| Summary: | We point out the emergence of magnetism from the interplay of electron quasi-itinerancy and quantum order by disorder in pyrochlore iridates. Like other Mott insulating iridates, the Ir^{4+} ion in pyrochlore iridates develops an effective J=1/2 moment from the on-site spin-orbit coupling. We consider the generic symmetry-allowed exchange between these local moments on a pyrochlore lattice and obtain the mean-field phase diagram. Assuming the superexchange is mediated by direct and/or indirect electron hopping via intermediate oxygens, we derive the exchange interactions in the strong-coupling regime from the Hubbard model. This exchange has a degenerate classical ground-state manifold, and quantum fluctuation selects a noncoplanar ground state, known as quantum order by disorder. Extending to the intermediate-coupling regime, the same noncoplanar order is selected from the degenerate manifold by the kinetic energy, which is dubbed “electron quasi-itinerancy.” We discuss the experimental relevance of our results and electron quasi-itinerancy among other iridates and 4d/5d magnets.
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