Double perovskite-like materials which include magnetic transition elements have relevance due to the technological perspectives in the spintronics engineering. In this study, we report the studies of the electronic and magnetic properties of Sr2CrWO6 and Sr2FeReO6 as spintronics materials at room temperature by using the linear muffin- tin orbitals (LMTO) method through the atomic-sphere approximation (ASA) within the local spin density approximation (LSDA). The interchange-correlation potential was included through the (LSDA+U) method. The band structure results at room-temperature predict half-metallic ferrimagnetic ground state for Sr2CrWO6 and Sr2FeReO6 with total magnetic moment of 1.8780μB and 3.1841μB per formula unit, respectively, agreement with the previous theoretical and experimental results.

Keywords: spintronics, double perovskites, half-metallic, LMTO-ASA, LSDA+U method

Spintronics, analogous to the electronics science and engineering, is a complex term means spin-transport electronics, also named magneto-electronics. Spintronics is an emerging technology in solid-state devices,^1‒3 exploits both the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, i.e. Spin (S=±½)+Charge (e^-)=Spintronics. Spintronics came into view from the observations: (i) spin-polarized electron injection from a ferromagnetic (FM) metal to a normal metal,⁴ (ii) giant magnetoresistance (GMR) phenomenon in Fe/Cr super-lattice and in Fe–Cr–Fe trialed,^5,6 and (iii) magnetic tunnel junctions (MTJ).^7,8 Materials with high spin-polarization (P), preferably 100%, are promising as materials for spintronics devices and thus have been searched enthusiastically. The ratio of spin-polarization (P) can be defined by means of the spin-up and spin-down density of states (D↑, D↓) around the Fermi level (E_F), as:

$P=\frac{D_{\uparrow }(E_F)-D_{\downarrow }(E_F)}{D_{\uparrow }(E_F)+D_{\downarrow }(E_F)}$ (1)

This is extremely interesting as a promising candidate of a spin injector in spintronics. The material with perfect spin-polarization is characterized as a half-metal (HM); HM materials are good candidates because they can have high spin polarization, P=±1 (P=100%), at high temperature.

The thin insulator sandwiched between two FM contacts (FM/I/FM) generates tunnel current due to quantum effect by using small voltage; insulating layer provides quantum mechanical tunnelling of electrons from one ferromagnetic layer to another.⁸ Consequently, the electrical resistance will be low when the magnetizations of two FM layers are parallel (FM↑/I/FM↑) or (FM↓/I/FM↓). On the other hand, resistance (R) rises for antiparallel magnetization of the FM layers, (FM↑/I/FM↓) or (FM↓/I/FM↑). This phenomenon is known as tunnelling magneto resistance (TMR) effect.⁷ The low-field GMR in granular materials is dominated by the inter-grain spin-dependent TMR through insulating grain boundaries, reflecting the spin-polarization of the ferromagnetic grains.⁷ Of course, TMR is favorited by the alignment of the magnetization of the neighboring grains under application of the magnetic field. Based on the resistivity of the material, the magneto resistance (MR) can be defined as⁷

$MR=\frac{\Delta \rho }{{\rho }_0}=\frac{\rho \left(H\right)-\rho \left(0\right)}{\rho \left(0\right)}$ (2)

Where, and are the resistivity with (H>0) and without (H=0) applied magnetic field, respectively. Therefore, the MR phenomenon is being the field-dependent resistance (R) as a function of the applied magnetic field. However, TMR is a pure interface effect and does not require spin transportation in insulator layer. The corresponding TMR in an FM₁/I/FM₂ magnetic tunnel junction (MTJ) can be described by the relative fraction:

$TMR=\frac{\Delta R}{R_{\uparrow \uparrow }}=\frac{R_{\uparrow \downarrow }-R_{\uparrow \uparrow }}{R_{\uparrow \uparrow }}$ (3)

Where, the resistances R are labeled by the relative orientations of the magnetization in FM₁ and FM₂, and it is possible to change the relative orientations between ↑↑ and ↓↓, even at small-applied magnetic fields. Using Julliere model which assumes constant tunneling matrix elements and those electrons without spin flip-flop,^7,8 Equations. (1) and (3) yield:

$TMR=\frac{2P_1{P}_2}{1-P_1{P}_2}$ (4)

Double perovskites have the chemical formula A₂BB'O₆ crystallize in the rock-salt (NaCl) structure with alternate perovskite units ABO₃ and AB'O₃ along three crystallographical axes.⁹ The corner of each perovskite unit cell are in turn occupied by different transition-metal atoms B and B' with oxygen atoms located in between forming alternate BO₆ and B'O₆ octahedra.^9,10 The large alkaline-earth metal atoms A²⁺ occupied the body-centered site with 12-fold oxygen coordination in each unit cell.¹¹ In the ionic model of alkaline-earth metal based double perovskites, the pair of transition-metal ions are in the 8+ valence state, (BB')⁸⁺. The interaction between two magnetic ions B and B' in double perovskites A²BB'O⁶ controls by the long-range super exchange (–B–O–B'–) instead of double-exchange (–B–O–B–) in perovskite ABO₃.^12,13

Materials with high spin-polarization of the charge carriers, the current, have attracted a great deal of attention owing to their technological applications in spintronics,¹⁴ magnetotransport devices as well as their rich and challenging physical properties.^9‒14 In particular, an ideal material with 100% spin-polarization is called a half-metal.¹⁵ Such materials can be found in several materials classes; in classic inorganic oxides, such as magnetite (Fe₃O₄)¹⁶ and chromium dioxide (CrO₂),¹⁷ in manganite perovskites as in (LaMnO₃)¹⁸ and in Heusler alloy compounds as in (Co₂Cr_1-xFe_xAl),^19,20 as well as in the group of double perovskites.^9,12,13 Double perovskites are of special attention, since within this group half-metals with above room-temperature (RT) are found, such as in (Ca₂FeMoO₆), (Sr₂FeMoO₆), (Ba₂FeMoO₆),^21,22 and in (Sr₂CrMoO₆).^21,22 The ordered double perovskites, such as (Sr₂FeMoO₆), (Sr₂FeReO₆), (Sr₂CrWO₆), etc., are among the very few materials that allow electrons of one spin direction to move through them as though they were passing through a normal metal, while blocking electrons of the opposite spin. Materials that behave this way at RT are even more exotic, so their conduction bands have a fully spin-polarization.⁹ (Sr₂FeReO₆), (Sr₂CrWO₆) double perovskites, in particular, have attracted more attention due to their fairly high transition temperature from a paramagnetic (PM) to ferromagnetic (FI) state, which makes them and their related compounds candidates for future spintronics applications.

The first-principles linear muffin-tin orbital (LMTO) method with atomic-sphere approximation (ASA) has been employed to perform self-consistent band structure calculations within the local spin density approximation (LSDA). In LMTO-ASA, which is similar to the multiple-scattering Korringa-Kohn-Rostoker (KKR) method,²⁴ the potential is approximated by a muffin tin potential, i.e., it is spherically symmetric around the atomic sites and constant in the interstitial volume. Moreover, ASA takes the one-electron potential and charge density to be spherically symmetric inside space-filling Wigner-Seitz (WS) spheres whose overlap is neglected, the interstitial volume, now integrating to zero.²⁴ The von Barth–Hedin parameterization for exchange-correlation potential is used in the calculations.^9,25 The Hartree potential is expanded in term of spherical harmonic up to 6, therefore, Sr (5s 4p 4d), Cr/Fe (4s 4p 3d), Mo (5s 5p 4d), W (6s 6p 5d) and O (2s 2p) LMTOs were input as valance states, while Sr (4s), Cr/Fe (3p), Mo (4s 4p), W (5p 4f) fixed as semicore states in the unit cells. It has been established that the structures are close enough, that no empty sphere (ES) is needed to introduce in the unit cells.¹⁷ The numbers of divisions along reciprocal lattice vector which will set up the mesh for integrating valence state are selected as 6×6×6. Special k points of 120 in the irreducible Brillouin zone (IBZ) was used in band structure and density of states calculations. A single kappa LMTOs basis set expanded in spherical harmonic up to the angular momentum l_max=6, was used for the valence-band charge densities and potential inside the non-overlapping muffin-tin spheres.²⁴ The interchange-correlation potential was included through the LSDA+U method, where the on-site Coulomb energy (U) has been in used. The correlation parameters, Coulomb energy (U) and Hund's rule exchange (J), were utilized for strongly correlated 3d and weakly 5d electrons in the calculations. The Hubbard parameters (U=4 eV, J=0.98 eV) are used for Cr/Fe (3d) states,^9,25 even as ( U=1 eV, J=0.96 eV) are used for W/Re (5d) states.^1,17 The resolving of spin up and down in total and partial densities of states for Sr₂CrWO₆ and Sr₂FeReO₆ were calculated and obtained from the LSDA+U calculations.

Crystal structures

In the present study we report systematic studies on the Cr/Fe (3d) and W/Re (5d) orbitals contributions to the electronic and magnetic structures of two close relative members of strontium double perovskites, Sr₂CrWO₆ and Sr₂FeReO₆. Where, W and Re are neighboring 5d transition-metal elements in periodic table with the ordinary electronic configurations of [Xe] 6s²4f¹⁴5dⁿ, where n=4 for W (Z=74) or n=5 for Re (Z=75), [Xe] denotes the configurations of the noble gas Xenon core. For chromium and iron Cr/Fe, Cr has an odd electron configuration of [Ar] 4s¹3d⁵ owing to the lower energy of the high spin configuration, not [Ar] 4s²3d⁴ as it might expect, where a half-filled d sublevel is more energetically favorable than a half-filled s sublevel, so one of the 4s electrons is promoted to a 3d orbital. On the other hand, iron (Fe) has ordinary electron configuration of [Ar] 4s²3d⁵. Cr and Fe exhibit a wide range of possible oxidation states, where the +3 state is most stable energetically.^25‒27 Accordingly, the valence configurations of transition-metal ions in Sr₂CrWO₆ are; Cr³⁺ (3d³) and W⁵⁺(5d¹) in high spin state with valence spin magnetic moments of S=3/2 and S=1/2 according to the Hund's rule, respectively. Consequently, the theoretical total magnetic moment is 2 μ_B per formula unit cell for the ferrimagnetic ground state. In other compound, Sr₂FeReO₆, where the ion Fe₃₊ (3d₅) is in high spin state of S=5/2, ion Re⁵⁺(5d²) is highly ionized with valence spin magnetic moment of S=1. As a result, the total magnetic moment for the ferrimagnetic ground state is 3 μ_B per Sr₂FeReO₆.

For cubic Sr₂CrWO₆ and Sr2FeReO6 perovskites with space group Fm-3m (No. 225), we used the experimental lattice constants of a=7.890Å from²⁸ and a=7.832Å from,⁹ respectively, closed to the theoretical values calculated using SPuDS²⁷ 7.8587Å and 7.8858Å, correspondingly, see Table 1. The magnetic structure in double perovskites can be assign to the AFM superexchange interactions between two very different transition magnetic ions, ^9,25 such as Cr/Fe (3d) and W/Re (5d) in this study, via intermediated O^2-(2p) ions (Cr/Fe –O– W/Re). In addition to, the naturally small magnetic moment at W/Re (5d), is believed to be not intrinsic, but is induced by the strong magnetic ions Cr/Fe(3d) (Table 2).

Electronic and magnetic structures

Figure 1 illustrates the total densities of states (TDOSs) of Sr₂CrWO₆ and Sr₂FeReO₆ from band structure LSDA+U calculations. In spin-up TDOSs, there are energy gap of about 1.33 eV in Sr₂CrWO₆ and 2.18 eV in Sr₂FeReO₆ between the occupied Cr/Fe (3d) and unoccupied W/Re (5d) partial bands. Since the energy gap in the spin-up produces from the antiferromagnetic coupling between Cr/Fe (3d) and W/Re (5d) states, as shown in Figure 2, this situation emerge as peaks of 3d and 5d bands polarized antiferromagnetically demonstrate the Cr/Fe (3d) ↑ and W/Re (5d)↓ form. Therefore, the spin-up electrons are insulating while the spin-down electrons are metallic, resulting in full (100%) spin-polarized of the conduction electrons at E_F. For that reason, Sr₂CrWO₆ and Sr₂FeReO₆ materials allow electrons of spin-down direction to move through them as though they were passing through a normal metal, while blocking electrons of the spin-up. The obtained results of Sr₂CrWO₆ and Sr₂FeReO₆ are agreement with previous LSDA+U calculations.^9,25,29 As seen in Figure 2, the conduction bands in spin-down orientation is attributed mainly to the contributions of W (5d) and Re (5d) ions with tiny contributions of Cr (3d) and Fe (3d), correspondingly. Compare TDOSs with PDOSs, the level distributions in of Sr₂CrWO₆ and Sr₂FeReO₆ are overall very similar, except a peak between 1 eV and 3 eV, above EF, is higher in Sr₂FeReO₆ than in Sr₂CrWO₆. This dissimilarity, as seen in Figure 2, due to the extra electron in Re (5d²) than in W (5d¹).

In order to understand in some more detail the origin of the electronic and magnetic characters of Sr₂CrWO₆ and Sr₂FeReO₆, we critically examine the partial electronic density of states (PDOS) of these systems. The basic critical ingredients in the TDOS are the d states of the Cr/Fe and W/Re atoms, which in turn are split into t_2g and e_g states by the octahedral crystal field (OCF) produced by the oxygen octahedra. The t_2g states having lower energy and place for three electrons per spin channel, whereas the e_g states are higher in energy and have place for two electrons per spin channel. Furthermore, due to the exchange splitting, t_2g bands degenerate into double orbitals (d_xz and d_yz) and one singlet orbital (d_xy), while e_g bands degenerate into two singlet orbitals (d_x2 –y₂ and d_z2), as seen in Figure 3, which show the partial densities of states of t_2g, e_g and 2p orbitals in Sr₂CrWO₆ and Sr₂FeReO₆.

From the PDOS in Figure 3A, the three-fold degenerate Cr t_2g states of the spin-up channel are filled Cr³⁺ (3d^3:t_2g³↑); consequently the d_xy↑, d_xz↑ and d_yz↑ orbitals are at the energy range, about -7 eV~-1.5 eV in the valance bands. Therefore, the EF ends up in the CF gap of ∆_o≈1.5 eV between Cr t_2g and e_g states. A similar situation is observed in the half-metallic close-relative Sr₂FeReO₆.^29,30 Due to the antiferromagnetic coupling in Cr (3d) –W (5d), it is the spin-down channel in W (5d) which is the occupied one, and it contains one electron in t_2g states W⁵⁺ (5_d¹:t_2g¹↓). This means that the W (5d) t_2g spin-down states are only filled to about one-two, resulting in high density of states of d_xy and d_yz at the EF in spin-down channel. In addition to, due to hybridization between states in Sr₂CrWO₆, Cr t_2g↓ states achieved small occupation, while W (5d) states in the spin-up channel are essentially empty; hybridization with Cr t_2g↑ states results nevertheless in a finite, small occupation above EF.

On the other hand, from the PDOS in Figure 3B, the Fe t_2g and e_g states are full-filled in the spin-up orientation; Fe³⁺ (3d⁵: t_2g³↑ e_g²↑) in the high spin state; the electronic configuration can be set of orbitals as (d_xy↑)¹, (d_xz↑ and d_yz↑)², (d_x2–y₂)¹ and (d_z2)¹ extend from -8.0 eV to -2.0 eV in the valance bands. The exchange splitting is about 7.5 eV, larger than the CF splitting, ∆_o ≈ 2.25 eV, resulting in the high-spin of Fe (3d) states. At the same time, spin-down channel in Re (5d) which is the occupied one, and it contains two electron in t_2g states Re⁵⁺(5d²: t_2g²↓). Therefore, the Re t2g spin-down states are only filled to about two-three, emerged as a high spin-down DOS of d_xy and d_yz at EF. Inversely, neither Fe t_2g ↓ nor Re (5d) ↑ states have contribution to the bands around EF, while the O(2p) bands are at a much lower energy from -9 to -2 eV.

Finally, the magnetic structure in Sr₂CrWO₆ and Sr₂FeReO₆ double perovskites can be assign to the antiferromagnetic superexchange interactions between Cr/Fe(3d) and W/Re(5d) via intermediated oxygen atoms in the 180^o long-chain Cr (3d-t_2g↑)–O(2p_π)–W(5d-t_2g↓) and Fe (3d-t_2g↑)–O (2p_π) – Re (5d-t_2g↓), correspondingly. The calculated spin magnetic moments from LSDA+U for Sr₂CrWO₆ are; 2.9188μ_B / Cr, -1.0435μ_B / W with a total magnetic moment of 1.8780μ_B, which is 94% agreement to the later LSDA+U result, 2.01μ_B.^27,29 For Sr₂FeReO₆, 4.5778μ_B for Fe, -1.3438μ_B for Re, and the total magnetic moment found to be 3.1841μ_B, also agreement to the LSDA+U result, 3.06μ_B.⁹ The bands scheme for both compounds are illustrated in Figure 4, the results can be to resume by means the simple model describes the effect of filling t_2g and e_g orbitals in 3d and 5d bands for spin-up and -down configurations.

Figure 4 Representation of the electronic density of spin-up and spin-down states in 100% electronic spin-polarization half-metallic in Sr₂CrWO₆ and Sr₂FeReO₆. The quantity of filling signifies the effect of t_2g and e_g orbitals in 3d and 5d bands per unit volume and per unit energy; E. E_F is the Fermi energy.

We have comparatively studied the electronic and magnetic characterizations of double perovskites Sr₂CrWO₆ and Sr₂FeReO₆ by using the linear muffin- tin orbitals through the atomic-sphere approximation method within the local spin density approximation, including the interchange-correlation potential through the LSDA+U method. The band structure results demonstrated half-metallic ferrimagnetic ground state for Sr₂CrWO₆ and Sr₂FeReO₆ with total magnetic moment of 1.8780μ_B and 3.1841μ_B per formula unit, respectively, in exact agreement with the theoretical and experimental results. The obtained HM-FiM feature in double perovskites Sr₂CrWO₆ and Sr₂FeReO₆ makes these materials suitable for many applications. It established that they have a high degree of electronic spin polarization which means that they will have potential spin transport electronics (spintronics), where spin currents are utilized as well as charge currents.

None.

The authors declare no conflict of interest.