2 Method of Calculation
We have performed our calculations to determine the alloys RE2SnFeO6 (Re=Ca,Ba) for their potential stand in thermoelectric technology and future spintronic applications. This piece of work is carried out by means of spin-polarized full potential argumented plane wave (FPLAPW) as intregrated in WEIN2k program [24]. The density functional theory (DFT) calculations has been conveniently performed in the form of PBE-GGA parameterization [25] for the exact treatment of exchange correlation potential. Since the calculation within the first GGA implementation is somehow inadequate to do the functionality of the systems mainly assembled withd /f electrons particularly the underestimation of band gap problem due to the reason of insufficient potential for highly localized states and also self-interaction between the electrons which misplaces to produce the actual band profile formation. So, in order to have a complete and concise study on these systems Hubbard model (GGA+U) [26] has been noteworthy applied which specifically handles such large complex systems. Hence, an empirical method which is under controlled to correct the energy band gaps by varying the potentials corresponding to experimental band gaps. It is worthy to mention here, due to lack of the experimental evidence we have established the effective potential Ueff = U-J where U was calibrated to 15 Ry and 20 Ry on Fe-3d orbitals of RESnFeO6 (RE =Ca, Ba) and J labels exchange parameters was slightly varied from 0 to 0.04 eV to know the exact magnetic interaction between the various constituents. However, the standard Hubbard Hamiltonian in an extended form can be written as: [27]
(1)
where, the symbol in the equation abbreviates the creation and annihilation of electron on site i with the spin = or and U is the onsite coulomb repulsion between the electrons (two e’s) at the same location. The symbol t which is particularly hybridization between the nearest neighbours allows the particles to jump at the adjacent sites. Muffintin potential for the basis set defined as a product of R mt K max = 7 has been selected in a proper way to prevent electron hopping as well as charge leakage from the intersititial regions between atomic spheres. The valence shell and deep lying core electrons are separated at default value of -6.0 Ry of energy. The crystal potential as well as charge density is expanded up to an orbital quantum no ‘lmax’=10 . The self-consistent field (SCF) for calculating the electronic ground state density can be determined until the charge and energy convergence reaches up to 0.0001(eV) and 0.0001(Ry) respectively. The transport coefficients as well as thermodynamical were manifested via their respective packages.
3 Results and discussions
The WIEN2k simulation enables to figure out relaxed lattice constants suitably from their conventional unit cells which therefore decides the various physical properties of RE2SnFeO6 (RE=Ca,Ba) debated as below: