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

Research output: Contribution to journalArticle

305 Citations (Scopus)

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 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
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume69
Issue number13
DOIs
StatePublished - Apr 2004
Externally publishedYes

Fingerprint

Magnetization reversal
torque
Fokker Planck equation
Torque
Fokker-Planck equation
magnetization
Energy barriers
numerical integration
thermal energy
Temperature
temperature
Magnetization
Pumps
pumps
energy

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

@article{6d898e85e7f847ba9002fcaaefb34e00,
title = "Thermally assisted magnetization reversal in the presence of a spin-transfer torque",
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 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.",
author = "Z. Li and Shufeng Zhang",
year = "2004",
month = "4",
doi = "10.1103/PhysRevB.69.134416",
language = "English (US)",
volume = "69",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Institute of Physics Publising LLC",
number = "13",

}

TY - JOUR

T1 - Thermally assisted magnetization reversal in the presence of a spin-transfer torque

AU - Li, Z.

AU - Zhang, Shufeng

PY - 2004/4

Y1 - 2004/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=37649033021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=37649033021&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.69.134416

DO - 10.1103/PhysRevB.69.134416

M3 - Article

VL - 69

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 13

M1 - 134416

ER -