### A Solution of Fourth Order Perturbed Heisenberg Hamiltonian with Seven Magnetic Parameters

#### Abstract

For the first time, the fourth order perturbed Heisenberg Hamiltonian with all seven magnetic energy parameters was solved for simple cubic structured ferromagnetic ultrathin films. Spin exchange interaction, magnetic dipole interaction, second order magnetic anisotropy, fourth order magnetic anisotropy, applied magnetic field, demagnetization energy and stress induced anisotropy were considered. 3D graphs of total magnetic energy versusstressinduced anisotropy and angle were plotted for different values of second order and fourth order magnetic anisotropy constants. Each second and fourth order magnetic anisotropy constants was considered as a variable in the film. All other magnetic energy parameters were fixed at constant values. In addition, graphs of energy versus angle were plotted to find the magnetic easy and hard directions. The angle between magnetic easy and hard directions were found to be 90 degrees in each case as expected. These results were compared with the results obtained using second and third order perturbed Heisenberg Hamiltonian.

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