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.