Spin Currents in Rashba Altermagnets: From Equilibrium to Nonlinear Regimes

We investigate equilibrium (background), linear, and nonlinear spin currents in two-dimensional Rashba spin-orbit coupled altermagnet systems, using a modified spin current operator that includes anomalous velocity from non-zero Berry curvature. The background spin current, stemming from spin-orbit coupling and modulated by the altermagnet term ($t_j$), exhibits in-plane polarization, increases linearly with Fermi energy ($\epsilon_F$), and is enhanced by both the altermagnet ($t_j$) and the Rashba parameter ($\lambda$). Linear spin current is always transverse with out-of-plane polarization and can be viewed as Spin Hall current, primarily driven by band velocity, with $t_j$ enabling a band-induced contribution (previously absent in simple Rashba systems ($t_j=0$)). This highlights altermagnet system as a promising source of spin Hall current generation. For linear spin Hall current, its band contribution's magnitude increases linearly with $\epsilon_F$, while the magnitude of anomalous component saturates at higher $\epsilon_F$. Further, the magnitude of spin Hall current is enhanced by $t_j$ but reduced by $\lambda$. Nonlinear spin currents feature both longitudinal and transverse components with in-plane polarization. Both the nonlinear longitudinal spin current from band velocity and the nonlinear transverse spin current from anomalous velocity initially decrease with $\epsilon_F$ before saturating at higher $\epsilon_F$. Importantly, $t_j$ reduces these currents while $\lambda$ enhances them. Meanwhile, the nonlinear transverse current from band velocity increases and then saturates with $\epsilon_F$, enhanced by $\lambda$ and showing non-monotonic variation with $t_j$. These findings highlight the tunability of spin current behavior through Rashba and altermagnet parameters, offering insights for spintronic applications.