Kibble-Zurek mechanism in a quenched ferromagnetic Bose-Einstein condensate

The spin vortices are shown to be created through the Kibble-Zurek (KZ) mechanism in a quantum phase transition of a spin-1 ferromagnetic Bose-Einstein condensate, when the applied magnetic field is quenched below a critical value. It is shown that the magnetic correlation functions have finite correlation lengths, and magnetizations at widely separated positions grow in random directions, resulting in spin vortices. We numerically confirm the scaling law that the winding number of spin vortices is proportional to the square root of the length of the closed path, and for slow quench, proportional to $\tau_{\rm Q}^{-1/6}$ with $\tau_{\rm Q}$ being the quench time. The relation between the spin conservation and the KZ mechanism is discussed.