RESUMO
Stripy states, consisting of a collection of stripy spin textures, are the precursors of skyrmion crystals (SkXs). The common belief is that stripy states and SkXs are topologically unconnected and that transitions between SkXs and stripy states are phase transitions. Here, we show that both stripy states and SkXs are skyrmion condensates and they are topologically equivalent. By gradually tuning the stripe whose width goes from smaller than to larger than skyrmion-skyrmion separation, the structure of a skyrmion condensate transforms smoothly and continuously from various stripy phases, including helical states and mazes, to crystals, showing that stripy states are topologically connected to SkXs.
RESUMO
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 the parameter κ, which measures the relative Dzyaloshinskii-Moriya interaction (DMI) strength, is large enough. The lowest energy state of an infinite film is a long zig-zag ramified stripe skyrmion occupying 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 κ is above a critical value. The lowest energy state is still a stripy helical state no matter with or without a field when κ is below the critical value. The multi-metastable states explain the thermodynamic path dependences of the various metastable states of a film. The decrease of the κ value with the temperature explains why SkXs become metastable at low temperatures in many skyrmion systems. These findings open a new avenue for SkX manipulation and skyrmion-based applications.