Abstract
For the first time, the 2nd order perturbed Heisenberg Hamiltonian with all the seven magnetic energy parameters was solved for fcc structured ferromagnetic films with five layers. Previously, the 2nd order perturbed Heisenberg Hamiltonian was solved for four layered ferromagnetic films under some special assumptions by us. However, the exact solution of 2nd order perturbed Heisenberg Hamiltonian without any special assumption is formulated in this manuscript. The magnetic easy and hard directions were determined using the angles corresponding to the energy minimum and maximum in the 3-D and 2-D plots. The shape of the 3-D plots doesn’t change with the number of layers except the position of spikes. However, the magnetic easy direction varies with the number of layers. Most of the theoretical data obtained by our model agree with the experimental data of ferromagnetic thin films.
Highlights
Ferromagnetic films are prime candidates of magnetic memory and microwave devices
Total energy was found using equation 6. 3-D plot of total magnetic energy versus stress induced anisotropy and azimuthal angle of spin
The Heisenberg Hamiltonian was solved for sc ferromagnetic film with three layers by assuming that the C+ is the normal inverse of the matrix C (Samarasekara 2006)
Summary
Ferromagnetic films are prime candidates of magnetic memory and microwave devices. The orientation of easy and hard directions is important in all these applications. The Heisenberg Hamiltonian with few magnetic energy parameters has been employed to explain the ultra thin ferromagnetic films The exact pseudo inverse was found using equation 7 for the Heisenberg Hamiltonian with all seven magnetic energy parameters. 3-D plot of total magnetic energy versus stress induced anisotropy and azimuthal angle of spin
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