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

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