Derivation of spin hamiltonians by tensor decomposition

Abstract

The spin Hamiltonian of a paramagnetic system is derived from the decomposition of spherical tensors having appropriate symmetry properties. Although no explicit use of group theory is involved, the Hamiltonian obtained is similar to that derived from purely group theoretical methods. Since perturbation theory is not invoked, the derivation applies regardless of the relative magnitude of the interactions, regardless of whether the lowest state of the free ion is an S-state, and regardless of whether the interaction of interest is linear, quadratic or of higher order.