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

TL;DR

This paper develops a generalized stochastic model for magnetization dynamics influenced by spin transfer torque, introducing an effective temperature concept that aligns with experimental observations and extends classical thermal relaxation theories.

Contribution

It proposes a new stochastic Landau-Lifshitz framework incorporating spin transfer torque and defines an effective temperature for non-equilibrium conditions.

Findings

Effective temperature linearly depends on spin torque.

Néel-Brown relaxation law remains valid with modified temperature.

Numerical results agree with experimental data.

Abstract

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.