  In this theoretical investigation, we analyze light-induced nonlinear spin
Hall currents in a gated single-layer 1T$'$-WTe$_2$, flowing transversely to
the incident laser polarization direction. Our study encompasses the
exploration of the second and third-order rectified spin Hall currents using an
effective low-energy Hamiltonian and employing Kubo's formalism. We extend our
analysis to a wide frequency range spanning both transparent and absorbing
regimes, investigating the influence of light frequency below and above the
optical band gap. Additionally, we investigate the influence of an out-of-plane
gate potential on the system, disrupting inversion symmetry and effectively
manipulating both the strength and sign of nonlinear spin Hall responses. We
predict a pronounced third-order spin Hall current relative to its second-order
counterpart. The predicted nonlinear spin currents show strong anisotropic
dependence on the laser polarization angle. The outcomes of our study
contribute to a generalized framework for nonlinear response theory within the
spin channel will impact the development of the emerging field of
opto-spintronic.
