Abstract
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.
Highlights
In recent years, there has been a lot of activity on the Ir-based transition-metal oxides
We primarily focus on the magnetic properties and avoid touching the band structure topology that has been invoked in early works
II, we study a generic symmetry-allowed exchange Hamiltonian on the pyrochlore lattice with the effective spin1/2 originating from Kramers degeneracy, which is relevant for R2Ir2O7 in the strong-coupling regime
Summary
There has been a lot of activity on the Ir-based transition-metal oxides. For example, a quantum spin liquid phase was proposed for an Ir-based hyperkagomé lattice in Na4Ir3O8 [5], and a ferromagnetic ground state with a large ferromagnetic moment was discovered in Sr2IrO4 with the Ir4+ ions forming a square lattice [6] In these Mott insulating systems, the presence of strong SOC drastically changes the local spin physics. For the realistic exchange model obtained from an extended Hubbard model relevant for R2Ir2O7, there are only two ordered phases, which are the four-in–four-out state and the continuously degenerate manifold spanned by two basis vectors (v1, v2) For the latter, we find that the quantum fluctuation selects a noncoplanar spin configuration by a linear spin-wave expansion. IV, we discuss the relevant experiments and other related works
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