Core structure of static ferrodark solitons in a spin-1 Bose-Einstein condensate

We develop an analytical description of static ferrodark solitons, the Z(2) topological defects in the magnetic order, in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed Anstitze show excellent agreement with numerical results. Spin-singlet amplitudes, nematic tensor densities, and nematic currents of ferrodark solitons are also discussed. The Z(2) topological defects in the mass superfluid order, dark-dark-dark vector solitons, are obtained exactly in the parameter regime where exact ferrodark solitons exist. The dark-dark-dark vector soliton has higher excitation energy than ferrodark solitons.