Tailoring the electronic structure and magnetic properties of pyrochlore Co2Ti1−x Ge x O4: a GGA + U ab initio study

Abstract

We report the electronic structure and magnetic properties of Co2Ti1−x Ge x O4 (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-degenerate and states (e g orbitals) of the B-site Co. We observe large exchange splitting (ΔEX ∼ 9 eV) between the up and down spin bands of t 2g and e g states, respectively, of tetrahedral and octahedral Co2+ (4A2(g)(F)) and moderate crystal-field splitting (ΔCF ∼ 4 eV) and the Jahn–Teller distortion (ΔJT ∼ 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 to J AA (∼−2.2 meV, for (x, y) = (0.25, 0)) and J 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 increasing x due to the imbalance of Co spins between the A- and B-sites.