Electron quasi-itinerancy intertwined with quantum order by disorder in pyrochlore iridate magnetism

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 non-coplanar ground state, known as quantum order by disorder. Extending to the intermediate coupling regime, the same non-coplanar 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.