Melting the skyrmion lattice - from solid to liquid via a hexatic phase*

The most commonly seen phase transition is possibly "melting", a transition from ordered crystalline solids to disordered isotropic liquids. While melting in three-dimensions is always a single, fist-order phase transition, in two-dimensional systems a scenario of two continuous phase transitions separated by an intermediate "oriented liquid" state, the so-called hexatic phase, has been proposed theoretically and evidenced experimentally in colloidal systems, Wigner solids and liquid crystals. Fundamentally different from these real-matter particles, skyrmions are countable soliton configurations localized in continuous filds with non-trivial topology, and these emergent quasi-particles can form two-dimensional lattices, whose melting dynamics remains unexplored. Here we show, by direct imaging with cryo-Lorentz transmission
electron microscopy, that the phase of the skyrmion ensembles in the material Cu2OSeO3 can be tuned by magnetic fild from two-dimensional skyrmion solids, through the long-speculated skyrmion hexatic phase, to skyrmion liquids, with the local spin order preserved throughout the whole process. Remarkably, our quantitative analysis demonstrates that this mesoscopic phase transition can be well described as topological-defect-induced crystal melting in two dimensions. By uncovering the novel phase behaviors of skyrmionic quasi-particles, we demonstrate skyrmion ensembles as an ideal platform for exploring novel properties in two-dimensions.