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Density functional studies of magneto-optic properties of Sr2GdReO6
expand article infoSaadi Berri, Sabah Chami§, Mourad Attallah|, Mouloud Oumertem, Djamel Maouche
‡ Laboratory for Developing New Materials and their Characterizations, University of Setif, Setif, Algeria
§ Laboratory of Electro-Mechanic Systems (LASEM), National School of Engineers of Sfax (ENIS) Univrsity of Sfax, Sfax, Tunisia
| Department of Physics, Faculty of Sciences, University of Biskra, Biskra, Algeria
¶ Department of Physics, Faculty of Sciences, University of M’sila, M’sila, Algeria
Open Access

Abstract

The electronic structure and magneto-optic properties of the Sr2GdReO6 double perovskite were investigated using the full-potential linearized augmented plane wave (FPLAPW) method. Exchange correlation effects are treated using the generalized gradient approximations GGA, GGA + U and GGA + U + SOC approachs. At ambient conditions, these calculation predict a half-metallic character for Sr2GdReO6 material. The electronic band structures and density of states demonstrate that Sr2GdReO6 is HM with a magnetic moment of 9 µB/fu and HM flip gap of 1.82 eV. The half metallicity is attributed by the double-exchange interaction mechanism via the Gd(4f)–O(2p)–Re(t2g) π-bounding. These new double perovskite may become ideal candidate material for future spintronic applications. The analysis charge densities show that bonding character as a mixture of covalent and ionic nature. The optical properties are analyzed and the origin of some peaks in the spectra is described. Besides, the dielectric function ε(ω), refractive index n (ω) and extinction coefficient K (ω) for radiation up to 14 eV have also been reported.

Keywords

Double perovskite, Half-metallic, Magnetic properties, Optical properties, Electronic structure

1. Introduction

Many works have been focused on the double-perovskite structure with different compositions and structures because of to their possible applications in numerous industrial and engineering domains [1–5]. These compounds have many interesting properties such as tunnelling magnetoresistance [6], colossal magnetoresistance [7], ferromagnetism [8, 9], magneto-optic properties [10], metallicity [11], multiferroicity [12] and magnetodielectric properties [13]. The observation of high magneto-resistance in half-metallic for Sr-based double perovskite with fairly high transition temperature [14] of 410 K indicates the promise in double perovskite materials as candidates for high temperature half metallic magnets [15].

Many double-perovskite compounds are found to possess the half-metallic band structure as revealed by the ab-initio calculations [16–22]. Samanta et al. [23] calculated the electronic structures and magnetic properties of Sr2CrOsO6 using full-potential linearized augmented plane wave (FPLAPW) scheme within the (GGA) + U. Jeng and Guo [24] calculated magnetic and electronic structure of Sr2FeMoO6, Sr2FeReO6, and Sr2CrWO6 using full-potential linear muffin-tin orbital method within the GGA + U and LSDA + U methods. The electronic structure calculations predicted a HMF band structure with spin magnetic moment of 4μB, 3μB, and 2μB per formula unit for Sr2FeMoO6, Sr2FeReO6, and Sr2CrWO6, respectively. Faizan et al. [25]. also predicted that Sr2XOsO6 (X = Li, Na, Ca) were HM ferromagnets. The electronic structure calculations predicted a HMF band structure for Sr2XOsO6 (X = Li, Na, Ca), with energies band gap of 1.90, 1.83 and 2.24 eV for Sr2LiOsO6, Na and Ca respectively. The structural and electronic properties have been investigated at zero and elevated pressure for the double perovskite Sr2GdReO6 using the density functional theory (GGA) + U approach [26].

In the present paper, the magnetic, electronic and optical properties of Sr2GdReO6 are reported. As far as the electronic structure and optical properties of materials are concerned, these features play a crucial role in determining their magneto-optic properties for devices. Therefore, accurate knowledge of these properties is very important for the application. The aim of this work is to examine the electronic band structure of Sr2GdReO6, with emphasis on its derived properties. The calculations are performed using ab initio a full relativistic version of the full-potential augmented plane-wave scheme within GGA and GGA + U approachs. The rest of the paper is organized as follows: The theoretical background is presented in Section 2. Results and discussions are presented in Section 3. A summary of the results is given in Section 4.

2. Method of calculations

For the present computational study, we have considered the experimental crystal parameters [27] as reported by Baud and Capestan. Sr2GdReO6 crystallizes in the (Fm3m cubic space group), with Z = 4 formula unit per unit cell having a lattice parameters of 8.279 Å. The Wyckoff positions of atoms with an occupancy of 1 are as follows: Sr 8c (0.25, 0.25, 0.25), Gd 4b (0.5, 0.5, 0.5), Re 4a (0, 0, 0) and O 24e (0.25, 0, 0). The crystal structures of these compounds are shown in Fig. 1. We have used the full-potential linearized augmented plane wave (FP-LAPW) and local orbitals method through a density functional theory approach [28, 29]. Here, the Kohn–Sham equations are solved by expanding the wave functions in the spherical harmonics form inside the atom spheres. Plane wave expansion is used in the interstitial regions of atoms inside the unit cell. We have used lmax = 10 for angular momentum expansion and RMTKmax = 8 as a plane wave cut-off with 2000 k points to achieve self-consistency. Here RMT is the average muffin-tin (MT) radius and Kmax is the wave function cut-off. The radii RMT of the muffin tins (MT) are chosen to be approximately proportional to the corresponding ionic radii. The energy between successive iterations is converged to 0.0001 Ry and forces are minimized to 1 mRy Bohr-1. The Monkhorst–Pack (MP) technique is used for Brillouin zone integrations. Exchange-correlation effects are treated using generalized gradient approximation (GGA) as parameterized by Perdew et al. [30] and GGA + U by Anisimov et al. [31] with an approximate correction for the self-interaction correction. This is probably best suited for our system and for a full potential method we use an effective Ueff = U + J, setting J = 0.5 and U = 7.4 eV, for Gd atoms and J = 0.3, U = 3 eV for Re atoms quoted from Refs. [32] and [33], respectively. To treat the interactions of heavier elements like Gd and Re one needs to consider SOC during the calculations. A dense k-mesh with 5000 k-points was used in the first Brillouin zone to calculate the linear optical properties.

Figure 1.

The crystal structures of Sr2GdReO6 compound.

Optical properties of a solid are usually described in terms of the complex dielectric function ε(w) = ε1(w) + iε2(w). The imaginary part ε2(w) was calculated from the momentum matrix elements between the occupied and unoccupied wave functions within the selection rules. The real part ε1(w) of the dielectric function was calculated by the Kramers–Kronig transformation [34] of the imaginary part ε2(w). Other optical constants were computed from the values of ε(w). The frequency dependent complex dielectric tensor ε2(w) components are calculated by using the following mathematical expressions [35]:

(1)

(2)

where is the polarization vector of light. is the optical transition matrix from valence to conduction states and P is the principal value of the integral and the integral is over irreducible Brillouin zone. The optical constants such as refractive index n (w) and the extinction coefficient k (w), are calculated interms of the real and the imaginary parts of the complex dielectric function as follows [36]:

(3)

(4)

3. Results and discussion

As presented in Fig. 2, the electronic properties of the Sr2GdReO6 compound are assessed the band structures, total and partial densities of states of Gd f, Re eg and t2g, Sr eg and t2g and O pz and d electrons in FM phase. Note that the density of states was presented only for GGA + U method because it is similar to that of GGA and GGA + U + SOC method with a small difference. It is clear that the majority-spin band is metallic, while the minority spin band shows a semiconducting gap around the Fermi level. The energy band gap (Eg↓ = 2.02 eV) in spin down channel is formed by the nonbonding states Re 4d of the conduction band and the bonding states O p of valence band. The present study show that the energy gap for spin-down electrons for Sr2GdReO6 compound is 2.02 eV, and close to the energy gap values for the La2CrZnO6 compound [37]. This energy gap in the minority-spin band gap leads to 100% spin polarization at the Fermi level, resulting in the half-metallic behavior at equilibrium state.

We have calculated the band structure along symmetry directions in the first Brillouin zone with/without SOC and this is shown in Fig. 3. Note that, there is an overall topological resemblance for Sr2GdReO6 compound for both methods.

Figure 2.

Spin-polarized a) band structure, partial and b) total densities of states (TDOS) of Sr2GdReO6 compound.

Figure 3.

The calculated band structure for GGA, GGA + U and GGA + U + SOC of Sr2GdReO6 compound.

The half-metallic gap [38, 39], which is determined as the minimum between the lowest energy of majority (minority) spin conduction bands with respect to the Fermi level and the absolute values of the highest energy of the majority (minority) spin valence bands, is 1.82 eV, for both method.

The hybridisation bonding states pz and d electrons of O element (See Fig. 2a), which contribute to the TDOS in the energy region from –8.0 to –2.0 eV for both spin channels, are mainly formed by Gd-4f and t2g states of Re atoms creates fully occupied bands with a positive spin-splitting (the exchange-splitting between the spin-up and spin-down sub-bands of the Gd 4f states is approximately 4.75 eV, which is the main contributor in the magnetic moment of these compound).

For unoccupied states of both spin channels above the Fermi level, the nonbonding hybridisation state in spin- down channel of TDOS is 4F-Gd and eg electron of Re atoms situated in the range from 0.5 to 4.0 eV, and the eg and t2g states of Sr atoms contribute to the majority and minority spin states mix with eg electron of Re atom in the region from 4.0 to 8.0 eV.

The calculated total and atom-resolved magnetic moments, using GGA, GGA + U and GGA + U + SOC for Sr2GdReO6 compound, are summarized in Table 1. The present study shows that the total magnetic moment for Sr2GdReO6 compound is ≈ 9 µB/fu for both approximations. Here, the main contribution to the total magnetic moment is due to Gadolinium and Rhenium atom, and the magnetic moment on the Strontium and Oxygen atoms are small. Our results for magnetic moment for Gadolinium atoms which is in agreement with previous studies [40, 41]. The magnetic moments of the Rhenium atoms are in agreement with theoretical data [42].

The calculated total and partial magnetic moment (in μB) for Sr2GdReO6 compound.

m Gd m Re m Sr m O m interstitial m Total
GGA 6.72563 1.31451 0.0088 0.04382 0.67677 9.00
GGA + U 6.75414 1.34922 0.0072 0.03992 0.64067 9.00
GGA + U + SOC 6.77910 1.33155 0.0070 0.04507 0.62448 9.00

Normally, exchange interactions are very short-ranged, confined to electrons in orbitals on the same atom or nearest neighbor atoms but longer-ranged interactions can occur via intermediary atoms and this is termed superexchange. The double-exchange mechanism is a type of a magnetic exchange that may arise between ions in different oxidation states. First proposed by Clarence Zener [43] and later developed by Anderson an d Hasegawa [44], by Kubo and Ohata [45] and by Furukawa [46], is generally agreed to provide a description of the FM ground state this theory predicts the relative ease with which an electron may be exchanged between two species. Electronic structures from a full-potential linearized augmented plane wave method also demonstrated that the half-metallic character is not caused by direct Gd-Gd or Re-Re interactions but by indirect O–Gd–O–Re pf and π–d couplings, which are simulate ane ously responsible for their ferrimagnetic character [46].

In order to understand the nature of chemical bonding, we display, in Fig. 4 the contours of charge densities in (110) plane for Sr2GdReO6 compound. From Fig. 4, we can see that the near spherical charge distribution around the Sr atoms site is negligible and as a result the Sr atoms are fairly isolated, indicating that the bonding Sb-O has expected to be some ionic character. On an other hand, the O atoms hybridization with Gd and Re atoms for spin-up and spin-down (See Fig. 2a), happen with an interaction between the Gd and Re with O atom, indicating that a covalent interaction occurs between Gd and Re with O atoms. The bonding character may be described as a mixture of covalent and ionic character. To our knowledge, there are no experimental or theoretical data reported for the electronic structure for the material of interest, and hence our results are predictions.

Figure 4.

Charge density distribution in the plane (110) of Sr2GdReO6 compound.

Magneto-optical effects comprise various changes in the polarization state if light upon interaction with materials possessing a net magnetic moment, including rotation of the plane of linearly polarized light (Faraday, Kerr rotation), and the complementary differential absorption of left and right circularly polarized light (circular dichroism) [47].

Mainly, the first Microscopic dielectric function describes the behaviour of linear response of a material to the electromagnetic radiation field applied which displays the absorptive character of that material. The real part of the dielectric function describes how much material polarized as a result of induced electric dipole creation when an electric field is applied while the imaginary part indicates how much material absorption photon energy. There are two contributions to ε2(ω), namely, intraband and interband transitions. The contribution from intraband transitions is important only for metals. The interband transitions can further be split in to direct and indirect transitions. We neglect the indirect interband transitions, which involve scattering of phonons and are expected to give only a small contribution to ε2(ω).

In Fig. 5a we present the dielectric function of Sr2GdReO6 as calculated by FP-LAPW method. For energies up to 14 eV, based on our calculated band structure it would be worthwhile to identify the interband transitions that are responsible for the structure in ε2(ω). Our analysis of the ε2(ω) spectra shows that the threshold energy (first critical point) of the dielectric function occurs at about 2.39, 2.62 and 3.83 eV, respectively. These points are mainly coming from the electron transition from the Gd 4f (VB), O-d (VB) and O-pz (VB) to Re t2g (CB) orbitals. We note that in Sr2GdReO6 compound, ε2(ω) shows peaks located at 6.64 eV and 7.51 eV, respectively. This point is mainly derived from the transition from Gd 4f (VB) and O-d (VB) to Sr t2g (CB) orbitals. The behaviour of ε1(ω) (See Fig. 5b) seems to be rather similar to that of ε2(ω). Below the reststrahlen region in the optical spectra, the real part of the dielectric function asymptotically approaches the static or low-frequency dielectric constant ε0, in the present contribution, the calculated static dielectric constant ε0 for spin-down is 2.93 for Sr2GdReO6 compound.

Figure 5.

The calculated a) real parts of dielectric function, b) imaginary parts of dielectric function, c) refractive index and d) extinction coefficient.

The refractive index is a quantity that describes how much light is refracted after entering material [48, 49]. The calculated refractive index n (ω) and the extinction coefficient k (ω) using GGA approach are displayed in Fig. 5 (c and d). From the refractive index plot, we remark that the material possesses high refractive index within Infrared region and decreases at higher energy in the Ultraviolet lointain. Note that in this compound the extinction coefficient has resonance in the low energy region. Our results of k (ω) show that Sr2GdReO6 has strong extinction effects at Infrared region and then decreases with photon energy forming the maximum peak at 0.8 eV. In the absence of both experimental and theoretical data of the dielectric function, refractive index and extinction coefficients for the material of interest, to the best of our knowledge, no comment can be ascribed to used method and hence our results may serve only for a reference.

4. Conclusion

For the Sr2GdReO6 compound, The electronic structure and magneto-optic properties the electronic structure and magnetic has been studied by using first-principle FPLAPW calculation method..At ambient conditions, these calculation predict a half-metallic character for Sr2GdReO6 material. The electronic band structures and density of states demonstrate that Sr2GdReO6 is HM with a magnetic moment of 9 µB/fu and HM flip gap of 1.82 eV. The half metallicity is attributed by the double-exchange interaction mechanism via the Gd(4f)–O(2p)–Re(t2g) π-bounding. The analysis of charge densities contours leads us to conclude that the bonding character in Sr2GdReO6 compound is a mixture between covalent and ionic nature. To complete the fundamental characteristics of this compound we have analyzed their optical properties such as the dynamic dielectric function, refractive index, extinction coefficient for a wide range of 0–14 eV.

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