Quantum unidirectional magnetoresistances

We show that a unidirectional magnetoresistance effect of quantum origin may arise in a bilayer composed of a nonmagnetic metal and a ferromagnetic insulator, whereby both longitudinal and transverse resistances vary when the direction of the applied electric field is reversed or the magnetization of the magnetic layer is rotated. In the presence of spin-orbit coupling, an electron wave incident on the interface of the bilayer undergoes a spin rotation and a momentum-dependent phase shift. Quantum interference between the incident and reflected waves furnishes the electron with an additional velocity that is even in the in-plane component of the electron's wavevector, giving rise to the unidirectional magnetoresistance–a nonlinear magnetotransport effect that is rooted in the wave nature of electrons. We have calculated both the longitudinal and transverse nonlinear conductivities using a quantum approach, which allows us to determine their dependencies on disorder and magnetization direction as well as other relevant materials properties. Possible ways to distinguish these nonlinear conductivities–which rely on quantum interference–from their semiclassical counterparts will also be discussed.