  We predict unidirectional magnetoresistance effects arising 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 ferromagnetic 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 quadratic
magnetotransport that is rooted in the wave nature of electrons. The
corresponding unidirectional magnetoresistances exhibit decay lengths at the
scale of the Fermi wavelength$-$distinctive signatures of the quantum nonlinear
magnetotransport effect.
