TY - JOUR

T1 - Magnetic elements at finite temperature and large deviation theory

AU - Kohn, R. V.

AU - Reznikoff, M. G.

AU - Vanden-Eijnden, E.

N1 - Funding Information:
We would like to thank Weinan E, Geoff Grinstein, and Roger Koch for stimulating conversations that contributed to the development of this work. This article derives from work done as part of the Ph. D. thesis of M. G. Reznikoff, while partially supported by NSF grant DMS01-01439. R. V. Kohn was partially supported by NSF grants DMS01-01439 and DMS03-13744. E. Vanden-Eijnden was partially supported by NSF grants DMS01-01439, DMS02-09959, and DMS02-39625, and ONR grant N00014-04-1-0565.

PY - 2005/8

Y1 - 2005/8

N2 - 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.

AB - 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.

KW - Landau-Lifshitz-Gilbert equation

KW - action minimization

KW - large deviation theory

KW - micromagnetics

KW - rare events

KW - stochastic perturbation

KW - stochastic resonance

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U2 - 10.1007/s00332-005-0671-z

DO - 10.1007/s00332-005-0671-z

M3 - Article

AN - SCOPUS:84867946760

SN - 0938-8974

VL - 15

SP - 223

EP - 253

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 4

ER -