Floquet-induced anisotropic magnetoresistance and anomalous Hall effect in 2D $d$-wave altermagnets with Rashba spin-orbit coupling

Altermagnets (AMs) combine momentum-dependent spin splitting with zero net magnetization, making them promising for spintronics. Periodic driving enables dynamic symmetry engineering beyond static, material-specific control. We show that Floquet engineering in 2D $d$-wave AMs with out-of-plane N\'eel order and Rashba spin-orbit coupling unlocks equilibrium-forbidden transport responses. Monochromatic driving produces purely out-of-plane magnetization, yielding longitudinal anisotropic magnetoresistance (AMR) and an anomalous Hall effect, whereas bichromatic driving generates both in-plane and out-of-plane magnetizations and additionally activates transverse AMR via the second harmonic of the secondary beam. Comparable static magnetic fields would require hundreds of tesla, avoided in Floquet driving. These effects persist across linear, circular, and mixed light polarizations and are tunable via light parameters. Our results establish multi-color Floquet engineering for controlling magnetization and symmetry-protected transport in AMs.