### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 223-253 |

Number of pages | 31 |

Journal | Journal of Nonlinear Science |

Volume | 15 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2005 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Engineering(all)

### Cite this

*Journal of Nonlinear Science*,

*15*(4), 223-253. https://doi.org/10.1007/s00332-005-0671-z

**Magnetic elements at finite temperature and large deviation theory.** / Kohn, Robert; Reznikoff, M. G.; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

*Journal of Nonlinear Science*, vol. 15, no. 4, pp. 223-253. https://doi.org/10.1007/s00332-005-0671-z

}

TY - JOUR

T1 - Magnetic elements at finite temperature and large deviation theory

AU - Kohn, Robert

AU - Reznikoff, M. G.

AU - Vanden Eijnden, Eric

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 - action minimization

KW - Landau-Lifshitz-Gilbert equation

KW - large deviation theory

KW - micromagnetics

KW - rare events

KW - stochastic perturbation

KW - stochastic resonance

UR - http://www.scopus.com/inward/record.url?scp=84867946760&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867946760&partnerID=8YFLogxK

U2 - 10.1007/s00332-005-0671-z

DO - 10.1007/s00332-005-0671-z

M3 - Article

VL - 15

SP - 223

EP - 253

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 4

ER -