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.

最通常观察到的相变可能是熔化，即从有序结晶固体到无序各向同性液体的转变。在三个维度上，熔化是单个的一级相变。然而，在二维系统中，理论预测了由连续的，定向的液态分隔的两个连续相变的一般情况，即所谓的具有短程平移和准长程取向阶的六价相。此类六方相出现在胶体系统，维格纳固体和液晶中，它们全部由实物颗粒组成。相比之下，天体离子是具有非平凡拓扑的可数孤子构型，这些准粒子可以形成二维晶格。在这里，我们展示了通过低温洛伦兹透射电子显微镜的直接成像，₂ OSeO ₃从二维固体经过长时预测的Skyrmion六方相转变为液体。本地旋转顺序将在整个过程中持续存在。值得注意的是，我们的定量分析表明，上述拓扑缺陷引起的晶体熔化情况很好地描述了观察到的相变。