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(𝜔) . Normal metal–magnetic insulator heterostructures also exhibit a characteristic nonlinear response quadratic in 𝐸(𝜔) , 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 𝜔 of the driving field and for four contributions that have been previously considered in the literature: Joule heating, phononmediated 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.
