Skyrmion Lattice in Two-Dimensional Chiral Magnet

TL;DR

This paper develops a theoretical framework for understanding the formation of Skyrmion crystal states in two-dimensional chiral magnets under magnetic fields, aligning well with recent experimental observations in thin films.

Contribution

It introduces a CP^1 representation-based Ginzburg-Landau functional to analyze Skyrmion states and derives a phase diagram matching experimental results.

Findings

Identifies a sequence of magnetic phases with increasing magnetic field.

Reproduces Skyrmion crystal state using a mean-field solution analogous to vortex lattices.

Provides a theoretical basis for Skyrmion formation in thin film chiral magnets.

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 $\rightarrow$ Skyrme crystal $\rightarrow$ 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.