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The field-induced reorientation of the magnetization of ferromagnetic filmsis treated within the framework of many-body Green's function theory byconsidering all components of the magnetization. We present a new method forthe calculation of expectation values in terms of the eigenvalues andeigenvectors of the equations of motion matrix for the set of Green'sfunctions. This formulation allows a straightforward extension of the monolayercase to thin films with many layers and for arbitrary spin and moreoverprovides a practicable procedure for numerical computation. The modelHamiltonian includes a Heisenberg term, an external magnetic field, asecond-order uniaxial single-ion anisotropy, and the magnetic dipole-dipolecoupling. We utilize the Tyablikov (RPA) decoupling for the exchangeinteraction terms and the Anderson-Callen decoupling for the anisotropy terms.The dipole coupling is treated in the mean-field approximation, a procedurewhich we demonstrate to be a sufficiently good approximation for realisticcoupling strengths. We apply the new method to monolayers with spin $S\geq 1$and to multilayer systems with S=1. We compare some of our results to thosewhere mean-field theory (MFT) is applied to all interactions, pointing out somesignificant differences.Comment: 14 pages, 11 figures, EPJ-B style fil

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