Electronic, magnetic and optical properties of XScO3 (X=Mo, W) perovskites

Density Functional Theory (DFT) full potential linearized augmented plane wave (FP-LAPW) method with the Modified Becke-Johnson (mBJ) approximation is used to perform spin polarised calculations of the transition metal perovskites MoScO3 and WScO3. Both depict half metallic behaviour with semiconducting and metallic in the minority and majority spins respectively. MoScO3 and WScO3 have indirect R− Γ band gaps in the minority spin channels of 3.61 and 3.82eV respectively. Moreover, they both show substantial magnetic moments of 2.99μB. In addition, we calculate the dielectric function, optical conductivity and the optical constants, namely, the refractive index, the reflectivity, the extinction and absorption coefficients.


Introduction
The recent years has seen a lot of research on perovskites for potential applications in electronics, photovoltaics, renewable energy and innumerable other industries [1][2][3]. The universal structural formula of a perovskite is ABX 3 and the cubic form is the most ideal case. X atom is usually oxygen. It could also be a halide. A/B atoms are in general alkali, alkali earth, rare earth or transition metals [4,5]. Thus, an enormous variety of structural modifications and variants are possible which can accommodate almost all of the elements in the periodic Table. The flexibility in choice of atom types gives rise to a multitude of perovskite structures with interesting electronic, magnetic and optical properties and motivates the continued interest in this family [6][7][8]. Transition metals (TM) are exceptionally valuable and allow for complex magnetic interactions depending upon the local environment and dimensionality to give intriguing magnetic, magnetoelectric, multiferroic, piezoelectric properties [9][10][11] and even induce non-magnetic materials to become magnetic [12,13]. Thus, transition metal (TM) perovskites are of special interest and past research show a wide range of electronic, magnetic and optical properties owing to the complex nature of TM ion interactions with oxygen or halides [14,15]. It is mainly the unfilled or filled'd' bands of the TM that are responsible for the electronic/magnetic and dielectric properties respectively. In most of the previous studies on TM perovskites, the TM occupies the B site. Recently, we explored the effect of 3d-filling on the electronic, magnetic and optical properties on TMScO 3 perovskites where the TM (from Ti to Zn) sits on the A site [16]. The materials show half metallic behavior with wide band gaps, except for TiScO 3 and VScO 3 which are metallic and semiconducting. As, a further study, in the current work we explore the electronic, magnetic and optical properties with TM Mo and W which are isoelectric to Cr in group VI i.e. MoScO 3 and WScO 3 perovskites. The purpose of the paper is to give the essential and accurate theoretical information of the optoelectronic properties of these perovskite compounds, which are being investigated for the first time for possible technological applications and further research. The perovskites MoScO 3 and WScO 3 are investigated using the full-potential linearized augmented plane wave (FP-LAPW) DFT method with the wein2k software program. The paper is arranged as follows: section 2 gives the Calculation details, section 3 is devoted to the Discussion of results under the sub headings_ Structural and electronic; Magnetic and Optical properties, finally section 4 presents the Conclusions.

Calculation details
The full-potential linearized-augmented plane wave (FP-LAPW) method as implemented in the WIEN2k [17] code based on DFT [18] is used to calculate the spin polarized ground states of the pervoskites. We have used generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) [19] to calculate the optimized structures at a 10×10×10 kpoint grid. The optimized lattice constant values have then been used with the more accurate Modified Becke-Johnson (mBJ) exchange correlation of Trans Blaha [20] to evaluate the electronic, magnetic and optical properties using denser grids of 15×15×15 and 30×30×30 for electronic/magnetic and optical properties respectively. In order to achieve energy eigenvalues convergence, the wave functions in interstitial region were expanded in plane waves with a cutoff of Kmax set to 8; Kmax gives the magnitude of the largest K vector in the plane-wave expansion. The muffin-tin radii (RMT), which denotes the smallest atomic sphere radius are taken to be 2.5 and 2.7 a.u for Mo, W respectively and 1.60 a.u for Sc and O atoms. The Brillouin zone integrations within the self-consistency cycle are performed via a tetrahedron method [21] using 120 k points in the irreducible wedge of the Brillouin zone (IBZ) for all compounds. The self-consistence calculations have convergence tolerance thresholds of less than 10 -4 Ry in energy and 10 -4 in electron charges.

Structural and electronic properties
The MoScO 3 and WScO 3 Perovskites in the cubic form with space group is Pm-3m (#221) contains one formula unit and the Mo/W, Sc and O atoms are positioned at 1a (0, 0,0), 1b (½, ½,½) and 3c (0,½, ½) sites of Wyckoff coordinates, respectively. The lattice constants of XScO 3 structures are optimized using Murnaghan equation of state [22] and the energy vs volume curves are presented in Figure1 along with the structure visualization. Since, the structure is cubic only volume optimization is required. The optimized lattice constants, bulk moduli, Fermi and total energies at the minimum energy equilibrium state are shown in Table 1. We notice that the lattice constant of the perovskites decreases slightly with increasing atomic numbers of the TM. Although, the individual ionic radii of Mo and W are comparable the decrease in size of the compounds can be attributed to the change in electronic density and changes in the occupation of the band orbitals in new molecular environment. The mbj exchange potential has consistently proved to give accurate and very reliable band structures comparable to that of GW or hybrid functionals. After the structural optimization using GGA-PBE, our electronic and optical calculations have been performed using mBJ to obtain highly accurate band structures of the perovskites and reliable results for all the optical properties under investigation. The MoScO 3 and WScO 3 band structures along the high symmetry points are shown in Figures 2 and 3 respectively. As seen from Fig. 2, MoScO 3 shows interesting semi-conducting behavior in the minority spin with an indirect R−Γ of 3.61eV which predominates over the direct Γ−Γ gap of 3.64eV. In fact we see that the difference between valence band maximum (VBM) at the R and Γ points are very close, with just a difference of 0.033eV. A direct bandgap is very favorable since excitation is possible with photons of energy equivalent or higher than the band gap, and gives stronger emission or absorption properties for potential applications in photovoltaics (PV), light emitting diodes (LED) etc. The indirect band gap requires both a photon and phonon for excitation of electrons from the valence to conduction band; nevertheless, it has also useful applications in optoelectronics. The Majority channel in Fig.2 (b) shows a slight metallic behavior with only very few valence bands at the beginning of the conduction band. In Fig. 3 the WScO 3 band structures are depicted and in contrast to MoScO 3 we see a more pronounced half metallic behavior. The minority band shows an indirect R−Γ gap of 3.82 eV and the majority spin band is strongly metallic with valence bands deep in the conduction band. Such a feature has potential application in spintronics. Table 2 presents a summary of the band structure results. For the sake of comparison the values for CrScO 3 is also shown from reference [16].

Magnetic properties
Although the TM are paramagnetc and individually do not show any magnetism, the Mo/WScO 3 pervoskites are magnetic. This is due the local environment and the complex interactions of the TM d orbitals with the Sc and O 2 atoms. Sc does not seem to play any major role in the magnetism as indicated by the spin polarized total density of states (TDOS) plots Fig. 3 and 4.  The TDOS for WScO3 in Fig.5 Table 3. Table 3 lists the total magnetic moments: atom wise, interstitial and of the perovskite compounds. We notice from the table that the perovskites have very similar total moments. This is as expected since Mo and W belong to the same group VI elements and are isoelectric. The magnetic moment of the compounds arises mainly from the TM with unfilled d bands. For the sake of comparison the corresponding values for CrScO 3 has been included from reference [16].

Optical properties
Knowledge of the optical properties of a compound is crucial and fundamental for many applications and applied research. It is highly important to have a very dense grid and an accurate exchange correlation in the FP-LAPW to calculate the complex dielectric function that takes into account the self-energy and local field corrections. The TB-mBJ proves to be an excellent choice with a 30×30×30 grid for our optical properties calculations to obtain a high degree of accuracy of results. In this section we present the results for the dielectric function, optical conductivity and the important optical constants namely, the refractive index, the reflectivity, the extinction and absorption coefficients. The complex dielectric function (ε = ε 1 + iε 2 ) is a function of the amount of light absorbed by the material. The imaginary part of dielectric function, ε 2 (ω) , which represents absorption behavior, can be calculated from the electronic band structure of solids [23]. The real part of dielectric function, ε 1 (ω), can be calculated according to Kramers-Kroing relation [24,25] which represents the electronic polarization under incident light. Fig. 6 shows the real and imaginary plots for the dielectric function for the Mo/WScO 3 perovskites in the photon energy range of 0-14eV. We see from the plots that the active spectral region is within 2eV, beyond which the graphs are flat. The static dielectric constants are those at ω=0, and we notice that the ε 1 value of MoScO 3 is more than double that of WScO 3 indicating a very much higher dielectric constant.
The negative values for ε 1 (ω) indicate a metal like behavior in these very low photon energies with complete reflection of light. Moreover, in Fig.6(b) the ε 2 (ω) peaks are also more than twice that of WScO 3 , implying much higher absorption capabilities. The peaks occur at low photon energy around 1 eV and indicate transitions of valence oxygen '2p' electrons to low lying conduction 4/5d bands. The complex index of refraction of the medium N is defined as Where, n is the usual refractive index and k is the extinction coefficient. Using the values of ε 1 and ε 2 we can obtain the refractive index n, reflectivity, and the extinction and absorption coefficients from the equations (2) The refractive index and reflectivity plots are shown in Fig. 7(a) and (b) respectively in the photon energy range 0-14eV, which captures all the necessary features. Refractive index is a function of incident frequency and the graphs display maximum peak values around ω =0, with a decrease in values as we go towards higher frequencies. Both MoScO 3 and WScO 3 have large refractive index values of 10.6 and 5.7 respectively as a result of the high electron densities in these materials [5]. The refractive index shows an almost constant and optically isotropic behavior at high energies > orange. The reflectivity is a maximum in the visible energy range, and the materials could be used be used as reflective coatings in this range. Beyond this we observe an almost constant region with very small reflectance values in 3-8 and 2-8eV for MoScO 3 and WScO 3 respectively. This region of the spectra therefore provides good ultraviolet (UV) and higher energy absorption. It is well known that the materials with band gaps larger than 3.1 eV as in the present case, work well for applications in the UV region of the spectrum [26]. After 8eV we see steady increases to reach ~0.6 for both compounds. In Table 4 we list the energies of the zeros of ε 1 (ω) and static values of the refractive index, the reflectivity and absorption coefficients. Table 4 The zero y-values of ε 1 (ω) and the static optical constants at ω=zero; dielectric constant ε 1 (0), static refractive index n(0), static reflectivity R(0) and static absorption coefficient I(0) XScO3 perovskite compounds.

Compound
Zeros of ε 1 (ω) [eV] ε 1 (0) n(0) R(0) I(0) The optical conductivities and absorption coefficients are shown in Fig 8. From the graphs we notice that both the pervoskites have good optical conductivities in the visible range and also high absorption coefficients making them excellent for optoelectronic applications.

Conclusions
In conclusion, this is the first investigation of the pervoskites Mo/WScO 3 using DFT, full potential linearized augmented plane wave method with mBJ approximation to obtain accurate electronic, band structures, magnetic and optical properties. The results indicate that the compounds are half metals with semiconducting in the minority and metallic behaviour in the majority spin channels. Moreover the considerable band gap and sizeable magnetic moment makes these materials very suitable for spintronic applications.
In addition the optical spectral properties in the energy range of 0-14eVfor the dielectric function and optical constants gives a reliable and through understanding of potential application of these