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

摘要

Third order perturbation of Heisenberg Hamiltonian has been investigated for ultrathin ferromagnetic films with two and three layers in details. If the second and fourth orderanisotropy constants do not vary within the ultra thin film, films with two layers behave asoriented ferromagnetic films. But when the anisotropy constants change within the film, thefilms indicate non-zero second and third order perturbations. But the films with three layerscontribute non-zero second and third order perturbations, even if the second and fourth orderanisotropy 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 and122.40 with film normal, respectively. The main easy and hard directions of sc(001) thin filmsof three layers with the effect of second order anisotropy are 770 and 1670, respectively. Aftertaking fourth order anisotropy into consideration, the positions of maximums and minimumschanges. Although the angle between easy and hard directions is not 900, the angle betweenany two consecutive maximums or minimums is 1800 in this case.