A theory of skyrmion crystal formation

A generic theory about skyrmion crystal (SkX) formation in chiral magnetic thin films and its fascinating thermodynamic behaviours is presented. A chiral magnetic film can have many metastable states with an arbitrary skyrmion density up to a maximal value when a parameter $\kappa$, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zagged ramified stripe skyrmion occupied the whole film in the absence of a magnetic field. Under an intermediate field perpendicular to the film, the lowest energy state has a finite skyrmion density. This is why a chiral magnetic film is often in a stripy state at a low field and a SkX only around an optimal field when $\kappa$ is above a critical value. The lowest energy state is still a stripy helical state no matter with or without a field when $\kappa$ is below the critical value. The multi-metastable states explains the thermodynamic path dependences of various metastable states of a film. Decrease of $\kappa$ value with the temperature explains why SkXs become metastable at low temperature in many skyrmion systems. These findings open a new avenue for SkX manipulation and skyrmion-based applications.