Nonreciprocal coherent all-optical switching between magnetic multistates

We present experimental and computational findings of the laser-induced nonreciprocal motion of magnetization during ultrafast photomagnetic switching in garnets. We found distinct coherent magnetization precession trajectories and switching times between four magnetization states, depending on both directions of the light linear polarization and initial magnetic state. As a fingerprint of the topological symmetry, the choice of the switching trajectory is governed by an interplay of the photomagnetic torque and magnetic anisotropy. Our results open a plethora of possibilities for designing energy-efficient magnetization switching routes at arbitrary energy landscapes.