  We interpret the recently observed spatial domain formation in spin-1 atomic
condensates as a result of dynamical instability. Within the mean field theory,
a homogeneous condensate is dynamically unstable (stable) for ferromagnetic
(antiferromagnetic) atomic interactions. We find this dynamical instability
naturally leads to spontaneous domain formation as observed in several recent
experiments for condensates with rather small numbers of atoms. For trapped
condensates, our numerical simulations compare quantitatively to the
experimental results, thus largely confirming the physical insight from our
analysis of the homogeneous case.
