Ferromagnetic thin Films with Simple Cubic Structure as Described by Fourth Order Perturbed Heisenberg Hamiltonian

For the first time, fourth order perturbed Heisenberg Hamiltonian has been applied to study the properties of simple cubic structured ferromagnetic ultrathin films with two spin layers. Only the spin exchange interaction, second order magnetic anisotropy constant and the short-range magnetic dipole interaction were taken into account. Only when the second order anisotropy constant varies from one spin plane to the other spin plane, perturbation becomes nonzero. 3-D plots of total energy versus spin exchange interaction and angle, total energy versus second order anisotropy constant in bottom spin layer and angle, and total energy versus second order anisotropy constant in top layer and angle were plotted. Peaks in the plots are closely packed in fourth order perturbed case compared to the plots obtained using third order perturbed case. All the graphs were plotted using MATLAB program