A novel theoretical design of electronic structure and half-metallic ferromagnetism in the 3d (V)-doped rock-salts SrS, SrSe, and SrTe for spintronics

Abstract

The exploration of new dilute magnetic semiconductors (DMSs) designed for the development of practical semiconductor spintronics devices has attracted increasing interest in recent years. In the present study, we have investigated the structural, electronic and magnetic properties of strontium chalcogenide semiconductors (SrS, SrSe and SrTe) doped with the transition metal vanadium (V) in the rock-salt structure as Sr_1−xV_xZ (Z = S, Se and Te) ternary DMSs at a concentration x = 0.125, using first-principles calculations of density functional theory with the generalized gradient approximation functional of Wu and Cohen (GGA-WC). The electronic structure of each compound revealed half-metallic (HM) ferromagnetic behavior with a HM gap and 100% spin polarization. The HM gap is an important parameter in determining the importance of DMSs in spintronics; it is 0.937, 0.585 and 0.245 eV for Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te, respectively. Therefore, the Sr_0.875V_0.125Z (Z = S, Se and Te) seems to be a new potential candidate for future spintronics applications.

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1. Introduction

In electronics, electrical charges are used to store information and perform logic operations; however in addition to their charges, electrons have magnetic moments (spins), but this property is not used in conventional solid-state electronic devices.¹ Spintronics (spin transport electronics or spin-based electronics) is a new generation of microelectronics, which aims to use the spin degree of freedom of charge carriers in the development of an emerging field of promising materials for spin-based multifunctional devices.^2,3 Diluted magnetic semiconductors (DMSs) are particularly relevant to spintronics devices due to the fact that their Curie temperatures are higher than room temperature and because of their half-metallic ferromagnetic (HMF) behavior.⁴ They show stable ferromagnetism at temperatures above room temperature.^5,6 The HMF character is considered an important factor with respect to spin injection carriers for spintronics; however, the electronic structure of DMSs combines both metallic and semiconductor characteristics, having a metallic nature in one spin channel and a band gap at the Fermi level in the opposite spin direction,⁷ and thus the DMS shows a HMF feature.

Recently, DMSs based on III–V and II–VI semiconductors doped with magnetic elements have been intensively studied experimentally^8–14 as well as theoretically^15–23 to predict their magnetic properties with respect to their use in spintronics applications. The (II = Be, Mg, Ca, Sr, and Ba; VI = O, S, Se, and Te) alkaline-earth-chalcogenides belong to the II–VI group and they are important semiconductors due to significant properties such as large band gaps and valence-band widths.²⁴ These semiconductors form closed-shell ionic systems that crystallize in the rock-salt NaCl-type (B1) crystal structure under ambient conditions, except for beryllium chalcogenides, which crystallize in the zinc-blende structure; the BeO and MgTe crystallize in the wurtzite structure.^25–27 Among these compounds, SrZ (Z = S, Se and Te) strontium chalcogenide semiconductors have attracted increasing attention due to their wide range of technological applications in many fields such as catalysis, microelectronics, luminescent devices, radiation dosimetry, fast high-resolution optically stimulated luminescence imaging and infrared-sensitive devices.^28–30 In the last few years, several theoretical studies have investigated half-metallic ferromagnetism in alkaline-earth-chalcogenides doped with magnetic and nonmagnetic impurities; much attention has been focused on N, P, As and Sb-doped alkaline-earth sulfides such as AeS_0.875X_0.125 (Ae = Mg, Ca and Sr; X = N, P, As and Sb),³¹ and nonmagnetic sp element (B, C and N)-doped AeSe (Ae = Mg, Ca, Sr and Ba) alkaline earth selenides³² and C, Si, Ge and Sn-doped alkaline-earth sulfides such as AeS_1−xM_x (Ae = Mg, Ca and Sr; M = C, Si, Ge and Sn)³³ and Sr_1−xCr_xZ (Z = S, Se and Te).³⁴ To the best of our knowledge, there have been no experimental and theoretical studies on the electronic and magnetic properties of V-doped SrZ (Z = S, Se and Te).

The aim of the present study was to investigate the electronic and magnetic properties of Sr_1−xV_xZ (Z = S, Se and Te) at concentration x = 0.125 of atomic vanadium (V) in the rock-salt phase, using first-principles calculations of density functional theory^35,36 within the framework of a full-potential linearized augmented plane-wave method with a generalized gradient approximation functional proposed by Wu and Cohen.³⁷ We have predicted the half-metallic behavior and discussed the origin of ferromagnetism in Sr_0.875V_0.125Z (Z = S, Se and Te), induced by the transition-metal vanadium impurity, based on simple ordered Sr₇VS₈, Sr₇VSe₈ and Sr₇VTe₈ supercells of 16 atoms.

2. Method of calculations

The calculations are carried out using the framework of density functional theory (DFT)^35,36 within the first-principles full-potential linearized augmented plane-wave (FP-LAPW) method as implemented in the WIEN2K package.³⁸ The generalized gradient approximation functional proposed by Wu and Cohen (GGA-WC)³⁷ was used for the exchange correlation potential. Based on the Sr₇VS₈, Sr₇VSe₈ and Sr₇VTe₈ supercells of 16 atoms, we have determined the structural parameters and the electronic and magnetic properties of the SrZ (Z = S, Se and Te) strontium chalcogenides doped with vanadium (V) in the form of Sr_1−xV_xZ (Z = S, Se and Te) ternary compounds at concentration x = 0.125.

We have taken the averages of non-overlapping muffin-tin radii (R_MT) of Sr, S, Se, Te and V in such a way that the muffin-tin spheres do not overlap. The wave functions are expanded in the interstitial region to plane waves with a cut-off of K_max = 8.0/R_MT (where K_max is the magnitude of the largest K vector in the plane wave and R_MT is the average radius of the muffin-tin spheres), and the maximum value for partial waves inside the atomic sphere was l_max = 10, while the charge density was Fourier-expanded up to G_max = 14 (a.u.)⁻¹, where G_max is the largest vector in the Fourier expansion. For the sampling of the Brillouin zone, we utilized the Monkhorst–Pack mesh^39,40 of (4 × 4 × 4) k-points for SrZ^34,41 and (4 × 4 × 2) for Sr_0.875V_0.125Z (Z = S, Se and Te),³⁴ where the self-consistent convergence of the total energy was at 0.1 mRy.

3. Results and discussions

The SrZ (Z = S, Se and Te) semiconductors have a rock-salt (B1) structure with a space group of 225 Fm3̄m, where the Sr atom is located at (0, 0, 0) and the (S/Se/Te) atom at the (0.5, 0.5, 0.5) position. We obtain the concentration x = 0.125 by substitution of one Sr cation site at the (0, 0, 0) position by a V impurity in Sr₈Z₈ (Z = S, Se and Te) supercells of 16 atoms. We obtain Sr_0.875V_0.125Z (Z = S, Se and Te) (1 × 1 × 2) supercells of 16 atoms with concentration x = 0.125 as a tetragonal structure with space group 123 (P4/mmm), as shown in Fig. 1.

Fig. 1 The crystal structure of a Sr_1−xV_xZ supercell of 16 atoms with (Z = S, Se and Te) and x = 0.125.

The abovementioned structures were optimized by fitting the variations of total energies as a function of equilibrium volumes with the empirical Murnaghan's equation of state⁴² to compute the structural parameters, such as the equilibrium lattice constants (a), bulk modules (B) and pressure derivatives (B′), for SrZ and Sr_0.875V_0.125Z (Z = S, Se and Te) compounds. Our results, as well as various theoretical^43,44 and experimental^45–47 data, are given in Table 1.

Table 1 Calculated values of lattice constant (a), bulk modulus (B), and its pressure derivative (B′) for SrS, SrSe, SrTe, Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te

Compound	a (Å)	B (GPa)	B′
a Theoretical values from ref. 43.b Theoretical values from ref. 44.c Experimental values from ref. 45.d Experimental values from ref. 46.e Experimental values from ref. 47.
SrS	5.992, 6.05^a, 5.988^b, 6.024^c	52.83, 58^c	4.34
SrSe	6.204, 6.29^a, 6.204^b, 6.234^d	43.23, 45^d	4.22, 4.5^d
SrTe	6.624, 6.71^a, 6.621^b, 6.659^e	34.77, 39.5^e	4.40, 5^e
Sr0.875V0.125S	5.877	55.94	4.41
Sr0.875V0.125Se	6.103	47.60	4.44
Sr0.875V0.125Te	6.509	37.26	4.56

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The calculated lattice constants of binary SrZ (Z = S, Se and Te) semiconductors are better than the theoretical calculations⁴³ with a generalized gradient approximation using the Perdew, Burke, and Ernzerhof (GGA-PBE) method.⁴⁸ This is owing to the better performance of the GGA-WC approximation used in structural optimization,^49–51 which results from the fourth-order gradient expansion of the exchange-correlation functional.^37,50 Moreover, the lattice parameters of binary SrZ (Z = S, Se and Te) are very close to the theoretical calculations⁴⁴ with the same GGA-WC method²⁸ and are in good agreement with experimental data.^45–47 Furthermore, the lattice constants of ternary Sr_0.875V_0.125Z (Z = S, Se and Te) systems are smaller than those of binary compounds because the ionic radius of a V atom is smaller than that of Sr. As a consequence, the bulk modules of Sr_0.875V_0.125Z (Z = S, Se and Te) are higher than those of SrZ (Z = S, Se and Te) and therefore SrZ (Z = S, Se and Te) is easily compressible compared to the Sr_0.875V_0.125Z (Z = S, Se and Te) compounds.

Moreover, we noticed that there are no experimental and theoretical GGA-WC calculations of structural parameters for Sr_0.875V_0.125Z (Z = S, Se and Te) to compare with the results of our study. In the following calculations, we have used the computed lattice constants to determine the electronic and magnetic properties of the compounds under study.

The plots of spin-polarized total densities of states (TDOS) and partial densities of states (PDOS) for Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te are displayed in Fig. 2(a)–(c), respectively. The PDOS show that the five-fold degenerate 3d (V) states are divided into two parts: the three-fold degenerate low-lying t_2g (d_xy, d_xz, and d_yz) and the two-fold generate high-lying e_g (d_z² and d_x²−y²) symmetry states; this is due to the effect of the octahedral crystal field formed by surrounding (S, Se and Te) ligands. For the 3d (V) majority-spin states, the t_2g (V) are completely filled non-bonding states that cut the Fermi level (E_F) and the e_g states occur in the bottom of conduction bands, which are empty anti-bonding states located above E_F. In contrast, in the study of Cr-doped SrZ (Z = S, Se and Te),³⁴ the t_2g (Cr) are completely filled states located below E_F and do not cut the Fermi level and the e_g (Cr) partially occupied states cross E_F. In both the V and Cr cases, the e_g states move to higher energies than the t_2g states, meaning that the vanadium impurity is situated in an octahedral environment.³⁴

Fig. 2 Spin-polarized total and partial DOS of Sr_0.875V_0.125Z (Z = S, Se, Te). (a) Sr_0.875V_0.125S, (b) Sr_0.875V_0.125Se and (c) Sr_0.875V_0.125Te. The Fermi level is set to zero (vertical dotted line).

The PDOS for both spin directions of Sr_0.875V_0.125Z (Z = S, Se and Te) show that the lower part of the valence bands are principally formed by the main contributions of p (S, Se and Te) and minor s (Sr) states in the ranges from −4 to −1, −3.8 to −0.6, and −3.5 to −0.4 eV for Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te, respectively. The upper parts of conduction bands of two spin channels are dominated by small contributions of the p (S, Se and Te) states. Furthermore, the top of the majority-spin valence bands and the bottom of the minority-spin conduction bands mainly originate from the 3d (V) states. However, the Sr_1−xV_xZ (Z = S, Se and Te) compounds exhibit half-metallic behavior due to the presence of a band gap in the minority spin and metallic nature of majority spin. The metallic character of the majority spin results from the large hybridization between p (S, Se and Te) and 3d-t_2g (V) states that occur in the upper part of the valence band and crosses the Fermi level, whereas the 3d (V) minority-spin states vanish at the Fermi level, resulting in a semiconducting band gap.

Moreover, Sato et al.^52–54 explained the ferromagnetism of III–V and II–VI semiconductors doped with tetrahedrally bonded transition metals (TM). They suggested that the ferromagnetic state is stabilized by the double-exchange mechanism when the 3d-t_2g (TM) anti-bonding states are partially occupied. In the octahedrally-bonded vanadium (V)-doped Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te compounds, we understand that partially filled 3d (V) majority-spin states lower the total energy to stabilize a ferromagnetic ground state arrangement associated with the double-exchange mechanism.⁵⁵ We know that this suggestion is analogous to the one proposed by Sato et al.^52–54 in the case of the III–V and II–VI semiconductors doped with tetrahedrally bonded TMs. As we have mentioned that both p-d exchange and the double-exchange mechanism contribute to the stabilization of the ferromagnetic ground state configuration in the Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te doping systems.

Furthermore, Fig. 3(a)–(c), represent the spin-polarized band structures of Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te, respectively, along the high symmetry points of the first Brillouin zone. The band structures of majority and minority spin are different; the half-metallic behavior arises from the metallic nature of the majority spin and band gap of minority-spin, leading to 100% magnetic spin-polarization at the Fermi level. We can also notice that the large spin splitting occurs through the p (S, Se and Te) and 3d (V) states around the Fermi level. Therefore, we deduce that p-d exchange interaction is responsible for creating the half-metallic ferromagnetic (HMF) band gap (E_g) and the half-metallic (HM) gap (G_hm) in the minority spin. The HM gap G_hm is determined as the minimum energy gap between the lowest energy of majority (minority)-spin conduction bands with respect to the Fermi level and the absolute value of the highest energy of majority (minority)-spin valence bands.^56,57 It is a very significant parameter in recognizing the importance of the diluted magnetic semiconductor, which determines the minimal energy gap of a spin excitation for generating a hole or an electron in minority spin.³⁴

Fig. 3 Spin-polarized band structures of majority spin (up) and minority spin (dn) for Sr_0.875V_0.125Z. (a) Sr_0.875V_0.125S, (b) Sr_0.875V_0.125Se and (c) Sr_0.875V_0.125Te. The Fermi level is set to zero (horizontal dotted line).

The calculated HMF gaps E_g and HM gaps G_hm of minority-spin states for Sr_0.875V_0.125Z (Z = S, Se and Te) compounds are given in Table 2. From Fig. 3(a)–(c), the minority-spin band for each compound exhibits a direct HMF gap located at the Γ symmetry point, which decreases from Sr_0.875V_0.125S to Sr_0.875V_0.125Se to Sr_0.875V_0.125Te, as shown in Table 2. The HM gap (spin-flip gap) of each compound is created between the valence band maximum (VBM) and the Fermi level (0 eV) and describes the minimal energy band gap of a spin-flip excitation required to flip a minority spin electron from the top of the occupied valence band to the Fermi level of the majority spin.^58,59 However, the minimal energy band gaps are 0.937, 0.585 and 0.245 eV for Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te, respectively, corresponding to the HM gaps of these materials. Moreover, the HM gap decreases from Sr_0.875V_0.125S to Sr_0.875V_0.125Se to Sr_0.875V_0.125Te as the energy level of the p (Z) states shifts to high energy towards the Fermi level from the 3p (S) to 4p (Se) to 5p (Te) states. The wide HM gap suggests true half-metallic ferromagnets and therefore the Sr_0.875V_0.125S with a higher HM gap (0.937 eV) is predicted to be a better potential candidate than Sr_0.875V_0.125Se or Sr_0.875V_0.125Te for exploring half-metallic ferromagnetic properties for possible future semiconductor spintronics applications.

Table 2 Calculated half-metallic ferromagnetic band gap (E_g) and half-metallic gap (G_hm) of minority-spin bands for Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te

Compound	Eg (eV)	Ghm (eV)
Sr0.875V0.125S	2.198	0.937
Sr0.875V0.125Se	1.955	0.585
Sr0.875V0.125Te	1.583	0.245

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The Sr_0.875V_0.125Z (Z = S, Se and Te) compounds are obtained by the substitution of one (S/Se/Te) cation site with one vanadium V (4s²3d³-t_2g³e_g⁰) impurity, where the new V constituent contributes two electrons to the bonding states of the host valence band carriers of the semiconductors. Consequently, the electronic valence configuration of the V atom in Sr_0.875V_0.125Z (Z = S, Se and Te) compounds becomes V²⁺ (4s⁰3d³-t_2g³e_g⁰), having three electrons in the t_2g³ (V) states and empty e_g⁰ (V) states. In contrast, for Cr-doped SrZ (Z = S, Se and Te),³⁴ where the valence configuration of the chromium ion is Cr²⁺ (4s⁰3d^​4-t_2g³e_g¹) having four electrons in majority spin: three in t_2g³ (Cr) states and one electron in e_g¹ (Cr) states. According to Hund's rule, the 3d (V) are empty minority-spin states and the 3d (V) majority-spin states are partially occupied with three electrons, whereas for the 3d (Cr) majority-spin states, the t_2g (Cr) states are completely filled with three electrons and e_g (Cr) states are partially occupied with one electron. Comparing to our findings, the results for Cr-doped SrZ (Z = S, Se and Te)³⁴ show that the 3d (V) and 3d (Cr) majority-spin states have three and four electrons, respectively, meaning that 3d (Cr) have one more electron than 3d (V). The unpaired electrons, such as three for 3d (V) and four for 3d (Cr), give rise to the total magnetic moments of 3 μ_B and 4 μ_B (μ_B is the Bohr magneton) for Sr_0.875V_0.125Z (Z = S, Se and Te) and Cr-doped SrZ (Z = S, Se and Te) compounds, respectively.

The calculated total and local magnetic moments (MMs) within the muffin-tin spheres of the relevant atoms and in the interstitial sites for Sr_0.875V_0.125Z (Z = S, Se and Te) are summarized in Table 3. It shows that the local MMs of vanadium impurities, such as 2.658, 2.705 and 2.752 μ_B, are smaller than the predicted Hund's rule values of 3 μ_B for the total MMs due to the p-d exchange interactions. The total MMs are integral multiples of the Bohr magneton of 3 μ_B, confirming the true half-metallic behavior of Sr_0.875V_0.125Z (Z = S, Se and Te) compounds. The local MMs of vanadium impurities mainly contributed to the total MMs and less important MMs are induced at the nonmagnetic (Sr, S, Se and Te) sites. On the other hand, the negative sign of the MMs of S, Se and Te described the anti-ferromagnetic interaction between vanadium (V) and S, Se and Te magnetic spins; this implies that the valence band carriers containing the p (S, Se and Te) states interact anti-ferromagnetically with vanadium magnetic spins. In addition, the ferromagnetic interaction between V and Sr atoms is explained by the positive MMs of Sr atoms.

Table 3 Calculated total and local magnetic moments (in Bohr magneton μ_B) within the muffin-tin spheres and in the interstitial sites for Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te

Compound	Total (μB)	V (μB)	Sr (μB)	S/Se/Te (μB)	Inters. (μB)
Sr0.875V0.125S	3.00	2.658	0.007	−0.078	0.414
Sr0.875V0.125Se	3.00	2.705	0.013	−0.101	0.386
Sr0.875V0.125Te	3.00	2.752	0.004	−0.114	0.362

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4. Conclusions

The first-principles calculations of density functional theory with the full-potential linearized augmented plane-wave method and the generalized gradient approximation functional of Wu and Cohen were used to investigate the electronic and half-metallic ferromagnetic properties of Sr_0.875V_0.125Z (Z = S, Se and Te) compounds in the rock-salt phase. We have found that Sr_0.875V_0.125Z (Z = S, Se and Te) compounds are half-metallic ferromagnets with 100% magnetic spin polarization, wherein the ferromagnetic state is stabilized by the 3d (V) partially filled states associated with the double-exchange mechanism. Therefore, Sr_0.875V_0.125S, Sr_0.875V_0.125Se and Sr_0.875V_0.125Te are predicted as new promising materials for spintronics. Moreover, the half-metallic (HM) gaps are 0.937, 0.585 and 0.245 eV, decreasing from Sr_0.875V_0.125S to Sr_0.875V_0.125Se to Sr_0.875V_0.125Te as the p (Z) valence band shifts to high energy towards the Fermi level, going from 3p (S) to 4p (Se) to 5p (Te) states. Thus, Sr_0.875V_0.125S with a high HM gap seems to be a better potential candidate than the other compounds to explore half-metallic ferromagnetism for possible future spintronics applications. An experimental study is needed in future to confirm the predictions of our theoretical study.

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