  We investigate the long-term dynamics of spin textures prepared by cooling
unmagnetized spinor gases of F=1 $^{87}$Rb to quantum degeneracy, observing
domain coarsening and a strong dependence of the equilibration dynamics on the
quadratic Zeeman shift $q$. For small values of $|q|$, the textures arrive at a
configuration independent of the initial spin-state composition, characterized
by large length-scale spin domains, and the establishment of easy-axis
(negative $q$) or easy-plane (positive $q$) magnetic anisotropy. For larger
$|q|$, equilibration is delayed as the spin-state composition of the degenerate
spinor gas remains close to its initial value. These observations support the
mean-field equilibrium phase diagram predicted for a ferromagnetic spinor
Bose-Einstein condensate, but also illustrate that equilibration is achieved
under a narrow range of experimental settings, making the F=1 $^{87}$Rb gas
more suitable for studies of nonequilibrium quantum dynamics.

Quantum Gases;Other Condensed Matter;Atomic Physics