Skyrmion lattice in a two-dimensional chiral magnet

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 Fe0.5Co0.5Si and in the A phase of MnSi. Ginzburg-Landau functional of the chiral magnet rewritten in the CP1 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 -> Skyrme crystal -> 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 CP1 mean-field equation is solved and shown to reproduce the Skyrmion crystal state.