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A formation of tetrahedral spin clusters is discovered by Monte Carlosimulation for a spin-ice type double-exchange model on a pyrochlore lattice.The spin-cluster phase is magnetically disordered, but breaks spatial inversionsymmetry spontaneously by developing noncoplanar four-spin moleculesperiodically on the pyrochlore lattice. We find that the system exhibits anonzero spin Hall conductivity in the spin-cluster phase. The result suggeststhat an intersite-multipole order induces the unconventional spin Hall statewithout the spin-orbit interaction.

Spontaneous Spatial Inversion Symmetry Breaking and Spin Hall Effect in a Spin-ice Double-exchange Model on a Pyrochlore Lattice