Quantum mechanical motion of off-center ion in external magnetic field

We consider the magnetostatic response to an external magnetic field of a crystal containing off-center ions, such as Li^+ in KCl and KBr or the apical oxygens O(A) in the LaSCO family of layered perovskites. Magnetic dipoles are deduced from the matrix elements of the energy operator of a spinning particle in a magnetic field which particle also satisfies the nonlinear Mathieu equation. The magnetic moments are found to increase in magnitude as the system goes from the lowest energy ground state to the higher lying excited states. Our conclusions are in concert with earlier studies of magnetic dipoles from circular currents based on Ampere's theorem.