Exchange interactions between ions with different orbitally degenerate crystal field ground states (2T2g and 3T1g)

Abstract

The effects of orbital degeneracy on magnetic exchange interactions between two ions, with electronic configuration t¹_2g(τ) and t²_2g(τ′), respectively, are examined starting from Anderson's hamiltonian. We suppose these ions to interact through a common trigonal face of their octahedra. In the suggested treatment, we consider only kinetic exchange mechanisms and assume that the jump of one electron from site τ′ to site τ requires an excitation energy U. The general problem is complex but great simplifications are allowed by symmetry. The final result differs from the usual expression of Heisenberg–Dirac–Van Vleck (H.D.V.V.) which only involves spin operators S_τ and S_τ′. In particular, a biquadratic interaction term appears between orbital momenta so that the lowest energy level of the binuclear cluster is a four-fold degenerate state when spin–orbit coupling is neglected. A critical analysis of the system shows that this degeneracy is not removed even when a distortion of the cubic crystal field is taken into account.