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Modified second order perturbed Heisenberg Hamiltonian was employed todescribe the magnetic properties of ferromagnetic films with three to twentyspin layers for the first time. Previously, the solution of second orderperturbed Heisenberg Hamiltonian was found for ferromagnetic films with two tofive layers under some assumptions by us. In this report, the exact solution ispresented without any assumptions by calculating the pseudo inverse of matrixC. All eight magnetic parameters such as spin exchange interaction, secondorder magnetic anisotropy, fourth order magnetic anisotropy, stress inducedmagnetic anisotropy, demagnetization factor, in plane magnetic field, out ofplane magnetic field and magnetic dipole interaction were taken into account.The easy and hard directions were found using 3-D and 2-D plots of totalmagnetic energy versus these magnetic parameters. Angle between easy and harddirections was nearly 107 degrees in many cases. The magnetic easy axisgradually rotates from out of plane to in plane direction by indicating apreferred in plane orientation of magnetic easy axis for films with highernumber of spin layers. These theoretical results agree with some experimentalresearch data of ferromagnetic thin films.

Ferromagnetic films with three to twenty spin layers as described using second order perturbed Heisenberg Hamiltonian