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Title: Stochastic hysteresis and resonance in a kinetic Ising system

Abstract

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below T{sub c}. For these restricted parameters, the magnetization switches through random nucleation of a {ital single} droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for themore » interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise. {copyright} {ital 1998} {ital The American Physical Society}« less

Authors:
;  [1]; ; ;  [2]; ;  [3]
  1. Center for Materials Research and Technology and Department of Physics, Florida State University, Tallahassee, Florida 32306-4350 (United States)
  2. Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4130 (United States)
  3. Colorado Center for Chaos and Complexity, University of Colorado, Boulder, Colorado 80309-0216 (United States)
Publication Date:
Research Org.:
Florida State Univ., Tallahassee, FL (United States)
OSTI Identifier:
664951
DOE Contract Number:  
FG02-85ER25000
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Additional Journal Information:
Journal Volume: 57; Journal Issue: 6; Other Information: PBD: Jun 1998
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; RESONANCE; PROBABILITY; FERROMAGNETISM; FERROMAGNETIC RESONANCE; HYSTERESIS; ISING MODEL; KINETICS; STOCHASTIC PROCESSES; SPIN; FERROMAGNETIC MATERIALS; MONTE CARLO METHOD; SIMULATION; CRITICAL TEMPERATURE; MAGNETIZATION; RANDOMNESS; NUCLEATION; MARKOV PROCESS

Citation Formats

Sides, S W, Rikvold, P A, Sides, S W, Rikvold, P A, Novotny, M A, Sides, S W, and Rikvold, P A. Stochastic hysteresis and resonance in a kinetic Ising system. United States: N. p., 1998. Web. doi:10.1103/PhysRevE.57.6512.
Sides, S W, Rikvold, P A, Sides, S W, Rikvold, P A, Novotny, M A, Sides, S W, & Rikvold, P A. Stochastic hysteresis and resonance in a kinetic Ising system. United States. https://doi.org/10.1103/PhysRevE.57.6512
Sides, S W, Rikvold, P A, Sides, S W, Rikvold, P A, Novotny, M A, Sides, S W, and Rikvold, P A. Mon . "Stochastic hysteresis and resonance in a kinetic Ising system". United States. https://doi.org/10.1103/PhysRevE.57.6512.
@article{osti_664951,
title = {Stochastic hysteresis and resonance in a kinetic Ising system},
author = {Sides, S W and Rikvold, P A and Sides, S W and Rikvold, P A and Novotny, M A and Sides, S W and Rikvold, P A},
abstractNote = {We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below T{sub c}. For these restricted parameters, the magnetization switches through random nucleation of a {ital single} droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise. {copyright} {ital 1998} {ital The American Physical Society}},
doi = {10.1103/PhysRevE.57.6512},
url = {https://www.osti.gov/biblio/664951}, journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 6,
volume = 57,
place = {United States},
year = {1998},
month = {6}
}