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

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${}_7$.

10 pages, 7 figures, added more refs

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• First-principles studies of spin-orbital physics in pyrochlore oxides
• Experimental signatures of versatile Weyl semimetal in pyrochlore iridate with spin-ice like magnetic orders
• Optical response of Luttinger semimetals in the normal and superconducting states
• Competing magnetic orders and multipolar Weyl fermions in 227 pyrochlore iridates
• Phonon spectrum of Pr${}_2$Zr${}_2$O${}_7$ and Pr${}_2$Ir${}_2$O${}_7$ as an evidence of coupling of the lattice with electronic and magnetic degrees of freedom
• Multi-scale Quantum Criticality driven by Kondo-lattice Coupling in Pyrochlore Systems
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• Quasiuniversality from all-in-all-out Weyl quantum criticality in pyrochlore iridates
• Electron quasi-itinerancy intertwined with quantum order by disorder in pyrochlore iridate magnetism
• Many-body electronic structure in pyrochlore superconductor CsBi2 and spin liquid Pr2Ir2O7
• Three-dimensional Sandglass Magnet with Non-Kramers ions
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• Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions