Characterization of electronic properties, exchange splitting and ferromagnetic arrangement in new Ti-doped BaO

We have studied the electronic structures, ferromagnetic properties, half-metallicity and exchange splitting in BaO doped with titanium such as Ba 1-x Ti x O at concentration x = 0.125. The structural parameters of BaO and Ba 0.875 Ti 0.125 O compounds are calculated with generalised gradient approximation of Wu and Cohen, while their electronic structures, accurate band gaps and magnetic properties are evaluated by the use of the Tran-Blaha-modified Becke-Johnson potential. The changes of lattice parameter and bulk modulus of Ba 0.875 Ti 0.125 O are discussed with respect to the BaO. We have found that the Ba 0.875 Ti 0.125 O has a wide half-metallic ferromagnetic gap of 2.701 eV and a half-metallic gap of 0.803 eV with integral Bohr magneton of 2 μ B , where its ferromagnetic state is characterised by the main contribution of the direct exchange splitting. Therefore, the Ba 0.875 Ti 0.125 O is true half-metallic ferromagnet with spin polarisation of 100 % and appears to be promising material for spintronics applications.


Introduction
Spintronics known as spin electronics is based on the use of the spin of electron plus its charge; it is an attractive field of research into spin-based physical phenomena and electronics [1,2]. In recent years, the diluted magnetic semiconductors (DMS) have been widely investigated as promising candidates for several spintronics applications. These compounds are characterised by intermediate properties that combine non-magnetic semiconductor and magnetic behaviours, which are obtained by doping non-magnetic semiconductors with magnetic elements for example transition metals and rare-earth [3][4][5]. The half-metallic ferromagnets DMS with spin polarisation of 100 % have been considered an important class of materials for spintronics because their electronic structures show a semiconductor feature in one direction of spins and a metallic character in the other spin channel [6,7]. However, spintronics processes the spin of the electron as well as its charge to obtain new functionalities in spin-based devices. The advantages of spintronics devices with respect to the conventional electronics are the non-volatility, high data processing speed, decreased electrical power consumption and high transistor density [8][9][10].
The barium oxide (BaO) is one of the alkaline-earth-metal binary oxides; it has wide band gap owing to its high ionicity [11]. This compound has several technological applications for example it is used as a buffer layer in the epitaxial growth of multifunctional perovskite oxides directly on silicon [11,12]. The alkaline-earth-metal binary oxides have been considered as potential materials for spintronics and optoelectronics applications [13][14][15]. The half-Metallic ferromagnetic property was predicted in the new class of DMS based on Cdoped MgO, SrO and BaO [13] and CaO doped with C and N atoms [14]. E. Albanese et al., [15] have investigated magnetic interaction and nature of isolated Nitrogen-dopants in bulk BaO (N-BaO) by the use of first-principles calculations of functional density theory. The BaO is a potential candidate for spintronics according to first-principle study carried out on its halfmetallic ferromagnetic behavior under the doping effect of magnetic chromium (Cr) impurities [16].
In this study, we investigated the structural properties, electronic structures, half-metallic ferromagnetic behaviour, exchange splitting and crystal field energy in titanium (Ti)-doped BaO such as Ba1-xTixO compound at concentration x = 0.125. The calculations were carried out by the first-principle approaches of full-potential linearised augmented plane-wave (FP-LAPW) method [17] within density functional theory (DFT) [18,19].

2 Method of calculations
The properties of the BaO and Ba1-xTixO compound at concentration x = 0.125 were investigated using the first-principle concepts of the FP-LAPW method and the DFT implemented in WIEN2k code [20]. The structural parameters of BaO and Ba0.875Ti0.125O are determined by the use of the generalised gradient functional of Wu and Cohen (GGA-WC) [21], while the Tran-Blaha-modified Becke-Johnson exchange potential (TB-mBJ) combined with the local density approximation [22,23] is employed to determine the magnetic moments, exchange constants, exchange splitting, crystal field energy and perfect electronic structures with accurate bands gaps of compounds under study.
The wave functions were extended in the interstitial region to plane waves with a cut-off of

Structural properties
The structural properties such as the lattice constants (a), bulk modules (B) and their pressure derivatives (B') of BaO and Ba0.785Ti0.125O compounds have calculated by fitting the empirical Murnaghan's equation of state [25]. The obtained results are given in Table 1 with other experimental data [26][27][28][29] and theoretical values [11,16,[30][31][32]. We have noticed that there are changes in the structural parameters (a) and (B) of Ba0.875Ti0.125O doping material compared to the BaO. This is due to the difference between the ionic radii of the Ba and O atoms. However, the lattice constant of Ba0.785Ti0.125O decreases with respect to the BaO, leading to the increase of its bulk modulus. Therefore, the Ba0.785Ti0.125O becomes harder than BaO. The behaviours of these two parameters of Ba0.785Ti0.125O compound were observed for BaO doped with Cr [7] and CaO doped with Ti [16]. It should be noted that there are no experimental and theoretical studies on Ba0.785Ti0.125O material in order to compare them with our results of structural parameters.
Moreover, the results of the lattice constant and bulk modulus of BaO are in good concordance with the experimental values [26][27][28] and theoretical calculations [16] found by GGA-WC [21]. Also, these parameters are better than the theoretical values [11,16,[30][31][32] calculated with generalised gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) [33] and the local density approximation (LDA) [34] with respect to the experimental values, meaning that the GGA-WC [21] provides good results for the structural parameters. The performance of GGA-WC potential compared to other approximations for determining structural properties results from the fourth order of expansion of its gradient of exchange and correlation functional [21,[35][36][37].   Table 2 summarise the values of direct band gap E XX of BaO, HMF gap GHMF and HM gap GHM of minority-spin bands of Ba0.875Ti0.125O with other theoretical [11,16,30,38,39] and experimental [40][41][42] values. The Ba0.875Ti0.125O has direct HMF gap of 2.701 eV situated at the  high symmetry point and its HM gap is 0.803 eV located between the valence band maximum and Fermi level. The wide gap of BaO of 3.5 calculated with the TB-mBJ is more improved with respect to the theoretical values [11,16,30,38,39] found by the GGA-WC [21], GGA-PBE [33] and LDA [34] approximations. The better gap of BaO is due to the performance of TB-mBJ semi-local exchange correlation potential for predicting band gaps of semiconductors and insulators [23,43,44].

Electronic structures and Half-metallic characteristic
The projected total and partial densities of states (DOS) of Ba0.875Ti0.125O are given by the states as shown in Fig. 4. In addition, the 3d states of titanium (Ti) ion are splitted into t2g partially occupied states and eg empty states due to the octahedral crystal field environment produced by neighbouring oxygen (O) ions. From Fig. 3, we can see clearly that the total-DOS is metallic for the majority spins but a band gap occurs around Fermi level (EF) for the minority spins. Therefore, the Ba0.875Ti0.125O is half-metallic ferromagnetic with 100 % spin polarisation and it can be considered as a potential compound for spintronics applications.

Magnetic Moments
The origin of magnetism in the compound Ba0.875Ti0.125O is due to the localisation of the partially occupied 3d states of Ti of the majority spins around EF. The Fig. 4 of partial DOS of majority spins shows that the eg states are unoccupied, while the t2g states are two-thirds filled which means that they are partially occupied by two electrons. Therefore, the two unpaired electrons created a total magnetic moment of 2 μB, where the μB is the Bohr magneton. The computed total and partial magnetic moments of Ba, Ti and O atoms and in the interstitial sites of Ba0.875Ti0.125O compound are given in Table 3. We have found that the magnetic moment of Ti of 1.778 μB is reduced less than 2 μB and small magnetic moments are induced at the Ba, O and interstitial sites owing to the p-d interaction. The negative magnetic moment of oxygen (O) means that the interaction is anti-ferromagnetic between the (Ba, Ti) and O 6 magnetic spins. The ferromagnetic interaction is generated between Ba and Ti owing to their positive magnetic moments.

Exchange couplings
The exchange couplings between the conduction and valence bands and 3d (Ti) states are explained by the N0α and N0β exchange parameters. The N0α determines the s-d exchange coupling between the s-type conduction and 3d (Ti) states, whereas the p-d exchange coupling between the p-type valence and 3d (Ti) states is described by the N0β. These two important parameters are calculated by using the mean-field theory, given by the following expressions [45,46] : correspond respectively to the conduction and valence band-edge spin-splittings at Γ high symmetry point of spin-polarised band structures of Ba0.875Ti0.125O. The  s is the half computed total magnetic moment per Ti and x = 0.125 is the concentration of Ti atom [45]. Table 4 gives the calculated N0α and N0β exchange parameters of Ba0.875Ti0.125O compound. Its shows that the N0α is positive and N0β is negative, which suggest that the exchange couplings between 3d (Ti) and conduction and valence bands are respectively ferromagnetic and anti-ferromagnetic.

Crystal field energy and exchange splitting
The magnitude of ferromagnetism is measured by the use of other factors such as crystal field energy and direct exchange splitting. The crystal field energy ) ( . This result is revealed by the smaller value of 3.755 eV of the direct exchange splitting compared to the crystal field energy of 4.136 eV as seen in Table 4. This kind of process means that the ferromagnetism state is more favourable by the contribution of the crystal field energy compared to the indirect exchange.

Conclusion
We have used the GGA-WC approximation and the TB-mBJ semi-local exchange correlation potential to characterise the structural properties, electronic structures, half-metallic Ba0.875Ti0.125O is more favourable by the crystal field contribution than that of the direct exchange splitting. Therefore, the Ba0.875Ti0.125O doping material is an accurate half-metallic ferromagnet and it can be predicted as a potential candidate for possible applications in semiconductors spintronics.

Disclosure statement
No potential conflict of interest was reported by the author(s).