The recent discovery of a Skyrmion crystal phase in an insulating multiferroic compound Cu${}_2$OSeO${}_3$ calls for new ways and ideas to manipulate the Skyrmions in the absence of spin transfer torque from the conduction electrons. It is shown here that the position-dependent electric field, pointed along the direction of the average induced dipole moment of the Skyrmion, can induce the Hall motion of the Skyrmion with its velocity orthogonal to the field gradient. Finite Gilbert damping produces longitudinal motion. Inter-Skyrmion interaction leads to the reduction of the drift speed. We find a rich variety of resonance modes excited by an ac electric field.

• Received 14 September 2012

DOI:https://doi.org/10.1103/PhysRevB.87.100402