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 ${\mathrm{Ir}}^{4+}$ 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.

中文翻译：

---

拟烧绿石铱酸盐磁性中的无序电子准量子纠缠

我们指出了由吡咯氯铱酸盐的电子准瞬变和量子序的无序相互作用引起的磁性。像其他莫特绝缘铱酸盐一样，${铱}^{4+}$ 烧绿石铱酸盐中的离子发展有效 $Ĵ=\mathrm{1个}/2$现场自旋轨道耦合的瞬间。我们考虑了烧绿石晶格上这些局部矩之间的一般对称允许交换，并获得了平均场相图。假设超交换是通过中间氧通过直接和/或间接电子跳跃来介导的，我们从哈伯德模型得出强耦合体系中的交换相互作用。这种交换具有退化的经典基态流形，并且量子涨落选择非共面基态，称为无序量子阶。扩展到中间耦合机制，通过简并的动能从简并流形中选择相同的非共面阶，该动能被称为“电子准瞬变”。我们讨论了实验结果与其他铱酸盐和其他准电子的准相关性。$4d/5d$ 磁铁。