We investigate Floquet-engineered topological phases in two-dimensional $d_{x^2-y^2}$-wave altermagnets irradiated by circularly polarized light in the off-resonant regime. These materials exhibit large momentum-dependent spin splitting governed by distinctive magnetic symmetries. Using a lattice model combined with Floquet theory, we demonstrate that irradiation induces light-tunable quantum anomalous Hall phases with Chern numbers up to $\pm 3$. The resultant phase diagram is verified by calculating the anomalous Hall conductivity and also the edge modes inside the band gap of a nanoribbon version of the altermagnet. Our findings establish $d$-wave altermagnets as promising platforms for realizing nonequilibrium topological states of matter. The low-energy continuum limit of the lattice-based Floquet Hamiltonian results in linear and higher-order-in-momentum spin-orbit couplings, and also a Zeeman-like magnetization, all arising from light-induced virtual photon processes. The resulting higher-order spin-orbit coupling generates additional gapless Dirac points which, together with high-symmetry gap closings, yield enhanced Berry curvature and high Chern numbers. The light irradiation effectively breaks the static $d_{x^2-y^2}$-wave magnetic symmetry mixing in an isotropic photoinduced $s$-wave correction.

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• Altermagnetism
• Anomalous Hall effect
• Berry curvature
• Chern insulators
• Edge states
• Phase transitions
• Quantum anomalous Hall effect
• Altermagnets
• Floquet systems
• Topological materials
• Bloch-Floquet theorem