Magnetic properties of ferromagnetic thin films with three spin layers as described by fourth-order perturbed Heisenberg Hamiltonian

The magnetic properties of ferromagnetic thin films with three spin layers were investigated for the first time using fourth-order perturbed Heisenberg Hamiltonian. Total magnetic energy was determined for ferromagnetic materials with simple cubic lattice. The simulation was carried out for Heisenberg Hamiltonian with different second-order magnetic anisotropy constants in different spin layers. The total magnetic energy periodically varies with spin-exchange interaction, azimuthal angle of spin and the secondorder magnetic anisotropy constant in each spin layer. The peaks along the axis of the angle are closely packed except in the 3-D plot of energy versus angle and second-order magnetic anisotropy constant of the middle spin layer. 2-D plots were perceived by rotating 3-D plots in MATLAB. According to the 3-D plot, the angle between magnetic easy and hard directions is 90 degrees. The minimum energy range was found in the 3-D plot of energy versus angle and the second order anisotropy constant of the middle spin layer. The samples with the minimum magnetic anisotropy energies have potential application in transformer cores, magnetic switching and magnetic amplifiers.