  Motivated by a recent experiment, we study non-equilibrium quantum phenomena
taking place in the quench of a spinor Bose-Einstein condensate through the
zero-temperature phase transition separating the polar paramagnetic and planar
ferromagnetic phases. We derive the typical spin domain structure (correlations
of the effective magnetization) created by the quench arising due to spin-mode
quantum fluctuations, and establish a sample-size scaling law for the creation
of spin vortices, which are topological defects in the transverse
magnetization.
