# Linear and nonlinear spin current response in anisotropic spin-orbit coupled systems

## TL;DR

This paper investigates the linear and second harmonic spin current responses in anisotropic 2D systems with spin-orbit coupling, revealing how sample orientation and spin-orbit strengths influence spin current polarization and enabling control over spin transport.

## Contribution

It introduces a detailed analysis of anisotropic spin responses in 2D electron systems with Rashba and Dresselhaus couplings, highlighting conditions for vanishing spin conductivities and potential for nonlinear spin Hall effects.

## Key findings

- Vanishing spin conductivity tensors under SU(2) symmetry.
- Control of spin current polarization via sample orientation.
- Distinct linear and nonlinear responses in anisotropic systems.

## Abstract

We calculate the linear and the second harmonic (SH) spin current response of two anisotropic systems with spin orbit (SO) interaction. The first system is a two-dimensional (2D) electron gas in the presence of Rashba and k-linear Dresselhaus SO couplings. The dependence of the anisotropic spin splitting on the sample growth direction introduces an additional path to modify the linear and nonlinear spectra. In particular, vanishing linear and second order spin conductivity tensors are achievable under SU(2) symmetry conditions, characterized by a collinear SO vector field. Additional conditions under which specific tensor components vanish are posible, without having such collinearity. Thus, a proper choice of the growth direction and SO strengths allows to select the polarization of the linear and SH spin currents according to the direction of flowing. The second system is an anisotropic 2D free electron gas with anisotropic Rashba interaction, which has been employed to study the optical conductivity of 2D puckered structures with anisotropic energy bands. The presence of mass anisotropy and an energy gap open several distinct scenarios for the allowed optical interband transitions, which manifest in the linear and SH response contrastingly. The linear response displays only out-of-plane spin polarized currents, while the SH spin currents flow with spin orientation lying parallel to the plane of the system strictly. The models illustrate the possibility of the nonlinear spin Hall effect in systems with SO interaction, under the presence or absence of time-reversal symmetry. The results suggest different ways to manipulate the linear