Theory of nonlinear magnetoelectric transport effects in normal-metal $-$ magnetic-insulator heterostructures

TL;DR

This paper develops a theoretical framework for understanding nonlinear magnetoelectric effects in normal-metal magnetic-insulator heterostructures, focusing on their frequency dependence and distinguishing features of various contributions.

Contribution

It introduces a comprehensive theory of bilinear responses in FN and NFN heterostructures, analyzing multiple nonlinear effects and their dependencies, advancing understanding of complex magnetoelectric phenomena.

Findings

Identifies distinct frequency and magnetization dependencies of nonlinear effects.

Provides a scaling analysis with magnetic field and geometry.

Offers a framework for experimental differentiation of effects.

Abstract

Heterostructures of normal metals (N) and magnetic insulators (F) show paradigmatic effects, such as spin-Hall magnetoresistance and electric drag currents. These effects are linear in the applied electric field $E(\omega)$. Normal-metal $-$ magnetic-insulator heterostructures also exhibit a characteristic nonlinear response quadratic in $E(\omega)$, referred to as unidirectional spin-Hall magnetoresistance or spin-torque diode effect. In this article, we develop a theory of the bilinear response of FN bilayers and NFN trilayers for finite frequencies $\omega$ of the driving field and for four contributions that have been previously considered in the literature: Joule heating, phonon-mediated unidirectional magnetoresistance, the spin-torque diode effect, and magnonic unidirectional spin-Hall magnetoresistance. We identify their distinct dependencies on frequency and the magnetization direction of the magnetic insulator and examine their scaling with magnetic field and system geometry, providing a framework for experimental differentiation.