  We develop an analytical description of static ferrodark solitons, the
$\mathbb{Z}_2$ 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 ansatzes show excellent
agreement with numerical results. Spin-singlet amplitudes, nematic tensor
densities and nematic currents of ferrodark solitons are also discussed. The
$\mathbb{Z}_2$ 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.
