Electronic structure and optical properties of Er5Si3Yu.V. Knyazev a, A.V. Lukoyanov a,b,n, Yu.I. Kuz‘min a

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

a r t i c l e i n f o

Article history:Received 10 January 2014Received in revised form17 February 2014Accepted 18 February 2014Available online 25 February 2014

Keywords:Electronic structureRare-earth compoundsIntermetallicsAb initio calculationsOptical measurementsOptical conductivity

a b s t r a c t

We report a joint experimental and theoretical investigation of optical properties and electronic struc-ture of Er5Si3. Rare-earth alloy optical constants have been measured in the wavelength range0:22–15 μm ð0:083–5:64 eVÞ, as well as other spectral and electronic characteristics. Spin-polarizedcalculations of the electronic structure have been performed employing the LSDAþUmethod accountingfor electronic correlations in the 4f shell of Er. All main features of the experimental optical conductivityin the interband region have been well interpreted using the convolution of the calculated densities ofstates of Er5Si3.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Binary compounds RE5M3, where RE is the rare-earth metaland M is the p element, are characterized by a great diversity ofmagnetic and transport properties, manifesting themselves viastrong anomalies near phase transition temperatures. These alloyscrystallize in hexagonal crystal structure with the RE ions found in(4d) and (6g) positions forming different sublattices. Due to thisfact, inner magnetic interactions in RE5M3 are anisotropic thatpromotes complicated magnetic structures as well as sharp jumpsin kinetic and thermal properties, especially well-pronounced atlow temperatures [1–6]. Characteristic features of physical proper-ties of these materials often have unusual behaviour in externalfields, doping, pressure and temperature. In many cases thesefeatures are associated with strong interrelation between struc-tural, charge and spin degrees of freedom. Compound Er5Si3investigated in this paper is characterized by a sine modulatedantiferromagnetic ordering below Néel temperature values 30 and15 K corresponding to different periods of magnetic structure[7–9]. In this alloy, thermal hysteresis was found in magnetizationand electrical resistance, and the low-temperature behaviour ofmagnetoresistance in the presence of magnetic field of 12–18 kOepoints out on a metamagnetic AFM-FM transition [10].

As it follows from the previous studies, physical propertiesof Er5Si3 are rather unique. In the present paper we continueinvestigations of the electronic structure combining the bandstructure computations and experimental optical measurementsin a wide wave-length range. Based on the calculated density ofstates, all main features of the experimental optical conductivityare interpreted.

2. Methods

The samples studied in this work were investigated usingelastic neutron diffraction in [8] and prepared following [7].Single-phase hexagonal Mn5Ge3�type structure was confirmedby structural X-ray analysis. Crystal structure lattice parametersa¼8.290 Å and c¼6.228 Å are close to the previously reportedone in Refs. [7,9]. Er5Si3 crystallizes in a hexagonal Mn5Si3�typestructure (space group P63/mcm). Erbium atoms occupy twononequivalent crystallographic positions: Er1 – (4d) (1/3, 2/3, 0)and Er2 – (6g) (xEr, 0, 1/4), silicon atoms occupy only (6g) positionswith coordinates (xSi, 0, 1/2).

Optical properties were measured at room temperature for thewavelength λ¼ 0:22–15 μm (0.083–5.64 eV). Ellipsometric methodwas used to measure optical constants – refractive index n(λ) andabsorption coefficient k(λ) for the angles of reflection of light fromthe mirror of the sample within 70–801. From these constantsreflectivity was obtained as

R¼ ðn�1Þ2þk2

ðnþ1Þ2þk2: ð1Þ

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Physica B

http://dx.doi.org/10.1016/j.physb.2014.02.0280921-4526 & 2014 Elsevier B.V. All rights reserved.

n Corresponding author at: Institute of Metal Physics, UrB RAS, 18,S. Kovalevskaya St., 620990 Yekaterinburg, Russia. Tel.: þ7 3433783886;fax: þ7 3433745244.

E-mail address: lukoyanov@imp.uran.ru (A.V. Lukoyanov).

Physica B 442 (2014) 12–15

In the present work the electronic structure of Er5Si3 wasinvestigated using ab initio approach. Self-consistent calculationswere performed within LSDAþUmethod [11] in the TB-LMTO-ASApackage (Tight Binding, Linear Muffin-Tin Orbitals, Atomic SphereApproximation) [12] accounting for electronic corrections in the 4fshell of erbium. The values of direct Coulomb UEr¼6.5 eV andHund exchange JEr¼0.6 eV interactions for the 4f states of Er weretaken as in Ref. [13]. Orbital basis included 6s, 6p, 5d, and 4f statesof Er (REr1

MT ¼ 3:4 a:u: and REr2MT ¼ 3:8 a:u:), 4s and 4p states of Si

(RSiMT ¼ 2:6 a:u:).

3. Results and discussions

3.1. Electronic structure

In the electronic structure calculations we obtained an AFMsolution with magnetic moments of the Er ions equal to 3μB, thisvalue does not account for a large orbital moment of Er, sincespin–orbit coupling was not included in our calculations. Hence,noncollinear magnetic ordering at low temperatures [7–9] wasneglected. The Er 4f effective magnetic moments can be estimatedas μeff ¼ g

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiJðJþ1Þ

paccounting for an orbital moment contribution

in a way of [14], it equals to 9:6μB, the same value was estimatedfrom the experimental magnetic measurements in [10].

Spin-polarized total densities of states (DOS) of Er5Si5 areshown in the upper panel of Fig. 1a. Other panels of Fig. 1 containpartial Er 4f and 5d densities of states, as well as Si 3s and 3pstates. The many-peaks structure of DOS is almost identical forboth spin directions. Above the Fermi energy (EF), it is mostlydefined by the Er 5d states, whereas in 1–4.5 eV below EF it is amixture of the Si 3s and 3p and Er 5d states. Strong narrow peaksat 6–8.5 eV below EF and some maxima just above EF belong to theoccupied and empty Er 4f states in both spin directions. Silicon 3s

and 3p states have almost the same shape in both spin directionsand located 6.5–9 eV and 1–4.5 eV below the Fermi level, respec-tively. Above EF, the contribution of these bands to the totaldensity of states is small and decreases gradually with the increaseof energy.

The energy dependence of the densities of states of Er5Si5below the Fermi energy in Fig. 1 in general is found in a goodagreement with previous X-ray photoemission study of thiscompound [15]. The significant features of photoemission spec-trum related to the 4f, 5d and 3p states are located close to theones calculated in this work.

3.2. Optical properties

Refractive index n(λ) and absorption coefficient k(λ) resultsobtained in this work for Er5Si3 are shown in Fig. 2. Except for theshort-wave interval up to 1:5 μm, almost for all wavelength valuesthese constants gradually increase. Also k4n, it is typical for amedia with metallic conductivity. This kind of behaviour of opticalconstants results in negative values of the real part of complexpermittivity, and also the reflectivity increases with the decreaseof light wave energy, see the inset of Fig. 3.

Optical conductivity s¼ nkω=2π, where ω is the angular freq-uency, of Er5Si3 is shown in Fig. 3. This is the most sensitivespectral parameter that characterizes the frequency dependenceand intensity of optical response of medium. In the spectrum ofsðωÞ two frequency ranges are well defined that correspond totwo different types of electronic excitations by light: intra- and

-10 -8 -6 -4 -2 0 2 4 6 8 10

4

0

E (eV)

0

4

4

00

4

8040

0

DO

S (s

tate

s eV

-1)

04080

2010

001020

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) 5dstates (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 tocolour in this figure caption, the reader is referred to the web version of this paper.)

1234

0 1 2

2 4 6 8 10 12 14 16

4

8

12

16

20

24

28

n,k

λ (μm)

n

kn

k

0

λ(μm)

n,k

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

0 2 4 6

0.4

0.6

0.8

1.0

0 1 2 3 4 5 610

20

30

40

σ x

10-1

4 (s

-1)

E (eV)

R

E (eV)

Fig. 3. The energy dependence of optical conductivity of Er5Si3. In the inset opticalreflectivity R is shown.

Yu.V. Knyazev et al. / Physica B 442 (2014) 12–15 13

inter-band ones. In the low-energy infrared range, a rapid increasein optical conductivity is caused by the Drude mechanism ofinteraction of electromagnetic waves with free electrons(s�ω�2). With the increase of light frequency (visible light andultraviolet), quantum absorption starts to dominate, and almostmonotonous decrease of sðωÞ is replaced by the increase forenergies above 1 eV and then by a group of maxima. Two mostintense peaks of the interband absorption are found at 1.3 and1.8 eV, above these peaks the optical conductivity drops nonmo-notonously with energy. Other three broad maxima at 2.4, 3.3 and4.4 eV can be distinguished in this energy range. Noteworthy,there are two “shoulders” on the Drude slope below 1 eV. Thesefeatures of sðωÞ are formed by interband transitions between theelectronic states above and below the Fermi energy and reflect theactual structure of the electronic spectrum of a particular compound.

To understand the nature of these structural features of theinterband optical conductivity (sibðωÞ) obtained from the totaloptical conductivity subtracting the Drude contribution, it isinteresting to compare it to the corresponding theoretical curvecalculated from the densities of states in Fig. 1. It is well knownthat the overall structure of interband optical absorption in bothferromagnets and antiferromagnets can be presented as a super-position of electron excitations in both spin subsystems. Each ofthese contributions is related to its structure in sibðωÞ formed byquantum transitions between energy bands of that subsystem. Thetheoretical interband optical conductivities of Er5Si3 correspond-ing to different spin directions were made according to [16] usingtotal convolutions N↑ðEÞ and N↓ðEÞ below and above EF with equalprobabilities of all types of the electronic transitions. Thus, thetotal calculated interband conductivity sibðωÞ ¼ s↑ðωÞþs↓ðωÞ, aswell as the contributions from both spin subsystems, is presentedin Fig. 4.

A further comparison reveals that the theoretical curve sibðωÞreproduces all the main features of the experimental interbandoptical conductivity rather well. Noteworthy, an intense structurecentered at 0.5 eV remained after the Drude contribution subtrac-tion. An analysis of all contributions to the interband opticalconductivity allows us to interpret this and another intensepeak at 1.3 eV as direct quantum p, f-f transitions in the↑�spin subsystem. Such electronic excitations in the ↓�spinsubsystem are formed on the slope of the high-energy absorptionstructure at 0.8 eV and near 1.8 eV. Thus, the main structuralfeatures of the experimental interband conductivity, namely, themaxima below 2 eV, are caused by quantum transitions with theinvolvement of the Er 4f electrons. These maxima are

characterized by large intensity and abrupt decrease that corre-sponds to localized character of the 4f states in the electronicstructure of Er5Si3. For the higher photon energies, including nearultraviolet, the large width of the d band and significant s, p and dhybridization of Er and Si states in the Mn5Ge3�type lattice alsopromote the formation of the intense (p, d-d, p) interbandtransitions. In this energy range, three broad maxima at 2.4,3.3 and 4.4 eV can be determined. As it is clearly follows fromFig. 4, these features stem from the electronic transitions in the ↓�spinsubsystem. The calculation also has demonstrated that in this energyrange (E42 eV) contributions to sibðωÞ from both spin-polarizedbands are comparable.

In general, one can notice a smoother character of the experi-mental frequency dependence of the interband optical conductiv-ity in comparison with the theoretical one. Such a character couldbe a cooperative result of partial contributions of a large number ofelectronic transitions with different lifetimes of excited state, aswell as experimental factors related with the preparation of thesamples surfaces.

Using the experimental values of optical constants n and k,kinetic characteristics of conduction electrons, namely, dampingconstant γ and plasma ωp frequency, were estimated in the low-energy range where the effects of interband transitions on opticalproperties are minimal. For Er5Si3, their numerical values stabilizein the wavelength range of 11–15 μm and equal to γ¼1.9�10�14 s�1, ωp¼4.5�10�15 s�1. The Drude contribution to opticalconductivity estimated for these values is shown as a dotted linein Fig. 4.

4. Conclusions

The electronic structure and optical properties of Er5Si3 wereinvestigated for the first time, damping constant and plasmafrequency were estimated from the intraband region of opticalconstants. The spin-polarized densities of states were calculatedself-consistently within the LSDAþU method taking into accountstrong electronic correlations in the Er 4f shell. It was demon-strated that the dispersion of experimental interband opticalconductivity is well described by the theoretical optical conduc-tivity. Namely, the positions and widths of the main peaks of theexperimental curve sðωÞ were well reproduced by the theoreticalcurve and identified with the certain electronic states transitionsin both spin subsystems of Er5Si3.

Acknowledgements

This study was partially supported by the Russian Foundationfor Basic Research, research Project nos. 13-02-00256-a, 14-02-92713-IND_a, 13-02-00050-a, the Presidential Program of Grantsin Science, Project no. SP-506.2012.2, the Dynasty Foundation,calculations were performed using “Uran” supercomputer of IMMUrB RAS.

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1 2 3 4 5 6

10

20

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σ x

10-1

4 (s

-1)

E (eV)0

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

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