Analytical Derivations for the Description of Magnetic Anisotropy in Transition Metal Complexes

This chapter is dedicated to the rationalization of magnetic anisotropyMagnetic anisotropy in metal complexes. Analytical derivations allow one to predict the nature and magnitude of both the zero-field-splitting and the anisotropies of magnetic exchangeMagnetic exchange. The first section is devoted to mononuclear complexesMononuclear complexes. It addresses the effect of spin–orbit coupling (SOC) in two different cases: (i) when the ground state is non-degenerate and a second-order SOC applies. The effect of the SOC can then be modeled by an energy splitting of the MS components of the ground spin state. Illustrations of the power of these analytical derivations for the rationalization of the ZFSZero-field splitting of various complexes are presented; (ii) when the ground state is (almost) degenerate, a first-order SOCFirst-order SOC applies. A more sophisticated model is here derived which rationalizes the obtaining of a giant value of the ZFS in a Ni(II) complex. The second section is devoted to the derivation of multi-spin models for binuclear complexesBinuclear complexes. We will determine the physical content of both the symmetric and the antisymmetricAntisymmetric exchange tensors in the case of two centers with spin S = 1/2. A peculiar derivation concerns the Dzyaloshinskii–Moriya (antisymmetric exchange) interaction in case of a local degeneracy of the orbitals and shows how the first-order SOCFirst-order SOC can generate giant values of this anisotropy of exchange. In the last subsection, we will show that the usual multi-spin model for spin S = 1 centers is not valid and derive an appropriate model involving a four-rank exchange tensor.