Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix fur the set of Green's functions. This formulation allows a straight forward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotrophy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotrophy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin S greater than or equal to 1 and to multilayer systems with S = 1. We compare some of our results to those where mean-field theory (RIFT) is: applied to all interactions, pointing out some significant differences.