Recent Insights Into Electronic Performance, Magnetism and Exchange Splittings in the Cr-substituted CaO

The first-principles computations of density functional theory are employed to characterize the structural properties, electronic structures, and ferromagnetism induced by Cr impurities in Ca1-xCrxO compounds at concentrations x = 0. 25, 0.5, and 0.75. The dynamic stability is performed by the phonon spectra calculations. The structural parameters are computed by using Wu-Cohen generalized gradient approximation, while the electronic and magnetic properties are determined by the accurate Tran–Blaha-modified Becke–Johnson exchange potential. The crystal field, direct and indirect exchange splittings were investigated to determine the origin and stability of ferromagnetic state configuration. The Ca1-xCrxO systems have right half-metallicities, which are verified by the spin polarization of 100% and the integer values of total magnetic moments. The Ca0.75Cr0.25O, Ca0.5Cr0.5O, and Ca0.25Cr0.75O are half-metallic ferromagnetic with flip-gaps of 1.495, 0.888, and 0.218 eV, respectively. Therefore, the Ca1-xCrxO materials are suitable candidates for possible applications of spin-injection in future semiconductors spintronics.


INTRODUCTION
In recent years, the exploitation of new materials for technological development has become an attractive area of research for the scientific community. Spintronics is a modern field emerging from quantum electronics relating to exploration and control of the electron spin; it is currently an important research topic because the spin-based devices have interesting multifunctional characteristics such as non-volatility, data-processing speed, higher integration densities (Elilarassi and Chandrasekaran, 2017;Rai et al., 2018). In the last years, the half-metal ferromagnetic (HMF) materials have attracted considerable interest due to their wide application in spintronic devices as magnetic sensors, tunnel junctions, and spin injection sources of electrons (Özdemir and Merdan, 2019). The diluted magnetic semiconductors (DMSs) are obtained from the III-V, II-VI, or IV-VI semiconductors doped with magnetic elements, inducing changes in their structural, electronic, and magnetic properties, which are related to the concentration of magnetic impurities. These materials have received a lot of attention for scientific research because they are promising candidates for innovative applications in spintronics, as an example for non-volatile memories, optical switches, and magneto-optical devices (Ohno, 1998;Dietl et al., 2000;Wolf et al., 2001;Zuti et al., 2004;Sato et al., 2010;Kumar et al., 2014).
Alkaline earth chalcogenides are important materials with a wide technological application ranging from catalysis to microelectronics as well as in the area of electro-and photoluminescent devices (Hakamata et al., 2005;Speziale et al., 2006;Murtaza et al., 2014). Among these compounds, the CaX (X = O, S, Se) has a closed-shell ionic environment, crystallizing in the rock-salt NaCl-type (B1) structure at ambient conditions (Doll et al., 1996;Mishra et al., 2012). Under high pressure, they undergo a first-order structural phase transition from the NaCltype (B1) to the CsCl-type (B2) crystal structure (Luo et al., 1994;Doll et al., 1996;Dadsetani and Doosti, 2009;Mishra et al., 2012). The CaO calcium oxide can be a potential candidate as a DMS material according to several theoretical studies (Kenmochi et al., 2004;Kemmochi et al., 2005;An Dinh et al., 2006). Kenmochi et al. (2004) have studied a new class of DMSs based on CaO without transition metals, where the substituted CaO by C and N at the oxygen sites shows room-temperature ferromagnetism with half-metallic property. The ferromagnetism in C-doped CaO is explained by the exchange coupling constants, where it is induced by the strong hybridization between 2p states of carbon and 2p states of oxygen (An Dinh et al., 2006). Further, Kemmochi et al. (2005) have found that the stability of ferromagnetic state in the C-doped CaO is originated from the Zener's double-exchange mechanism.
In this study, we have investigated the structural parameters, electronic performance, magnetism, and exchange splittings of Ca 1-x Cr x O materials at various concentrations x = 0, 0.25, 0.5, and 0.75. The calculations are performed by the use of first-principle approaches of density functional theory (DFT) (Hohenberg and Kohn, 1964;Kohn and Sham, 1965) as implemented in the WIEN2k package (Blaha et al., 2001). The phonon spectra are used to verify the dynamic stability of Ca 1-x Cr x O materials. The exchange and correlation potential is evaluated by the generalized gradient approximation of Wu and Cohen (GGA-WC) (Wu and Cohen, 2006), and the Tran-Blaha-modified Becke-Johnson potential (TB-mBJ) (Tran and Blaha, 2009).

COMPUTATIONAL METHODS
The calculations of structural, electronic, and magnetic properties of Ca 1-x Cr x O are carried out using the WIEN2k code (Blaha et al., 2001) based on the first-principle computations of DFT and the full-potential linearized augmented planewave (FP-LAPW) method (Singh and Nordstrom, 2006). We have computed the structural parameters using GGA-WC approximation (Wu and Cohen, 2006), while the electronic and magnetic properties are determined by employing the TB-mBJ exchange potential (Becke and Johnson, 2006;Tran and Blaha, 2009). The phonon frequencies are determined by the phonopy code (Togo and Tanaka, 2015) based on the density functional perturbation theory (Giannozzi et al., 1991;Gonze and Lee, 1997). The phonon spectra are calculated using the WIEN2k and the phonopy packages to verify the dynamic stability of Ca 1-x Cr x O doping compounds.
The averages of Muffin-tin spheres radii are selected for Ca, Cr, and O atoms in condition that Muffin-tin spheres do not overlap. The cutoff of −6 Ry is utilized to separate between the valence and core states. The basic functions and the potentials are extended in combination of spherical harmonics around the atomic sites, that is to say, the atomic spheres with a cutoff l max = 10, and in the interstitial region are extended into plane waves with a cutoff R MT k max = 8 (where R MT is the average radius of the Muffin-tin spheres). We have expanded the charge density in Fourier up to G max = 14 (a.u.) −1 , where G max represents the largest vector in the Fourier expansion. The calculations were performed for structures of eight (8) (Monkhorst and Pack, 1976) using the special k-points of (10 × 10 × 10) for CaO and (5 × 5 × 5) for Ca 0.75 Cr 0.25 O, Ca 0.5 Cr 0.5 O, and Ca 0.25 Cr 0.75 O compounds. The self-consistent is achieved when the total energy convergence condition was set to be 10 −1 mRy.

Crystal Structures
The calcium oxide CaO is known as a wide-band gap II-VI semiconductor, crystallizing in rock-salt NaCl (B1) structure at ambient conditions (Doll et al., 1996;Mishra et al., 2012). The primitive unit cell of CaO contains two atoms such as the calcium (Ca) and the oxygen (O), which belong, respectively, to the main groups II and VI of the periodic table. Our study is based on the conventional NaCl structure of eight atoms of CaO such as Ca 4 O 4 , where the Ca is located at (0, 0, 0) position and the O atom at (0.5, 0.5, 0.5) with space group of Fm3m No. 225. The Ca 3 CrO 4 , Ca 2 Cr 2 O 4 , and CaCr 3 O 4 supercells are created by substituting one, two, and three Cr impurities at Ca sites, respectively. Consequently, we have obtained three supercells such as

Structural Stability
The structural stability of the Ca 1-x Cr x O compounds in the ferromagnetic rock-salt NaCl (B1) structure is verified by computing the formation energies. The formation energies (E form ) of the Ca 4-y Cr y O 4 materials are determined using the following expression (Bai et al., 2011;Doumi et al., 2015a): where E total (Ca 4-y Cr y O 4 ) corresponds to the minimum total energy of Ca 4-y Cr y O 4 per atom, and E(Ca), E(Cr), and E(O) refer to the minimum total energies per atom of bulks Ca, Cr, and O, respectively. The y = 1, 2, and 3 are the number of substituted Cr impurities in Ca 4-y Cr y O 4 supercells. We have found that the formation energies are −5.99, −6.37, and −6.76 eV, respectively, for Ca 0.75 Cr 0.25 O, Ca 0.5 Cr 0.5 O, and Ca 0.25 Cr 0.75 O. Therefore, the negative values of formation energies suggest that these compounds are thermodynamically stable in the ferromagnetic rock-salt structure. Furthermore, we have used the phonon spectra to demonstrate the dynamic stability of the Ca 1-
The results of lattice constants and bulk modulus of CaO are closed to theoretical values of Tran et al. (2007) and Fan et al. (2015) calculated with GGA-WC potential (Wu and Cohen, 2006). We see that there is a good agreement between our calculations and experimental results (Mammone et al., 1981;Kaneko et al., 1982;Richet et al., 1988) and theoretical value found by GGA-PBE sol (Perdew et al., 2008). On the other hand, the obtained values of these parameters with GGA-WC (Wu and Cohen, 2006) 2015), and Santana et al. (2016) found, respectively, by GGA-PBE (Perdew et al., 1996) and LDA approximation (Perdew and Zunger, 1981;Perdew and Wang, 1992). The performance of GGA-WC approximation for predicting structural parameters is due to the fourth-order gradient expansion of exchangecorrelation functional (Doumi et al., 2015b;Sajjad et al., 2015).

Band Structures and Half-Metallicity
We have used the predicted structural parameters to characterize the electronic structures and the half-metallicity in Ca 1- According to Figure 4, the CaO is a semiconductor because both majority and minority spins revealed the analogous band structures with indirect gaps. The CaO has an indirect gap(E ŴX ) between the valence bands maximum and conduction bands minimum situated, respectively, at Γ and X high symmetry points. Figures 5-7 demonstrate that the Ca 1-x Cr x O for all concentrations are metallic and semiconductors, respectively, for majority-and minority-spin bands. Consequently, the Ca 1-x Cr x O doping materials are half-metallic ferromagnets. The metallic character is due to localized partially filled 3d-Cr states of majority spins around Fermi level (E F ), which interact with carriers of valence states of host semiconductor. For minority spins, the Ca 1-x Cr x O doping systems keep a semiconductor behavior as CaO compound because the 3d-Cr empty minorityspin states arise in the bottom of conduction band minimum at Γ high symmetry point far than E F . Thus, the gap nature shifted from indirect band gap for CaO to direct gap for Ca 1-x Cr x O doping systems.
The minority spins of Ca 1-x Cr x O systems are characterized by direct wide-band gaps called half-metallic ferromagnetic (HMF) gaps located at the Γ high symmetry point. The minimal energies that separate the Fermi level (zero eV), and the conduction band minimums determine the half-metallic (HM) gaps. Table 2 shows the computed band gaps such as the direct HMF gaps   (Fan et al., 2015;Nejatipour and Dadsetani, 2015;Yang et al., 2016;Tran and Blaha, 2017;Salam, 2018) and experimental data (Whited et al., 1973). The result of wideindirect gap of 5.392 eV of CaO is in good agreement with recent calculated value of 5.35 eV of Tran and Blaha (2017) study using the same TB-mBJ potential (Becke and Johnson, 2006;Tran and Blaha, 2009), and it is better than the values ranging from 3.437 to 3.67 eV of Fan et al. (2015), Nejatipour and Dadsetani (2015), Yang et al. (2016), Tran and Blaha (2017), Salam (2018) found by the LDA (Perdew and Zunger, 1981;Perdew and Wang, 1992), GGA-WC (Wu and Cohen, 2006), GGA-PBE (Perdew et al., 1996), and GGA-PBEsol exchange potentials (Perdew et al., 2008). The TB-mBJ provides accurate gap for CaO because he is known for its performance in the calculation of electronic structures of insulators and semiconductors with respect to LDA and all forms of GGA approximations (Bhattacharjee and

Densities of States and Spin Polarization
In order to understand the origin of half-metallic feature induced by the substituting effect of Cr, we have plotted the total and partial densities of states (DOS) of Cr, Ca, and O atoms of Ca 1-x Cr x O compounds. Figures 8-10    The spin-polarized material is known by its spin polarization of electronic structures, which is an important factor for characterizing a half-metal. The polarization (P) of half-metal compound results from the different contributions of numbers of DOS around E F . It is determined from the following expression (Soulen et al., 1998;Wang et al., 2017): where N ↑ (E F ) and N ↓ (E F ) indicate, respectively, the DOS of majority and minority spins at E F . From Figures 8-10A, the density of states N ↓ (E F ) equals zero because the DOS do not cross E F , leading to a spin polarization of 100%. Therefore, the Ca 1-x Cr x O compounds appear to be suitable candidates for possible spin-injection in spintronics applications.

Magnetic Moments
The spin-polarized electronic structures show an asymmetric character, indicating that the Ca 1-x Cr x O compounds are magnetic in nature. The magnetism is induced by the magnetic spins arising from the localized 3d-Cr majority-spin states around E F . The Cr impurity contributes two electrons to host carriers of valence bands, resulting in Cr +2 ion. Thus, the 3d-Cr states become partially filled with four electrons. Therefore, the magnetism is originated from the four itinerant electrons of Cr +2 ions in Ca 1-x Cr x O doping materials. From the DOS of majority spins, one can see that the nonbonding states enclose three low-lying t 2g levels, which are completely occupied by three electrons. In contrast, the two highlying e g states have an anti-bonding nature, which are partially occupied by one electron because they are crossed by Fermi level in the middle. According to the Hund's rule, the 3d-Cr states generate a total magnetic moment of 4 µ B per Cr ion. Consequently, the Ca 0.75 Cr 0.25 O, Ca 0.5 Cr 0.5 O, and Ca 0.25 Cr 0.75 O compounds have total magnetic moments of 4, 8, and 12 µ B , respectively, for one, two, and three Cr doping impurities.
The calculated total and partial magnetic moments of Ca, Cr, and O atoms and in the interstitial sites for Ca 0.75 Cr 0.25 O, Ca 0.5 Cr 0.5 O, and Ca 0.25 Cr 0.75 O are given in Table 3. The total magnetic moment per Cr atom is an integer number of 4 µ B . It is a typical feature of half-metallic materials Zhang et al., 2017). All compounds have negative partial magnetic moments for O atoms, revealing that carriers of host valence bands enclosing p-O states interact anti-ferromagnetically with 3d-Cr states. Besides, the positive partial magnetic moments of Cr and Ca atoms describe the ferromagnetic interaction between Cr and Ca magnetic spins.

Exchange Splitting Mechanisms
The ferromagnetism is created from the localized electrons of t 2g and e 2g of 3d-Cr states mediated by holes, where the empty holes of e g states occur at the top of valence band and generate an acceptor hole type carrier hybridizing with carriers of host valence band (Doumi et al., 2013). The degenerate 3d-Cr into t 2g and e 2g is due to crystal field generated from the electrostatic environment of surrounding oxygen (O) ions, where the 3d-Cr majority-spin levels contain four unpaired electrons (Noor et al., 2018). According to the Hund's rule, this kind of process mediates magnetism in Ca 1-x Cr x O materials (Yaqoob et al., 2019). It is understood that both exchange splitting of 3d-Cr states and crystal field take part in the contribution of ferromagnetism in Ca 1-x Cr x O doping materials.
The magnitude of crystal field energy ( E CF ) is defined as a difference between E eg and E t2g energies of e g and t 2g states E CF = E eg − E t2g . The direct exchange splitting energy  The values of E CF , x (d), and x (pd) exchange splitting are shown in Table 4. The obtained values of ( E CF and x (d)) are (1.71 and 4.98 eV), (2.97 and 4.90 eV), and (1.74 and 5.17 eV), revealing that the direct exchange splittings are more dominated compared to the crystal field splittings. Therefore, the ferromagnetism state is mainly favored by the contribution of direct exchange splitting mechanism than that of crystal field (Amin et al., 2018)  x (pd), meaning that magnetic moment of Cr is directly related to the indirect exchange splitting. On the other hand, the attraction nature of spin-polarized electrons is measured from the indirect exchange splitting (Verma et al., 2011;Mahmood et al., 2016Mahmood et al., , 2018. The indirect exchange splittings x (pd) have negative values because the valence band maximums of minority-spins are situated at lower energies with respect to the valence band maximums of majority-spins. This means that the minority-spins have more attractive (negative) potential than that of majority-spins, leading to perfectly localized magnetic states. Consequently, the ferromagnetism is preferred in the Ca 1-x Cr x O compounds. In the DMS based on III-V and II-VI semiconductors doped with transition metals, when the d states of magnetic dopants are partially occupied (Sato and Katayama-Yoshida, 2002;Sato et al., 2003a,b), the stability of ferromagnetism is described by the double-exchange mechanism (Akai, 1998). According to this rule, the anti-bonding states of partially filled 3d-Cr atoms associated with double-exchange mechanism stabilize the ferromagnetic state configuration in Ca 1-x Cr x O.
The magnitudes of valence and conduction band edge splitting are measured by the two sp-d exchange constants N 0 α and N 0 β. The N 0 α parameter determines the s-d exchange interaction between the s carriers of conduction bands and d-Cr levels, while the N 0 β describes the p-d exchange coupling between the p states of carriers of valence bands and d-Cr levels. We have used the mean field theory (Sanvito et al., 2001;Raebiger et al., 2004) to calculate the exchange constants of Ca 1-x Cr x O compounds given by the following relations. The c difference energies correspond, respectively, to the valence band-edge and conduction band-edge spin-splittings at Γ high symmetry point. The s and x are the half total magnetic moment per Cr and the concentration of Cr, respectively (Sanvito et al., 2001). The calculated E v , E c , N 0 α, and N 0 β are summarized in Table 5. Yaqoob et al. (2019) have predicted that the negative values of N 0 α and N 0 β are due to the quantum confinement effect or structural symmetry changes that modify the coupling of different states. For Ca 1-x Cr x O materials, the negative values of N 0 α and N 0 β describe the anti-ferromagnetic coupling between the valence and conduction bands and the 3d states of magnetic Cr atoms.

CONCLUSIONS
We have characterized the structural properties, the spinpolarized electronic structures, and ferromagnetic performance induced by the Cr impurities in Ca 1-x Cr x O compounds at concentrations x = 0, 0.25, 0.5, and 0.75. The Ca 1-x Cr x O doping materials are dynamically stable due to their positive phonon frequencies. The structural parameters and indirect gap of CaO are very significant with respect to the recent calculations found by GGA-WC and TB-mBJ. For Ca 1-x Cr x O, the lattice constant decreases with increasing Cr concentration, leading to the increase in bulk modulus, where the sizes of the ionic radii of Ca and Cr atoms are the factors determining these changes. The Ca 1-x Cr x O systems have a half-metallic ferromagnetic feature, where the ferromagnetism is favored by the large contribution of direct exchange splitting than that of the crystal field. The analysis of magnetic properties shows that both double-exchange and p-d exchange mechanisms participate to stabilize ferromagnetic state configuration. The half-metallic ferromagnets Ca 1-x Cr x O compounds maintain a half-metal gap feature for all concentrations with spin polarization of 100%, making them suitable spin-injection candidates for possible exploration in semiconductors spintronics.

DATA AVAILABILITY STATEMENT
All datasets presented in this study are included in the article/supplementary material.

AUTHOR CONTRIBUTIONS
With the submission of this manuscript, all authors declare that the manuscript is original. All authors of this research paper have contributed to this manuscript. All authors of this paper have read and approved the final version submitted. The contents of this manuscript have not been copyrighted or published previously. The contents of this manuscript are not now under consideration for publication elsewhere.