Abstract
The variation of energy of ferromagnetic ultra-thin films with second and fourth order anisotropy was investigated using Heisenberg Hamiltonian with second order perturbation. The study was limited to sc(001) film with three layers. Graphs indicate energy minimums at certain values of second order anisotropy, fourth order anisotropy and angle. Films with fourth order anisotropy (Dm(4))/ω=4 can be easily oriented in the direction given by angle of 2.66 radians for the values of other energy terms used in this simulation. When the second order anisotropy (Dm(2))/ω is 3.1, preferred direction is 0.754 radians. When the second order anisotropy varies at a constant value of fourth order anisotropy, the graph indicates more energy minimums.Keywords: Heisenberg Hamiltonian; magnetic thin films; magnetic anisotropies; spinDOI: 10.4038/josuk.v3i0.2740J. Sci. Univ. Kelaniya 3 (2007) : 73-82
Highlights
Earlier the energy of ferromagnetic thin films was studied using Heisenberg Hamiltonian with second order perturbation for limited number of energy terms such as exchange interaction, second order anisotropy and stress induced anisotropyP Samarasekara (Samarasekara, 2006)
When the second order anisotropy varies at a constant value of fourth order anisotropy, the graph indicates more energy minimums
All the energy terms are considered for simulations
Summary
Earlier the energy of ferromagnetic thin films was studied using Heisenberg Hamiltonian with second order perturbation for limited number of energy terms such as exchange interaction, second order anisotropy and stress induced anisotropy. The angle between easy and hard directions was found to be 900 for all sc(001), fcc(001) and bcc(001) ferromagnetic lattice types. All the energy terms are considered for simulations. The energy of perfectly oriented thick ferromagnetic films up to 10000 layers has been investigated earlier and reported that easy and hard directions for bcc(001) lattice were θ=450 and 1350, respectively (Samarasekara, 2006). The Hamiltonian in Heisenberg model has been solved using Green functions (Ze-Nong Ding et al, 1993)
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