Modelling magnetic anisotropy in molecular magnets

In this mini-review we develop and apply methods for computing magnetic anisotropy constants of single molecule magnets starting from the exchange Hamiltonian. In the small anisotropy limit, we treat the exchange Hamiltonian as the unperturbed Hamiltonian and the fine structure Hamiltonian as the perturbation. We describe methods for solving the exchange Hamiltonian for huge Hilbert spaces and develop a perturbation method for computing the anisotropy constants of the multinuclear SMM in the weak anisotropy limit. When the anisotropy is large the perturbation method breaks down and we have to include the single-ion anisotropy contribution to the unperturbed Hamiltonian. In this case, the total spin is only an approximate quantum number and excited spin states can intrude into the ground state spin manifold and the SMM anisotropy constants can be obtained from a partial set of spin multiplet states. We also discuss modelling the energy barrier U_B to magnetization relaxation using a rejection free kinetic Monte Carlo method on an assembly of SMMs which are also interacting via spin-dipolar interactions. We note that both exchange anisotropy and spin-dipolar interactions have a strong influence on U_B.