Dynamical Generation of Higher-order Spin-Orbit Couplings, Topology and Persistent Spin Texture in Light-Irradiated Altermagnets

Altermagnets have been identified as the third category of magnetic materials, exhibiting momentum-dependent spin splitting characterized by even powers of momentum. In this study, we show that when subjected to elliptically polarized light, these materials serve as an exemplary framework for the dynamic generation of topological bands featuring higher-order spin-orbit coupling (SOC). Notably, while the generated Zeeman field remains invariant to the particular altermagnetic ordering, the induced higher-order SOCs are related to the magnitude and symmetry of the altermagnetic order. Specifically, we show that an altermagnet exhibiting $k^n$-spin splitting can generate spin-orbit couplings up to $k^{n-1}$. In the limit of circularly polarized light, the only correction is $k^{n-1}$, with all lower-order contributions being nullified. Interestingly, light-induced SOCs significantly impact the low-energy band topology, where their Chern numbers change by $\Delta C =\pm 1,2,3$ for $d,g,f$-wave altermagnets. Finally, we find a critical field in which a persistent spin texture is realized, a highly desirable state with predicted infinite spin lifetime. Our work showcases light as a powerful, controllable tool for engineering complex and exciting phenomena in altermagnets.