Stochastic Hysteresis and Resonance in a Kinetic Ising System

TL;DR

This paper investigates stochastic hysteresis and resonance phenomena in a small, two-dimensional kinetic Ising model under oscillating magnetic fields, combining Monte Carlo simulations with analytical theory to reveal unique behaviors at low temperatures.

Contribution

It introduces a parameter-free analytical theory that accurately predicts stochastic hysteresis in small Ising systems, highlighting differences from mean-field and larger system behaviors.

Findings

Stochastic hysteresis differs qualitatively from mean-field models.

Average hysteresis-loop area exhibits logarithmic decay at low frequencies.

Evidence of stochastic resonance in magnetization dynamics.

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 $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a 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.