Investigation of magnetic properties of ferromagnetic thin films with three spin layers using fourth order perturbed Heisenberg Hamiltonian

The magnetic properties of ferromagnetic thin films with three spin layers were investigated using fourth order perturbed Heisenberg Hamiltonian with all seven magnetic energy parameters for simple cubic lattice. Total Magnetic energy was formulated in terms of spin exchange interaction, second order and fourth order anisotropy, in plane and out plane applied magnetic fields, demagnetization energy and stress induced anisotropy in three spin layers. 3D plot of total magnetic energy versus angle and stress induced anisotropy were plotted for the different values of second order magnetic anisotropy constants. All other magnetic energy parameters were kept at constant values. All the peaks are closely packed in the graphs plotted using fourth order perturbed Heisenberg Hamiltonian compared to peaks in the graphs plotted using second and third order perturbed Heisenberg Hamiltonian. The order of magnetic energy changed when the values of second order anisotropy constants of three spin layers are varied. The order of magnetic energy is higher, when the second order magnetic anisotropy constant in the top spin layer is less than those of the bottom and middle spin layers. The order of magnetic energy is lower, when the second order magnetic anisotropy constant in the bottom spin layer is less than those of the top and middle spin layers. In addition, the angle between consecutive magnetic easy and hard direction is nearly 90 degrees for all the cases.