Order parameter fluctuation effects on current-induced magnetization

We investigate the impact of order parameter fluctuations on magnetoelectric effects in metallic systems using classical Monte Carlo simulations. We focus on a a chiral quadrupole order in a distorted kagome lattice in a model incorporating conduction electrons and classical orbital moments. The ordered orbital moments break mirror symmetry and couple with the conduction electrons, leading to a current-induced magnetization driven by the quadrupole order. Our findings reveal that order parameter fluctuations significantly affect the current-induced magnetization, strongly suppressing the response over a broad temperature range below the transition temperature. Additionally, we analyze the influence of Fermi surface properties and associated matrix elements on this phenomenon. Our results highlight the crucial role of fluctuation effects, demonstrating a qualitatively distinct temperature dependence of the current-induced magnetization compared to that of the order parameter itself.