Optical magnetic switching in odd-parity magnets with spin-orbit coupling

$p$-wave magnets exhibit odd-parity spin polarization in momentum space, with spin splitting that reverses under $\vec{k}\rightarrow -\vec{k}$, while preserving zero net magnetization. Here we show that, in odd-parity magnets with spin-orbit coupling, elliptically polarized light generates a momentum-independent spin-dependent term that dynamically switches a zero-net-magnetization $p$-wave state into a finite spin-polarized state. The Floquet-engineered bands also acquire a nonzero Chern number whose sign is controlled by the light polarization. For $f$-wave magnets, circularly polarized light induces a net out-of-plane magnetization, offering a direct experimental signature. Our results establish light as an efficient means of controlling magnetic states, with potential applications in spintronics and quantum information.