Physics – Condensed Matter – Materials Science
Scientific paper
2003-02-17
Physical Review B69, 134416 (2004)
Physics
Condensed Matter
Materials Science
5 figures
Scientific paper
10.1103/PhysRevB.69.134416
We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin transfer torques. Since the spin transfer torque can pump a magnetic energy into the magnetic system, the equilibrium temperature of the magnetic system is ill-defined. We introduce an effective temperature based on a stationary solution of the Fokker-Planck equation. In the limit of high energy barriers, the law of thermal agitation is derived. We find that the N\'{e}el-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent of the spin torque. We carry out the numerical integration of the stochastic Landau-Lifshitz equation to support our theory. Our results agree with existing experimental data.
Li Zaidong
Zhang Sheng
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