Transformations from stripy states to skyrmion crystals

Transformations from condensed stripe skyrmions to skyrmion crystals (SkXs) in perpendicularly magnetized chiral films are investigated in order to clarify a widely spread misconception that stripy phases and SkXs are not topologically connected. Based on our new understanding of skyrmion nature of most stripes in chiral magnetic films, we show that a stripy state, including the helical state, and a SkX are topologically the same. The morphology of a skyrmion condensate is determined only by the ratio of stripe width and skyrmion-skyrmion separation. When stripe width is much smaller than skyrmion-skyrmion separation, the skyrmion condensate is in various stripy phases such as periodically arranged helical states and mazes. The skyrmion condensate has a crystal structure in which individual skyrmions are disk-like objects when stripe width is larger than skyrmion-skyrmion separation. We demonstrated how a collection of given number of stripe skyrmions transforms smoothly and continuously into a SkX no matter whether initial configurations of a set of nucleation domains are randomly or orderly arranged and whether stripe width is gradually or suddenly tuned. This finding does not support the notion of a phase transition from a helical state to a SkX.