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

Xu-Ping Yao, Gang Chen|arXiv (Cornell University)|Dec 18, 2017

Advanced Condensed Matter Physics4 citations

TL;DR

This paper proposes that the ordered 'Melko-Hertog-Gingras' spin ice state in Pr₂Ir₂O₇ generates an internal magnetic field that reconstructs the band structure of Ir 5d electrons, inducing symmetry-protected Dirac cones at time-reversal invariant momenta and stabilizing Weyl nodes. The f-d exchange coupling between Pr 4f moments and Ir conduction electrons enables magnetic field control of topological band features, offering a tunable platform for engineering topological semimetals in correlated electron systems.

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$_7$.

Motivation & Objective

• To investigate the interplay between Ir 5d conduction electrons and Pr 4f local moments in Pr₂Ir₂O₇.
• To understand how the ordered 'Melko-Hertog-Gingras' spin ice state of Pr moments influences the topological band structure of Ir electrons.
• To propose that the magnetic translation symmetry of the Pr spin order protects Dirac cones at time-reversal invariant momenta in the Ir band structure.
• To demonstrate that external magnetic fields can tune the system between semimetallic and insulating phases via f-d exchange coupling.
• To provide testable predictions for ARPES, optical, and magneto-transport experiments in ordered Pr₂Ir₂O₇ samples.

Proposed method

• Theoretical modeling of the band structure in Pr₂Ir₂O₇ using a tight-binding Hamiltonian incorporating f-d exchange coupling between Pr 4f moments and Ir 5d electrons.
• Analysis of the magnetic translation symmetry of the 'Melko-Hertog-Gingras' spin ice state and its impact on time-reversal symmetry protection of Dirac nodes.
• Use of group theory and momentum-space symmetry analysis to identify protected band touchings at high-symmetry points.
• Construction of phase diagrams in the parameter space of f-d exchange couplings to map topological phase transitions.
• Prediction of Weyl node formation under external magnetic fields due to symmetry breaking.
• Suggestion of experimental probes: ARPES for direct band structure mapping, optical spectroscopy for inter-band transitions, and magneto-transport for anomalous Hall effect and metal-insulator transitions.

Experimental results

Research questions

• RQ1 How does the ordered 'Melko-Hertog-Gingras' spin ice state of Pr 4f moments affect the band structure of Ir 5d conduction electrons in Pr₂Ir₂O₇?
• RQ2 What symmetries protect the emergence of Dirac cones in the Ir band structure when the Pr moments are ordered in the 'Melko-Hertog-Gingras' state?
• RQ3 Can external magnetic fields tune the topological nature of the Ir band structure in Pr₂Ir₂O₇, and if so, how?
• RQ4 What experimental signatures can distinguish the topological features induced by the Pr spin ice order from those in the paramagnetic phase?
• RQ5 How does the f-d exchange coupling mediate a field-driven metal-insulator transition in this system?

Key findings

• The 'Melko-Hertog-Gingras' spin ice order in Pr₂Ir₂O₇ generates an internal magnetic field that reconstructs the Ir 5d band structure, leading to symmetry-protected Dirac cones at time-reversal invariant momenta.
• The magnetic translation symmetry of the Pr spin order protects Dirac nodes at specific high-symmetry points in the Brillouin zone.
• Weyl nodes of different types are generically present in both the ordered Pr₂Ir₂O₇ sample and under external magnetic fields.
• Applying an external magnetic field lifts the protection of Dirac cones, causing them to disappear, which provides a sharp experimental signature.
• The phase diagram shows a field-driven metal-insulator transition, with a large portion of the semimetallic region converting to an insulating phase under strong f-d exchange coupling.
• ARPES, optical measurements, and magneto-transport are proposed as viable experimental probes to detect the predicted topological features and transitions.