{'fraction_non_alphanumeric': 0.01399825021872266, 'fraction_numerical': 0.0, 'mean_word_length': 5.850299401197605, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Third order perturbed modified Heisenberg Hamiltonian of fcc structured ferromagnetic films with seventy spin layers

Magnetic properties of fcc structured ferromagnetic films with the number of spin layers up to seventy was described using third order perturbed Heisenberg Hamiltonian. The variation of magnetic easy direction, magnetic energies in easy and hard directions, magnetic anisotropy energy and the angle between easy and hard directions was investigated by varying the number of spin layers. Spin exchange interaction, magnetic dipole interaction, second and fourth order magnetic anisotropies, in and out of plane applied magnetic fields, demagnetization factor and stress induced anisotropy were considered in the model. Because magnetic dipole interaction and demagnetization factor represent microscopic and macroscopic properties of the sample, respectively, both these terms were incorporated in our theoretical model. Although our model is a semi-classical model, some discrete variations of angle of easy axis were observed. Our theoretical data qualitatively agree with experimental data of Fe and Ni ferromagnetic films.