  We have experimentally observed the emergence of spontaneous
antiferromagnetic spatial order in a sodium spinor Bose-Einstein condensate
that was quenched through a magnetic phase transition. For negative values of
the quadratic Zeeman shift, a gas initially prepared in the F = 1, mF = 0 state
collapsed into a dynamically evolving superposition of all 3 spin projections,
mF = 0, +/-1. The quench gave rise to rich, nonequilibrium behavior where both
nematic and magnetic spin waves were generated. We characterized the
spatiotemporal evolution through two particle correlations between atoms in
each pair of spin states. These revealed dramatic differences between the
dynamics of the spin correlations and those of the spin populations.
