First And Second Order Rotational Transitions Of Skyrmion Crystal In Multiferroic Cu2oseo3 Under Electric Field

We investigate the electric-field-induced rotations of a skyrmion crystal (SkX) in multiferroic Cu2OSeO3. We perform our analysis within a free energy model that incorporates both the exchange anisotropy and the fourth order magnetocrystalline anisotropy, and both the deformation and rotation of SkX are taken into account. We find that for a background magnetic field along the direction [110], (i) electric fields out of the (1 (1) over bar0) plane lead to continuous rotations of SkX, which explains the experiments [White et al., Phys. Rev. Lett. 113, 107203 (2014)] and (ii) electric fields in the (1 (1) over bar0) plane may lead to 30 degrees rotations of SkX. Our results provide an understanding of manipulation of SkX by the electric field, which may contribute to the applications of skyrmion-based spintronic devices without Joule heating energy losses.