Wave-nature and metastability of emergent crystals in chiral magnets

Topological spin textures emerging in magnetic materials usually appear in crystalline states. A long-standing dilemma is whether we should understand these emergent crystals as gathering particles or coupling waves, the answer of which affects almost every aspect of our understanding on the subject. Here we prove that 2-D emergent crystals with long-range order in helimagnets, such as skyrmion crystals and dipole skyrmion crystals, have a wave nature. We systematically study their equilibrium properties, metastability, and phase transition path when unstable. We show that the robustness of a skyrmion crystal derives from its metastability, and that its phase transition dynamics at low (high) magnetic field is mediated by a soft mode which breaks (maintains) its hexagonal symmetry. Different from ordinary crystals which are formed by. and breaks into atoms, emergent crystals have a new formation (destruction) mechanism: they appear from (turn to) single-Q spin-density-wave states through nonlinear mode-mode interactions.