Spontaneous Vortex Lattices in Quasi 2D Dipolar Spinor Condensates

Motivated by recent experiments (Vengalattore et al. in Phys. Rev. Lett. 100: 170403, 2008; Vengalattore et al., arXiv: 0901.3800), we study quasi 2D ferromagnetic condensates with various aspect ratios. We find that in zero magnetic field, dipolar energy generates a local energy minimum with all the spins lie in the 2D plane forming a row of circular spin textures with alternating orientation, corresponding to a packing of vortices of identical vorticity in different spin components. In a large magnetic field, the system can fall into a long lived dynamical state consisting of an array of elliptic and hyperbolic Mermin-Ho spin textures, while the true equilibrium is an uniaxial spin density wave with a single wave-vector along the magnetic field, and a wavelength similar to the characteristic length of the long lived vortex array state.