Abstract
A formation of tetrahedral spin clusters is discovered by Monte Carlo simulation for a spin-ice type double-exchange model on a pyrochlore lattice. The spin-cluster phase is magnetically disordered but breaks spatial inversion symmetry spontaneously by developing noncoplanar four-spin molecules periodically on the pyrochlore lattice. We find that the system exhibits a nonzero spin Hall conductivity in the spin-cluster phase. The result suggests that an intersite-multipole order induces the unconventional spin Hall state without the spin-orbit interaction.
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