First-principles study on half-metallic properties of the Sr2GdReO6 double perovskite

Journal of Magnetism and Magnetic Materials 385 (2015) 124–128

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First-principles study on half-metallic properties of the Sr2GdReO6 double perovskite Saadi Berri Laboratory for Developing New Materials and their Characterizations, University of Setif, Algeria

art ic l e i nf o

a b s t r a c t

Article history: Received 13 September 2014 Received in revised form 4 March 2015 Accepted 6 March 2015 Available online 7 March 2015

A first-principles approach is used to study the structural, electronic and magnetic properties of Sr2GdReO6, using full-potential linearized augmented plane wave (FP-LAPW) method within the spin density functional theory. At the equilibrium lattice constant, our calculations predict that Sr2GdReO6 is half-metallic (HM) with a magnetic moment of 9 mB/fu and HM flip gap of 1.82 eV. In addition, the ferromagnetic phase is found to be energetically more favorable than paramagnetic phase. Therefore, the Sr2GdReO6 compound is a promising material for future spintronic application. & 2015 Elsevier B.V. All rights reserved.

Keywords: Sr2GdReO6 Half-metallic Magnetic properties Electronic structure

1. Introduction Double perovskite oxides of general formula A2BB’O6 attracted a great deal of attention followed by the discovery of exotic properties such as tunnelling magnetoresistance (TMR) [1], colossal magnetoresistance [2], ferromagnetism [3,4], magneto-optic properties [5], metallicity [6], multiferroicity [7] and magnetodielectric properties [8]. Half-metallic ferromagnets represent a new class of materials which absorbed a lot of attention considering their possible applications in spintronics [9]. These materials behave like metals with respect to the electrons of one spin direction and like semiconductors with respect to the electrons of the other spin direction. Recently, half-metallic ferromagnetism has been found in CrO2 [10], NiMnSb [11], Fe3O4 [12], La0.67Sr0.33MnO3 [13], Co2MnSi [14], Pb2FeMoO6 [15], Sr2FeWO6 [16], Sr2CoMoO6 [17], Sr2CrWO6 [18], Sr2FeReO6 [19, 20], Sr2MnMoO6 [20], Sr2CuOsO6 [21], Sr2VOsO6 [22], Sr2NiRuO6 [23], Sr2FeTiO6 [24], Sr2CrMoO6 [25], RbX (X ¼Sb, Te) [26], Al1  xMnxP [27], and nearly 100% high spin-polarization has been observed experimentally in the cases of CrO2 and La0.67Sr0.33MnO3 materials [28]. Sr2GdReO6 is cubic at room temperature with space group Fm3¯ m [29]. The cubic unit cell contains one molecule with the Wychoff positions of the atoms are 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. In the present E-mail address: [email protected] http://dx.doi.org/10.1016/j.jmmm.2015.03.025 0304-8853/& 2015 Elsevier B.V. All rights reserved.

paper, the structural, electronic and magnetic properties of Sr2GdReO6 compound are reported. Our main goal in this work is to evaluate examine the validity of the predictions of half metallicity for Sr2GdReO6 compound, The calculations are performed using ab initio full-potential linearized augmented plane wave (FP-LAPW) scheme within GGA and GGA þU approaches. Our paper is organized as follows. The theoretical background is presented in Section 2. Results and discussion are presented in Section 3. A summary of the results is given in Section 4.

2. Method of calculations The calculations are carried out first-principles calculations [30, 31] with both full potential and linear augmented plane wave (FPLAPW) method [32] as implemented in the WIEN2k code [33] within the density functional theory (DFT). The Perdew–Burke– Ernzerhof generalized gradient approximation GGA [34, 35]. In the calculations reported here, we use a parameter RMTKmax ¼8, which determines matrix size (convergence), where Kmax is the plane wave cut-off and RMT is the smallest of all atomic sphere radii. We have chosen the muffin-tin radii (MT) for Re, Gd, Sr and O to be 2.2, 2.1, 2.0 and 1.8 a.u. respectively. Within the spheres, the charge density and potential are expanded in terms of crystal harmonics up to angular momenta L ¼10, and a plane wave expansion has been used in the interstitial region. The value of Gmax ¼14, where Gmax is defined as the magnitude of largest vector in charge density Fourier expansion. The Monkorst-Pack special k-points

S. Berri / Journal of Magnetism and Magnetic Materials 385 (2015) 124–128

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Table 1 Lattice constant a (Å), bulk modulus B (GPa), pressure derivative of bulk modulus B′, ΔE(eV) ¼ E(FM)-E(PM), total and partial magnetic moment (in μB) for Sr2GdReO6 compound. a

B

B′

ΔE

FM PM FM PM – mGd

8.369 8.294 8.376 8.291 8.279 mRe

142.73 146.43 144.69 146.34 – mSr

4.36 4.42 4.14 4.85 – mO

 6.99 – –  6.83 – minterstitial

– – – – – mTotal

6.72563 6.75414

1.31451 1.34922

0.04382 0.03992

0.67677 0.64067

9.00 9.00

Compound GGA GGA þ U EXP[29]

GGA GGA þ U

0.0088 0.0072

3. Results and discussion

Fig. 1. Crystal structure of Sr2GdReO6 compound.

were performed using 1000 special k-points in the Brillouin zone. The cut off energy, which defines the separation of valence and core states, was chosen as  6 Ry. We select the charge convergence as 0.0001e during self-consistency cycles. The 4f orbital for the Gd atom were treated using the GGA þU approach [36]. The GGA þU calculations used an effective parameter Ueff ¼U þJ, where U is the Hubbard parameter and J is the exchange parameter. We set U¼7.07 eV, and J ¼0.95 eV. These parameters were sufficient to give good electronic structure and magnetic properties.

Our basic procedure in this work is to calculate the total energy as a function of the unit-cell volume around the equilibrium cell volume V0 for Sr2GdReO6 double perovskite in both paramagnetic and ferromagnetic state. We present, in Fig. 2, structural optimization curves obtained in both phases, and the data are fitted to the Murnaghan's equation of state [37] so as to determine the ground state properties, such as equilibrium lattice constant a, bulk modulus B and its pressure derivative B′. The calculated structural parameters of Sr2GdReO6 are reported in Table 1. The optimal lattice parameter obtained by this procedure are in agreement with the experimental value [29]. To our knowledge, there are no experimental or theoretical data reported for the bulk modulus and its pressure derivative for the material of interest, and hence our results are predictions. In addition, the ferromagnetic phase is found to be energetically more favorable than paramagnetic phase. The calculated spin-polarized band structures of Sr2GdReO6 compound at the theoretical equilibrium lattice constant along high-symmetry directions of the first Brillouin zone are displayed in Fig. 3. The total and partial densities of states, in which the spinup and spin-down sub-bands, are shown in Fig. 4. The Fermi level set as 0 eV. The density of states was presented only for GGA þU

Fig. 2. Volume optimization for the Sr2GdReO6 compound.

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S. Berri / Journal of Magnetism and Magnetic Materials 385 (2015) 124–128

Fig. 3. The band structures of the Sr2GdReO6 compound for the spin-up and spin-down electrons.

Fig. 4. Spin-polarized total densities of states (TDOS) and atom-projected DOS of Sr2GdReO6 compound.

method because it is similar to that of GGA method with a small difference. In Fig. 2, it is clear that the majority-spin band is metallic, while the minority spin band shows a semiconducting gap around the Fermi level. In the minority-spin band, the valance band maximum (VBM) is located at Г point, and the conduction band minimum (CBM) is located at Г point for both method. 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 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 [40]. 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. Fig. 4 shows the total density of states and atom projected as a function of energy for the Sr2GdReO6 compound at its equilibrium lattice constant. To illustrate the nature of the electronic band structures, we have plotted the partial density of states (Fig. 5) of Gd f, Re eg and t2g, Sr eg and t2g and O pz and d electrons for the

spin-up and spin-down sub-bands. For Sr2GdReO6 compound, in both spin channels, significant contributions to the total density of states in the energy range between  8.0 to  2.0 eV, come from pz and d electrons of O element, at the Fermi energy the situation is markedly different, where the f orbital of Gd and t2g states of Re atoms creates fully occupied bands (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). In the energy range between 2.0 to 6.0 eV, the eg and t2g were states of Sr atoms contribute to the majority and minority spin states mix with eg electron of Re atom. The calculated total and atom-resolved magnetic moments, using GGA and GGA þU of Sr2GdReO6 compound, are summarized in Table 1. The present study shows that the total magnetic moment for Sr2GdReO6 compound is E 9 mB/fu for the GGA and GGA þU approximation. 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 [41, 42]. The magnetic moments of the Rhenium atoms are in agreement with theoretical data [43]. In Fig. 6, the TDOS of Sr2GdReO6 at different lattice constants are presented. In minority spin,with lattice expanding, a clear change of the Fermi level position is observed. It is clearly seen in Fig. 6 that the Sr2GdReO6 has half-metallic nature above the lattice constant value of 8.37 Å. Therefore, the lattice constant variation does not affect half-metallic behavior of the Sr2GdReO6 compound.

4. Conclusion For the Sr2GdReO6 compound, the electronic structure and magnetic properties have been calculated using the first principles full-potential linearized augmented plane waves (FPLAPW) method within the spin density functional theory. Features such as the lattice constant, bulk modulus and its pressure derivative are reported. Also, we have presented our results of the band structure and the density of states. At the equilibrium lattice constant, our calculations predict that Sr2GdReO6 is half-metallic (HM) with a magnetic moment of 9 mB/fu and HM flip gap of 1.82 eV. In addition, the ferromagnetic phase is found to be energetically more favorable than paramagnetic phase. Therefore, the Sr2GdReO6

S. Berri / Journal of Magnetism and Magnetic Materials 385 (2015) 124–128

Fig. 5. Spin-polarized partial densities of states (DOS) of Sr2GdReO6 compound.

Fig. 6. Total TDOS for the Sr2GdReO6 compound as a function of the lattice constant.

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compound is application.

S. Berri / Journal of Magnetism and Magnetic Materials 385 (2015) 124–128

a

promising

material

for

future

spintronic

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