Spin anomalous-Hall unidirectional magnetoresistance

We predict a spin anomalous-Hall unidirectional magnetoresistance (AH-UMR) in conducting bilayers composed of ferromagnetic layer and nonmagnetic layer, which does not rely on the Hall effect normal metal layer---in stark contrast to well-studied spin-Hall magnetoresistance---but instead arises from anomalous layer. Physically, it is charge-spin conversion induced by that conspires with structural inversion asymmetry generate net nonequilibrium density which, turn, modulates resistance bilayer when direction applied current or magnetization reversed. The dependencies AH-UMR materials geometric parameters are analyzed compared other nonlinear magnetoresistances. In particular, we show that, magnetic where effects comparable, overall UMR may undergo sign change thickness either varied, suggesting scheme quantify angle via transport measurement.