Melting of a skyrmion lattice to a skyrmion liquid via a hexatic phase.

The phase transition most commonly observed is probably melting, a transition from ordered crystalline solids to disordered isotropic liquids. In three dimensions, melting is a single, first-order phase transition. In two-dimensional systems, however, theory predicts a general scenario of two continuous phase transitions separated by an intermediate, oriented liquid state, the so-called hexatic phase with short-range translational and quasi-long-range orientational orders. Such hexatic phases occur in colloidal systems, Wigner solids and liquid crystals, all composed of real-matter particles. In contrast, skyrmions are countable soliton configurations with non-trivial topology and these quasi-particles can form two-dimensional lattices. Here we show, by direct imaging with cryo-Lorentz transmission electron microscopy, that magnetic field variations can tune the phase of the skyrmion ensembles in Cu2OSeO3 from a two-dimensional solid through the long-speculated skyrmion hexatic phase to a liquid. The local spin order persists throughout the process. Remarkably, our quantitative analysis demonstrates that the aforementioned topological-defect-induced crystal melting scenario well describes the observed phase transitions.