Tailoring the electronic structure and magnetic properties of pyrochlore Co₂Ti_{1- x}Ge_xO₄: a GGA + Uab initio study

We report the electronic structure and magnetic properties of Co₂Ti_1-xGe_xO₄(0 ⩽x⩽ 1) spinel by means of the first-principle methods of density functional theory involving generalized gradient approximation along with the on-site Coulomb interaction (U_eff) in the exchange-correlation energy functional. Special emphasis has been given to explore the site occupancy of Ge atoms in the spinel lattice by introducing the cationic disorder parameter (y) which is done in such a way that one can tailor the pyrochlore geometry and determine the electronic/magnetic structure quantitatively. For all the compositions (x), the system exhibits weak tetragonal distortion (c/a≠ 1) due to the non-degeneratedz2anddx2-y2states (e_gorbitals) of the B-site Co. We observe large exchange splitting (Δ_EX∼ 9 eV) between the up and down spin bands oft_2gande_gstates, respectively, of tetrahedral and octahedral Co²⁺(⁴A_2(g)(F)) and moderate crystal-field splitting (Δ_CF∼ 4 eV) and the Jahn-Teller distortion (Δ_JT∼ 0.9 eV). These features indicate the strong intra-atomic interaction which is also responsible for the alteration of energy band-gap (1.7 eV ⩽E_g⩽ 3.3 eV). The exchange interaction (J_BB∼ -4.8 meV, for (x,y) = (0.25, 0)) between the Co²⁺dominates the overall antiferromagnetic behaviour of the system for all 'x' as compared toJ_AA(∼-2.2 meV, for (x,y) = (0.25, 0)) andJ_AB(∼-1.8 meV, for (x,y) = (0.25, 0)). For all the compositions without any disorderness in the system, the net ferrimagnetic moment (Δμ) remains constant, however, increases progressively with increasingxdue to the imbalance of Co spins between the A- and B-sites.