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Hwang K, Trivedi N, Randeria M. Topological Magnons with Nodal-Line and Triple-Point Degeneracies: Implications for Thermal Hall Effect in Pyrochlore Iridates. PHYSICAL REVIEW LETTERS 2020; 125:047203. [PMID: 32794830 DOI: 10.1103/physrevlett.125.047203] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2018] [Revised: 12/19/2019] [Accepted: 06/29/2020] [Indexed: 06/11/2023]
Abstract
We analyze the magnon excitations in pyrochlore iridates with all-in-all-out (AIAO) antiferromagnetic order, focusing on their topological features. We identify the magnetic point group symmetries that protect the nodal-line band crossings and triple-point degeneracies that dominate the Berry curvature. We find three distinct regimes of magnon band topology, as a function of the ratio of Dzyaloshinskii-Moriya interaction to the antiferromagnetic exchange. We show how the thermal Hall response provides a unique probe of the topological magnon band structure in AIAO systems.
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Affiliation(s)
- Kyusung Hwang
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Nandini Trivedi
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - Mohit Randeria
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
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Shinaoka H, Motome Y, Miyake T, Ishibashi S, Werner P. First-principles studies of spin-orbital physics in pyrochlore oxides. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:323001. [PMID: 31140447 DOI: 10.1088/1361-648x/ab162f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
The pyrochlore oxides [Formula: see text]O7 exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling (SOC), due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical challenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4d and 5d pyrochlore oxides with B = Mo, Os, and Ir. In these studies, the SOC and local electron correlations are treated within the local density approximation (LDA) + U and LDA + dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations.
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Affiliation(s)
- Hiroshi Shinaoka
- Department of Physics, Saitama University, Saitama 338-8570, Japan
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Wang Y, Weng H, Fu L, Dai X. Noncollinear Magnetic Structure and Multipolar Order in Eu_{2}Ir_{2}O_{7}. PHYSICAL REVIEW LETTERS 2017; 119:187203. [PMID: 29219540 DOI: 10.1103/physrevlett.119.187203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2017] [Indexed: 06/07/2023]
Abstract
The magnetic properties of the pyrochlore iridate material Eu_{2}Ir_{2}O_{7} (5d^{5}) have been studied based on first principles calculations, where the crystal field splitting Δ, spin-orbit coupling (SOC) λ, and Coulomb interaction U within Ir 5d orbitals all play significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction U, where a stable antiferromagnetic ground state with all-in-all-out (AIAO) spin structure has been found. In addition, another antiferromagnetic state with energy close to AIAO has also been found to be stable. The calculated nonlinear magnetization of the two stable states both have the d-wave pattern but with a π/4 phase difference, which can perfectly explain the experimentally observed nonlinear magnetization pattern. Compared with the results of the nondistorted structure, it turns out that the trigonal lattice distortion is crucial for stabilizing the AIAO state in Eu_{2}Ir_{2}O_{7}. Furthermore, besides large dipolar moments, we also find considerable octupolar moments in the magnetic states.
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Affiliation(s)
- Yilin Wang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hongming Weng
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Xi Dai
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100190, China
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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Jaubert LDC, Lin T, Opel TS, Holdsworth PCW, Gingras MJP. Spin ice Thin Film: Surface Ordering, Emergent Square ice, and Strain Effects. PHYSICAL REVIEW LETTERS 2017; 118:207206. [PMID: 28581768 DOI: 10.1103/physrevlett.118.207206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2016] [Indexed: 06/07/2023]
Abstract
Motivated by recent realizations of Dy_{2}Ti_{2}O_{7} and Ho_{2}Ti_{2}O_{7} spin ice thin films, and more generally by the physics of confined gauge fields, we study a model spin ice thin film with surfaces perpendicular to the [001] cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges. This surface ordering may also be expected on the surfaces of bulk crystals. For ultrathin films made of one cubic unit cell, once the surfaces have ordered, a square ice phase is stabilized over a finite temperature window. The square ice degeneracy is lifted at lower temperature and the system orders in analogy with the well-known F transition of the 6-vertex model. To conclude, we consider the addition of strain effects, a possible consequence of interface mismatches at the film-substrate interface. Our simulations qualitatively confirm that strain can lead to a smooth loss of Pauling entropy upon cooling, as observed in recent experiments on Dy_{2}Ti_{2}O_{7} films.
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Affiliation(s)
- L D C Jaubert
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France
| | - T Lin
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - T S Opel
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - P C W Holdsworth
- Université de Lyon, Laboratoire de Physique, École normale supérieure de Lyon, CNRS, UMR5672, 46 Allée d'Italie, 69364 Lyon, France
| | - M J P Gingras
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
- Perimeter Institute for Theoretical Physics, 31 Caroline North, Waterloo, Ontario N2L 2Y5, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
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Laurell P, Fiete GA. Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films. PHYSICAL REVIEW LETTERS 2017; 118:177201. [PMID: 28498709 DOI: 10.1103/physrevlett.118.177201] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2016] [Indexed: 06/07/2023]
Abstract
We theoretically study the magnetic properties of pyrochlore iridate bilayer and trilayer thin films grown along the [111] direction using a strong coupling approach. We find the ground state magnetic configurations on a mean field level and carry out a spin-wave analysis about them. In the trilayer case the ground state is found to be the all-in-all-out (AIAO) state, whereas the bilayer has a deformed AIAO state. For all parameters of the spin-orbit coupled Hamiltonian we study, the lowest magnon band in the trilayer case has a nonzero Chern number. In the bilayer case we also find a parameter range with nonzero Chern numbers. We calculate the magnon Hall response for both geometries, finding a striking sign change as a function of temperature. Using a slave-boson mean-field theory we study the doping of the trilayer system and discover an unconventional time-reversal symmetry broken d+id superconducting state. Our study complements prior work in the weak coupling limit and suggests that the [111] grown thin film pyrochlore iridates are a promising candidate for topological properties and unconventional orders.
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Affiliation(s)
- Pontus Laurell
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Gregory A Fiete
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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Zhang H, Haule K, Vanderbilt D. Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates. PHYSICAL REVIEW LETTERS 2017; 118:026404. [PMID: 28128605 DOI: 10.1103/physrevlett.118.026404] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2015] [Indexed: 06/06/2023]
Abstract
Combining density functional theory (DFT) and embedded dynamical mean-field theory (DMFT) methods, we study the metal-insulator transition in R_{2}Ir_{2}O_{7} (R=Y, Eu, Sm, Nd, Pr, and Bi) and the topological nature of the insulating compounds. Accurate free energies evaluated using the charge self-consistent DFT+DMFT method reveal that the metal-insulator transition occurs for an A-cation radius between that of Nd and Pr, in agreement with experiments. The all-in-all-out magnetic phase, which is stable in the Nd compound but not the Pr one, gives rise to a small Ir^{4+} magnetic moment of ≈0.4 μ_{B} and opens a sizable correlated gap. We demonstrate that within this state-of-the-art theoretical method, the insulating bulk pyrochlore iridates are topologically trivial.
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Affiliation(s)
- Hongbin Zhang
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
- Institute of Materials Science, Technische Universität Darmstadt, 64287 Darmstadt, Germany
| | - Kristjan Haule
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - David Vanderbilt
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
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Schaffer R, Kin-Ho Lee E, Yang BJ, Kim YB. Recent progress on correlated electron systems with strong spin-orbit coupling. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:094504. [PMID: 27540689 DOI: 10.1088/0034-4885/79/9/094504] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The emergence of novel quantum ground states in correlated electron systems with strong spin-orbit coupling has been a recent subject of intensive studies. While it has been realized that spin-orbit coupling can provide non-trivial band topology in weakly interacting electron systems, as in topological insulators and semi-metals, the role of electron-electron interaction in strongly spin-orbit coupled systems has not been fully understood. The availability of new materials with significant electron correlation and strong spin-orbit coupling now makes such investigations possible. Many of these materials contain 5d or 4d transition metal elements; the prominent examples are iridium oxides or iridates. In this review, we succinctly discuss recent theoretical and experimental progress on this subject. After providing a brief overview, we focus on pyrochlore iridates and three-dimensional honeycomb iridates. In pyrochlore iridates, we discuss the quantum criticality of the bulk and surface states, and the relevance of the surface/boundary states in a number of topological and magnetic ground states, both in the bulk and thin film configurations. Experimental signatures of these boundary and bulk states are discussed. Domain wall formation and strongly-direction-dependent magneto-transport are also discussed. In regard to the three-dimensional honeycomb iridates, we consider possible quantum spin liquid phases and unusual magnetic orders in theoretical models with strongly bond-dependent interactions. These theoretical ideas and results are discussed in light of recent resonant x-ray scattering experiments on three-dimensional honeycomb iridates. We also contrast these results with the situation in two-dimensional honeycomb iridates. We conclude with the outlook on other related systems.
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Affiliation(s)
- Robert Schaffer
- Department of Physics and Center for Quantum Materials, University of Toronto, Toronto, Ontario M5S 1A7, Canada
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Hwang K, Kim YB. Theory of Multifarious Quantum Phases and Large Anomalous Hall Effect in Pyrochlore Iridate Thin Films. Sci Rep 2016; 6:30017. [PMID: 27418293 PMCID: PMC4945933 DOI: 10.1038/srep30017] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Accepted: 06/27/2016] [Indexed: 11/11/2022] Open
Abstract
We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect.
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Affiliation(s)
- Kyusung Hwang
- Department of Physics and Centre for Quantum Materials, University of Toronto, Toronto, Ontario M5S 1A7, Canada
| | - Yong Baek Kim
- Department of Physics and Centre for Quantum Materials, University of Toronto, Toronto, Ontario M5S 1A7, Canada
- Canadian Institute for Advanced Research/Quantum Materials Program, Toronto, Ontario M5G 1Z8, Canada
- School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea
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