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We investigate the spontaneous generation of crystallized topological defectsvia the combining effects of fast rotation and rapid thermal quench on thespin-1 Bose-Einstein condensates. By solving the stochastic projectedGross-Pitaevskii equation, we show that, when the system reaches equilibrium, ahexagonal lattice of skyrmions, and a square lattice of half-quantized vorticescan be formed in a ferromagnetic and antiferromagnetic spinor BEC, respetively,which can be imaged by using the polarization-dependent phase-contrast method.

Spontaneous Crystallization of Skyrmions and Fractional Vortices in the Fast-rotating and Rapidly-quenched Spin-1 Bose-Einstein Condensates