Deterministic manipulation of multi-state polarization switching in multiferroic thin films

Deterministically controllable multi-state polarizations in ferroelectric materials are promising for the application of next-generation non-volatile multi-state memory devices. However, the achievement of multi-state polarizations has been inhibited by the challenge of selective control of switching pathways. Here we report an approach to selectively control 71{\deg} ferroelastic and 180{\deg} ferroelectric switching paths by combining the out-of-plane electric field and in-plane trailing field in multiferroic BiFeO3 thin films with periodically ordered 71{\deg} domain wall. Four-state polarization states can be deterministically achieved and reversibly controlled through precisely selecting different switching paths. Our studies reveal the ability to obtain multiple polarization states for the realization of multi-state memories and magnetoelectric coupling based devices.