Pr$_2$Ir$_2$O$_7$: when Luttinger semimetal meets Melko-Hertog-Gingras spin ice state

TL;DR

This paper investigates how the interplay between local moments and itinerant electrons in Pr$_2$Ir$_2$O$_7$ influences its band topology, revealing protected Dirac points and potential control via magnetic fields, with implications for topological properties.

Contribution

It introduces the concept that the Pr local moments' spin ice order reconstructs the band structure of the Luttinger semimetal, predicting protected Dirac points and controllable topological features.

Findings

Pr$_2$Ir$_2$O$_7$ hosts a Luttinger semimetal with magnetic order affecting its band structure.

The spin ice order of Pr moments can protect Dirac band touchings at specific momenta.

Magnetic fields can tune the Pr magnetic structure and influence the Ir electrons' topological properties.

Abstract

We study the band structure topology and engineering from the interplay between local moments and itinerant electrons in the context of pyrochlore iridates. For the metallic iridate Pr$_2$Ir$_2$O$_7$, the Ir $5d$ conduction electrons interact with the Pr $4f$ local moments via the $f$-$d$ exchange. While the Ir electrons form a Luttinger semimetal, the Pr moments can be tuned into an ordered spin ice with a finite ordering wavevector, dubbed "Melko-Hertog-Gingras" state, by varying Ir and O contents. We point out that the ordered spin ice of the Pr local moments generates an internal magnetic field that reconstructs the band structure of the Luttinger semimetal. Besides the broad existence of Weyl nodes, we predict that the magnetic translation of the "Melko-Hertog-Gingras" state for the Pr moments protects the Dirac band touching at certain time reversal invariant momenta for the Ir conduction electrons. We propose the magnetic fields to control the Pr magnetic structure and thereby indirectly influence the topological and other properties of the Ir electrons. Our prediction may be immediately tested in the ordered Pr$_2$Ir$_2$O$_7$ samples. We expect our work to stimulate a detailed examination of the band structure, magneto-transport, and other properties of Pr$_2$Ir$_2$O$_7$.