Altermagnets have been identified as the third category of magnetic materials, exhibiting momentum-dependent spin splitting characterized by even powers of momentum. In this Letter, 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 ${\mathbf{k}}^{2n}$-spin splitting can generate odd-in-$\mathbf{k}$ spin-orbit couplings up to ${\mathbf{k}}^{2n-1}$. In the limit of circularly polarized light, the only correction is $k^{2n-1}$, with all lower-order contributions being nullified. Interestingly, light-induced SOCs significantly impact the low-energy band topology, where their Chern numbers change by $\mathrm{\Delta }C=\pm 1$, 2, 3 for $d$, $g$, $i$-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 Letter showcases light as a powerful, controllable tool for engineering complex and exciting phenomena in altermagnets.

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• Spin texture
• Topological phases of matter
• Altermagnets
• Bloch-Floquet theorem