Universal scaling laws for dynamical-thermal hysteresis

TL;DR

This paper uncovers universal scaling laws governing the area of dynamic hysteresis loops in materials, revealing how they depend on the sweep rate and thermal fluctuations, with broad experimental and theoretical validation.

Contribution

It introduces a universal crossover framework for hysteresis scaling laws, resolving previous inconsistencies and guiding material design for hysteresis-based applications.

Findings

Hysteresis loop area scales as R^{1/3} below R* and R^{2/3} above R*

The crossover rate R* is proportional to temperature over critical temperature (T/Tc)

Universal scaling laws are validated across experiments, simulations, and analytical models.

Abstract

Dynamic hysteresis, the rate-dependent lagged response of materials to external fields, underpins applications from energy-efficient transformers to gas storage systems. A fundamental yet unresolved question is how the hysteresis loop area $A$ scales with the field sweep rate $R$. Here, we reveal that a competition between the field sweep and thermal fluctuations governs a universal crossover between two scaling regimes: $A - A_0 \propto R^{1/3}$ for $R < R^*$ and $A - A_0 \propto R^{2/3}$ for $R > R^*$, where $A_0$ is the quasi-static area and the crossover rate $R^* \propto T/T_c$ depends on the temperature $T$ and the material's critical temperature $T_c$. We demonstrate these scaling laws universally across experiments of magnetic materials, simulations of Ising and metal-organic framework models, and analytical solutions of a stochastic Langevin equation. This framework not only resolves the long-standing non-universality of reported scaling exponents but also provides a direct design principle for the application of dynamic hysteresis.