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Supertransferred hyperﬁne interactions in layer LaSrGa0.995Cu0.005O4 O.A. Anikeenoka, M.A. Augustyniak-Jab"okowb, T.A. Ivanovac, P. Reiched, R. Ueckerd, Yu.V. Yablokovb,* b

a Kazan State University, Kremljevskaja 18, 420008 Kazan, Russia Institute of Molecular Physics, Polish Academy of Sciences, Radiospectroscopy of Solid State, Smoluchowskiego 17, ! Poland PL-60179 Poznan, c Kazan Physical–Technical Institute, Russian Academy of Sciences, Sibirskii Trakt 10/7, 420029 Kazan, Russia d Institute of Crystal Growth, D-12489 Berlin, Germany

Received 17 May 2002; received in revised form 29 July 2002; accepted 16 September 2002

Abstract The EPR allowing a direct observation of supertransferred hyperﬁne ﬁelds on the nuclei of the next-nearest cations to copper ion in the structure of LaSrGa0.995Cu0.005O4 isomorphous to the superconducting cuprates prove the far delocalisation of the spin density. The theoretical analysis of the value and mechanisms of this process by the method of conﬁgurational interaction leads to a good agreement with the experiment. It is shown that the cascade processes involving simultaneous electron transfers from the oxygen to the copper atom and from the neighbouring cation to the same oxygen, in the fragment considered bring a substantial contribution into polarisation of 3s-shell of gallium ion. A comparison of the supertransferred hyperﬁne ﬁelds and g-tensor values in the studied, diluted LaSrGa0.995Cu0.005O4 crystal and in the La2CuO4 cuprate conﬁrms the validity of the local centre approach in the analysis of cuprate properties. r 2002 Elsevier Science B.V. All rights reserved. PACS: 33.15.P; 33.35.+r; 71.20.b Keywords: Supertransferred hyperﬁne interaction; Method of conﬁgurational interactions; Cuprates

1. Introduction We have recently reported [1] an observation of the magnetic superhyperﬁne structure due to the interaction of the unpaired electron of Cu2+ ion *Corresponding author. Tel.: +48-61-8695205; fax: +48-618684524. E-mail address: [email protected] (Y.V. Yablokov).

with nuclear magnetic moments of Ga3+ ions, which are the next nearest cations of Cu2+ ions in the LaSrGa0.995Cu0.005O4 crystal belonging to the K2NiF4 structure type. The study of the local magnetic ﬁelds at the nuclei of diamagnetic cations in the crystals doped with magnetic ions allows elucidation of the mechanisms of the electron density transfer from the metal ion into the orbitals of the neighbouring ions in the crystals. Such a transfer is usually realised indirectly

0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 5 3 5 - 1

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through the intervening diamagnetic anions and is known as the supertransferred hyperﬁne interaction [2]. Presently available experimental data show a small difference between the anisotropic part of the supertransferred hyperﬁne interaction tensor and that of the purely dipole–dipole one. At the same time, a noticeable isotropic interaction As ðSIÞ is observed, which has usually been the subject of consideration. The ﬁrst calculations of the supertransferred magnetic ﬁelds were performed in analysis of the results of ENDOR measurements [3 and references therein] of the 27Al hyperﬁne structure in Cr3+:LaAlO3 and Fe3+: LaAlO3. It was found in Ref. [3] that the greatest contribution to the observed isotropic hyperﬁne interaction originates from the overlapping of the external 2s orbital Al3+ with the electron shells of the oxygen ion. The nonzero spin density on the oxygen atom comes from the overlapping and covalence effects with the partly ﬁlled shells of Fe3+ or Cr3+. Such a mechanism was also assumed [2] in the calculations of the contribution to the hyperﬁne ﬁeld at 55Mn nuclei in antiferromagnetic KMnF3 and MnO. The possibilities of the charge transfer from oxygen onto the external orbitals of the diamagnetic cation were discussed. For Cr3+ and Ni2+ ions introduced into MgO, the contribution of such processes was shown to be inessential [4]. However, in order to ﬁt to the local magnetic ﬁelds on 25Mg, the author of Ref. [4] took into consideration the overlapping of both 2s and 1s orbitals of 25Mg with O2. The conclusions drawn in Refs. [3,4] are in agreement with the results of the NMR study of the cations nuclei in diamagnetic crystals [5]. In Ref. [6] the calculations performed by the conﬁgurational interaction method in order to explain the local ﬁelds in crystals of ﬂuorite type with the Eu2+ and Gd3+ rare earth ions, are reported. These theoretical results are confronted with ENDOR experiment [5]. The results have shown an important role of the cascade charge transfer processes (electron transfer from the ligand into the unﬁlled level of the paramagnetic ion and simultaneous transition from the diamagnetic cation to ligand). Supertransferred hyperﬁne ﬁelds at the nuclei of various diamagnetic ions have been also studied in a series of articles for yttrium iron garnet and its diluted

247

analogue [7]. After discovery of the high temperature superconductivity in cuprates La2xSrxCuO4 and YBa2Cu3O6+d, studies of the local magnetic ﬁeld on the copper nuclei by the methods of nuclear magnetic resonance and relaxation have become an important source of information about the properties of these materials [8–14]. In this paper, we report our experimental EPR observations of the supertransferred hyperﬁne interaction in the LaSrGa0.995Cu0.005O4 crystal, which follow the preliminary report [1], and their theoretical analysis performed by the method of conﬁgurational interaction. The detailed results of the experimental study of the supertransferred hyperﬁne interaction in the LaSrGa0.995Cu0.005O4 crystal are presented in the second section of this work. The theoretical analysis of the supertransferred hyperﬁne ﬁelds on the gallium nuclei and the mechanisms of their appearance in the studied crystal are given in Section 3. These theoretical predictions are compared with the experiments. In the last part of this section, we compare our experimental parameters of the hyperﬁne and superhyperﬁne couplings in the LaSrGa0.995Cu0.005O4 crystal to the corresponding, literature parameters obtained for La2xSrxCuO4 from the analysis of the Knight shift in NMR spectra and nuclear relaxation rates tensor.

2. Crystal growth and crystallography Crystals of LaSrGa0.995Cu0.005O4 have been grown using the automatised Czochralski pulling technique with RF-induction heating. Due to the high melting temperature of this material (15161C), an iridium crucible had to be used, and therefore, the growth had to be performed under ﬂowing nitrogen. The pulling rate of 1.0 mm h1 and the crystal rotation of 10 min1 were chosen. To avoid cracking, an active afterheater was applied to establish an axial temperature gradient of about 10 K cm1 above the melting point. The seed orientation was /1 1 0S and the obtained crystal was 16 mm in diameter and 75 mm in length. The crystal was yellowish in colour and it showed {0 0 1} facets at the cylinder and {1 0 1}

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facets at the interface. In contrast to other compounds of the ABCO4 type (e.g. PrSrGaO4) the LaSrGaO4 crystal has a stoichiometric composition, however, because this material melts incongruently; the melt composition must differ from that of the crystal by a lower SrO content [15]. Due to the incongruent melting behaviour, the crystal showed the eutectic structure in its lower part. LaSrGaO4 crystal belongs to the structural type of K2NiF4 with the symmetry group I4/mmm with Z ¼ 1 and unit cell parameters: a ¼ 0:38437 nm and c ¼ 1:2688 nm [16]. Its crystal structure consist of oxygen-linked octahedrons GaO4O2 intergrown with La(Sr)O layers which include apical oxygens of the GaO4O2 octahedrons. The octahedrons are weakly distorted along the c-axis: GaOplane=0.1922 nm and GaOapic= 0.2134 nm. The distance between the apical oxygen and La/Sr position along the c-axis (La/ Ga)cOapic=0.2458 nm while the distance to the La/Sr position in the layer (La/Sr)layer Oapic=0.2745 nm [17]. The ions La3+ and Sr2+ are statistically disordered [18]. The Cu2+ ions occupy the positions of the Ga3+ ions with nonlocal compensation of deﬁcient positive charge and are under the inﬂuence of the tetragonal ligand ﬁeld disturbed by the disorder in the La–Sr system. The structure of the closest surrounding of Cu2+ is shown in Fig. 1.

Fig. 1. A fragment of LaSrGaO4 crystal structure with the introduced Cu2+ cation. The CuO6 complex is shown together with the Ga3+ cations interacting via O2 anions.

3. EPR measurements EPR measurements of LaSrGa0.995Cu0.005O4 single crystal were performed on an X-band RADIOPAN SE/X-2547 spectrometer with 100 kHz magnetic modulation and an Oxford ESR 900 ﬂowing helium cryostat in the temperature range 4.2–300 K. The samples studied were oriented by X-ray diffraction with additional correction according to the EPR spectra. The spectra were collected in the (1 1 0) and (0 0 1) planes. The EPR spectra recorded for the magnetic ﬁeld oriented along [0 0 1], [1 1 0] and [1 0 0] directions are presented in Fig. 2. The number of lines is evidently higher than expected for the interaction

Fig. 2. The experimental EPR spectra recorded for the magnetic ﬁeld directed along: (a) [0 0 1]; (b) [1 1 0] and (c) [1 0 0] axes.

with the nuclei of 63,65Cu, with nuclear spin I ¼ 3=2: The nuclear magnetic moment of the closest 16 O (with natural abundance 99.98%) ligands IO ¼ 0: Consequently, the additional splitting of

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the observed spectrum can be due solely to the four Ga3+ (IGa ¼ 3=2) ions located in the next coordination sphere of the copper ion (see Fig. 1). This supposition is conﬁrmed by the analysis of the best-resolved spectrum recorded for B8½1 1 0 (Fig. 2). In this orientation all the four Ga3+ ions are equivalent and the 13 components of the superhyperﬁne structure, which can be distinguished, correspond to the number N ¼ ð2nI þ 1Þ expected for the interaction with four equivalent nuclei of 69,71Ga with I ¼ 3=2: In this case, the expected intensity rate is 1:4:10:20:31:40:44:40:31:20:10:4:1. However, the two isotopes 69Ga and 71Ga with natural abundance of 60.4% and 39.6%, respectively, differ in the nuclear g-factors: gn ð69 GaÞ ¼ 1:34439 and gn ð71 GaÞ ¼ 1:70818 (their gyromagnetic ratio g71 =g69 ¼ 1:2701 [19]) and their interaction with the unpaired Cu2+ electron. The spectrum is moreover complicated because of the different probabilities of various combinations of 69Ga and 71 Ga isotopes in the structural fragment Cu(OGa)4 and differences in the splitting of

249

their energy levels [20]. These facts were taken into account in the process of the spectra simulation, although, they result mainly in the broadening of the observed resonance lines and in the departure of their relative intensities from the expected ones. Down to B15 K the spectra parameters (g; ACu ; AGa and dB) are independent of temperature. The observed spectra can be described by the spin-Hamiltonian including the term describing the superhyperﬁne interaction with four planar Ga3+ ions: H ¼ bBfggS þ ICu fACu gS þ

4 X

ðjÞ ðjÞ IGa fAGa gS;

ð1Þ

j¼1

where S ¼ 1=2; ICu ¼ 3=2; IGa ¼ 3=2: As the quadrupole effects have not been observed in the experimental spectra, the term describing quadrupole electric interaction is not included in Eq. (1). The angular dependencies of the spectra recorded in the (1 1 0) and (0 0 1) planes were analysed. In spite of the relatively broad EPR lines with dBE1:2 mT, estimation of the

Fig. 3. Comparison of the (a) experimental and (b) theoretical ﬁts for the magnetic ﬁeld along [1 1 0] direction (01) and inclined at 101 and 201 from this direction. The ﬁtted spectra parameters are (all A values are in 104 cm1); for 01: g ¼ 2:0554; A63;65Cu ¼ 3; A69Ga ¼ 19:5; A71Ga ¼ 24:7; dB ¼ 1:22 mT, shape 0:95L þ 0:05G; for 101: g ¼ 2:064; A63Cu ¼ 19:5; A65Cu ¼ 20:7; A69Ga ¼ 19:6; A71Ga ¼ 25; dB ¼ 1:22 mT, shape 0:95L þ 0:05G: For 201 the ﬁt is a superposition of three spectra resulting from a nonstatistical La3+ and Sr2+ distribution: (i) g ¼ 2:084; A63Cu ¼ 43:3; A65Cu ¼ 46:7; (ii) g ¼ 2:080; A63Cu ¼ 39:6; A65Cu ¼ 42:8; and (iii) g ¼ 2:090; A63Cu ¼ 47:9; A65Cu ¼ 51:0: In all cases A69Ga ¼ 19:8; A71Ga ¼ 25:1; dB ¼ 1:22 mT, shape 0:95L þ 0:05G:

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superhyperﬁne splitting AGa in the (1 1 0) plane was possible in the whole angular range. The hyperﬁne ACu splitting in this plane was measurable directly in the angular range 7501 from the c-axis direction. For the remaining angles, the ACu values were obtained by ﬁtting the experimental spectra. The experimental and theoretical spectra for the magnetic ﬁeld directed along [1 1 0] and inclined to this direction at 101 and 201, are shown in Fig. 3. The angular dependencies of the measured parameters g; ACu and AGa in (1 1 0) plane are shown in Fig. 4. The angular dependence of AGa indicates the existence of small anisotropic superhyperﬁne interaction between the unpaired electron of Cu2+ and the magnetic moments of gallium nuclei. This also explains a decrease of the spectrum resolution in the (0 0 1) plane when the magnetic ﬁeld B deviates from the [1 1 0] direction (Fig. 2). It is the smallest in the [1 0 0] direction when the magnetic ﬁeld is parallel to the interionic Cu–O–Ga axes of the two Ga2+ ions, while the axes of the two other ions are perpendicular to B: ð2Þ ð3Þ ð4Þ We can write: Að1Þ Ga x ¼ AGa y ¼ AGa x ¼ AGa y and ð1Þ ð2Þ ð3Þ ð4Þ AGa y ¼ AGa x ¼ AGa y ¼ AGa x : It is obvious that AðiÞ Ga z are equal. In the further discussion, the analysis of the Ga3+ superhyperﬁne interactions is performed for the structural fragment Cu– OGa(1). In the (0 0 1) plane, no angular dependence of {g} tensor is observed and the EPR spectra do not suggest any angular dependence of the Cu2+ hyperﬁne interaction. Therefore, we can assume that both {g2 } and {g2 A2Cu } tensors are axial and their principal axes coincide with each other and with the axes of the {g2 A2Ga } tensor. The experiment does not allow the determination of the values of AGa x and AGa y and we assume that {g2 A2Ga } tensor is axial too with AGa z ¼ AGa y : Then the value of AGa x can be determined from the formula A2Ga ½1 1 0 ¼ ðA2Ga x þ A2Ga y Þ=2: The obtained experimental parameters are presented in Table 1. The most noticeable feature of the EPR spectra in the crystal studied is their distinct asymmetry (Figs. 2 and 3). Practically, only the spectrum recorded for B8½1 1 0 can be treated as the symmetric one. The essential asymmetry of the spectrum recorded for B8½0 0 1 direction was

Fig. 4. The angular dependencies of (a) g values, (b) ACu the copper hyperﬁne splitting and (c) AGa the gallium superhyperﬁne splitting in the (1 1 0) plane.

explained to be as a result of the distribution of La3+ and Sr2+ ions, which are the next nearest neighbours in the [0 0 1] direction [1]. As shown in Fig. 5, the asymmetric spectrum is a sum of the three symmetric spectra, with different values of g and ACu : The same method can be used for the other asymmetric spectra as it was done for the

O.A. Anikeenok et al. / Physica B 325 (2003) 246–255 Table 1 Parameters of the EPR spectra of LaSrGa0.995Cu0.005O4 crystal (A in 104 cm1) Parameter

g8 g> A8Cu A>Cu AzGa ¼ AyGa A½1 1 0Ga AxGa

Experiment

2.32070.005 2.05870.005 14371 E3 18.4 22.1 25.3

Ligand SHFS parameters Ga69

Ga71

Theory for Ga71

16.8 19.5 21.9

21.3 24.7 27.7

21.50 27.66

251

The isotropic AGa s interaction arises from the delocalisation of the unpaired electron spin density of Cu2+ on the s orbital(s) of the Ga3+ ion (whose electron conﬁguration is 1s22s22p63s23p6). The anisotropic part of the superhyperﬁne interaction AGa p ; which in the usual notation [21] can be written as AGa p ¼ Ad þ AGa s AGa p ; which represents the sum of the effect of the delocalisation on the ps and pp orbitals of Ga3+ and the dipolar interaction Ad between the 69,71Ga nucleus and the electron spin on the neighbouring Cu2+ ion. In a point-dipole model Ad ¼ ðgn bn gbÞR3 ; and for g> ¼ 2:058 and R ¼ 0:38437 nm [17] the dipole– dipole interaction Ad ¼ 0:012 mT. As follows from Table 2, the isotropic contribution AGa s is by more than an order of magnitude greater than AGa s AGa p :

4. Theory and comparison with experiment 4.1. The method of calculation

Fig. 5. The theoretical spectra (a–c) are generated on the assumption that the nonstatistical distribution of La3+ and Sr2+ cations affects the crystal ﬁeld around the introduced Cu2+. The spectra parameters are the following (all A values are in 104 cm1): (i) g ¼ 2:320; A63Cu ¼ 140:0; A65Cu ¼ 149:8; (ii) g ¼ 2:327; A63Cu ¼ 41:8; A65Cu ¼ 150:6; g ¼ 2:312; A63Cu ¼ 138:0; A65Cu ¼ 147:0: In all cases A69Ga ¼ 16:8; A71Ga ¼ 21:3; dB ¼ 1:2 mT, shape 0:8L þ 0:2G:

theoretical ﬁtting of the spectrum recorded for the magnetic ﬁeld direction at 201 to the [1 1 0] direction in the (1 1 0) plane shown in Fig. 3. Table 2 presents the estimated values of the isotropic and anisotropic contributions to the parameters of the gallium superhyperﬁne interaction obtained according to Ref. [21] for the experimental values shown in Table 1. In the system of the magnetic axes shown in Fig. 1: AGa s ¼ 13ðAGa x þ 2AGa zðyÞ Þ; AGa p ¼ 13ðAGa x AGa zðyÞ Þ:

ð2Þ

We have obtained the operator of the supertransferred hyperﬁne interaction HSTHI by the method of conﬁgurational interaction as in Ref. [22]. The existence of the supertransferred spin density on Ga3+ ion distinguishes the chain of ions Cu2+O2Ga3+ in the crystal lattice. Therefore, it is natural to take their ionic states for the ground conﬁguration. The following excited conﬁgurations are taken into account: (1) that with an electron transferred from the ligand onto the paramagnetic ion, and (2) that with an electron transferred from the diamagnetic cation onto a partly vacated orbital of the ligand. The processes discussed are described by the terms proportional to the fourth and higher powers of the overlapping integrals. We shall limit our considerations to those in the fourth power. In contrast to the procedure used in Ref. [22], we construct the system of many-electron orthonormalised wave functions in the following way. As shown in Ref. [29], the matrix element of an arbitrary operator calculated on the Slater determinants composed of partly nonorthogonal

O.A. Anikeenok et al. / Physica B 325 (2003) 246–255

252

Table 2 Parameters of superhyperﬁne interaction with gallium nuclei (in 104 cm1)

For the experimental values For the 71Ga isotope

AðjÞ Ga s

AðjÞ Ga p

Ad (estimated)

AGa s AGa p

20.7 23.4

2.3 2.13

0.12 0.12

2.18 2.01

one-electron orbitals is 8 2 3 9 < = X 0 5 0 0 /mjV jm0 S ¼ /mjN exp4 aþ x ax /xjx S n jm S; : ; 0 xax

ð3Þ þ þ jmS ¼ aþ x1 ax2 ?axn j0S;

ð4Þ

where V is a single-particle or two-particle 0 operator in a second quantisation form, aþ x ðax Þ is the operator of creation (annihilation) of electron, N is the sign of an normal product and /xjx0 S an overlapping integral. If V ¼ I; where I is a unity operator, Eq. (3) becomes [23] VI ¼ exp½Q; Q¼

X

aþ a /xj x0 x

ð5Þ N X Sn ð1Þnþ1 jx0 S: n n¼1

ð6Þ

Here /zjSjz0 S ¼ /zjz0 S is the matrix element of the overlapping matrix for the one-electron orbitals. Using expressions (3) and (4), the system of the ortho-normalised many-electrons functions jmS can be constructed as follows: X

jmS ¼ jnS/njhnj exp 12 Q jmS: ð7Þ Further, following the approach developed in Ref. [22], and restricting to the terms of the fourth-order perturbation theory, we shall obtain the following expression for the HSTHI operator: h X bc ca 9 ac cb HSTHI ¼ aþ Z aZ0 64 sZy sya /ba jnjbb SsbB sBZ0 bc ca * cb þ 38 ð*gac Zy g ya /ba jnjbb SsbB sBZ0 þ h:c:Þ

* ðhÞ jcy S; DZy

g* cb ya ¼ /cy j

* ðhÞ jba S; DZa

sac Zy ¼ /aZ jcb S:

ð9Þ

Here jaZ S; jcy S; jba S denote the orbitals of the paramagnetic ion, ligand and diamagnetic cation, respectively, DZy is the change of the energy of the system at the electron transfer from the orbital of one ion into the orbital of another ion, /ba jnjbb Sis the matrix element of the operator of the hyperﬁne interaction [24] and h* ¼ 12½ðI þ SÞ1 h þ hðI þ SÞ1 :

ð10Þ

If h is the operator deﬁned in Ref. [24], then g* ¼ g þ 12 s; where g is the covalence parameter and s is the overlapping integral. 4.2. Comparison of the theory with experiment The ground state wave function of the copper ion in the ﬁrst-order perturbation theory is jeS ¼ jx2 y2 S:

ð11Þ

Then spin Hamiltonian H* STHI corresponding to the HSTHI operator, determined by expression (8), can be written for Ga1 as follows: H* STHI ¼ Ax S* x Ix þ Ay S* y Iy þ Az S* z Iz ;

ð12Þ

where Ay ¼ Az ¼ Aa3s Ba3p ; ð13Þ

bc ca bc ca 27 ac 3 ac * 3d0;y scb s3d0;y scb A ¼ 256 y;3s s3s;z sz;3d0 þ 16 g y;3s s3s;z sz;3d0

1 ac cb * ca gZy g* ya /ba jnjbb Ssbc bz g zZ0 2 ð*

þ h:c:Þ i * cb * ca þ12 ð*gac gbc Zy g ya /ba jnjbb S* bz g zZ0 Þ ;

g* ac Zy ¼ /aZ j

Ax ¼ Aa3s þ 2Ba3p ;

cb bc ca þ 18 ð*gac Zy sya /ba jnjbb SsbB sBZ0 þ h:c:Þ

þ

where

bc ca bc ca 9 ac 3 ac * 3d0;y g* cb * z;3d0 þ 16 g* 3d0;y g* cb y;3s s3s;z sz;3d0 þ 4 g y;3s s3s;z g

ð8Þ

* cb * bc * ca þ 38 g* ac 3d0;y g y;3s g 3s;z g z;3d0 ;

ð14Þ

O.A. Anikeenok et al. / Physica B 325 (2003) 246–255 bc ca bc ca 27 ac 3 ac * 3d0;y scb B ¼ 256 s3d0;y scb y;3p0 s3p0;z sz;3d0 þ 16 g y;3p0 s3p0;z sz;3d0 bc ca 9 ac þ 16 g* 3d0;y g* cb y;3p0 s3p0;z sz;3d0 bc * cb * ca þ 34 g* ac 3d0;y g y;3p0 s3p0;z g z;3d0

þ

3 ac * * cb * bc * ca 8 g3d0;y gy;3p0 g3p0;z gz;3d0 ;

2 a3s ¼ 16 3 pbgn _jCð0Þj ;

ð15Þ

253

Table 3 Overlap integrals Cu2+O2

O2Ga3+

S3d0,2s=0.05237 S3d0,2p0=0.05452

S2s,3s=0.01875 S2s,3p0=0.01823

S2p0,3s=0.08558 S2p0,3p0=0.0352

a3p ¼ 45 bgn _/ 1=r3 S3p : ð16Þ

The a3s and a3p values represent the contact and dipole–dipole components of the hyperﬁne interactions of 3s and 3p electrons of gallium, respectively. It should be noted that Hamiltonian HSTHI is axial, as pz and py orbitals are orthogonal to dx2 y2 copper orbital and the p-bond is absent. The wave functions of the Cu2+, O2, Ga+ ions [25] were used as the zero-order orbitals. The calculated values of the needed overlap integrals are given in Table 3. The covalence parameters for the Cu2+O2 pair were taken as in [26] gs ¼ 0:032; gs ¼ 0:20: The parameters of the contact and dipole–dipole interactions were calculated from the functions in Ref. [25] as a3s ¼ 57:87 104 cm1, and a3p ¼ 3:067 104 cm1. The contribution from the 3d shell of gallium was found small and thus was neglected. To assess the relative importance of the processes, we assume the covalence parameters corresponding to the transfer process from gallium into the emptying orbital of oxygen, to be zero. This means that we will leave only the overlap integral for this pair of ions. Then the isotropic part of the H* STHI tensor will be equal to As ¼ Aa3s ¼ 11:46 104 cm1 whereas the experimental value Aexp ¼ 23:4 104 cm1. The s estimations of the isotropic part of the transferred hyperﬁne interaction show that taking into account only the overlap in the processes considered, gives B50% of the experimental value. At the same time, it is obvious that in the calculations of the spin density at the gallium nuclei, these processes should be taken into account. A good agreement with experiment (see Table 1) is obtained with the following values of the covalence parameters describing the electron transfer

from gallium into oxygen: g2s;3s ¼ 0;

g2s;3p0 ¼ 0;

g2p0;3s ¼ 0:0353;

g2p0;3p0 ¼ 0:137: The analogous parameters obtained by the authors of Ref. [6] are of the same order of magnitude. Thus, the above approach to the mechanisms of the spin density transfer on the nuclei of diamagnetic cations leads to values well consistent with the experiment. 4.3. Comparison with the data for cuprates We have obtained the data for the hyperﬁne interaction of an electron of the magnetic ion with its own nucleus (on-set hfs) and for the spin density delocalisation in a nonconducting crystal. It would be interesting to compare the obtained parameters with on-set and supertransferred hyperﬁne coupling parameters for the isostructural La2CuO4 crystal. The CuOCu fragment of interest is repeated in many oxides having CuO2 layers. Therefore, we also present some results for the YBa2Cu3O6+d compound. This is especially interesting when we take into account the great role of investigation of the hyperﬁne interactions in cuprates in the study of the fundamental problems of high-temperature superconductivity, ranging from magnetic behaviour of the planar excitations to the approaches in the electron Fermi liquid theory [8–11]. The parameters of on-site and supertransferred hyperﬁne interactions in cuprates have been obtained in the study of temperature and angular dependencies of the Knight shift NMR in external magnetic ﬁeld [12,13] and from the measurements of anisotropy of the Cu spin-lattice relaxation rates [11,13]. Some data are given in Table 4. There is deﬁnite scatter of parameters obtained by

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Table 4 On-site and supertransferred hyperﬁne coupling parameters for La2xSrxCuO4, YBa2Cu3O4+d and LaSrGa0.995Cu0.005O4 (in kG/mB) Source

Ac (ACu8 )

Aab (ACu> )

B {ðgGa =gCu ÞAðjÞ Ga> }

La2xSrxCuO4 Monien et al., Phys. Rev. B (1991) [29]; x ¼ 0:15 Zha et al., Phys. Rev. B (1996) [13]; x ¼ 0 Husser . et al., Phys. Rev. B (2000) [14]; Theory

163 185 188

34 18 29.4

40.8 36 44.5

LaSrGa0.995Cu0.005O4 This work

191

4

YBa2Cu3O6+d Mila and Rice, Physica C (1989) [8] Monien et al., Phys. Rev. B (1990) [10] Monien et al., Phys. Rev. B (1991) [30] Zha et al., Phys. Rev. B (1996) [13]

228 (180210) 195 163 172

5 (1732) 25 34.3 31

29

46.6 (3438) 37 40.8 43

We use here the notations Ac and Aab used in the references for ACu8 and ACu> previously used in the text as well as B for our ðjÞ ðgGa =gCu ÞAGa> :

different authors. We give preference to the review articles concerning La2CuO4. It can be concluded that the parameters Ac ; Aab and B reported in the references are comparable to those obtained from the ﬁrst-principle calculations and to correspondðjÞ ing parameters ACu8 ; ACu> and ðgGa =gCu ÞAGa> obtained in our experiment. This supports the usually accepted expectation that the inﬂuence of the crystal lattice on the copper centre does not vary substantially in cuprate and gallate crystals. More than that, the conﬁguration of CuO6 Jahn– Teller complex is determined by the inner vibronic forces, and small differences of the tetragonal crystal ﬁeld component in these compounds do not essentially affect the parameters. The full identity of our data with all parameters of EPR spectra of Cu2+ in aluminate and gallate ceramics [1,27] and very close values of g-tensor components extracted from magnetic measurements (g> ¼ 2:068 and g8 ¼ 2:306) [28] conﬁrm this approach. The parameters Ac and ACu8 as well as B and ðjÞ ðgGa =gCu ÞAGa> for La2CuO4 and LaSrGa0.995Cu0.005O4 practically coincide. For the other compositions B > ðgGa =gCu ÞAðjÞ Ga> and Ac tend to decrease with respect to ACu8 ; when in all cases Aab bACu> : All these considerations hold for both La2CuO4 and YBa2Cu3O6+d compounds. The coincidence of g-tensor components and similarity of the structure parameters of gallate

and cuprates show that the spin–orbital and dipole–dipole contributions to the hyperﬁne coupling parameters are also close. It seems that the reason for the differences in the values of Aab for cuprates and ACu> for gallate is the appearance of a small additional spin density on the 4s-orbital of the copper ion in cuprates. It would have the opposite sign with respect to the main 3s contribution. We have shown that this contribution is dominant in the gallate crystal. The same conclusion follows from the ﬁrst principal theory for La2CuO4 [14]. A large difference between Aab parameters for the hole-doped La1.85Sr0.15CuO4 and YBa2Cu3O6+d crystals and ACu> for our LaSrGa0.995Cu0.005O4 points to the transfer of electron density from oxygen p-band to copper 4sshell. The signiﬁcant difference between the Aab and ACu> (Aab bACu> ) parameters can be related to a very small difference between the core polarisation and all other contributions to ACu> of the opposite signs. This parameter is most strongly affected by the redistribution of the spin density in s shells.

5. Conclusions Direct observations of supertransferred hyperﬁne ﬁelds on the nuclei of the next-nearest cations

O.A. Anikeenok et al. / Physica B 325 (2003) 246–255

to copper ion in the structure isomorphous to the superconducting cuprates have proved the far delocalisation of the spin density as an experimental fact. Hitherto, the Mila and Rica idea on the core-polarisation transfer from the neighbourhood of Cu2+ ions [8], although highly effective and useful in analysis of Knight shift, measurements of nuclear relaxation rate tensor anisotropy for Cu [10,13] and supported by the ﬁrst principle calculations [14], have been treated as a useful suggestion only. Our theoretical analysis of the value and mechanisms of the spin density delocalisation by the method of conﬁgurational interaction leads to a good agreement with the experiment. It is shown that taking into account the covalence and overlapping effects only is not enough for the adequate description of the transfer effects. The cascade processes involving simultaneous electron transfers from the oxygen to the copper atom and from the neighbouring cation to the same oxygen, in the fragment considered, have been shown to bring a substantial contribution into polarisation of 3sshell of gallium ion. A comparison of the on-set and supertransferred hyperﬁne ﬁelds in the diluted LaSrGa0.995Cu0.005O4 crystal, measured directly, and for La2CuO4 cuprate, extracted from analysis of the nuclear magnetic resonance and nuclear relaxation rates data, shows that the supertransferred ﬁelds are very similar. Together with the g-tensor identity, this conﬁrms the validity of the local centre approach in the analysis of cuprate properties.

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