Recent discovery of Skyrmion crystal phase in 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 Skyrmion with its velocity orthogonal to the field gradient. Finite Gilbert damping produces longitudinal motion. We find a rich variety of resonance modes excited by a.c. electric field.
Skyrmions, once a hypothesized field-theoretical object believed to describe the nature of elementary particles, became common sightings in recent years among several non-centrosymmetric metallic ferromagnets. For more practical applications of Skyrmionic matter as carriers of information, thus realizing the prospect of Skyrmionics, it is necessary to have the means to create and manipulate Skyrmions individually. We show through extensive simulation of the Landau-Lifshitz-Gilbert equation that a circulating current imparted to the metallic chiral ferromagnetic system can create isolated Skyrmionic spin texture without the aid of external magnetic field.
We develop a theory of the magnetic field-induced formation of Skyrmion crystal state in chiral magnets in two spatial dimensions, motivated by the recent discovery of the Skyrmionic phase of magnetization in thin film of Fe$_{0.5}$Co$_{0.5}$Si and in the A-phase of MnSi. Ginzburg-Landau functional of the chiral magnet re-written in the CP$^1$ representation is shown to be a convenient framework for the analysis of the Skyrmion states. Phase diagram of the model at zero temperature gives a sequence of ground states, helical spin $rightarrow$ Skyrme crystal $rightarrow$ ferromagnet, as the external field $B$ increases, in good accord with the thin-film experiment. In close analogy with Abrikosovs derivation of the vortex lattice solution in type-II superconductor, the CP$^1$ mean-field equation is solved and shown to reproduce the Skyrmion crystal state.
