Three-dimensional skyrmion states in thin films of cubic helimagnets

A direct three-dimensional minimization of the standard energy functional shows that in thin films of cubic helimagnets, chiral skyrmions are modulated along three spatial directions. The structure of such three-dimensional skyrmions can be thought of as a superposition of conical modulations along the skyrmion axis and double-twist rotation in the perpendicular plane. We show that chiral modulations across the layer thickness radically change the skyrmion energetics and provide a thermodynamical stability of a skyrmion lattice in a broad range of applied magnetic fields. These results disclose a basic physical mechanism underlying the formation of skyrmion states recently observed in nanolayers of cubic helimagnets.