Effect of Third Order Perturbation on Heisenberg Hamiltonian for Non-Oriented Ultra-Thin Ferromagnetic Films

Abstract

Abstract: Third order perturbation of Heisenberg Hamiltonian has been investigated for ultra-thin ferromagnetic films with two and three layers in details. If the second and fourth order anisotropy constants do not vary within the ultra thin film, films with two layers behave as oriented ferromagnetic films. But when the anisotropy constants change within the film, the films indicate non-zero second and third order perturbations. But the films with three layers contribute non-zero second and third order perturbations, even if the second and fourth order anisotropy constants do not vary within the film. The easy and hard directions of sc(001) ultra-thin film with two layers and differed second order anisotropy constants makes 32.40 and 122.40 with film normal, respectively. The main easy and hard directions of sc(001) thin films of three layers with the effect of second order anisotropy are 770 and 1670, respectively. After taking fourth order anisotropy into consideration, the positions of maximums and minimums changes. Although the angle between easy and hard directions is not 900, the angle between any two consecutive maximums or minimums is 1800 in this case.