Electronic structure and optical properties of Er5Si3

Electronic structure and optical properties of Er5Si3

Physica B 442 (2014) 12–15 Contents lists available at ScienceDirect Physica B journal homepage: www.elsevier.com/locate/physb Electronic structure...

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Physica B 442 (2014) 12–15

Contents lists available at ScienceDirect

Physica B journal homepage: www.elsevier.com/locate/physb

Electronic structure and optical properties of Er5Si3 Yu.V. Knyazev a, A.V. Lukoyanov a,b,n, Yu.I. Kuz‘min a a b

Institute of Metal Physics, Russian Academy of Sciences–Ural Branch, 620990 Yekaterinburg, Russia Ural Federal University, 620002 Yekaterinburg, Russia

art ic l e i nf o

a b s t r a c t

Article history: Received 10 January 2014 Received in revised form 17 February 2014 Accepted 18 February 2014 Available online 25 February 2014

We report a joint experimental and theoretical investigation of optical properties and electronic structure of Er5Si3. Rare-earth alloy optical constants have been measured in the wavelength range 0:22–15 μm ð0:083–5:64 eVÞ, as well as other spectral and electronic characteristics. Spin-polarized calculations of the electronic structure have been performed employing the LSDAþ U method accounting for electronic correlations in the 4f shell of Er. All main features of the experimental optical conductivity in the interband region have been well interpreted using the convolution of the calculated densities of states of Er5Si3. & 2014 Elsevier B.V. All rights reserved.

Keywords: Electronic structure Rare-earth compounds Intermetallics Ab initio calculations Optical measurements Optical conductivity

1. Introduction Binary compounds RE5M3, where RE is the rare-earth metal and M is the p element, are characterized by a great diversity of magnetic and transport properties, manifesting themselves via strong anomalies near phase transition temperatures. These alloys crystallize in hexagonal crystal structure with the RE ions found in (4d) and (6g) positions forming different sublattices. Due to this fact, inner magnetic interactions in RE5M3 are anisotropic that promotes complicated magnetic structures as well as sharp jumps in kinetic and thermal properties, especially well-pronounced at low temperatures [1–6]. Characteristic features of physical properties of these materials often have unusual behaviour in external fields, doping, pressure and temperature. In many cases these features are associated with strong interrelation between structural, charge and spin degrees of freedom. Compound Er5Si3 investigated in this paper is characterized by a sine modulated antiferromagnetic ordering below Néel temperature values 30 and 15 K corresponding to different periods of magnetic structure [7–9]. In this alloy, thermal hysteresis was found in magnetization and electrical resistance, and the low-temperature behaviour of magnetoresistance in the presence of magnetic field of 12–18 kOe points out on a metamagnetic AFM-FM transition [10].

n Corresponding author at: Institute of Metal Physics, UrB RAS, 18, S. Kovalevskaya St., 620990 Yekaterinburg, Russia. Tel.: þ 7 3433783886; fax: þ7 3433745244. E-mail address: [email protected] (A.V. Lukoyanov).

http://dx.doi.org/10.1016/j.physb.2014.02.028 0921-4526 & 2014 Elsevier B.V. All rights reserved.

As it follows from the previous studies, physical properties of Er5Si3 are rather unique. In the present paper we continue investigations of the electronic structure combining the band structure computations and experimental optical measurements in a wide wave-length range. Based on the calculated density of states, all main features of the experimental optical conductivity are interpreted.

2. Methods The samples studied in this work were investigated using elastic neutron diffraction in [8] and prepared following [7]. Single-phase hexagonal Mn5 Ge3 type structure was confirmed by structural X-ray analysis. Crystal structure lattice parameters a¼ 8.290 Å and c ¼6.228 Å are close to the previously reported one in Refs. [7,9]. Er5Si3 crystallizes in a hexagonal Mn5 Si3 type structure (space group P63/mcm). Erbium atoms occupy two nonequivalent crystallographic positions: Er1 – (4d) (1/3, 2/3, 0) and Er2 – (6g) (xEr, 0, 1/4), silicon atoms occupy only (6g) positions with coordinates (xSi, 0, 1/2). Optical properties were measured at room temperature for the wavelength λ ¼ 0:22–15 μm (0.083–5.64 eV). Ellipsometric method was used to measure optical constants – refractive index n(λ) and absorption coefficient k(λ) for the angles of reflection of light from the mirror of the sample within 70–801. From these constants reflectivity was obtained as R¼

ðn  1Þ2 þ k 2

ðn þ 1Þ þ k

2 2

:

ð1Þ

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In the present work the electronic structure of Er5Si3 was investigated using ab initio approach. Self-consistent calculations were performed within LSDA þ U method [11] in the TB-LMTO-ASA package (Tight Binding, Linear Muffin-Tin Orbitals, Atomic Sphere Approximation) [12] accounting for electronic corrections in the 4f shell of erbium. The values of direct Coulomb UEr ¼ 6.5 eV and Hund exchange JEr ¼0.6 eV interactions for the 4f states of Er were taken as in Ref. [13]. Orbital basis included 6s, 6p, 5d, and 4f states Er2 of Er (REr1 MT ¼ 3:4 a:u: and RMT ¼ 3:8 a:u:), 4s and 4p states of Si (RSi ¼ 2:6 a:u:). MT

and 3p states have almost the same shape in both spin directions and located 6.5–9 eV and 1–4.5 eV below the Fermi level, respectively. Above EF, the contribution of these bands to the total density of states is small and decreases gradually with the increase of energy. The energy dependence of the densities of states of Er5Si5 below the Fermi energy in Fig. 1 in general is found in a good agreement with previous X-ray photoemission study of this compound [15]. The significant features of photoemission spectrum related to the 4f, 5d and 3p states are located close to the ones calculated in this work.

3. Results and discussions

3.2. Optical properties

3.1. Electronic structure

Refractive index n(λ) and absorption coefficient k(λ) results obtained in this work for Er5Si3 are shown in Fig. 2. Except for the short-wave interval up to 1:5 μm, almost for all wavelength values these constants gradually increase. Also k 4 n, it is typical for a media with metallic conductivity. This kind of behaviour of optical constants results in negative values of the real part of complex permittivity, and also the reflectivity increases with the decrease of light wave energy, see the inset of Fig. 3. Optical conductivity s ¼ nkω=2π , where ω is the angular frequency, of Er5Si3 is shown in Fig. 3. This is the most sensitive spectral parameter that characterizes the frequency dependence and intensity of optical response of medium. In the spectrum of sðωÞ two frequency ranges are well defined that correspond to two different types of electronic excitations by light: intra- and

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0

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2

λ(μm)

16

n

8 4

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0

0

2

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6

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10

12

14

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λ (μm)

40

Fig. 2. The wave-length dependence of refractive index n (blue diamonds) and absorption coefficient k (red circles). The inset shows n and k in the short-wave interval. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)

80 4 0

1.0

4

40

0.8

R σ x 10-14 (s-1)

4 0 4 -10

k

2

12

80

DOS (states eV-1)

n

3 1

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n,k

20 10 0 10 20

k

4

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n,k

In the electronic structure calculations we obtained an AFM solution with magnetic moments of the Er ions equal to 3μB , this value does not account for a large orbital moment of Er, since spin–orbit coupling was not included in our calculations. Hence, noncollinear magnetic ordering at low temperatures [7–9] was neglected.p The Er 4f effective magnetic moments can be estimated ffiffiffiffiffiffiffiffiffiffiffiffiffiffi as μeff ¼ g JðJ þ 1Þ accounting for an orbital moment contribution in a way of [14], it equals to 9:6μB , the same value was estimated from the experimental magnetic measurements in [10]. Spin-polarized total densities of states (DOS) of Er5Si5 are shown in the upper panel of Fig. 1a. Other panels of Fig. 1 contain partial Er 4f and 5d densities of states, as well as Si 3s and 3p states. The many-peaks structure of DOS is almost identical for both spin directions. Above the Fermi energy (EF), it is mostly defined by the Er 5d states, whereas in 1–4.5 eV below EF it is a mixture of the Si 3s and 3p and Er 5d states. Strong narrow peaks at 6–8.5 eV below EF and some maxima just above EF belong to the occupied and empty Er 4f states in both spin directions. Silicon 3s

-8

-6

-4

-2

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0.6 0.4

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E (eV) Fig. 1. Densities of states of Er5Si3. Total (a), partial Er (4d) 4f (purple area) and Er (6g) 4f states (cyan area) (b), partial Er (4d) 5d (green solid curve) and Er (6g) 5d states (red dashed curve) (c), partial Si 3s (green area) and 3p (blue curve) states (d). The Fermi level corresponds to zero. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.)

10

0

1

2

E (eV) Fig. 3. The energy dependence of optical conductivity of Er5Si3. In the inset optical reflectivity R is shown.

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inter-band ones. In the low-energy infrared range, a rapid increase in optical conductivity is caused by the Drude mechanism of interaction of electromagnetic waves with free electrons (s  ω  2 ). With the increase of light frequency (visible light and ultraviolet), quantum absorption starts to dominate, and almost monotonous decrease of sðωÞ is replaced by the increase for energies above 1 eV and then by a group of maxima. Two most intense peaks of the interband absorption are found at 1.3 and 1.8 eV, above these peaks the optical conductivity drops nonmonotonously with energy. Other three broad maxima at 2.4, 3.3 and 4.4 eV can be distinguished in this energy range. Noteworthy, there are two “shoulders” on the Drude slope below 1 eV. These features of sðωÞ are formed by interband transitions between the electronic states above and below the Fermi energy and reflect the actual structure of the electronic spectrum of a particular compound. To understand the nature of these structural features of the interband optical conductivity (sib ðωÞ) obtained from the total optical conductivity subtracting the Drude contribution, it is interesting to compare it to the corresponding theoretical curve calculated from the densities of states in Fig. 1. It is well known that the overall structure of interband optical absorption in both ferromagnets and antiferromagnets can be presented as a superposition of electron excitations in both spin subsystems. Each of these contributions is related to its structure in sib ðωÞ formed by quantum transitions between energy bands of that subsystem. The theoretical interband optical conductivities of Er5Si3 corresponding to different spin directions were made according to [16] using total convolutions N↑ ðEÞ and N ↓ ðEÞ below and above EF with equal probabilities of all types of the electronic transitions. Thus, the total calculated interband conductivity sib ðωÞ ¼ s↑ ðωÞ þ s↓ ðωÞ, as well as the contributions from both spin subsystems, is presented in Fig. 4. A further comparison reveals that the theoretical curve sib ðωÞ reproduces all the main features of the experimental interband optical conductivity rather well. Noteworthy, an intense structure centered at 0.5 eV remained after the Drude contribution subtraction. An analysis of all contributions to the interband optical conductivity allows us to interpret this and another intense peak at 1.3 eV as direct quantum p, f-f transitions in the ↑spin subsystem. Such electronic excitations in the ↓spin subsystem are formed on the slope of the high-energy absorption structure at 0.8 eV and near 1.8 eV. Thus, the main structural features of the experimental interband conductivity, namely, the maxima below 2 eV, are caused by quantum transitions with the involvement of the Er 4f electrons. These maxima are

characterized by large intensity and abrupt decrease that corresponds to localized character of the 4f states in the electronic structure of Er5Si3. For the higher photon energies, including near ultraviolet, the large width of the d band and significant s, p and d hybridization of Er and Si states in the Mn5 Ge3 type lattice also promote the formation of the intense (p, d-d, p) interband transitions. In this energy range, three broad maxima at 2.4, 3.3 and 4.4 eV can be determined. As it is clearly follows from Fig. 4, these features stem from the electronic transitions in the ↓spin subsystem. The calculation also has demonstrated that in this energy range (E 4 2 eV) contributions to sib ðωÞ from both spin-polarized bands are comparable. In general, one can notice a smoother character of the experimental frequency dependence of the interband optical conductivity in comparison with the theoretical one. Such a character could be a cooperative result of partial contributions of a large number of electronic transitions with different lifetimes of excited state, as well as experimental factors related with the preparation of the samples surfaces. Using the experimental values of optical constants n and k, kinetic characteristics of conduction electrons, namely, damping constant γ and plasma ωp frequency, were estimated in the lowenergy range where the effects of interband transitions on optical properties are minimal. For Er5Si3, their numerical values stabilize in the wavelength range of 11–15 μm and equal to γ ¼1.9  10  14 s  1, ωp ¼4.5  10  15 s  1. The Drude contribution to optical conductivity estimated for these values is shown as a dotted line in Fig. 4.

4. Conclusions The electronic structure and optical properties of Er5Si3 were investigated for the first time, damping constant and plasma frequency were estimated from the intraband region of optical constants. The spin-polarized densities of states were calculated self-consistently within the LSDA þU method taking into account strong electronic correlations in the Er 4f shell. It was demonstrated that the dispersion of experimental interband optical conductivity is well described by the theoretical optical conductivity. Namely, the positions and widths of the main peaks of the experimental curve sðωÞ were well reproduced by the theoretical curve and identified with the certain electronic states transitions in both spin subsystems of Er5Si3. Acknowledgements

σ x 10-14 (s-1)

30

This study was partially supported by the Russian Foundation for Basic Research, research Project nos. 13-02-00256-a, 14-0292713-IND_a, 13-02-00050-a, the Presidential Program of Grants in Science, Project no. SP-506.2012.2, the Dynasty Foundation, calculations were performed using “Uran” supercomputer of IMM UrB RAS.

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E (eV) Fig. 4. Spectra of the interband conductivity of Er5Si3. Blue circles correspond to the experiment, red solid curve is calculated from the total density of states, green dashed and purple dashed-dotted lines correspond to the partial interband contributions from spin up and spin down electronic subsystems, respectively. The black dotted curve corresponds to the calculated Drude contribution. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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