A theory of magnetoresistance of non-magnetic metal on magnon valves

One recent exciting development in the field of magnonics is the discovery of universal unusual anisotropic magnetoresistance (UAMR) in nanometer-thick non-magnetic (NM) metallic bars that are deposited on magnon valves of two ferromagnetic insulators (FIs) sandwiching an NM metal. This UAMR has the same angular dependencies as various bilayers consisting of at least one magnetic layer and at least one metallic layer. This suggests that the UAMR of different systems may originate from the same physics, which is yet to be fully understood. Here, we reveal the common feature shared by all these systems: two-vector dependencies of tensor quantities. Specifically, the resistivity of an NM metallic bar depends on the magnetization of its adjacent FI due to the quantum penetration of itinerant electrons of the metallic bar into the FI and on a perpendicular field at the interface of the bar and the FI. We demonstrate that the two-vector dependence of the resistivity tensor is responsible for the observed universal UAMR of metallic bars on magnon valves, independent of the details of the microscopic interactions in different materials. We also propose experiments that can test this theory.