  An effective Hamiltonian technique is used to investigate the effect of
applying curled electric fields on physical properties of stress-free BiFeO3
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. On a microscopic point of view, 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 as "magnetotoroidic" effect.
