Journal of Alloys and Compounds 578 (2013) 559–564

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Journal of Alloys and Compounds

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Ground state properties of filled skutterudite EuRu4P12: A first principlesstudy

0925-8388/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jallcom.2013.06.190

⇑ Corresponding author.E-mail address: amitshan2009@gmail.com (A. Shankar).

A. Shankar ⇑, D.P. Rai, Sandeep, R.K. ThapaCondensed Matter Theory Research Group, Physics Department, Mizoram University, Aizawl, Mizoram 796 004, India

a r t i c l e i n f o

Article history:Received 28 February 2013Received in revised form 26 June 2013Accepted 30 June 2013Available online 9 July 2013

Keywords:LSDADFTGGAFP-LAPWDOSRefractive index

a b s t r a c t

The electronic band structures and magnetic moments of filled skutterudite EuRu4P12 has been studiedby using full-potential linearized augmented plane wave (FP-LAPW) method based on density functionaltheory (DFT). Local spin density approximation (LSDA) is used for the exchange–correlation potential. Thespin–orbit interaction has significant influence on the band structures causing the splitting of f-bandshowing the ferromagnetic nature of this type of compound with effective magnetic moment of5.98 lB. Optical constants including dielectric function, optical reflectivity, refractive index, electronenergy loss and optical conductivity are calculated for photon energy radiation. The study of electronicband structures near the Fermi energy level shows the compound to be suitable for effective thermoelec-tric application.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

The skutterudite compounds named after Skutterud region inNorway, has chemical formula of MX3, where M is a metal and Xa pnictogen [1]. For structural stabilization of binary skutterudites(MX3) by electropositive elements leads to the ternary filled skutt-erudite with chemical formula of RM4X12 [1], where R is a lantha-nide element, M transitional element (Fe, Ru and Os) and Xpnictogen (P, As and Sb). Here for our study, we have consideredlanthanide element R as (Eu), transitional element M as (Ru) andX pnictogen is P. This types of compound having extremely largefigure of merit Z (=S2r/j, where S is the Seebeck coefficient, r isthe electrical conductivity and j is the thermal conductivity, whichis the main requirement for thermoelectric applications [2]), re-cently attracted much attention in the field of thermoelectricapplications for the industrial purpose. Several features like heavyfermion behavior, superconductivity [3,4], ferromagnetism, anti-ferromagnetism, magnetic ordering [5], semiconductivity withsmall hybridization gap [6], non-Fermi liquid behavior [7], and me-tal–insulator transition [8] have become the main interest for var-ious theoretical and experimental investigations of this type ofcompound. These filled ternary compounds also exhibit a largevariety of electronic and magnetic properties, where the magneticbehavior is dominated by the particular 4f electronic configurationof rare-earth elements. Several studies have been done previously

on filled-skutterudites. Nouneh et al. [9] have reported the semi-conductor and metallic nature of CeFe4Sb12 and LaFe4Sb12 respec-tively from band energy calculation using LDA and TB-LMTOapproach. Bauer et al. [10] have reported ferromagnetism in someof Eu-filled skutterudites. Jung et al. [11] have studied the elec-tronic properties of LaFe4P12 and related compounds using the ex-tended Huckel tight-binding (EHTB) method. Rosner et al. [12]have studied the structural, electronic and magnetic properties ofEuFe4As12 using LDA+U method.

We have found that till date there are no theoretical detailsregarding the structural, electronic, magnetic and optical proper-ties are available for EuRu4P12. In this report, we present the firstprinciples calculation of structural, electronic, magnetic and opti-cal properties in respect of filled skutterudite EuRu4P12 using FP-LAPW method within the framework of the LSDA approach. Wehave seen that the present calculations are more consistent to pre-dict the ferromagnetic nature and a wide possibility of thermoelec-tric applications of Eu-filled skutterudites.

2. Crystal structure

The electronic property of any system strongly depends on itscrystal structure. Filled skutterudite with chemical formula EuRu4-

P12 crystallizes in cubic structure having space group Im3 (No.204), where one Eu atom takes the atomic position of 2a (0,0,0)and the metal atoms Ru located at 8c (0.25,0.25,0.25), while theP atoms are located at the position of 24g (0,0.35,0.16). The posi-tions of the remaining atoms in the unit cell are determined by

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symmetry operations associated with Im3 space group. Fig. 1shows the crystal structure of EuRu4P12 in which Eu ions areloosely bound in their Ru–P cage and the movement of the rareearth atoms within these cages dampens lattice vibrations (pho-nons), reducing the thermal conductivity and thereby improvingthermoelectric efficiency. Each unit cell of a crystal is composedof eight similar cubes. Each cube with Ru atom at the center andis surrounded by six nearly square four member rings of P atoms.Six different P rings give octahedral structure of Ru, with each faceof a cube sharing quarter of one P ring. The space between octahe-dral are filled by the Eu. Each such ring runs parallel to the crystal-lographic axis and they are oriented in mutually orthogonal to eachother.

3. Computation details

For structural optimization, we have used PBE-GGA [14] and FP-LAPW [15]methods and for calculations of electronic structure and magnetic properties, FP-LAPW method is used, which is implemented in the WIEN2k code [16]. The ex-change–correlation potential is chosen in the local spin density approximation(LSDA) [17]. The convergence criterion is set to 0.0001 Ry. The self-consistentpotentials were calculated on a 21 � 21 � 21 k-mesh in the Brillouin zone, whichcorresponds to 451 k points in the irreducible Brillouin zone. The sets of valenceorbital in the calculations were selected as 4f, 6s for Eu atom, 4d, 5s for Ru atomand 5s, 5p for P atom and lower states were treated as core states. The multipleexpansions of wave function as well as electron density along with the potential in-side the muffin–tin (MT) spheres was cut at l = 10. Nonspherical contributions tothe charge density and potential within the MT spheres were considered up tolmax = 6. The plane wave cut-off parameter was RMT � Kmax = 7 (where Kmax is themaximum value of the wave vector K = k + G). In the interstitial region, the chargedensity and the potential were expanded as a Fourier series with wave vectors upto Gmax = 12 a.u.�1. The different MT sphere radii (RMT) used were 2.5 a.u.,2.26 a.u. and 2.24 a.u. for Eu, Ru and P atoms respectively.

4. Structural optimization

We performed the structural optimization of EuRu4P12 usingGGA, the optimized lattice parameter (ao), isothermal bulk modu-lus (B), the equilibrium volume (V0) corresponding to minimumenergy (E0) and the pressure (P) are calculated by fitting the totalenergy to the Murnaghan’s equation of states [18]. The results ofthe variation of equilibrium lattice parameters and energy forEuRu4P12 is shown in Fig. 2a. All physical properties are relatedto the total energy. For example, the lattice constant that mini-mizes the total energy is the equilibrium lattice constant of a crys-tal. The detailed values of the optimized lattice parameter and bulkmodulus are given in Table 1. The optimized equilibrium latticeparameters were slightly different than the experimental latticeparameter [1] (see Table 1), in which the change in the latticeparameter is given by D(ao). Bulk modulus is a measure of

Fig. 1. Left: unit cell structure of EuRu4P12, key: Eu in grey, Ru in red and P in yellow. Rigare recognizable, key: Ru in purple, P in blue, and Eu in golden. (For interpretation of thethis article.)

resistance to volume change by an applied pressure. From Table 1,we can see that EuRu4P12 has the highest resistance to uniformcompression with highest value of bulk modulus compared toEuFe4P12 and EuOs4P12 (bulk modulus for EuFe4P12 = 115.995 GPaand EuOs4P12 = 175.268 GPa). A series of calculated total energiesas a function of volume can be fitted to an equation of statesaccording to Murnaghan’s equation as follows:

EðVÞ ¼ E0 þðV0=VÞB

00

B00 � 1þ 1

" #� B0V0

B00 � 1ð1Þ

where E0 is the minimum energy at T = 0 K, B0 is the bulk modulusat the equilibrium volume and B00 is pressure derivative of the bulkmodulus at the equilibrium volume. Here pressure is given by fol-lowing equation:

P ¼ � dEdV

; bulk modulus; B0 ¼ �VdPdV¼ V

d2E

dV2 :

The enthalpy (H) of the system has been calculated by using thefollowing equation:

H ¼ E0 þ PV0 ð2Þ

In Fig. 2b we have plotted enthalpy (H) as function of latticeconstant (ao) and compared with enthalpy of other Eu-filled skutt-erudites (namely EuFe4P12 and EuOs4P12). It is seen that EuRu4P12

has the minimum enthalpy compared to other in its equilibriumposition. The calculated negative and lower value of enthalpy indi-cates this compound have a better alloying ability. The lower valueof enthalpy may be due to the presence of Ru atom in the center ofthe P4-rings in the crystal.

5. Electronic properties and magnetic moment

The thermoelectric materials are semiconductor or semimetalwith optimal charge carrier concentration of around 1019 cm�3 asreported by Chen et al. [19]. To understand the thermoelectricapplication of the Eu-filled skutterudites we performed DOS andband structures calculation of this type of compounds. The severalauthors have reported electronic structure calculations for variousfilled-skutterudites by using various techniques [9,20,21]. The totaland partial electronic DOS for EuRu4P12 are shown in Fig. 3 for bothspin channels. These DOS plots are relatively similar to previouslyreported plots [20,21]. From the total DOS plot (Fig. 3a) we can seethat there are three distinct regions separated from each other bysmall energy gaps. The core region (below �6.0) is primarilyformed by 3s and 3p state electrons of phosphorus atom (Fig. 3d)for both spin channels. From the same figures we can see that

ht [13]: EuRu4P12 unit cell where the pnictogen P4-rings along with the filled voidsreferences to color in this figure legend, the reader is referred to the web version of

Fig. 2. (a) Volume optimization plot for EuRu4P12 and (b) enthalpy against lattice constant.

Table 1Lattice parameters, bulk modulus and equilibrium energy.

Compounds Lattice constants, ao (Å) Bulkmodulus, B(GPa)

EquilibriumEnergy (Ry)

Previous Calculated D(ao)

EuRu4P12 8.041[1]

8.026 �0.01 201.662 �66141.686

A. Shankar et al. / Journal of Alloys and Compounds 578 (2013) 559–564 561

the contribution of phosphorus atom in the valence region is neg-ligible for both spin channels. The valence region is mainly contrib-uted by 4f state electrons of Eu giving a sharp peak at around�0.4 eV with very small contribution of 4d state electrons of Ruatom for spin up channel (Fig. 3b and c). For spin down channelthe valence region is mainly contributed by Ru-4d state electrons(Fig. 3b and c). The conduction region is mainly contributed byEu-4f state electrons giving a sharp peak at 4.1 eV in the spin down

Fig. 3. Total and partial DOS for EuRu4P12 (positive D

channel (Fig. 3b). To understand the electronic properties of EuRu4-

P12 the relative calculation of the electronic band structure alongthe high symmetry direction in the Brilllouin zone are shown inFig. 4 for both spin channels. The calculated band structuresshowed trends relatively similar to the previously calculated forskutterudite by Nouneh et al. [9] and Lovvik et al. [22]. From theband structure plots we can see that the energy bands are highlypopulated just below the Fermi level for spin up channel whichis mainly contributed by the Eu-4f with Ru-d electrons as seenfrom the partial DOS plots. Similarly for spin down channel the en-ergy region of 4.0 eV is highly populated by the bands due to Eu-4felectrons. The band structures also show these filled skutteruditesposses the energy gap above the Fermi level. EuRu4P12 have indi-rect band gap of about 0.05 eV and 0.2 eV respectively for spinup and spin down channels between C and N symmetry pointsof BZ.

OS for spin up and negative DOS for spin down).

Fig. 4. Band structure plot for EuRu4P12.

Table 2Total and partial magnetic moments.

Compounds Magnetic moment (lB)Previous Calculated

Eu Ru P TotalEuFe4P12 6.30 [1] 6.56 �0.01 �0.01 5.98

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The important feature of the DOS plot is the presence of a regionwhere the DOS is very small above the Fermi level for both spinchannels. The presence of such a low density of states region is atypical characteristic of the skutterudites [9,21,23]. The densityof state is very low in this region but not zero and it is referredto as the pseudogap. In the band structure plot more or less welldefined pseudogap appears above the Fermi level. In EuRu4P12 forthe pseudogap is crossed by two bands from the conduction regionthat touches the valence region in accordance with the previouswork [24] and the interaction between the Eu and Ru atoms withthe bands of light holes crossing the pseudogap will be manifestedin a shift of and change in the energy gap compared to binaryskutterudites. In case of EuRu4P12 this band of light holes interactswith the localized f-states of the conduction band similar to homo-atomic system LaFe4X12(X = Sb,P) [22,24–26]. This interaction willalso create indirect energy band gap [24,26]. The Fermi energy le-vel is not inside the gap but within the valence band at an energycorresponding to the filling of this band by holes, as well as thecontribution from 4f state of Eu atom in the spin up channel show-ing the characteristic of skutterudites compound, which also im-plies the metallic nature of this compound. From the DOS plot(Fig. 3b and c) it is also clear that there is very negligible hybridiza-tion between the Eu-4f and Ru-3d states in the valence regionagain indicating the metallic nature of this compound. In case ofEuRu4P12 the Fermi energy level is located in the vicinity of bandsoriginating mainly from f of Eu and d of metal atom. The density ofstates on the Fermi level is relatively high in this types of com-pounds possessing superconducting behavior, which forms a largerelectronic specific heat for EuRu4P12 [27,28]. The presence of thesmall pseudo gap above EF and metallic character with larger elec-tronic specific heat of EuRu4P12 in our calculation indicates thiscompound to be effective material for the thermoelectricapplications.

The splitting of the DOS in the spin-up and spin-down channelswere found to occur for Eu-4f state, which contribute to the ferro-magnetic (FM) nature of the compound similar to previous report[10] and is supported by the individual magnetic moments calcu-lated (see Table 2). The calculated Eu magnetic moments is

(6.56 lB) in qualitative agreement with the previously reportedvalues [10]. In EuRu4P12, Ru moment (�0.01 lB) have very negligi-ble AFM coupling with Eu giving the ferromagnetic nature of thesecompounds as reported by Bauer et al. The calculated total mag-netic moments are in qualitative agreement with reported value[1] but quantitatively the Eu moments and the total magnetic mo-ments are slightly lower than the previous values [1]. The choice ofLSDA method and the exclusion of Coulomb interaction in our cal-culation can be responsible for the lower magnetic moment in ourcalculation. The LSDA method has a tendency to underestimate theintra-atomic correlation between the 4f electrons and hence over-estimate the hybridization [29] between the states of Eu-4f and Ru-d which leads to a less prominent splitting of the 4f states givingrise to lower magnetic moment for Eu atoms. Treating the d-statesof Ru and f-states of Eu as strongly localized states by means ofLSDA+U method [30] (where U is Coulomb repulsion), we can havethe magnetic moment close to previously reported value.

6. Optical properties

Since Eu-filled skutterudites have cubic symmetry, to character-ize completely the linear optical properties of this type of systemwe need to calculate only one dielectric tensor component. Thiscomponent is the imaginary part of the frequency dependentdielectric function e2(x) [20]:

e2ðxÞ ¼e2h

pm2x2

Xv;c

ZBZjMcvðkÞj2d½xcvðkÞ �x�d3k ð3Þ

A. Shankar et al. / Journal of Alloys and Compounds 578 (2013) 559–564 563

The integral is taken over the first Brillouin zone, Mcv(k) = huck|-d � r|uvki is the momentum dipole elements, where d is the poten-tial vector defining the electric field, are matrix elements for directtransitions between valence (uvk(r)) and conduction band (uck(r))states, ⁄xcv(k) = Eck � Evk is the corresponding transition energy.The real part e1(x) of the frequency dependent dielectric functioncan be obtained from the imaginary part e2(x) using the Kramers–Kronig dispersion relation:

e1ðxÞ ¼ 1þ 2p

PZ 1

0

x0e2ðx0Þx02 �x2 dx0 ð4Þ

where P implies the principal value of the integral. From the realand imaginary parts of the frequency dependent dielectric functionwe can calculate the refractive index n(x).

nðxÞ ¼ e1ðxÞ2þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie2

1ðxÞ þ e22ðxÞ

q2

24

35

1=2

ð5Þ

To calculate the optical properties the Brillouin zone integrationwas performed with a dense mesh of uniformly distributed21 � 21 � 21 k-mesh in the Brillouin zone, which corresponds to451 k points in the irreducible Brillouin zone.

Hachemaoui et al. [20] have reported the optical properties forCe-filled skuterudites using FP-APW+lo method. Mutou et al. [31]calculated the optical conductivity spectrum for Ce based skutter-udites using tight binding model. We present here the calculationof optical properties of Eu filled skutterudites using FP-LAPWmethod. Our calculated plots are similar to plots for isostructuralcompounds CeFe4As12 and CeFe4Sb12 [20]. Unfortunately, for thepresent crystal there are no theoretical or experimental results tocompare with the present calculated values. Our theoretically cal-culated absorptive (imaginary) and dispersive (real) part of theelectronic dielectric function spectrums are shown in Fig. 5a, for

Fig. 5. Calculated (a) real and imaginary parts of the dielectric functions, (b) refractive indoptical conductivity spectra EuRu4P12.

energy radiation up to 5.0 eV. The peak for real part is maximumat close to Fermi level. Thus the critical points (thresholds) areembedded at the EF. These were followed by small flat structures�2.0 eV (Fig. 5a). The peak reproduced in our calculation, are thegeneral form of the spectra. The trends in e2 may be linked to thetrends observed in the DOS and band structures. Since many directand indirect transitions take place, for the interpretation it is notrealistic to give single transition assignment to peaks present inthe optical spectrum of the corresponding energy.

The dispersive part of the dielectric function (e1) is obtainedfrom the absorptive part e2 using Kramers–Kronig conversion (Eq.4). In the zero frequency limit e1(0) is the static dielectric constant,where there is no contribution from the lattice vibration and thecalculated value of e1(0) is 9 for EuRu4P12. The refractive index(n), reflectivity and electron loss spectra are shown in Fig. 5b–drespectively. The refractive index reaches a maximum value of7.4 at 0 eV of photon energy (Fig. 5b). We have also calculatedthe frequency dependent reflectivity, shown in Fig. 5c. From thefigure it is visible that the strong maximum is present close to0 eV. Similarly the strong minimum is present near 1 eV. At zeroenergy the energy loss spectra (Fig. 5d) is minimum, since e2 ismaximum at this energy. However the real and imaginary part ofdielectric function goes on decreasing with energy and loss spec-trum increases with the increase in photon energy. Analysis ofFig. 5b–d, shows that the 0–0.75 eV photon-energy range is charac-terized by small absorption and maximum reflectivity. The 0.8–2.5 eV photon energy range is characterized by high transparencyno absorption and small reflectivity. The photon-energy from2.5 eV is characterized by appreciable reflectivity with smallabsorption. Fig. 5e summarizes the optical conductivity of EuRu4-

P12. We can see from the figure that the real (r) increases withthe increase in photon energy showing a maximum peak near4.1 eV. However, imag (r) decreases with the increase in the pho-ton energy and negative giving a valley for 2.9 eV of energy and

ex, (c) reflectivity and (d) electron loss spectra and (e) real and imaginary part of the

564 A. Shankar et al. / Journal of Alloys and Compounds 578 (2013) 559–564

then a sharp increase towards zero and crosses the real part athigher energy.

7. Conclusions

We have performed structural optimization and electronicstructure calculation for the filled skutterudites EuRu4P12, usingFP-LAPW method to evaluate theoretical lattice parameter anddensity of electron states near Fermi energy level. The smallpseudogap is present in between the valence band and the conduc-tion band. The Fermi level is not inside the pseudo gap but withinthe valence region indicating semi metallic nature of this com-pound and likely to be the candidate for thermoelectric applica-tions. The spin–orbit interaction has significant influence on theband structures causing the splitting of f-band showing the ferro-magnetic nature of this type of compounds. The calculated mag-netic moments are lower than the previously reported values,which is mainly contributed by Eu-4f states. The study of opticalspectra suggested the system exhibits small absorption and appre-ciable reflectivity just above EF which is followed by high transpar-ency and small reflectivity in the conduction region.

Acknowledgement

AS acknowledges fellowship, Sandeep a DST FASTRACK projectand RKT a research grant from UGC (New Delhi, India).

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