Symmetry-protected difference between spin Hall and anomalous Hall effects of a periodically driven multiorbital metal

Nonequilibrium quantum states can be controlled via the driving field in periodically driven systems. Such control, which is called Floquet engineering, has opened various phenomena, such as light-induced anomalous Hall effect. There are expected to some essential differences between and spin effects of systems because difference time-reversal symmetry. However, these remain unclear due lack engineering Here we show that when helicity circularly polarized light changed a $t_{2g}$-orbital metal, current generated by effect remains unchanged, whereas charge reversed. This protected symmetry time reversal operation. Our results offer way distinguish could experimentally observed pump-probe measurements Sr$_{2}$RuO$_{4}$.