Magnetic elements at finite temperature and large deviation theory

R. V. Kohn, M. G. Reznikoff, E. Vanden-Eijnden

Research output: Contribution to journalArticlepeer-review


We investigate thermally activated phenomena in micromagnetics using large deviation theory and concepts from stochastic resonance. We give a natural mathematical definition of finite-temperature astroids, finite-temperature hysteresis loops, etc. Generically, these objects emerge when the (generalized) Arrhenius timescale governing the thermally activated barrier crossing event of magnetic switching matches the timescale at which the magnetic element is pulsed or ramped by an external field; in the special and physically relevant case of multiple-pulse experiments, on the other hand, short-time switching can lead to non-Arrhenius behavior. We show how large deviation theory can be used to explain some properties of the astroids, like their shrinking and sharpening as the number of applied pulses is increased. We also investigate the influence of the dynamics, in particular the relative importance of the gyromagnetic and the damping terms. Finally, we discuss some issues and open questions regarding spatially nonuniform magnetization.

Original languageEnglish (US)
Pages (from-to)223-253
Number of pages31
JournalJournal of Nonlinear Science
Issue number4
StatePublished - Aug 2005


  • Landau-Lifshitz-Gilbert equation
  • action minimization
  • large deviation theory
  • micromagnetics
  • rare events
  • stochastic perturbation
  • stochastic resonance

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Engineering
  • Applied Mathematics


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