Thermally assisted magnetization reversal in the presence of a spin-transfer torque

Z. Li, S. Zhang

Research output: Contribution to journalArticlepeer-review

369 Scopus citations


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 Néel-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent on 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.

Original languageEnglish (US)
Article number134416
Pages (from-to)134416-1-134416-6
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number13
StatePublished - Apr 2004

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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