Dynamic hysteresis at a noisy saddle-node shows power-law scaling but nonuniversal exponent

TL;DR

This paper investigates dynamic hysteresis in a thermally-driven metal-insulator transition, revealing that noise influences the hysteresis scaling exponent, which varies from the mean-field prediction of 2/3 to as low as 0.2, explaining observed experimental variations.

Contribution

The study combines experimental measurements and Langevin dynamics simulations to show how noise affects the hysteresis scaling exponent in a saddle-node bifurcation system.

Findings

Experimental exponent ~1/3 in NdNiO3 thin films

Simulations show noise lowers the exponent from 2/3 to 0.2

Power law scaling persists despite exponent variation

Abstract

Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response around a saddle-node bifurcation. As a consequence, the hysteresis area increases with the sweep rate. Mean-field theory, relevant for noise-free situations, predicts power law scaling with the area scaling exponent of 2/3. We have experimentally investigated the dynamic hysteresis for a thermally-driven metal-insulator transition in a high quality NdNiO$_3$ thin film and found the scaling exponent to be about 1/3, far less than the mean field value. To understand this, we have numerically studied Langevin dynamics of the order parameter and found that noise, which can be thought to parallel finite temperature effects, influences the character of dynamic hysteresis by systematically lowering the dynamical exponent to as small as 0.2. The power law scaling character, on the other hand, is unaffected in the range of chosen parameters. This work rationalizes the ubiquitous power law scaling of the dynamic hysteresis as well as the wide variation in the scaling exponent between 0.66 and 0.2 observed in different systems over the last 30 years.