  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.
