Tunable Odd-Parity Spin Splittings in Altermagnets

Momentum-dependent spin splitting and its relation to inversion ($P$) and time-reversal ($T$) symmetries are central to nonrelativistic spintronics. Representative examples include collinear altermagnets with $(P,T)=(+,-)$ and non-collinear odd-parity magnets with $(P,T)=(-,+)$. In this work, we develop a theoretical framework to induce odd-parity spin splittings in the more abundant collinear altermagnets through two mechanisms: driving by a two-color linearly polarized light field or coupling to a $P$-odd loop-current order. Properly phase-locked two-color driving induces a static $(P,T)=(-,-)$ order, symmetry-equivalent to a translationally invariant $P$-odd loop-current order. Coupling this order to an altermagnet produces a controllable mixed-parity spin texture, opening new avenues for the electrical and optical manipulation of spin-polarized currents in spintronics applications. The same mechanism applied to a collinear $PT$-symmetric magnet induces a distinct $(P,T)=(+,+)$ state with a nonrelativistic dissipationless anomalous spin Hall conductivity. We present group-theory and microscopic Floquet theory to highlight the emergent responses.