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Magnetic skyrmions have attracted considerable attention recently for theirhuge potential in spintronic applications. Generally skyrmions are big comparedto the atomic lattice constant, which allows for the Ginzburg-Landau typedescription in the continuum limit. Such a description successfully capturesthe main experimental observations on skyrmions in B20 compound withoutinversion symmetry. Skyrmions can also exist in inversion-symmetric magnetswith competing interactions. Here we derive a general Ginzburg-Landau theoryfor skyrmions in these magnets valid in the long wavelength limit. We study theunusual static and dynamical properties of skyrmions based on the derivedGinzburg-Landau theory. We show that an easy axis spin anisotropy is sufficientto stabilize a skyrmion lattice. Interestingly, the skyrmion ininversion-symmetric magnets has a new internal degree of freedom associatedwith the rotation of helicity, i.e. the "spin" of the skyrmion as a particle,in addition to the usual translational motion of skyrmions (orbital motion).The orbital and spin degree of freedoms of an individual skyrmion can couple toeach other, and give rise to unusual behavior that is absent for the skyrmionsstabilized by the Dzyaloshinskii-Moriya interaction. The derivedGinzburg-Landau theory provides a convenient and general framework to discussskyrmion physics and will facilitate the search for skyrmions ininversion-symmetric magnets.

Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions