Hysteresis scaling of uniaxially anisotropic Heisenberg model

We simulate by the Monte Carlo method the dynamic hysteresis and hysteresis scaling of two-dimensional uniaxially anisotropic Heisenberg model submitted to a time-oscillating magnetic field $h$ of frequency $f$ and amplitude $h0$⁠. It is revealed that the hysteresis area as a function of $f$ and $h0$ exhibits well-defined power law behaviors over the low-$f$ and high-$f$ regimes as long as $h0$ is high enough. The power law exponents for the low-$f$ regime depend on the uniaxially anisotropic factor $K$⁠, but the exponents for the high-$f$ regime are universal. The single-peaked hysteresis dispersions at different $h0$ follow both the empirical scaling approach and the single-variable scaling hypothesis, respectively, demonstrating the existence of a single characteristic time for spin reversal mode given the amplitude $h0$⁠. However, the scaling may be broken when $h0$ is low, due to the coexistence of spin reversal and spin tilting resonances.