. J. B 33, 173.

220 Handbook of Magnetic Materials

parameters and relaxation times, as function of temperature, were deduced from the measurements. It was found that at T ¼ 4K from the hyperfine field that Dy3þ has values for the hyperfine field and the electric quadrupolesplitting, indicating a JZ ¼ 15/2 Kramers doublet. At higher temperatures, magnetic relaxation broadening was observed. In this respect, Dy2Ti2O7 resembles the same relaxation behavior as DyPO4 and DyVO4 as described in Section 4.4. In Section 3.6.2, Yb2Ti2O7 was already discussed. Recently, the Higgs ferromagnetic phase has recently been proposed for this compound at low temperature by Chang et al. (2012), since a longstanding controversy exists as to the intrinsic presence of magnetic Bragg reflections in Yb2Ti2O7 as discussed by several authors (e.g., Hodges et al., 2002; Ross et al., 2009). Beside the R2Ti2O7 series, the pyrochlore rare-earth stannates R2Sn2O7 have also attracted strong interest since both series share similar R anisotropies and a nonmagnetic M sublattice. Comparing the two series, it seems that the titanates are more influenced by exchange interactions beyond the nearest neighbors than the stannates. Therefore, Yb2Sn2O7 is a better test than Yb2Ti2O7 for the current theoretical works dedicated to quantum spin liquids. For Yb2Sn2O7, bulk macroscopic properties were studied first. Then microscopic results were obtained from 170Yb Mo¨ssbauer spectroscopy, powder neutron diffraction and muon spin relaxation (mSR) as studied by Yaouanc et al. (2013). The heat capacity, measured in the range 0.08e4K, is shown in Fig. 37A. Its most important result is a fairly symmetric narrow peak at the transition at Tt z 0.15K, and a broad hump centered at about 2K. This hump is ascribed to the exchange splitting of the ground-state Kramers doublet associated with the onset of magnetic correlations, which is a commonly observed feature in frustrated magnets. The 170Yb Mo¨ssbauer spectroscopy measurements on Yb2Sn2O7 as shown in Fig. 37B were measured down to T ¼ 0.045K. At 4.2K a pure quadrupole hyperfine spectrum is observed with a temperature-independent size and symmetry. With decreasing temperature, the line shapes broaden progressively as shown in Fig. 37B at 0.2K due to the increase of the short-range correlations among the Yb3þ moments as also evidenced by the specific-heat measurements. These correlations lead to a decrease of the Yb3þ spin fluctuation rate vcM so that it enters the 170Yb Mo¨ssbauer frequency window as displayed in Fig. 38. As the temperature is further lowered through Tt, an additional magnetic hyperfine interaction initially appears on some of the Yb3þ spins. The relative weight of this fraction increases as the temperature is decreased as shown in Fig. 37D. At T ¼ 0.09K the pure quadrupole subspectrum has disappeared and only the mixed quadrupole with magnetic hyperfine spectrum was observed. This behavior evidences that paramagnetic and magnetically ordered moments coexist in a small temperature range around the transition, which is an indication of first-order transition. Below the transition, the fluctuation rate is below the sensitivity limit of this technique (108 s1).

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FIGURE 37 (A) Low-temperature heat capacity of Yb2Sn2O7. (B) 170Yb absorption Mo¨ssbauer spectra at selected temperatures. The decomposition of the spectra at 0.12 and 0.10K in terms of two subspectra, pure quadrupole and quadrupole with magnetic hyperfine interactions, is indicated. (C) Thermal evolution of the magnitude of the Yb3þ magnetic moments detected by Mo¨ssbauer spectroscopy and (D) the percentage fraction of the Yb3þ ions carrying a magnetic moment. Here the lines are guides to the eye. The behaviors shown in panels (C) and (D) are the signatures of first-order transitions. This figure is earlier published by Yaouanc, A., Dalmas de Re´otier, P., Bonville, P., Hodges, J.A., Glazkov, V., Keller, L., Sikolenko V., Bartkowiak, M., Amato, A., Baines, C., King, P.J.C., Gubbens, P.C.M., Forget, A., 2013, Phys. Rev. Lett. 110, 127207.

The hyperfine field of the Yb3þ ion, proportional to the spontaneous magnetic moment, amounts 110  2T, which corresponds to 1.1 mB. These moments are parallel to the hyperfine field and lie at an angle of 65 relative to their local [111] direction. The spectroscopic g-factors of the anisotropic Yb3þ groundstate Kramers doublet are determined. For Yb2Sn2O7 gz y 1.1 and gt y 4.2, which gives a stronger XY anisotropy than in Yb2Ti2O7. The neutron diffraction measurements show magnetic reflections observed at the position of the nuclear Bragg peaks. Therefore, a long-range magnetic order is found characterized by a k ¼ 0 propagation wave vector. A Rietveld refinement was performed according to a linear combination of two basis vectors of the sixth-order irreducible representation, of which only one of the four possibilities exist for a k ¼ 0 magnetic structure in the Fd3m space group

222 Handbook of Magnetic Materials

FIGURE 38 Temperature dependence of the fluctuation rates of the correlated Yb3þ moments in Yb2Sn2O7 obtained from 170Yb Mo¨ssbauer and mSR spectroscopies, and comparison with the Yb2Ti2O7 data studied by Yaouanc et al. (2003). The full lines above the transition temperatures result from fits to activation laws. The dashed lines are guides to the eye. At the temperature of the respective specific heat peaks they are vertical, indicating a sharp change in the spin dynamics at those temperatures. The few points below Tt for Yb2Sn2O7 correspond to paramagnetic moments that coexist with ordered moments as shown in Fig. 37C. This figure is earlier published by Yaouanc, A., Dalmas de Re´otier, P., Bonville, P., Hodges, J.A., Glazkov, V., Keller, L., Sikolenko V., Bartkowiak, M., Amato, A., Baines, C., King, P.J.C., Gubbens, P.C.M., Forget, A., 2013, Phys. Rev. Lett. 110, 127207.

allowing for an angle between the ordered moment and the local [111] axis different from 0 and 90 . Setting this angle to 65 a very good fit of the data was obtained with a magnetic moment of 1.05  2 mB, a value close to the 170 Yb Mo¨ssbauer spectroscopy result shown above. Further information was derived from mSR measurements, which were performed in the temperature range from 0.014 to 2K. These measurements give access to the so-called asymmetry a0 Pexp Z ðtÞ, where a0 is an experimental parameter and Pexp the muon polarization function, which reflects the physics Z of the compound under study. All the spectra were fitted to a0 Pexp Z ðtÞ ¼ as PZ ðtÞ þ abg , where the second time-independent component accounts for the muons implanted in the sample surroundings. Above Tt PZ(t) ¼ exp (lZt), where lZ is the muon spin-lattice relaxation rate. This means the system is in the fast fluctuation limit, that is, the fluctuation rate vc,m of the Yb3þ dipolar field at the muon site verifies the relation vc,m [ gmDpara, where Dpara is the root-mean-square of the field distribution at the muon site and gm is the muon gyromagnetic ratio. It was found that lZ increases on cooling. This is a usual behavior reflecting the slowing down of the fluctuations of exchange-coupled Yb3þ moments in Yb2Sn2O7. In this temperature range, Dpara can be taken to be temperature-independent and it was found that Dpara y 73 mT, which is close to the value of 80 mT for Yb2Ti2O7 from

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Yaouanc et al. (2003). Fig. 38 displays vc,m deduced from the above analysis together with vc,M. An activation law is rather well obeyed, with an activation energy of 0.20K in temperature units. Below Tt y 0.15K, that is, in the presence of long-range magnetic order, it might be expected that the spectral shape would show rapid depolarization or pronounced oscillations due to muon spin precession in the spontaneous field. Instead the spectral shape shows little change on crossing Tt. A similar unusual behavior was already found, for example, Tb2Sn2O7 (Dalmas de Re´otier et al., 2006) and explained by a persistent dynamics in the ordered state, with a fluctuation rate larger than the muon precession frequency. Since there is no evidence of spontaneous precession below Tt, the spectral shape has changed and it no longer follows a simple exponential form. It means that the fast fluctuation limit no longer applies and therefore the Yb3þ spins have undergone a drastic slowing down at Tt. This is confirmed by weak longitudinal field measurements. The weak minimum seen below 1 ms indeed reveals the presence of a field distribution at the muon site with dynamics in the microsecond time scale. The shape of the spectra recorded below Tt is reminiscent of the dynamical Kubo-Toyabe function, however, with a slight modification as shown by Hodges et al. (2002). The main result of the mSR study is the abrupt decrease of vc,m to an essentially temperature-independent value in the megahertz range below Tt y 0.15K. It is consistent with the upper bound of 108 s1 derived from Mo¨ssbauer spectroscopy measurements. In this respect, Mo¨ssbauer spectroscopy and mSR are partly overlapping and additive. This unusual transition in the dynamics in Yb2Sn2O7 is similar to that in Yb2Ti2O7 as shown in Fig. 38. The 170Yb Mo¨ssbauer measurements on Yb2GaSbO7 were performed over the temperature range from 0.03 to 80K. The results of these measurements were compared with mSR measurements on Yb2GaSbO7 as studied by Hodges et al. (2011). At 1.6K and above, the Mo¨ssbauer spectra are similar to the one measured at T ¼ 0.9K. They are all well described using only a quadrupole hyperfine interaction. The asymmetry parameter (h) as defined in Eq. (3) is not equal to zero as for the other crystallographically ordered pyrochlores. Another feature of these quadrupole spectra is that the measured line width is broader than that in crystallographically ordered Yb2Ti2O7 and Yb2Sn2O7. This broadening had to be attributed to the presence of a small distribution in the quadrupole interaction, which can be ascribed from a small distribution in the local crystal field parameters. These two effects have a common origin linked to the disorder in the Ga3þ/Sb5þ site occupancy. As the temperature is lowered below 0.9K, the line shape progressively broadens and then splits under the influence of a magnetic hyperfine interaction. The spectra from 0.03 up to 0.3K are characteristic of hyperfine field spectra, with large and inhomogeneous line broadenings due to the presence of a distribution in the hyperfine field, which again is related to the distribution of crystal field parameters produced by the Ga3þ/Sb5þ disorder.

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The data-fits of the 170Yb spectra were made with the quadrupolar interaction fixed at the value obtained above 0.9K. The saturated hyperfine field at 0.03K is Heff y 110T, which corresponds to a spontaneous moment of 1.1 mB per Yb3þ ion, identical to that in Yb2Ti2O7. The angle q of the hyperfine field with respect to the principal axis of the electric field gradient (the local [111] axis) is close to 55 . This measurement of the direction of the short-range correlated Yb3þ magnetic moments relative to the direction of the local principal anisotropy axis directly evidences that each moment is essentially oriented at the same angle relative to its local anisotropy axis. Because of the anticipated planar anisotropy of the ground-state g-tensor, the molecular field that gives rise to this moment is not aligned along the direction of the moment but is rather oriented much closer to the local [111] axis. The fact that the Yb3þ magnetic moment does not lie along the direction of the molecular field, which gives rise to the moment directly, shows that the exchange in Yb2GaSbO7 is anisotropic. The spectrum at 0.4K is only partially resolved. As the temperature is further increased, the line shape becomes narrower and tends to the quadrupolar hyperfine pattern observed above 0.9K. This line-shape change can be regarded as a fluctuation induced spectral narrowing due to the dynamic nature of the magnetic correlations. The spectra between 0.4 and 0.9K were fitted using a relaxational line shape involving stochastic fluctuations of the hyperfine field as shown by Hodges et al. (2001). On the same way as ascribed for Yb2Sn2O7 above, the magnetic dynamic time behavior sm can been determined from the measured value of lZ and the derived value of Dpara with the formula lZ ¼ 2g2m D2para sm . In Fig. 39 the composed results for the fluctuation rate of Yb2GaSbO7 and Yb2Ti2O7 are compared. The absence of any sharp anomaly in the temperature dependence of the fluctuation rate in Yb2GaSbO7 [there is also no sharp anomaly in the specific heat as shown by Blo¨te et al. (1969)] suggests that under the influence of the disorder, the thermal behavior is closer to that predicted for a classical collective paramagnet. However, the low-temperature behavior does not fully correspond to this state because the Yb3þ magnetic moments fluctuate only between a subset of the total possible directions since the moments retain a fixed angle of 55 relative to the local [111] axis. The relatively high fluctuation rate of 7  107 s1 observed at 0.02K indicates that the Ga3þ/Sb5þ disorder does not suppress the frustration-induced spin dynamics. The fact that frustration is operative both in ferromagnetic Yb2Ti2O7 (and Yb2Sn2O7) on the one hand and in antiferromagnetic Yb2GaSbO7 on the other hand may be linked to the fact that in both compounds the magnetic moments have components along a local [111] axis and in a local basal plane, so allowing different microscopic mechanisms to be operative in both cases. Hodges et al. (2003a) have examined the semiconducting pyrochlore compound Yb2Mo2O7, where the Mo sublattice is antiferromagnetic, with 170 Yb Mo¨ssbauer measurements down to z0.03K. The microscopic

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FIGURE 39 Temperature dependence of the fluctuation rates of the correlated Yb3þ moments in Yb2GaSbO7 and in Yb2Ti2O7 as studied by Yaouanc et al. (2003) obtained from the mSR measurements (vcm ¼ 1/sm, over a wide temperature span) and 170Yb Mo¨ssbauer measurements (vcM ¼ 1/shf, over a limited temperature span). The full line is a fit to an activation law as shown by Yaouanc et al. (2003) and the dashed line a guide to the eye. The variation in Yb2GaSbO7 does not result in evidence for a first-order transition, which is present in Yb2Ti2O7. The limiting low temperature fluctuation rate in Yb2GaSbO7 is much higher than the one found in Yb2Ti2O7. This figure is earlier published by Hodges, J.A., Dalmas de Re´otier, Yaouanc, A., Gubbens, P.C.M., King, P.J.C., Baines, C., 2011. J. Phys. Condens. Matter 23, 164217.

measurements evidence lattice disorder, which is important in Yb2Mo2O7. This behavior introduces distributions in the Yb3þ ground states and subsequently broadening in the measured 0.036K spectrum. Magnetic irreversibilities occur at 17K in Yb2Mo2O7. Below TN ¼ 17K, the Yb3þ ions carry magnetic moments that are induced through couplings with the Mo sublattice. The temperature dependence of the hyperfine is analyzed with a reduced exchange field in a self-consistent way with a Brillouin function for S ¼ 1 and s ¼ T/TN.

4.8 R3M5O12 Compounds The rare earth sublattice in garnets with the formula R3M5O12 with R is rare earth and M a metal, where the rare earth ions lie on two interpenetrating corner sharing triangular networks can lead to frustration. Therefore, magnetic frustration will be discussed in Gd3Ga5O12 and Yb3Ga5O12, which were studied respectively with 155Gd and 170Yb Mo¨ssbauer spectroscopy. The spin liquid properties of Gd3Ga5O12 have been examined using 155Gd Mo¨ssbauer spectroscopy down to 0.027K by Bonville et al. (2004). Information has been obtained concerning both the directional properties of the shortrange correlated moments and the thermal dependence of their spin fluctuation rates. The spectrum at the lowest temperature, 0.027K, is a partially resolved

226 Handbook of Magnetic Materials

mixed quadrupolar and magnetic hyperfine field pattern. For Gd3þ, the hyperfine field in insulating compounds is about 30T. The presence of a static hyperfine field, which is directly proportional to the Gd magnetic moment, shows that the Gd3þ spins are strongly correlated at 0.027K. As a long-range magnetic order is not observed down to 0.025K, the existence of dynamic short-range order has to be supposed, with a spin fluctuation rate that is below the lower limit of the 155Gd Mo¨ssbauer window of 3  107 s1. From the analysis of the spectrum at 0.027K, it was found that the short-range correlated Gd3þ spins fluctuate (with rates lower than 3  107 s1) in the YOZ plane of the orthorhombic structure such that they present equal probabilities along the electric field axes OY and OZ. For the three sites making up an elementary triangle of the rare earth sublattice, the three local YOZ planes are not parallel, and thus the fluctuations of the spins of a triangle are not coplanar. As the temperature is increased above 0.027K, the individual lines first broaden, and then above 0.2K a two-line spectrum is observed, with linewidths that decrease progressively. At 4.2K, a pure quadrupolar hyperfine spectrum is recovered. All these features are characteristic of the presence of electronic fluctuations with a rate that increases as the temperature increases. The relaxation line shape involves hyperfine field fluctuations along local axes, that is, the principal axes of the electric field gradient tensor. This line shape uses the random phase approximation that assumes that the jumps of the hyperfine field of the short-range correlated moments between the chosen directions are uncorrelated. The results of the relaxation model as described Bonville et al. (2004) are shown in Fig. 40. The only free parameters are (1/s) and the directions between which the hyperfine field fluctuates. The temperature dependence of the correlations could well be fitted with a T2.2 law as shown in Fig. 40. This law as well as a T linear law predicted at much lower temperatures is due to thermal excitations within correlated sin structures. At low temperatures, the Mo¨ssbauer derived relaxation rate lies far below those derived from the mSR measurements of both Dunsiger et al. (2000) (chained line) and Marshall et al. (2002) (dashed line). A clear explanation of this difference in behavior could not be given. In the garnet-structure compound Yb3Ga5O12, the Yb3þ ions with a ground-state effective spin S ¼ 1/2 are situated on two interpenetrating cornersharing triangular sublattices such that frustrated magnetic interactions are possible. Specific-heat measurements have evidenced the development of short-range magnetic correlations below w0.5K and a sharp transition at 54 mK as measured first by Filippi et al. (1980). 170Yb Mo¨ssbauer spectroscopy measurements down to 36 mK were performed by Hodges et al. (2003b). No static magnetic order at temperatures was found below the sharp specific transition. The 170Yb Mo¨ssbauer spectra were analyzed in a way comparable as performed for Gd3Ga5O12 as shown above. At 0.036K the line shape of spectrum of Yb3Ga5O12 is well broadened, and this makes it possible to obtain both the magnitude of the hyperfine field and its fluctuation rate. It was found

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FIGURE 40 Thermal variation of the fluctuation rate of the correlated Gd3þ moments in Gd3Ga5O12, obtained from the 155Gd Mo¨ssbauer data (black squares). Inset: Low-temperature behavior (same units as the main figure), where the horizontal dashed line defines the lower limit of the 155Gd Mo¨ssbauer frequency window of 3  107 s1. The solid line (main figure and inset) is the law: (1/s) ¼ aT2.2, with a ¼ 17  109 s1 K2.2. The chain and dashed lines schematically represent the data from the mSR measurements by Dunsiger et al. (2000) and Marshall et al. (2002), respectively. This figure is earlier published by Bonville, P., Hodges, J.A., Sanchez, J.P., Vulliet, P., 2004. Phys. Rev. Lett. 92, 167202.

that Heff x 140  10T, which corresponds to a Yb3þ moment of x1.4 mB and (1/s)hf ¼ 3  109 s1. The value for the Yb3þ moment is not far from the mean value expected both from the average g-tensor and from the saturated magnetization measured at 0.09K in of 1.7 mB as found by Filippi et al. (1980). In the fits for the spectra up to 0.2K, an intrinsic half-width of 1.35 mm/s was used, and assumed that the fluctuating hyperfine field has a size that remains constant at the value 140T derived at 0.036K. The thermal variation of (1/s)hf is shown in Fig. 41. As the temperature is lowered over the range 0.2 to 0.1K, the frequency decreases approximately linearly according to a law Zð1=sÞhf ¼ 0:3 kB T. Then, below about 0.1K, it tends to saturate toward the value 3  109 s1 as shown in Fig. 41. This is quite a high value and, in fact, Yb3Ga5O12 is the only known compound where the T / 0 spin fluctuation rate is rapid enough to fall within the 170Yb Mo¨ssbauer spectroscopy frequency window. There is essentially no difference between the rates either side of the sharp specific-heat transition at 54 mK as measured by Filippi et al. (1980) and shown in Fig. 42. Above w0.5K, the Yb3þ magnetic moments undergo paramagnetic fluctuations. Up to w150K, the fluctuation rate has a temperature-independent value of x3.8  1010 s1. Above 150K, additional temperature-dependent relaxation occurs through coupling to phonons, according to a two-phonon

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FIGURE 41 Thermal variations, in Yb3Ga5O12, of the Yb3þ hyperfine field fluctuation frequency extracted from the 170Yb Mo¨ssbauer spectra. The dashed line is the law Zð1=sÞhf ¼ 0:3 kB T. This figure is earlier published by Hodges, J.A., Bonville, P., Rams, M., Kro´las, K., 2003b. J. Phys. Condens. Matter 15, 4631.

Orbach process involving the excited crystal field states near 850K, which is quite a high value. From the 170Yb Mo¨ssbauer measurements on Yb3Ga5O12, it is clear that at TL ¼ 54 mK (the peak in the specific heat as shown in Fig. 42) no conventional magnetic phase transition was found. From the temperature dependence of LZ

FIGURE 42 Zero-field muon spin-lattice relaxation rate, lZ, versus temperature measured for Yb3Ga5O12. The solid line is the result of a fit to a model explained in the main text. The two straight dashed lines for T  0.4K down to 21 mK are guides to the eye. The specific heat (from Filippi et al., 1980) of Yb3Ga5O12 is also reproduced. A marked change of slope in lZ occurs at Tl ¼ 54 mK. This figure is earlier published by Dalmas de Re´otier, P., Yaouanc, A., Gubbens, P.C.M., Kaiser, C.T., Baines, C., King, P.J.C., 2003. Phys. Rev. Lett. 91 167201.

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measured with mSR, no onset of magnetic was found at Tl ¼ 54 mK by Dalmas de Re´otier et al. (2003). Furthermore, the observation of an exponential relaxation function below Tl is another important point. It implies that we are in the fast fluctuation limit and therefore the Yb3þ moments continue to fluctuate rapidly down to the lowest temperature investigated, which is in contrast with Yb2Ti2O7 and Yb2Sn2O7 as shown earlier, where the moments abruptly slow down below Tl and are here quasistatic. For a Heisenberg magnet at high temperature, if the thermal energy is larger than the exchange energy as explained by Dalmas de Re´otier et al. (2003) can simply be given by the Curie law. Then it can be deduced that lZ should be temperatureindependent as was effectively observed for 0.4  T  80K. However, above 80K, lZ(T) decreases steadily as the sample is heated. This behavior of lZ is due to the relaxation of the Yb3þ magnetic moments resulting from an Orbach process, which is a two-phonon real process with an excited crystal-field level as intermediate at an energy level at 850K as found by Hodges et al. (2003b). Combining the value of lZ in the range 0.4  T  80K and the value sc w 38 ps obtained from Mo¨ssbauer data in the same temperature interval, DZF x 0.16T which is of the expected magnitude. For comparison DZF x 0.08T was found for Yb2Ti2O7 above Tl as found by Yaouanc et al. (2003). Below T < Tl being in an interstitial site, the muon spin can be strongly influenced by magnetic pair correlations. In contrast, since a 170Yb Mo¨ssbauer nucleus is embedded in a Yb atom that is magnetic, it is mainly sensitive to self-correlations. Taking into account that the dynamics measured by Mo¨ssbauer spectroscopy is not very different above and below Tl it was inferred that the sharp increase of lZ occurring right below Tl is the signature of the building up of magnetic pair correlations as argued by Dalmas de Re´otier et al. (2003). In Sections 4.7 and 4.8 examples were shown, where pyrochlore and garnet lattice compounds show magnetic dynamic behavior down to very low temperatures. In Table 19 an overview of these oxide-based Gd and Yb compounds is given.

5. CONCLUSIONS, JUSTIFICATION, AND ACKNOWLEDGMENT In this overview, we saw quite interesting features. Rare earth Mo¨ssbauer spectroscopy gives clear information concerning crystal field effects and magnetic interaction. In this paragraph the author of this chapter will resume the most interesting results. First, a reanalysis of Tm2O3 Mo¨ssbauer results by Stewart et al. (1988) on the old measurements of Barnes et al. (1964) gives new information about the crystal field. Further, the results on Dy2O3 by Forester and Ferrando (1976b) and on PrO2 by Moolenaar et al. (1996) were discussed. For RMO3 the results of Hodges et al. (1984) and e.g., Salama and Stewart (2009) explain the

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TABLE 19 Transition Temperatures in Kelvin, Types of Transition, and Magnetic Moments in Bohr Magnetons in Gd and Yb Pyrochlore and Garnet Compounds Compound

Tl K

Type of Magnetic Transition

Magnetic Moment mB

Gd2Sn2O7

1.1

First order

7

Gd2Ti2O7

1.0

First order

7

Yb2Sn2O7

0.15

First order

1.1

Yb2Ti2O7

0.24

First order

1.1

Yb2GaSbO7

None

None

1.1

Gd3Ga5O12

None

None

7

Yb3Ga5O12

0.054

Second order

1.4

The values given in the table are approximate.

magnetic behavior based on the crystal field results. In the case of RMO4 the crystal field determinations on TmMO4 and YbMO4 were shown in relation to the existence of a JahneTeller effect, for example, by Hodges (1983). Furthermore, the magnetic interplay between rare earth and chromium as mainly studied by e.g., Jimenez-Melero et al. (2006) leads to some interesting features on magnetic and crystallographic behavior. In the SC RBa2Cu3O7 compounds, studies on magnetic and crystal field behavior by a diversity of authors lead to quite interesting results. The determination of the intermediary valency of 3.4 by Moolenaar et al. (1996) with help of the isomer shift interpolation from the 141Pr Mo¨ssbauer measurements on the PrxOy compounds is an exceptional, however, undervalued result. Crystal field-effect determination has been performed by cooperation of the Mo¨ssbauer groups in Delft (Netherlands) and Canberra (Australia) on the R2BaCuO5 compounds to explain its magnetic behavior. At last the Gd and Yb Mo¨ssbauer results, mainly performed by Joe Hodges and coworkers in Saclay on magnetic dynamic behavior in pyrochlore and garnet compounds, were discussed in combination with mSR results of cooperation between the groups in Grenoble, Delft, and Saclay. The author of this chapter thanks Glen Stewart, Steve Harker, Enrique Jimenez, Regino Sa´ez-Puche, Alain Yaouanc, Pierre Dalmas de Re´otier, Joe Hodges, Pierre Bonville, and others for their cooperation during many years on the field of Mo¨ssbauer spectroscopy on rare earth-based oxides. The author of this chapter thanks Ignatz de Schepper for critical reading the manuscript, Jouke Heringa for solving computer problems, and Ekkes Bru¨ck for pushing me forward to finish this chapter.

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REFERENCES Allenspach, P., Furrer, A., Bru¨esch, P., Marsolais, R., Unterna¨hrer, P., 1989a. Physica C 157, 58. Allenspach, P., Furrer, A., Hulliger, F., 1989b. Phys. Rev. B 39, 2226. Almog, A., Bauminger, E.R., Levy, A., Nowik, I., Ofer, S., 1973. Solid State Commun. 12, 693. Armon, H., Bauminger, E.R., Ofer, S., 1973. Phys. Rev. B 43, 380. Barnes, R.G., Mo¨ssbauer, R.L., Kankeleit, E., Poindexter, J.M., 1964. Phys. Rev. 136, A175. Bent, M.F., Cook, D.D., Persson, B.I., 1971. Phys. Rev. C 3, 1419. Bergold, M., Wortman, G., Stewart, G.A., 1990. Hyperfine Interact. 55, 1205. Bertaut, E.F., Mareschal, J., de Vries, J., Ale´onard, R., Pauthenet, R., Rebouillat, J.P., Zarubicka, V., 1966. IEEE Trans. Magn. MAG-2, 453. Bertin, E., Bonville, P., Bouchaud, J.P., Hodges, J.A., Sanchez, J.P., Vulliet, P., 2002. Eur. Phys. J. B 27, 347. Bertin, A., Chapuis, Y., Dalmas de Re´otier, P., Yaouanc, A., 2012. J. Phys. Condens. Matter 24, 256003. Blo¨te, H.W.J., Wielinga, R.F., Huiskamp, W.J., 1969. Physica 43, 549. Blume, M., 1965. Phys. Rev. Lett. 14, 96. Blume, M., Tjon, J.A., 1968. Phys. Rev. 165, 446. Bonville, P., Hodges, J.A., Imbert, P., Hartmann-Boutron, F., 1978. Phys. Rev. B 18, 2196. Bonville, P., Hodges, J.A., Ocio, M., Sanchez, J.P., Vulliet, P., Sosin, S., Braithwaite, D., 2003. J. Phys. Condens. Matter 15, 7777. Bonville, P., Hodges, J.A., Sanchez, J.P., Vulliet, P., 2004. Phys. Rev. Lett. 92, 167202. Bornemann, H.J., Czjzek, G., Ewert, D., Meyer, C., Renker, B., 1987. J. Phys. F Met. Phys. 17, L337. Bowden, G.J., 1998. Aust. J. Phys. 51, 201 (and references cited therein). Bradbury, M., Newman, D.J., 1967. Chem. Phys. Lett. 1, 44. Buisson, G., Bertaut, F., Mareschal, J., 1964. C. R. Acad. Sci. Paris 259, 411. Buisson, G., Tche´ou, F., Sayetat, F., Scheunemann, K., 1976. Solid State Commun. 18, 871. Cashion, J.D., Prowse, D.B., Vas, A., 1973. J. Phys. C Solid State Phys. 6, 2611. Campbell, I.A., 1972. J. Phys. F 2, L47. Cava, R.J., Batlogg, B., Chen, C.H., Rietman, E.A., Zahurak, S.M., Werder, D., 1987. Phys. Rev. B 36, 5719. Chang, L.-J., Onoda, S., Su, Y., Kao, Y.-J., Tsuei, K.-D., Yasui, Y., Kakurai, K., Lees, M.R., 2012. Nat. Commun. 3, 992. Clauser, M.J., Blume, M., 1971. Phys. Rev. B 3, 583. Coehoorn, R., Buschow, K.H.J., Dirken, M.W., Thiel, R.C., 1990. Phys. Rev. B 42, 4645. Coey, J.M.D., Donnelly, K., 1987. Z. Phys. B 67, 513. Cohen, R.L., Wernick, J.H., 1964. Phys. Rev. 134, B503. Cook, D.C., Cashion, J.D., 1976. J. Phys. C Solid State Phys. 9, L97. Cook, D.C., Cashion, J.D., 1980. J. Phys. C Solid State Phys. 13, 4199. Dalichaouch, D., Torikachvili, M.S., Early, E.A., Lee, B.W., Seaman, C.L., Yang, K.N., Zhou, H., Maple, M.B., 1988. Solid Sate Commun. 65, 1001. Dalmas de Re´otier, P., Yaouanc, A., Gubbens, P.C.M., Kaiser, C.T., Baines, C., King, P.J.C., 2003. Phys. Rev. Lett. 91, 167201. Dalmas de Re´otier, P., Yaouanc, A., Keller, L., Cervellino, A., Roessli, B., Baines, C., Forget, A., Vaju, C., Gubbens, P.C.M., Amato, A., King, P.J.C., 2006. Phys. Rev. Lett. 96, 17202. Dattagupta, D., 1981. Hyperfine Interact. 11, 77. Divis, M., Ho¨lsa¨, J., Lastusaari, M., Litvinchuk, A.P., Nekvasil, V., 2008. J. Alloy. Compd. 451, 662.

232 Handbook of Magnetic Materials Dunlap, B.D., 1971. in: Gruverman, I.J. (Ed.), Mo¨ssbauer Effect Methodology, vol. 7. Plenum, New York, p. 123. Dunsiger, S.R., Gardner, J.S., Chakhalian, J.A., Cornelius, A.L., Jaime, M., Kiefl, R.F., Movshovich, R., MacFarlane, W.A., Miller, R.I., Sonier, J.E., Gaulin, B.D., 2000. Phys. Rev. Lett. 85, 3504. Eibschu¨tz, M., Van Uitert, L.G., 1969. Phys. Rev. 177, 502. Eibschu¨tz, M., Murphy, D.W., Sunshine, S., Van Uitert, L.G., Zahurak, S.M., Grodkiewicz, W.H., 1987. Phys. Rev. B 35, 8714. Filippi, J., Lasjaunias, J.C., Hebral, B., Rossat-Mignod, J., Tcheou, F., 1980. J. Phys. C 13, 1277. Forester, D.W., Ferrando, W.A., 1976a. Phys. Rev. B 13, 3991. Forester, D.W., Ferrando, W.A., 1976b. Phys. Rev. B 14, 4769. Frauenfelder, H., 1962. in: The Mo¨ssbauer Effect edited by W.A.Benjamin, Inc., New York. Freeman, A.J., Desclaux, J.P., 1979. J. Magn. Magn. Mater. 12, 11. Fritz, L.S., Dixon, N.S., 1992. Hyperfine Interact. 72, 191. Fu¨rrer, A., Bru¨esch, P., Unterna¨hrer, P., 1988. Solid State Commun. 67, 69. Garcia, D., Faucher, M., 1984. Phys. Rev. B 30, 1703. Gardner, J.S., Dunsinger, S.R., Gaulin, B.D., Gingras, M.J.P., Greedan, J.E., Kiefl, R.F., Lumsden, M.D., MacFarlane, W.A., Jaju, N.P., Sonier, J.E., Swainson, I., Tun, Z., 1999. Phys. Rev. Lett. 82, 1012. Gardner, J.S., Gingras, M.P.J., Greedan, J.E., 2010. Rev. Mod. Phys. 82, 53. Goldanskii, V.I., Herber, R.H., 1968. in: Chemical Applications of Mo¨ssbauer Spectroscopy edited by Academic Press, New York and London, Chapter 1. Gonzalez-Jimenez, F., Imbert, P., Hartmann-Boutron, F., 1974. Phys. Rev. B 9, 95, 10, 2134. Gorobchenko, V.D., Lukashevich, I.I., Stankevich, V.G., Mel’nikopv, E.V., Filipov, N.I., 1973. Sov. Phys. Solid State 14, 2140. Greedan, J.E., Sato, M., Ali, N., Datars, W.R., 1987. J. Solid State Chem. 68, 300. Groves, J.L., DePasquali, G., Debrunner, P.G., 1973. Phys. Rev. B 7, 1974. Gruber, J.B., Leavitt, R.P., Morrison, C.A., Chang, N.C., 1985. J. Chem. Phys. 82, 5373. Gubbens, P.C.M., 2012. in: Buschow, K.H.J. (Ed.), Rare Earth Mo¨ssbauer Spectroscopy Measurements on Lanthanide Intermetallics: A Survey, vol. 20. Handbook of Magnetic Materials, Amsterdam, The Netherlands, pp. 227e335. Gubbens, P.C.M., Buschow, K.H.J., 1982. J. Phys. F 12, 2715. Gubbens, P.C.M., van der Kraan, A.M., Buschow, K.H.J., 1985a. edited by Gordon and Breach, New York. in: Proceedings of the International Conference on Applications of Mo¨ssbauer Effect (ICAME), Alma Ata (1984), pp. 297e318. Gubbens, P.C.M., van der Kraan, A.M., Buschow, K.H.J., 1985b. J. Less Common Met. 111, 301e312. Gubbens, P.C.M., van der Kraan, A.M., Buschow, K.H.J., 1985c. J. Magn. Mag. Mater. 50, 199. Gubbens, P.C.M., van der Kraan, A.M., Buschow, K.H.J., 1988a. J. de Phys. 49, C8eC525. Gubbens, P.C.M., van der Kraan, A.M., Buschow, K.H.J., 1989. Phys. Rev. B 39, 12548. Gubbens, P.C.M., van der Kraan, A.M., Buschow, K.H.J., 1990. Hyperfine Interact. 53, 37. Gubbens, P.C.M., van Loef, J.J., van der Kraan, A.M., de Leeuw, D.M., 1988b. J. Magn. Magn. Mater. 76 & 77, 615. Gubbens, P.C.M., Mulders, A.M., 1998. Aust. J. Phys. 51, 315e337. Gupta, R.P., Sen, S.K., 1973. Phys. Rev. A 7, 850. Harker, S.J., Stewart, G.A., Edge, A.V.J., 1996. Solid State Commun. 100, 307. Harker, S.J., Stewart, G.A., Gubbens, P.C.M., 2000. J. Alloy. Compd. 307, 70. Hodges, J.A., 1983. J. Phys. 44, 833.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

233

Hodges, J.A., Bonville, P., 2004. J. Phys. Condens. Matter 16, 8661. Hodges, J.A., Bonville, P., Forget, A., Andre´, G., 2001. Can. J. Phys. 79, 1373. Hodges, J.A., Bonville, P., Forget, A., Yaouanc, A., Dalmas de Re´otier, P., Andre´, G., Rams, M., Kro´las, K., Ritter, C., Gubbens, P.C.M., Kaiser, C.T., King, P.J.C., Baines, C., 2002. Phys. Rev. Lett. 88, 077204. Hodges, J.A., Bonville, P., Forget, A., Sanchez, J.P., Vulliet, P., Rams, M., Kro´las, 2003a. Eur. Phys. J. B 33, 173. Hodges, J.A., Bonville, P., Imbert, P., Je´hanno, G., 1994. Hyperfine Interact. 90, 187. Hodges, J.A., Bonville, P., Rams, M., Kro´las, K., 2003b. J. Phys. Condens. Matter 15, 4631. Hodges, J.A., le Bras, G., Bonville, P., Imbert, P., Je´hanno, G., 1993. Physica C 218, 283. Hodges, J.A., Dalmas de Re´otier, Yaouanc, A., Gubbens, P.C.M., King, P.J.C., Baines, C., 2011. J. Phys. Condens. Matter 23, 164217. Hodges, J.A., Imbert, P., Je´hanno, G., 1982. J. Phys. 43, 1249. Hodges, J.A., Imbert, P., Je´hanno, G., 1987. Solid State Commun. 64, 1209. Hodges, J.A., Imbert, P., Marimom da Cunha, J.B., Hammann, J., Vincent, E., Sanchez, J.P., 1988. Physica C 156, 143. Hodges, J.A., Imbert, P., Marimom da Cunha, Sanchez, J.P., 1989. Physica C 160, 49. Hodges, J.A., Imbert, P., Schuhl, A., 1984. J. Magn. Magn. Mater. 43, 101. Hodges, J.A., Sanchez, J.P., 1990. J. Magn. Magn. Mater. 92, 201. Jimenez, E., Bonville, P., Hodges, J.A., Gubbens, P.C.M., Isasi, J., Sa´ez-Puche, R., 2004a. J. Magn. Magn. Mater. 272e276, 571. Jimenez, E., Gubbens, P.C.M., Sakarya, S., Stewart, G.A., Dalmas de Re´otier, P., Yaouanc, A., Isasi, J., Sa´ez-Puche, R., Zimmermann, U., 2004b. J. Magn. Magn. Mater. 272e276, 568. Jimenez-Melero, E., Gubbens, P.C.M., Steenvoorden, M.P., Sakarya, S., Goosens, A., Dalmas de Re´otier, P., Yaouanc, A., Rodrı´guez-Carvajal, J., Beuneu, B., Isasi, J., Sa´ez-Puche, R., Zimmermann, U., Martı´nez, J.L., 2006. J. Phys. Condens. Matter 18, 7893. Kang, J.-S., Moritomo, Y., Xu, Sh, Olson, C.G., Park, J.H., Kwon, S.K., Min, B.I., 2002. Phys. Rev. B 65, 224422. Kapfhammer, W.H., Maurer, W., Wagner, F.E., Kienle, P., 1971. Z. Naturforsch. 26a, 357. Kasuya, T., 1956. Prog. Theor. Phys. (Kyoto) 16, 45. Katsufuji, T., Hwang, H.Y., Cheong, S.-W., 2000. Phys. Rev. Lett. 84, 1998. Kern, S., Loong, C.K., Faber Jr., J., Lander, J.H., 1984. Solid State Commun. 49, 295. Klencsa´r, Z., Kuzmann, E., Ve´rtes, A., Gubbens, P.C.M., van der Kraan, A.M., Bo´dogh, M., Kotsis, I., 2000a. Physica C 329, 1. Klencsa´r, Z., Kuzmann, E., Ve´rtes, A., Gubbens, P.C.M., van der Kraan, A.M., Bo´dogh, M., Kotsis, I., 2000b. J. Radioanal. Nucl. Chem. 246, 113. Knoll, K.D., 1971. Phys. Status Solidi B 45, 553. Kuzmann, E., Klencsa´r, Z., Homonnay, Z., Ve´rtes, A., Braga, G., De Oliveira, A.C., Garg, V.K., Bo´dogh, M., Kotsis, I., Nath, A., 2000. J. Radioanal. Nucl. Chem. 246, 313. Leavitt, R.P., Gruber, J.B., Chang, N.C., Morrison, C.A., 1982. J. Chem. Phys. 76, 4775. Li, W.H., Lynn, J.W., Skanthakumar, S., Clinton, T.W., Kebede, A., Jee, C.S., Engler, E.M., Grant, P.M., 1989. Phys. Rev. B 40, 5300. Lonkai, Th, Hohlwein, D., Ihringer, J., Prandl, W., 2002. Appl. Phys. A 74 (Suppl.), S843. Lytle, F.W., van der Laan, G., Greegor, R.B., Larson, E.M., Violet, C.E., Wong, J., 1990. Phys. Rev. B 41, 6655. Malkin, B.Z., Zakirov, A.R., Popova, M.N., Klinim, S.A., Chukilina, E.P., Antic-Fidancev, E., Goldner, E., Aschebourg, P., Dhalenne, G., 2004. Phys. Rev. B 70, 075112.

234 Handbook of Magnetic Materials Marshall, I.M., Blundell, S.J., Pratt, F.L., Husmann, A., Steer, C.A., Coldea, A.I., Hayes, W., Ward, R.C.C., 2002. J. Phys. Condens. Matter 14, L157. May, L., 1971. An Introduction to Mo¨ssbauer Spectroscopy. Adam Hilger, London. Meyer, C., Sanchez, J.P., Thomasson, J., Itie´, J.P., 1995. Phys. Rev. B 51, 12187. Mirebeau, I., Bonville, P., Hennion, M., 2007. Phys. Rev. B 76, 184436. Moolenaar, A.A., Gubbens, P.C.M., van Loef, J.J., Menken, M.J.V., Menovsky, A.A., 1994. Hyperfine Interact. 93, 1717. Moolenaar, A.A., Gubbens, P.C.M., van Loef, J.J., Menken, M.J.V., Menovsky, A.A., 1996. Physica C 267, 279. Moritomo, Y., Xu, Sh., Machida, A., Katsufuji, T., Nishibori, E., Takata, M., Sakata, M., Cheong, S.-W., 2001. Phys. Rev. B 63, 144425. Mulders, A.M., Gubbens, P.C.M., Gasser, U., Baines, C., Buschow, K.H.J., 1998. Phys. Rev. B 57, 10320. Mulder, F.M., Brabers, J.H.V.J., Coehoorn, R., Thiel, R.C., Buschow, K.H.J., de Boer, F.R., 1995. J. Alloy. Compd. 217, 118. Nagarajan, R., Grover, A.K., Dhar, S.K., Paulose, P.L., Nagarajan, V., Sampathkumaran, E.V., 1988. Hyperfine Interact. 42, 1227. Nekvasil, V., 1979. Czechoslov. J. Phys. B 29, 785. Nekvasil, V., 1988. Solid State Commun. 65, 103. Noakes, D.R., Shenoy, G.K., 1982. Phys. Lett. 91A, 35. Nowik, I., Williams, H.J., 1966. Phys. Lett. 154, 154. Orbach, R., 1961. Proc. R. Soc. Lond. Ser. A 264, 458. Olesen, M.C., Elbek, B., 1960. Nucl. Phys. 15, 134. Raju, N.P., Gmelin, E., Kremer, R.K., 1992. Phys. Rev. B 46, 5405. Ramirez, A.P., Shastry, B.S., Hayashi, A., Krajewski, J.J., Huse, D.A., Cava, R.J., 2002. Phys. Rev. Lett. 89, 067202. Rosenkranz, S., Ramirez, A.P., Hayashi, A., Cava, R.J., Siddharthan, R., Shastry, B.S., 2000. J. Appl. Phys. 87, 5914. Ross, K.A., Ruff, J.P.C., Adams, C.P., Gardner, J.S., Dabkowska, H.A., Qiu, Y., Coply, J.R.D., Gaulin, B.D., 2009. Phys. Rev. Lett. 103, 22720. Rudermann, M.A., Kittel, C., 1954. Phys. Rev. 96, 99. Rudowicz, C., Gnutek, P., Lewandowska, M., Orlowski, M., 2009. J. Alloy. Compd. 467, 98. Rushbrooke, G.S., Baker, G.A., Wood, P.I., 1974. Phase Transitions and Critical Phenomena, vol. 3, p. 246. Ryzhkov, M.V., Gubanov, V.A., Teterin, Y.A., Baev, A.S., 1985. Z. Pys. B 59, 7. Salama, H.A., Stewart, G.A., 2009. J. Phys. Condens. Matter 21, 386001. Salama, H.A., Stewart, G.A., Ryan, D.H., Elouneg-Jamroz, M., Edge, A.V., 2008. J. Phys. Condens. Matter 20, 255213. Salama, H.A., Stewart, G.A., Hutchison, W.D., Nishimura, K., Scott, D.R., O’Neill, H., 2010. Solid State Commun. 150, 289. Salama, H.A., Voyer, C.J., Ryan, D.H., Stewart, G.A., 2009. J. Appl. Phys. 2010 (5), 07E110. Savary, L., Balents, L., 2012. Phys. Rev. Lett. 108, 037202. Smit, H.H.A., Dirken, M.W., Thiel, R.C., de Jongh, L.J., 1987. Solid State Commun. 64, 695. Soderholm, L., Zhang, K., Hinks, D.G., Beno, M.A., Jorgensen, J.D., Segre, C.U., Schuller, I.K., 1987. Nature 328, 604. Sternheimer, R.M., 1966. Phys. Rev. 146, 140. Stevens, K.W.H., 1952. Proc. Phys. A65, 109. Stewart, G.A., 1985. Hyperfine Interact. 23, 1.

Mo¨ssbauer Spectroscopy on rare Earth-Based Oxides Chapter j 3

235

Stewart, G.A., 1994. Mater. Forum 18, 177. Stewart, G.A., 2010. J. Phys. Conf. Ser. 217, 012071. Stewart, G.A., Cadogan, J.M., 1993. J. Magn. Magn. Mater. 118, 322. Stewart, G.A., Day, R.K., Dunlop, J.B., Price, D.C., 1988. Hyperfine Interact. 40, 339. Stewart, G.A., Harker, S.J., Pooke, D.M., 1998. J. Phys. Condens. Matter 10, 8269. Stewart, G.A., Harker, S.J., Strecker, M., Wortmann, G., 2000. J. Phys. Rev. B 61, 6220. Stewart, G.A., Gubbens, P.C.M., 1999. J. Magn. Magn. Mater. 206, 17. Stewart, G.A., McPherson, I.M., Gubbens, P.C.M., Kaiser, C.T., Dalmas de Re´otier, P., Yaouanc, A., Cottrell, S.P., 2003. J. Alloy. Compd. 358, 7. Strecker, M., Hettkamp, P., Wortmann, G., Stewart, G.A., 1998. J. Magn. Magn. Mater. 177e181, 1095. Triplett, B.B., Dixon, N.S., Boolchand, P., Hanna, S.S., Bucher, E., 1974. J. Phys. 35, C6eC653. Wegener, H., 1964. in: Der Mo¨ssbauer-effekt und seine anwendungen in physik und chemie edited by Bibliographische Institut Mannheim. Wegener, H., 1965. Z. Phys. 186, 498. Wertheim, G.K., 1964. in: Mo¨ssbauer Effect, Principles and Application edited by Academic Press, New York and London. Wickman, H.H., Klein, M.P., Shirley, D.A., 1966. Phys. Rev. B 152, 345. Wit, H.P., Niesen, L., 1976. Hyperfine Interact. 1, 501. Wortman, D.E., Leavitt, R.P., Morrison, C.A., 1974. J. Phys. Chem. Solids 35, 591. Wortmann, G., Blumenro¨der, S., Freimuth, A., Riegel, D., 1988a. Phys. Lett. A 126, 434. Wortmann, G., Felner, I., 1990. Solid State Commun. 75, 981. Wortmann, G., Kolodziejczyk, A., Bergold, M., Staderrmann, G., Simmons, C.T., Kaindl, G., 1989. Hyperfine Interact. 50, 555. Wortmann, G., Kolodziejczyk, A., Simmons, C.T., Kaindl, G., 1988b. Physica C 153e155, 1547. Wortmann, G., Simmons, C.T., Kaindl, G., 1987. Solid State Commun. 64, 1057. Yaouanc, A., Dalmas de Re´otier, P., Bonville, P., Hodges, J.A., Glazkov, V., Keller, L., Sikolenko, V., Bartkowiak, M., Amato, A., Baines, C., King, P.J.C., Gubbens, P.C.M., Forget, A., 2013. Phys. Rev. Lett. 110, 127207. Yaouanc, A., Dalmas de Re´otier, P., Bonville, P., Hodges, J.A., Gubbens, P.C.M., Kaiser, C.T., Sakarya, S., 2003. Physica B 326, 456. Yosida, K., 1957. Phys. Rev. 106, 893. Zukrowski, J., Wasniowska, M., Tarnawski, Z., Przewoznik, J., Chmist, J., Kozlowski, A., Krop, K., Sawicki, M., 2003. Acta Phys. Pol. B 34, 1533.