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

It is shown that spin vortices are created through the Kibble-Zurek mechanism in the quantum phase transition of a spin-1 ferromagnetic Bose-Einstein condensate when the applied magnetic field is quenched to below a critical value. It is also shown that the spin correlation functions have finite correlation lengths, and that the magnetization at widely separated positions grows in random directions, resulting in spontaneous creation of spin vortices. We numerically confirm the scaling laws that the winding number of spin vortices is proportional to the square root of the length of a closed path and, for a slow quench, is proportional to ₐ^-1∕6 with ₐ being the quench time. The relevance of spin conservation to the Kibble-Zurek mechanism is discussed.