1 Introduction

Spintronics, also known as magnetoelectronics, is a new generation of microelectronics and involves utilizing both charge and spin degrees of freedom of electrons [1]. During the past decade, the development of diluted magnetic semiconductors (DMSs) for spintronics made revolution in the processing and storage information technologies. The half-metallic ferromagnets DMSs based on III–V doped with transition metals are the main ingredients of high-performance spintronic devices in the future [2, 3], because they are characterized with Curie temperature higher than room temperature and half-metallic ferromagnetic (HMF) behavior [4]. They have a band gap at the Fermi level for only one spin direction and conductor only from the charge carriers of the other spin channel [5]. Thus, the HMF character takes a significant role in the progress of new materials for the spintronic devices, especially as a source of spin-polarized injected carriers in the DMSs [6]. Recently, several theoretical works [7–24] focused on the investigation of HMF DMSs-based on II–VI and III–V semiconductors doped with transition metal elements in the intention to predict their use in the spintronic applications; further, new experimental studies were carried out in this area [25–30].

The GaP is an important semiconductor that belongs to III–V group, which crystallizes in the zinc-blende phase with a wide indirect band gap [31]. It has received significant attention as a material for exploitation in a wide range of important modern optoelectronic devices including photodetectors, light emitters, electroluminescent displays, and power diodes as well as being a model material with which to investigate the fundamental properties of semiconductors [32]. However, T. Dietl et al. [33] predicted that the p-type GaMnP DMS has a Curie temperature (T C) of roughly 100 K, and the manganese (Mn) plays a special role in the III-Mn–V compounds, as it is a relatively deep acceptor, whose level is 0.39 eV above the valence band maximum in GaP [34]. Although, several experimental studies considered gallium phosphide doped with manganese a best candidate as a DMS, M. A. Scarpulla et al. [35] reported that GaGa−x Mn x P represents a novel DMS alloy system where strongly localized carriers in a detached impurity band stabilize ferromagnetism, and F.J. Owens [36] found by both ferromagnetic resonance and AC magnetization measurements the existence of ferromagnetism in GaP hole doped with 3 % Mn and having a Curie temperature of 600 K. In addition, the half-metallic ferromagnetism has been theoretically predicted in GaGa−x Cr x P (x = 0.125, 0.25, and 0.5) [8], GaGa−x Cr x P (x = 0.03, 0.06, 0.125, and 0.25) [9], Ga0.875Mn0.125P [10], and Ga0.875Cr0.125P [11].

The aim of the present work is to study the ternary GaGa−x TM x P (TM = V, Cr, and Mn) DMSs, which the transition metal impurities (TM = V, Cr, and Mn)-doped GaP semiconductor give a particular half-metallic ferromagnetic property with 100 % spin polarization. We have explored the structural, electronic, and magnetic properties of GaGa−x TM x P (TM = V, Cr, and Mn) at concentrations x = 0.0625, 0.125, and 0.25, using first-principles calculations of density functional theory [37, 38] within the framework of full-potential linearized augmented plane-wave (FP-LAPW) method with generalized gradient approximation functional proposed by Wu and Cohen (GGA-WC) [39].

2 Method and Details of Calculations

The calculations are performed in the framework of the density functional theory (DFT) [37, 38] within the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code [40]. The generalized gradient approximation functional proposed by Wu and Cohen (GGA-WC) was used for the exchange correlation potential [39] to investigate the electronic and half-metallic ferromagnetic properties of (TM = V, Cr, and Mn)-doped GaP in zinc-blende (B3) structure, based on Ga15 TMP 16, Ga7 TMP 8, and Ga3 TMP 4 supercells of 32, 16, and 8 atoms, respectively. The GaP has a zinc-blende structure with space group \(F\overline {4}3m\), where the Ga atom is located at position (0, 0, 0) and P atom at (0.25, 0.25, 0.25). The GaGa−x TM x P (TM = V, Cr, and Mn) compounds with concentrations x = 0.0625, 0.125, and 0.25 are obtained by substituted one Ga atom with one (TM) atom in supercells of 32, 16, and 8 atoms, respectively. We get the Ga0.9375 TM 0.0625P (1 × 2 × 2) supercell of 32 atoms with x = 0.0625 of tetragonal structure with space group \(P\overline {4}2m\), Ga0.875 TM 0.125P (1 × 1 × 2) supercell of 16 atoms with x = 0.125 of tetragonal structure with space group \(P\overline {4}2m\), and Ga0.75 TM 0.25P (1 × 1 × 1) supercell of 8 atoms with x = 0.25 of cubic structure with space group \(P\overline {4}3m\).

We have taken the averages of non-overlapping muffin–tin radii (R MT) of Ga, P, V, Cr, and Mn in such a way that the muffin-tin spheres do not overlap. We have expanded the wave functions in the interstitial region to plane waves with a cutoff 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 = 12 a.u. -1, where G max is the largest vector in the Fourier expansion. The energy cutoff was chosen as - 6 Ry, which defines the separation of valence and core states. For the sampling of the Brillouin zone, (4×4×4), (4×4×2), and (2×2×5) Monkhorst–Pack mesh [41, 42] are utilized for supercells of 32, 16, and 8 atoms, respectively, where the self-consistent convergence of the total energy was at 0.1 mRy.

3 Results and Discussions

3.1 Optimization of Structures

To determine the analysis of the electronic and magnetic properties of GaGa−x TM x P (TM = V, Cr, and Mn) compounds, we calculated firstly the structural properties of compounds. The GaGa−x V x P, GaGa−x Cr x P, and GaGa−x Mn x P supercells are optimized by fitting empirical Murnaghan’s equation of state [43] of the variations of total energies as a function of equilibrium volumes. Our results of the equilibrium lattice constants (a), bulk modules (B) and its pressure derivatives (B ') of GaGa−x TM x P (TM = V, Cr, and Mn) compounds, various theoretical [8–10, 44], and experimental [45, 46] data are given in Table 1.

Table 1 Calculated of lattice constant (a), bulk modulus (B), and its pressure derivative (\(B^{\prime }\)) for GaP, and Ga ‘1-x TM x P (TM = V, Cr, and Mn) at concentrations (x = 0.0625, 0.125, and 0.25)
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The computed lattice constant (a = 5.446 Å) of GaP is very close to the theoretical value (5.448 Å) [44] by the same GGA-WC method [39] and stays in good agreement with experimental ones [45]. For the GaGa−x TM x P (TM = V, Cr, and Mn), we observed that the lattice constants decrease as the concentration of TM increases due to the smaller atomic radii of V, Cr, and Mn compared to the Ga atom, which signify that the local structure around the (V, Cr, and Mn) doping is slightly suppressed with the P atoms drawn closer to the (V, Cr, and Mn) atoms. We noticed that our computed lattice parameters of GaGa−x Cr x P and GaGa−x Mn x P with GGA-WC [39] are better than the theoretical calculations [8–10] with generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE) [47] due to better performance of GGA-WC approximation for structural optimization [22, 24, 48]. The calculated bulk modules of GaGa−x V x P, GaGa−x Cr x P and GaGa−x Mn x P increase with increasing of concentrations (x) of V, Cr, and Mn atoms, and this suggests that the compressibility of each compound increases with the increases in the concentration (x) of TM, and therefore the GaGa−x TM x P compounds become harder as the concentrations of vanadium, chromium, and manganese increase.

3.2 Electronic Properties with Half-Metallic Behavior

The plots of the spin-polarized band structures of GaGa−x V x P, GaGa−x Cr x P, and GaGa−x Mn x P with different concentrations (x = 0.0625, 0.125, and 0.25) are presented by Figs. 1, 2, 3, 4, 5, 6, 7, 8, and 9. They depicted that the top of valance band of the majority-spin crosses the Fermi level, while the minority-spin bands show a band gap around the Fermi level for GaGa−x V x P at concentrations (x = 0.0625, 0.125, and 0.25) and GaGa−x TM x P (TM = Cr and Mn) at (x = 0.0625 and 0.125). Consequently, these compounds show a half-metallic ferromagnetic (HMF) behavior. In contrast, the half-metallicity destroyed for GaGa−x Cr x P and GaGa−x Mn x P at higher concentration x = 0.25 because the majority-spin bands are metallic whereas for the minority spin bands the minimum of the conduction band broad strongly in the gap, resulting in metallic character, and thus the GaGa−x TM x P (TM = Cr and Mn) at x = 0.25 are metallic in nature.

Fig. 1
figure 1

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.9375 V 0.0625P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 2
figure 2

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.875 V 0.125P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 3
figure 3

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.75 V0.25P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 4
figure 4

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.9375Cr0.0625P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 5
figure 5

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.875Cr0.125P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 6
figure 6

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.75Cr0.25P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 7
figure 7

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.9375Mn0.0625P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 8
figure 8

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.875Mn0.125P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 9
figure 9

Spin-polarized band structures for majority spin (up) and minority spin (dn) for Ga0.75Mn0.25P. The Fermi level is set to zero (dotted line) (color figure online)

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Furthermore, for the HMF compounds the minority-spin bands exhibit two gaps; a half-metallic ferromagnetic (HMF) gap (E g) and a half-metallic (HM) gap (G hm). The HM gap is considered an important parameter to determine the application in spintronics [4], which is defined 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 majority (minority)-spin valence bands [49, 50]. The calculated HMF gap E g and the HM gap G hm of minority-spin channels with different concentrations are shown in Table 2. Our results show that the both HMF gap and HM gap decrease due to the broadening of the 3d (V, Cr, and Mn) bands in the gap as the concentrations of (V, Cr, and Mn) impurities increase. For GaGa−x Cr x P at concentrations x = 0.0625 and 0.125 and GaGa−x Mn x P at x = 125, the HMF gaps and HM gaps are lower than the other theoretical calculations [8, 9] due to the difference between our computed equilibrium lattice constants by the GGA-WC exchange correlation potential [39] and those found by GGA-PBE method [47]. Moreover, the minimal energy gap for a spin excitation is described by the HM gap [51], which has high values of 0.546, 4.64, and 0.43 eV at the lower concentration x = 0.0625 respectively for GaGa−x V x P, GaGa−x Cr x P, and GaGa−x Mn x P. The wide HM gap suggests a true half metallic ferromagnet and makes the GaGa−x TM x P (TM = V, Cr, and Mn) at low concentration potential candidates for spintronic applications.

Table 2 Calculated half-metallic ferromagnetic band gap E g, half-metallic gap G hm of minority spin, and half-metallic ferromagnetic (HMF) or metallic ferromagnetic (MF) behavior for GaGa−x TM x P (TM = V, Cr, and Mn) at concentrations (x = 0.0625, 0.125, and 0.25)
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The total (T) and partial (P) density of states (DOS) p of (Ga and P) and 3d (t 2g , e g ) of (TM = V, Cr, and Mn) for GaGa−x TM x P with different concentrations (x) are display by Figs. 10, 11, 12, 13, 14, 15, 16, 17, and 18. The 3 d(V, Cr, and Mn) minority-spin states are located above Fermi level, indicating that these states are empty, whereas the majority-spin states show strong hybridization between 3d (V, Cr, and Mn) and 3p (P) states that make the upper part of valence band. In this case, the t 2g states are situated above Fermi level for V atom, while they dominated the Fermi level for (Cr and Mn), and thus the 3 d − t 2g (TM) states are unoccupied and partially filled states respectively for GaGa−x V x P and GaGa−x TM x P (TM = Cr and Mn). However, in the DMS materials, the stabilization of ferromagnetic state is explained by the double-exchange mechanism when the delocalized anti-bonding states are partially occupied [52–54], and in the case of GaGa−x TM x P (TM = V, Cr, and Mn) doping systems, the partially filled 3d–t 2g (V, Cr, and Mn) majority-spin states suggest a ferromagnetic ground state associated with the double-exchange mechanism [55]. From the curves of the densities of states, we noted that GaGa−x V x P at concentrations (x = 0.0625, 0.125, and 0.25) and GaGa−x TM x P (TM = Cr and Mn) at (x = 0.0625 and 0.125) exhibit a half-metallic ferromagnetic character, this amounts to the presence of band gap in the minority spin and metallic nature of the majority spin that is a consequence of the strong p-d hybridization between two states as 3p (P) anions and 3d (V, Cr, and Mn) impurities. In contrast, for GaGa−x Cr x P and GaGa−x Mn x P at higher concentration x = 0.25, the 3d (Cr, and Mn) minority-spin states broaden strongly in the gap and cross the Fermi level, and hence these compounds are metallic ferromagnets.

Fig. 10
figure 10

Spin-polarized total and partial DOS of (3p) of P and (3d, 3d–e g , 3d– g ) of V in supercell for Ga0.9375 V 0.0625P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 11
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Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of V in supercell for Ga0.875 V 0.125P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 12
figure 12

Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of V in supercell for Ga0.75 V 0.25P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 13
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Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of Cr in supercell for Ga0.9375Cr0.0625P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 14
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Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of Cr in supercell for Ga0.875Cr0.125P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 15
figure 15

Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of Cr in supercell for Ga0.75Cr0.25P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 16
figure 16

Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of Mn in supercell for Ga0.9375Mn0.0625P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 17
figure 17

Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of Mn in supercell for Ga0.875Mn0.125P. The Fermi level is set to zero (dotted line) (color figure online)

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Fig. 18
figure 18

Spin-polarized total and partial DOS of (3p) of P and (3d, 3d– e g , 3d– t 2g ) of Mn in supercell for Ga0.75Mn0.25P. The Fermi level is set to zero (dotted line) (color figure online)

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3.3 Magnetic Properties

The computed total and local magnetic moments in the muffin–tin spheres and in the interstitial sites of the relevant (Ga, P) and transition metal (TM = V, Cr, Mn) atoms for all compounds are given in Table 3. In the GaGa−x TM x P DMSs, the each TM atom contributes three electrons to bonding states, and therefore the electronic configuration of tetrahedrally bonded (TM = V, Cr, and Mn) in GaGa−x TM x P systems are V +3 (\(d^{2}-e_{g}^{2} t_{2g}^{0}\)), Cr +3 (\(d^{3}-e_{g}^{2} t_{2g}^{1}\)), and Mn +3 (\(d^{4}-e_{g}^{2} t_{2g}^{2}\)). Based to Hund’s rule, the 3d (TM) majority-spin states are partially filled with two, three, and four electrons, respectively for V, Cr and Mn. This creates total magnetic moments of 2, 3, and 4 µ B (µ B is the Bohr magneton) respectively for GaGa−x V x P at concentrations (x = 0.0625, 0.125, and 0.25), GaGa−x Cr x P at (x = 0.0625 and 0.125), and GaGa−x Mn x P at (x = 0.0625 and 0.125), and hence these DMSs are true half-metallic ferromagnets.

Table 3 Calculated total and local magnetic moment (in Bohr magneton µ B) within the muffin–tin spheres and in the interstitial sites for GaGa−x TM x P (TM = V, Cr, and Mn) at concentrations (x = 0.0625, 0.125, and 0.25)
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Table 3 depicts that the magnetic moments of transition metal (V, Cr, and Mn) impurities are inferior to those predicted by Hund’s rule due to the p-d hybridization [18, 22, 23]. However, the major contributions of total magnetic moments are localized around the (V, Cr, and Mn) atoms and smaller local magnetic moments are induced in (Ga, P) and interstitial sites. The negative signs of the magnetic moments of (P) atoms revealed the anti-ferromagnetic interaction between valence band and 3d (V, Cr, and Mn) spins, while the ferromagnetic interaction is shown between Ga and 3d (V, Cr, and Mn) magnetic spins.

4 Conclusion

In this study, we have investigated the structural, electronic, and half-metallic ferromagnetic properties of GaGa−x TM x P (TM = V, Cr, and Mn) DMSs in zinc-blende phase at various concentrations x = 0.0625, 0.125, and 0.25 by using the FP-LAPW method within first-principles calculations of density functional theory with GGA-WC approximation. We found that GaGa−x V x P at concentrations (x = 0.0625, 0.125, and 0.25) and GaGa−x TM x P (TM = Cr and Mn) at (x = 0.0625 and 0.125) compounds are half-metallic ferromagnets (HMF) with 100 % spin polarization at the Fermi level. The HMF character destroyed for GaGa−x Cr x P and GaGa−x Mn x P at higher concentration x = 0.25. The HMF behavior is confirmed by the integral Bohr magneton of total magnetic moments of 2, 3, and 4 µ B respectively for V, Cr, and Mn doping systems, and the HMF materials exhibit high half-metallic gaps at low concentration x = 0.0625 of V, Cr, and Mn. Therefore, the GaGa−x TM xP DMSs at low concentrations (x) of (TM = V, Cr, and Mn) seem to be promising candidates for possible spintronic applications.