Spin superfluidity in noncollinear antiferromagnets

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.