Spin Hall effect originated from fractal surface

The spin Hall effect (SHE) has shown promising impact in the field of spintronics and magnonics from fundamental and practical points of view. This effect originates from several mechanisms of spin scatterers based on spin-orbit coupling (SOC) and also can be manipulated through the surface roughness. Here, the effect of correlated surface roughness on the SHE in metallic thin films with small SOC is investigated theoretically. Toward this, the self-affine fractal surface in the framework of the Born approximation is exploited. The surface roughness is described by the k-correlation model and is characterized by the roughness exponent H [Formula: see text], the in-plane correlation length ξ and the rms roughness amplitude δ. It is found that the spin Hall angle in metallic thin film increases by two orders of magnitude when H decreases from H  =  1 to H  =  0. In addition, the source of SHE for surface roughness with Gaussian profile distribution function is found to be mainly the side jump scattering while that with a non-Gaussian profile suggests both of the side jump and skew scatterings are present. Our achievements address how details of the surface roughness profile can adjust the SHE in non-heavy metals.