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 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 crystal, 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.