Electronic structure calculations of europium chalcogenides EuS and EuSe

phys. stat. sol. (b) 244, No. 6, 1988–1996 (2007) / DOI 10.1002/pssb.200642450

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Electronic structure calculations

of europium chalcogenides EuS and EuSe

D. Rached*, 1, M. Ameri1, M. Rabah1, R. Khenata1, 2, A. Bouhemadou3, N. Benkhettou1,

and M. Dine el Hannani1

1 Laboratoire des Matériaux Appliqués, Centre de Recherche (Ex: CFTE), Route de Mascara,

Université de Sidi-Bel-Abbès, Sidi Bel Abbès 22000, Algeria 2 Laboratoire de Physique Quantique et de Modélisation Mathématique de la Matière (LPQ3M),

Centre Universitaire de Mascara, Mascara 29000, Algeria 3 Département de Physique, Faculté des Sciences, Université Ferhat Abbès, 19000 Sétif, Algeria

Received 28 August 2006, revised 13 November 2006, accepted 20 November 2006 Published online 22 January 2007

PACS 61.50.Ks, 62.20.Dc, 71.15.Ap, 71.20.Nr

We have performed ab-initio self-consistent calculations on the full-potential linear muffin-tin orbital method with the local-density approximation and local spin-density approximation to investigate the structural and electronic properties of EuS and EuSe in its stable (NaCl-B1) and high-pressure phases. The magnetic phase stability was determined from the total energy calculations for both the nonmagnetic (NM) and magnetic (M) phases. These theoretical calculations clearly indicate that both at ambient and high pressures, the magnetic phase is more stable than the nonmagnetic phase. The transition pressure at which these compounds undergo the structural phase transition from NaCl-B1 to CsCl-B2 phase is calcu-lated. The elastic constants at equilibrium in both NaCl-B1 and CsCl-B2 structures are also determined.

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Rare-earth compounds attract considerable experimental and theoretical attention due to their interesting optical, magnetic and electronic properties [1–4]. These technologically important materials are semi-conducting if the rare-earth (Eu) ion is in the divalent state and metallic if trivalent [1–3]. Europium chalcogenides EuX (X = O, S, Se, Te) and most of the pnictides crystallize in the simple NaCl (rocksalt) structure with a decreasing lattice parameter as X varies from Te to O [4, 5]. Also, much of the interest was shown in these materials in increasing the magnetic ordering temperature with room temperature, as the final goal to make the practical applications of Eu chalcogenides realistic [6]. Among the europium chalcogenides compounds very little information is available for EuS and EuSe. From a theoretical point of view there exist a few reported studies on EuS and EuSe compounds. Horne et al. [7] used the ab-initio self-interaction corrected (SIC) method [8] to discuss the electronic structure of the Eu chalcogenides and pnictides in both the divalent and trivalent states. Kunes and Pickett [9] used the full-potential linearized augmented planes waves (FP-LAPW) method [10] to study the effective exchange parameters and the corresponding ordering temperatures of the (ferro)magnetic insulating Eu chalco-genides under ambient and elevated pressure conditions. Finally, the band-structure calculation and calculations of the structural stability of the high-pressure phases have been investigated by Singh et al. [11, 12] using the tight-binding linear muffin-tin orbital method within the atomic sphere approximation (ASA) [13, 14]. Different parameterizations or approaches have been used to determine the exchange-

* Corresponding author: e-mail: [email protected]

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correlation contribution [8, 15, 16] within the ab-initio technique. From the above it is clear that there is considerable theoretical work on EuS and EuSe compounds, but there are very few reported studies of the structural stability of high-pressure phases. Moreover, to the best of our knowledge, the elastic con-stants have been not yet calculated or measured in the NaCl and CsCl structures. We therefore think it worthwhile to perform these calculations. The aim of this paper is to provide a comparative study of structural, magnetic and elastic properties under high pressure using the full-potential linear muffin-tin orbital (FP-LMTO) method. Various quantities including lattice parameters, bulk modulus, magnetic moments and electronic structure, were obtained for these compounds. The organization of this paper is as follows: we describe the FP-LMTO computational details in Sec-tion 2, and in Section 3 the results and discussion for structural, phase transition, magnetic and electronic properties are presented. Finally, a conclusion is given in Section 4.

2 Computational methods

To study the structural and electronic properties of EuS and EuSe compounds we employ the first-principles full-potential linear muffin-tin orbital (FP-LMTO) within the (LDA) scheme [17–19]. This is an improved method compared to previous (LMTO) methods. The present one uses a more complete basis than its predecessors. Moreover, in the present method the space is partitioned into the nonoverlapp-ing muffin-tin spheres SR surrounding every atom and the remaining interstitial region Ωint. Within the spheres, the basis functions are represented in terms of numerical solutions of the radial Schrödinger equation for the spherical part of the potential multiplied by spherical harmonics. In the interstitial re-gion, they include Fourier transforms of LMTOs. The details of calculations are as follows: the charge density and the potential are represented inside the muffin-tin spheres (MTS) by spherical harmonics up to lmax = 6. The k integration over the Brillouin zone is performed using the tetrahedron method [20]. The values of the sphere radii (MTS) and the num-ber of plane waves (NPLW) used in our calculation are listed in Table 1. From these data, we have found that the MTS of the EuS in NaCl-B1 structure increases as the chalcogen atom increases, but we find the opposite situation for the CsCl-B2 structure.

3 Results and discussions

3.1 Ground-state and high-pressure properties

We first the calculated the NM (nonmagnetic) to M (magnetic) or M to NM transition, both spin and nonspin polarized, and the structural properties of the binary compounds EuS and EuSe in NaCl-B1

Table 1 Parameters used in the calculations. Total NPLW is the number of plane waves used, total Ecut

is the cut-off energy in Rydbergs and the muffin-tin sphere radii MTS in (a.u).

NPLW (total)

Ecut (Ry) (total)

MTS (a.u.)

EuS(B1) 2974 71.01 2.794a 2.478b

EuS(B2) 3266 86.81 2.912a 2.48b

EuSe(B1) 3942 79.26 2.86a 2.64b

EuSe(B2) 3558 87.34 2.873a 2.652b

a Eu atom parameters at different position of the structure. b Chalcogen atom parameters at different position of the structure.

1990 D. Rached et al.: Electronic structure calculations of EuS and EuSe

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Fig. 1 Calculated total energy as a function of volume in the NaCl-B1 for both nonmagnetic and mag-netic states of EuS and EuSe.

structure were investigated. The total energy of the primitive unit cell was calculated as a function of its volume, and then the results were fitted to the Birch equation of state [21]. The variation of total energy with cell volume for both the NM and M states of NaCl-B1 structure is displayed in Fig. 1. In view of this figure, it is clear that there is no M to NM transition and the magnetic state is stable at ambient con-dition, which is consistent with other theoretical works. From this result, we calculated the ground-state properties of EuS and EuSe in the magnetic states, the total energies are calculated in NaCl-B1 and CsCl-B2 structures for different volumes around the equilib-rium cell volume V0. The plots of calculated total energies versus reduced volume for these compounds in these structures are given in Fig. 2. The calculated total energies are fitted to the Birch equation of state [21] to determine the ground-state properties such as the equilibrium lattice constant a0, the bulk modulus B0 and its pressure derivative B0′. The calculated structural parameters of EuS and EuSe in both NaCl and CsCl structures are summarized in Table 1, together with the available experimental data and results of other calculations.

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Fig. 2 Calculated total energies as a function of volume in the NaCl-B1 and CsCl-B2 structures for EuS and EuSe.

It is clear from the E(V) curves (Fig. 2) that the NaCl-B1 structure is the most stable under ambient conditions, which is consistent with the experimental results and other theoretical works. In the present work, the optimized equilibrium volume V0 is taken to be 293.1395 (a.u.)3 and 332.896 (a.u.)3 for EuS and EuSe, respectively. The europium chalcogenides (EuS and EuSe) are observed to exhibit a pressure-induced structural transformation from low-pressure NaCl-B1 phase to high-pressure CsCl-B2 phase. The structural phase stability is determined by calculating the Gibbs free energy for both phases (G = Etot + PV – TS). Since the theoretical calculations are performed at 0 K, the Gibbs free energy be-comes equal to the enthalpy (H = Etot + PV) [22]. At a given pressure, a stable structure is one for which enthalpy has it lowest value and the transition pressure (Pt) is calculated at which the enthalpies for the two phases are equal. For EuS, the NaCl-B1 phase transforms to CsCl-B2 phase at 27.034 GPa, which is slightly higher than the 22 GPa suggested by the experimental trends [6]. For EuSe, the calculated value of Pt is 23.88 GPa, this value is higher than the experimental and theoretical values. These pressures transition are accompanied by a volume reduction of the B1 phase equal to 0.80 and 0.88 for EuS and



Table 2 Calculated lattice constant (in Å), bulk modulus (in GPa), pressure derivative (B0′) and transition

pressure of EuS and EuSe for B1 and B2 phases, and compared to experiment and other works.

EuS EuSe

present expt. TB-LMTOc SIC-LSDd present expt. TB-LMTOf

NaCl-B1 aeq (Å) B0 (Mbar) B0′

5.58 77.36 3.796

5.97a

5.71 68.48

53.6

5.82 66.33 3.96

52e

5.91 52.95

CsCl-B2 aeq (Å) B0 (Mbar) B0′

3.38 71.19 4.55

61 ± 5a

101.19

3.54 59.71 4.51

5.55 101.73

Pt (GPa) Vt(B1)/V0 Vt(B2)/V0 ∆V%

27.03 0.80 0.71 11.22

22b 21.1 11.6 23.88 0.88 0.71 10.57

15b 14.5 12.8

a Ref. [30]; b Ref. [6]; c Ref. [12]; d Ref. [31]; e Ref. [13]; f Ref. [11].

EuSe, respectively. It is interesting to note that the calculated transition pressure decreases with increase in the size of the cation atoms. A similar trend is noted in other rare-earth monochalcogenides and pnic-tides [23–26].

3.2 Elastic properties

It is well known that the elastic properties define the properties of material that undergoes stress, deforms, and then recovers and returns to its original shape after the stress ceases. Hence, to study the stability of these compounds in the NaCl-B1 and CsCl-B2 structures, we have calculated the elastic con-stants at the equilibrium lattice and compared our results to the stability criteria [27, 28] using the fol-

Table 3 Calculated elastic constants of EuS and EuSe in both NaCl-B1 and CsCl-B2 structures.

C11 (GPa) C12 (GPa) C44 (GPa) G (GPa) E (GPa)

EuS NaCl-B1 present others CsCl-B2 present others

211.06 201.85

10.47 15.85

174.25 207.07

144.66 163.44

267.34 277.75

EuSe NaCl-B1 present others CsCl-B2 present others

185.19 116.00a 127.71

6.90 25.99a 25.99

183.72 22.8a 187.74

145.89 132.98

252.00 228.97

a Ref. [29].

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Fig. 3 (online colour at: www.pss-b.com) Band structure along the symmetry lines of the Brillouin zone at the equilibrium lattice constant for NaCl-B1 structure of EuS and EuSe. The position of the Fermi Level is shown by the solid horizontal line.

lowing relations:

C11 – C12 > 0, C44 > 0, B0 > 0 .

We have found that in this structure these criteria are satisfied. The results of elastic constants are presented in Table 3. Since there are no available theoretical and experimental results for EuS, we com-pare our results for EuSe in NaCl-B1 with those of Wyckoff [29]. We note that these results are smaller to ours, and we note an increase of the nearest-neighbor distance from EuSe to EuS, a reverse situation was found for C44 results. We can also note that the hardness is inversely proportional to the atomic number of the chalcogen. On the other hand, the shear and the Young’s moduli are related to the micro-scopic elastic constants by means of the following equations: E = 9BG/(3B + G) and G = (C11 – C12 + 3C44)/5. It is important to note that the measurements of G and E are taken from polycrystalline sam-ples including defects and porosity. In our case, however, all calculations are related to a perfect crystal. From Table 3, we also note an increase of the Young’s moduli corresponding to a decrease of the near-est-neighbor distance from EuSe to EuS.

3.3 Electronic structures and magnetic properties

The calculated spin-polarized band structures of EuS and EuSe in NaCl-B1 phase at equilibrium lattice constants along the higher-symmetry directions in the BZ are shown in Fig. 3. The overall band profiles are quite similar for both compounds, with a small difference in detail. We distinguish three regions in the valence band: the states in the energy region from –19.20 eV to –17.49 eV for EuS (–20.16 eV to –17.63 eV for EuSe) come mainly from Eu-p states with minor contributions from chalcogen-s states. The second region is situated between –13.59 eV and –12.04 eV for EuS (–13.84 eV to –12.40 eV for EuSe) and is due essentially to the chalcogen valence s states. The third one, which ranges between –5.8 eV to –2.63 eV for EuS (–5.57 eV to –1.92 eV for EuSe) corresponds to chalcogen valence p states with minor contributions from chalcogen s and Eu-s. Finally the region including the Fermi energy arises predominantly from the Eu-f state with minor contributions from the Eu-d state. To further elucidate the nature of the electronic band structure, we have also calculated the total and the partial densities of states (DOS) of these compounds. These are displayed in Figs. 4 and 5. From the partial DOS we are able to identify the angular-momentum character of the different structures. Follow-



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Fig. 4 (online colour at: www.pss-b.com) Total and partial spin-polarized DOS of EuS in NaCl-B1: (a) The state contributions of the chalcogen (S) and (b) the state contributions of the europium (Eu). ing Figs. 4 and 5 we should emphasize that there are different distinct structures in the density of elec-tronic states separated from each other by gaps, confirming the discussion of the band structures (above) and show clearly the contribution of the states with spins up and down. From the density of states (DOS) of EuS spin up, we observe three regions; the first is situated between –13.43 eV and –11.79 eV. This structure arises entirely from chalcogen 3s states. The next structure localised between –5.64 eV and –2.36 eV below the zero of energy is dominated by the chalcogen 3p states. The structure above –1.13 eV up to the Fermi level is dominated by Eu (4f) states and beyond the Fermi energy it is domi-nated by Eu (5d) states. In the case of spin down, the region situated between –18.76 eV and –17.53 eV is mainly due to the europium 5p states and those beyond the Fermi energy are essentially dominated by the Eu (4f) states with a small contribution of Eu (4p) states. We note also the same contributions of the states for EuSe. The region situated between –13.67eV and –12.50 is dominated by Se (4s) and the second, ranging from –5.48 eV to –1.87 eV, is mainly due to the Se (4p) states.

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Fig. 5 (online colour at: www.pss-b.com) Total and partial spin polarized DOS of EuSe in NaCl-B1: (a) The state contributions of the chalcogen (Se) and (b) the states contributions of the europium (Eu).

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Table 4 Total and local magnetic moments as function of V/V0 for both compounds in NaCl-B1 struc-

ture.

V/V0 mEu mchalcogen (× 10–2) minterstitial (× 10–1) MEu (µB/cell)

EuS NaCl-B1

EuSe NaCl-B1

1.00 0.94 0.90 0.86 0.78 0.70 0.66 1.00 0.94 0.90 0.86 0.78 0.70 0.66

6.78 6.71 6.66 6.61 6.48 6.31 6.22 6.83 6.77 6.73 6.68 6.57 6.42 6.33

–3.93 –4.08 –4.20 –4.39 –4.79 –5.08 –5.16 –4.39 –4.47 –4.53 –4.62 –4.85 –5.00 –5.00

2.23 2.56 2.78 3.01 3.57 4.19 4.56 2.00 2.35 2.59 2.83 3.38 4.01 4.38

6.96 6.93 6.90 6.86 6.79 6.68 6.62 6.98 6.96 6.94 6.92 6.86 6.77 6.72

Spin-polarized self-consistent band-structure calculations have been very successful in calculating and predicting the magnetic moments using the (LSDA) approximation. The magnetic moments for EuS and EuSe are listed in Table 4. We note the very close values for both compounds in the NaCl-B1 structure (as for CsCl-B2), the magnetic moment of Eu is much higher, while the contribution of the chalcogen (S and Se) magnetic moment is negligible in comparison to that of Eu. From Table 4 it is clear that the magnetic moments decrease with the increase in pressure, except for the magnetic moment in the intersti-tial region, where the values are proportional to the pressure value.

4 Conclusion

We have performed first-principles FP-LMTO calculations of the structural, electronic and magnetic properties of europium chalcogenides (EuS and EuSe). The use of LDA and LSDA for the exchange-correlation potential permitted us to obtain good structural parameters. Under normal conditions EuS and EuSe are stable in the B1 structure. The calculated pressures at which these compounds undergo a struc-tural phase transition from B1 to B2 are found to equal 27.034 GPa and 23.88 GPa for EuS and EuSe, respectively. We are not aware of any experimental or theoretical data for the elastic properties of these compounds in both B1 and B2 phases and so our calculations can be used to cover this lack of data for these compounds.

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Documents

Electronic structure calculations of europium chalcogenides EuS and EuSe