  We explore the spin superfluid transport in exchange interaction dominated
three-sublattice antiferromagnets. The system in the long-wavelength regime is
described by an $SO(3)$ invariant field theory. Additional corrections from
Dzyaloshinskii-Moriya interactions or anisotropies can break the symmetry;
however, the system still approximately holds a $U(1)$-rotation symmetry. Thus,
the power-law spatial decay signature of spin superfluidity is identified in a
nonlocal-measurement setup where the spin injection is described by the
generalized spin-mixing conductance. We suggest iron jarosites as promising
material candidates for realizing our proposal.
