Phase diagram of solitons in the polar phase of a spin-1 Bose-Einstein condensate

We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose-Einstein condensate in the presence of quadratic Zeeman effect at zero temperature. The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase. The states are assorted into normal, antiferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the particle and spin densities in the core. The order of phase transitions between different solitons and the critical behavior of relevant continuous transitions are proved within the mean-field theory.