Orbitally dependent magnetic coupling between cobalt(II) ions: The problem of the magnetic anisotropy

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 exchang...