Skyrmion Lattice in Two-Dimensional Chiral Magnet

Abstract

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 $\to$ Skyrme crystal $\to$ ferromagnet, as the external field $B$ increases, in good accord with the thin-film experiment. In close analogy with Abrikosov's 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.

10 pages, 7 figures

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