Spin-domain formation in spinor Bose-Einstein condensation

The spatial structure of the spinor Bose-Einstein condensates with the spin degrees of freedom is analyzed based on the generalized Gross-Pitaevskii (GP) equation in light of the present spin-domain experiment on $m_F=\pm 1,$ and $0$ of the hyperfine state $F=1\mathrm{}$ of ${}^{23}\mathrm{Na}$ atom gases. The GP solutions in three- and one-spatial dimensional cases reproduce the observed spin-domain structures, revealing the length scale associated with the existence of the weak interaction of the spin-spin channel, other than the ordinary coherence length related to the density-density channel. The obtained domain structure in GP is compared with the result in the Thomas-Fermi approximation. The former solution is found to better describe the observed features than the latter.