Application of Second Order Perturbation Theory to AnalyzeHeisenberg Hamiltonian in Ultra-thin Films of Spinel Ferrite

Abstract The Heisenberg Hamiltonian’s solution with second-order perturbation is explored in the context of non-aligned cubic spinel ferrimagnetic materials. This investigation delves into perturbations stemming from alterations in angle at the boundary between adjacent cells. As the number of cells (N) increases from 2 to 3, the energy peaks exhibit sharper profiles, and their positions shift along the energy-angle curve. Interestingly, the intervals between successive major peaks remain consistent. Visualizing the relationship between total energy, angle, and stress in three dimensions, the plot’s smoothness improves with higher N values. Notably, the energy diminishes as the number of layers increases, suggesting disparate behaviors between oriented and non-oriented films. In the scenario where N=2, minor peaks adjacent to major peaks emerge. Furthermore, when the second-order anisotropy constant remains uniform across the film for N=2, the film’s behavior resembles that of an oriented film.