Competing orders and topology in the global phase diagram of pyrochlore iridates

Abstract

Strong electronic interactions and spin orbit coupling can be conducive for realizing novel broken symmetry phases supporting quasiparticles with nontrivial band topology. 227 pyrochlore iridates provide a suitable material platform for studying such emergent phenomena where both topology and competing orders play important roles. In contrast to the most members of this material class, which are thought to display "all-in all-out" (AIAO) type magnetically ordered low-temperature insulating ground states, Pr${}_2$Ir${}_2$O${}_7$ remains metallic while exhibiting "spin ice" (SI) correlations at low temperatures. Additionally, this is the only 227 iridate compound, which exhibits a large anomalous Hall effect (AHE) along [1,1,1] direction below 1.5 K, without possessing any measurable magnetic moment. By focusing on the normal state of 227 iridates, described by a parabolic semimetal with quadratic band touching, we use renormalization group analysis, mean-field theory, and phenomenological Landau theory as three complementary methods to construct a global phase diagram in the presence of generic local interactions among itinerant electrons of Ir ions. While the global phase diagram supports several competing multipolar orders, motivated by the phenomenology of 227 iridates we particularly emphasize the competition between AIAO and SI orders and how it can cause a mixed phase with "three-in one-out" (3I1O) spin configurations. In terms of topological properties of Weyl quasiparticles of the 3I1O state, we provide an explanation for the magnitude and the direction of the observed AHE in Pr${}_2$Ir${}_2$O${}_7$. We propose a strain induced enhancement of the onset temperature for AHE in thin films of Pr${}_2$Ir${}_2$O${}_7$ and additional experiments for studying competing orders in the vicinity of the metal-insulator transition.

25 pages, 11 Figures; replaced with the version published by Phys. Rev. B

References in corpus (13)

• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Magnetic orders and topological phases from f-d exchange in pyrochlore iridates
• Emergent topological phenomena in thin films of pyrochlore iridates
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Pyrochlore electrons under pressure, heat and field: shedding light on the iridates
• Slater to Mott crossover in the metal to insulator transition of Nd2Ir2O7
• Magnetic monopole condensation in pyrochlore ice quantum spin liquid: application to Pr2Ir2O7 and Yb2Ti2O7
• Topological phases in layered pyrochlore oxide thin films along the [111] direction
• Chiral RKKY interaction in Pr2Ir2O7
• Disordered and interacting parabolic semimetals in two and three dimensions
• Anomalous Hall effect from frustration-tuned scalar chirality distribution in Pr2Ir2O7
• First Principles Prediction of Topological Phases in Thin Films of Pyrochlore Iridates

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