Applied magnetic field and stress induced anisotropy dependence of energy for oriented ferromagnetic thick films

P Samarasekara

doi:10.4038/josuk.v4i0.2692

Abstract

The energy of perfectly oriented thick ferromagnetic films at different applied magnetic field and stress was studied using classical model of Heisenberg Hamiltonian. For the values of parameters used in this report, the energy required to orient the film with 1000 layers in 41.4° or 57.6° directions becomes minimum at applied magnetic fields of Hout/ω = 4.8 or Hin/ω = 4.8, respectively. The film can be easily oriented in 172° direction by applying the external stress Ks/ω = 3.6 perpendicular to the film plane, for the values of parameters used in this report. These final results mainly depend on the values of other parameters used for calculations. The energy becomes minimum and maximum at almost the same values of oriented angle (θ), in plane magnetic field, out of plane magnetic field and stress for both sc(001) and bcc(001 lattice types. But the values of energies corresponding to maxima and minima are slightly different for the sc(001) and bcc(001) lattices.Keywords: Magnetic thin films; ferromagnetism; Heisenberg Hamiltonian; stress induced anisotropy and spin DOI: 10.4038/josuk.v4i0.2692J Sci.Univ.Kelaniya 4 (2008): 1-10

Highlights

The solution of Hamiltonian for ferromagnetic thin films has been obtained using 2D XY model (Zhao et al, 2002), two-spin mean field theory (Jensen & Dreysse, 2002), spin half Ising model (Bentaleb et al, 2002) and classical HeisenbergP Samarasekara model (Shan-Ho et al, 2003; Usadel & Hucht, 2002) by some other researchers
Most of the films available in the applications of magnetic memory and microwave devices are thick films, no sufficient researches have been done on solution Heisenberg Hamiltonian of oriented ferromagnetic thick films
The classical Heisenberg Hamiltonian has been used to derive an equation for the energy of oriented ferromagnetic thin films in a previous publication (Samarasekara, 2006)

Summary

INTRODUCTION

The solution of Hamiltonian for ferromagnetic thin films has been obtained using 2D XY model (Zhao et al, 2002), two-spin mean field theory (Jensen & Dreysse, 2002), spin half Ising model (Bentaleb et al, 2002) and classical Heisenberg. The classical Heisenberg Hamiltonian has been used to derive an equation for the energy of oriented ferromagnetic thin films in a previous publication (Samarasekara, 2006). The energy curves for thick films with N=10000 has been given for these two lattice structures (Samarasekara, 2006). The dipole interaction is a microscopic parameter, demagnetization factor is a macroscopic parameter. MODEL AND DISCUSSION The Hamiltonian in Heisenberg model can be written in the following form for a ferromagnetic thin film

Applied magnetic field stress induced anisotropy

Hout cosθ

CONCLUSIONS