Hysteresis loop areas in kinetic Ising models: Effects of the switching mechanism

TL;DR

This paper investigates the low-frequency behavior of hysteresis loop areas in kinetic Ising models, deriving analytic expressions and highlighting a logarithmic frequency dependence relevant to experimental and simulation data.

Contribution

It provides the first theoretical derivation of the low-frequency asymptotic behavior of hysteresis loop areas in kinetic Ising models using droplet theory.

Findings

Hysteresis loop area approaches a logarithmic frequency dependence at low frequencies.

Derived analytic expressions for the asymptotic behavior of the loop area.

Results clarify the interpretation of experimental and simulation data on hysteresis.

Abstract

Experiments on ferromagnetic thin films have measured the dependence of the hysteresis loop area on the amplitude and frequency of the external field, $A$=$A(H_{0},\omega)$, and approximate agreement with numerical simulations of Ising models has been reported. Here we present numerical and theoretical calculations of $A$ in the low-frequency regime for two values of $H_{0}$, which bracket a temperature and system-size dependent crossover field. Our previous Monte Carlo studies have shown that the hysteretic response of the kinetic Ising model is qualitatively different for amplitudes above and below this crossover field. Using droplet theory, we derive analytic expressions for the low-frequency asymptotic behavior of the hysteresis loop area. In both field regimes, the loop area exhibits an extremely slow approach to an asymptotic, logarithmic frequency dependence of the form $A \propto - [\ln (H_{0} \omega)]^{-1}$. Our results are relevant to the interpretation of data from experiments and simulations, on the basis of which power-law exponents for the hysteresis-loop area have been reported.