Coarsening dynamics driven by vortex-antivortex annihilation in ferromagnetic Bose-Einstein condensates

In ferromagnetic Bose-Einstein condensates (BECs), the quadratic Zeeman effect controls magnetic anisotropy, which affects on magnetic domain pattern formation. While the longitudinal magnetization is dominant (similar to the Ising model) for a negative quadratic Zeeman energy, the transverse magnetization is dominant (similar to the XY model) for a positive one. When the quadratic Zeeman energy is positive, the coarsening dynamics is driven by vortex-antivortex annihilation in the same way as the XY model. However, due to superfluid flow of atoms, there exist several combinations of vortex-antivortex pairs in ferromagnetic BECs, which makes the coarsening dynamics more complicated than that of the XY model. We propose a revised domain growth law, which is based on the growth law of the two-dimensional XY model, for a two-dimensional ferromagnetic BEC with a positive quadratic Zeeman energy.