Orbitally dependent kinetic exchange in cobalt(II) pairs: origin of the magnetic anisotropy

Abstract

A comprehensive theoretical study of the magnetic exchange between Co2+ ions is reported. Using the microscopic background we deduce the general Hamiltonian for a corner-shared bioctahedral system involving kinetic exchange, spin–orbit coupling and low-symmetry local crystal field. This Hamiltonian acting within orbitally degenerate ground manifold 4(T1g)A⊗4(T1g)B of the cobalt pair is expressed in terms of orbital and spin operators. We elucidate the major electronic factors controlling the exchange anisotropy in the Co(II) pairs. The degree of the magnetic anisotropy is shown to depend on the strength of the cubic crystal field and on the relative efficiency of two kinds of electron transfer pathways (e–e and t2–t2) contributing to the kinetic exchange. An unusual role of spin–orbit interaction is revealed. This interaction tends to reduce the anisotropy caused by the orbitally dependent exchange. Finally, we discuss conditions of the applicability of the isotropic Lines’ model conventionally accepted in magnetochemistry of cobalt clusters.