Orbitally dependent magnetic coupling between cobalt(II) ions: The problem 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 the orbitally degenerate ground manifold (4T1g)A⊗(4T1g)B of the cobalt pair is expressed in terms of orbital and spin operators. The treatment of the Hamiltonian is performed with the use of the irreducible tensor operator technique. We elucidate the major electronic factors controlling the magnetic anisotropy in the Co(II) pairs. The degree of the exchange 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. Special attention is paid on the topical case when spin–orbit coupling exceeds the exchange interaction. In this case the effective Hamiltonian in its general form is projected onto the subspace of low-lying Kramers doublets and in such a way the pseudo-spin-12 Hamiltonian is derived. Unlike the commonly accepted phenomenological approaches based merely on the symmetry arguments the proposed procedure is grounded on the microscopic consideration and hence allows us to establish the interrelation between the idem parameters of the system and the effective parameters of the pseudo-spin-12 Hamiltonian. Finally, we discuss the applicability of the conventional Lines’ model.