The nonequilibrium dynamics of a rapidly quenched spin-1 Bose gas with spin-orbit coupling is studied. By solving the stochastic projected Gross-Pitaevskii equation, we show that crystallization of half-skyrmions (merons), can occur in a spinor condensate of
87Rb. The stability of such a crystal structure is analyzed. Likewise, inverted half-skyrmions can be created in a spin-polarized spinor condensate of
23Na. Our studies provide a chance to explore the fundamental properties of skyrmionlike matter.
We investigate the half-skyrmion excitations induced by spin-orbit coupling in the rotating and rapidly quenched spin-1 Bose-Einstein condensates. We give three expressions of the corresponding spin vectors to describe the half-skyrmion. Our results show that the half-skyrmion excitation depends on the combination of spin-orbit coupling and rotation, and it originates from a dipole structure of spin which is always embedded in three vortices constructed by each condensate component respectively. When both the strength of spin-orbit coupling and the rotation frequency are larger than some critical values, the half-skyrmions encircle the center with one or several circles to form a radial lattice, which occurs even in the strong ferromagnetic/antiferromagnetic condensates. We can use both the spin-orbit coupling and the rotation to adjust the radial lattice. The realization and the detection of the half-skyrmions are compatible with current experimental technology.