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A direct three-dimensional minimization of the standard energy functionalshows that in thin films of cubic helimagnets chiral skyrmions are modulatedalong three spatial directions. The structure of such 3D skyrmions can bethought of as a superposition of conical modulations along the skyrmion axisand double-twist rotation in the perpendicular plane. Numerical solutions forchiral modulations demonstrate that 3D skyrmion lattices and helicoids arethermodynamically stable in a broad range of applied magnetic fields. Ourresults disclose a basic physical mechanism underlying the formation ofskyrmion states recently observed in nanolayers of cubic helimagnets.

Three-dimensional skyrmion states in thin films of cubic helimagnets