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Cycloidal spin orders are common in multiferroics. One of the prototypicalexamples is BiFeO3 (BFO) which shows a large polarization and a cycloidalantiferromagnetic order at room temperature. Here we employ Landau theory andphase-field simulations to analyze the coupled switching dynamics ofpolarization and cycloidal antiferromagnetic orders in BFO. We are able toidentify 14 types of transitional spin structures between two cycloids and 9electric-field-induced spin switching paths. We demonstrate theelectric-field-induced rotation of wave vectors of the cycloidal spins anddiscover 2 types of cycloidal spin switching dynamics: fast local spin flipsand slow rotation of wave vectors. Also, we construct road maps to achieve theswitching between any two spin cycloids through multi-step applications ofelectric fields. The work provides a theoretical framework for thephenomenological description of spin cycloids and a fundamental understandingof the switching mechanisms to achieve electrical control of magnetic orders.

Theory and phase-field simulations on electrical control of spin cycloids in a multiferroic