Spin folding in the two-dimensional Heisenbergkagoméantiferromagnet

Spin-folding modes in the two-dimensional Heisenberg kagomé antiferromagnet favor coplanar spin configurations with three-spin tensor order and non-Abelian homotopy. With weak xy anisotropy, binding of the associated disclinations yields a coplanar state whose spin configuration depends on the order of pairing. The resulting metastable states exhibits a broad distribution of order parameters. Supporting numerical studies are presented and the related system ${\mathrm{SrCr}}_{8\mathrm{-}\mathit{x}}$ ${\mathrm{Ga}}_{4+\mathit{x}}$ ${\mathrm{O}}_{19}$ is discussed.