# Spin Hall effect originated from fractal surface

## TL;DR

This paper theoretically investigates how the statistical parameters of fractal surface roughness influence the spin Hall effect in thin films, revealing that surface texture significantly affects SHE magnitude and scattering mechanisms.

## Contribution

It introduces a comprehensive theoretical analysis of correlated fractal surface roughness effects on SHE, highlighting the role of roughness parameters like H, kesi, and distribution profile.

## Key findings

- Spin Hall angle can increase by an order of magnitude with decreasing H.
- Gaussian roughness profile mainly involves side jump scattering.
- Non-Gaussian profile involves both side jump and skew scattering.

## Abstract

Spin hall effect (SHE) in thin films is inherited by surface roughness. Although roughness effect on SHE has been studied in thin films, but roughness is not only parameter in rough surfaces. Our results show that how other statistical parameters of rough surface play important role in SHE. In this paper we investigate theoretically the effects of correlated surface roughness in the SHE with self affine fractal surface in non-heavy metallic thin films in the frame work of the Born approximation. The surface roughness is described by the k-correlation model and is characterized by the roughness exponent H (0 <= H <= 1), the in plane correlation length kesi and the rms roughness amplitude delta. We show that the spin Hall angle can increase by one order of magnitude when H decreasing from H = 1 to H = 0. We also demonstrate the SHE for surface roughness with distribution function of the Gaussian profile is mainly contributed by the side jump scattering while for that with a non-Gaussian profile, both side jump and skew scattering are present. our achievements demonstrate the important role of roughness texture profile for SHE in non-heavy metals.