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

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.