Parametrization of the magnetic energy at the atomic level -: art. no. 212405

We parametrize the adiabatic magnetic energy of generalized classical spins for the important special case of zero spin-orbit coupling and no applied external field. The expansion classifies the classical Heisenberg model as a first order approximation to the energy; extensions of the Heisenberg model in literature are shown to be of second order in the classical limit of our parametrization. The expressions for a third-order approximation to the magnetic energy are derived.