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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>E</a:mi> <a:mo>(</a:mo> <a:mi>ω</a:mi> <a:mo>)</a:mo> </a:mrow> </a:math> . Normal metal–magnetic insulator heterostructures also exhibit a characteristic nonlinear response quadratic in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>E</b:mi> <b:mo>(</b:mo> <b:mi>ω</b:mi> <b:mo>)</b:mo> </b:mrow> </b:math> , 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>ω</c:mi> </c:math> 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.