An effective Hamiltonian technique is used to investigate the effect of applying curled electric fields on physical properties of stress-free ${\mathrm{BiFeO}}_3$ dots being under open-circuit electrical boundary conditions. It is discovered that such fields can lead to a control of not only the magnitude but also the direction of the magnetization. Such control originates from the field-induced transformation or switching of electrical vortices and their couplings with oxygen octahedral tilts and magnetic dipoles. This control involves striking intermediate states and constitutes a novel phenomenon that can be termed a “magnetotoroidic” effect.

• Received 24 February 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.127202