3.3 Origin of Half-metallicity and magnetism
First principle calculations on electronic structure plays a pivotal role in understanding the multi-scale modelling of materials not only it revails accurately the physical as well as chemical properties of materials but also supports the adjustment of parametres (or potentials) in higher scale methods such as classical molecular dynamics, cluster dynamics etc. In a similar manner, electronic properties provides a wayout to define the possible applications of the materials in various subject areas of research. Therefore paves an adequate interests regarding their excellent properties. In this systematic report we have choosen exact and accurate relaxed lattice constants from their structural unit cell optimisations to forecast and justify the electronic nature in RE2SnFeO6 (RE=Ca,Ba) perovskite systems. The present study provides an superb description about the electronic properties of these alloys. The description of electronic nature of both these complex oxides within GGA and GGA+U functionals illustrates the half-metallic band characters with spin up-channels form as metal-type spectrum and the presence of gap demonstrates the semiconducting nature in spin-dn channel as displayed in Fig. (3, 4) . Seperatively, from the majority-up channels in case of Ca2SnFeO6 the valence band (top) and conduction band (bottom) in both of the correlation schemes are located at Г and X symmetry directions in the Brillouin zone with a indirect band gap of 0.81 eV and 1.51 eV respectively. Similarly, from the band structures of Ba2SnFeO6 the bottom of the conduction band and top of the valence band resides at X and Г within the two calculated functional schemes GGA and GGA+U thus describing the character of owing direct band gap with an approximate values of 0.81eV and 1.44 eV. Here in both the materials on the employment of GGA+U correction band gap increases due to the shifting of energy levels from the Fermi-level. Hence the over all trend revails its half-metallic nature in these present alloys. However, previous study divulges that these materials are reported theoretically as the semimetal ferromagnetic perovskites through LDA approximation [30]. Now showing the feature of band structures of these compounds interms of total density of states (TDOS) shown in Fig. 5 (a, b) which also incorporates its half-metallic nature in various exploiting schemes. In order to understand the elemental activeness of various energy states potrayed in Fig. 5 (c, d) which also points the occupancy of bands at the Fermi level. Insighting towards the partial density of states of Ca2SnFeO6 and Ba2SnFeO6 alloys. Crystal filed associated with FeO6 cage, generated by the Coloumb interactions are responsible for the spilliting of 3d degenerate state of Fe into non-degenerate states:dxy,dyz,dzx calledeg states anddx2-y2 ,dz2 are dt2g states. From the projected density of states (pDOS) for both the materials clealy predicts the presence of Fe-deg and O-p states being of their strong hybridization at the Fermi Level and are responsible to show the metallic behavior in all the up-spin cases, while trending down implies semiconducting behavior. However the low lying sates Ca-s, Ba-s, Sn-s , p which are far away from the Fermi level depicts negligible appearance. Hence the partial density of states potrays exclusively a clear environment of states being of active or deactive at the Fermi-level and also designates that p -d hybridization is predominant in these perovskites. Next we have tried to explore the magnetic properties and also the mechanisms which are responsible to describe the magnetism so far as these alloys is concerned. Hence this important property is directly linked to their structures especially electronic configuration. Within this study two exchange-correlation approximations were used in practice to know the appropriate knowledge among the interaction between various constituents which therefore enhances the magnetic character in these oxide based compounds. Here, we can see from Table 6 the magnetism was found and is found to be the integral value equivalent to 4.00 μB arises mostly from Fe atoms in both these perovskite systems. The obtained values of magnetic character of various atoms (Ca, Ba, Sn, Fe and O) is positive which hints the ferromagnetic interaction within the crystal structures of these alloys. The half-metallicity along with 100% spin polarization and quantized magnetism of these alloys projects a better stand in a new class of spintronics devices, spin filters, high performance electronic devices and spin injectors to meet the necessary demands of new spin based technologies.