Single molecule magnets (SMM) consist of several magnetic centers among which the exchange interactions are often frustrated. The nature of the super-exchange interaction between any pair of magnetic ions is itself sensitive to changes in the electron repulsion parameters and orbital energies. Even when all the exchange constants between pairs of magnetic centers are fixed, there are difficulties with predicting even the ground state of the spin. Approximate techniques for solving for the ground and low-lying states of such large Hilbert space system are unreliable. We have developed exact diagonalization techniques for solving such model Hamiltonians. Another important property of SMMs is the presence of a large negative magnetic anisotropy constant ‘D’ in the system. The individual ions have their own anisotropy constants oriented along their individual magnetic axis. We have developed a method of computing the molecular anisotropy constants in any given state of the SMM, using first order perturbation theory. We show that the relative orientation of the individual magnetic centers determines the sign of the anisotropy constant ‘D’ and that the molecular ‘D’ can be negative even when all the magnetic centers have a positive ‘D’. An important property of SMMs is the observation of quantum resonant tunneling (QRT). We study QRT using time-dependent quantum mechanics and show that the rates of ramping of the magnetic field as well as the presence of transverse fields determine the number and width of the magnetization plateaus in the M-H loop.
