Skyrmion lattice in a 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 ${\text{Fe}}_{0.5}{\text{Co}}_{0.5}\text{Si}$ and in the A phase of MnSi. Ginzburg-Landau functional of the chiral magnet rewritten in the ${\text{CP}}^{1}$ 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 $\text{spin}\ensuremath{\rightarrow}\text{Skyrme}$ $\text{crystal}\ensuremath{\rightarrow}\text{ferromagnet}$, 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 ${\text{CP}}^{1}$ mean-field equation is solved and shown to reproduce the Skyrmion crystal state.