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Wei C, Curnoe SH. Exact diagonalization for a 16-site spin-1/2 pyrochlore cluster. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 35. [PMID: 37054738 DOI: 10.1088/1361-648x/acccc8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 04/13/2023] [Indexed: 05/16/2023]
Abstract
We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore cluster with nearest neighbour exchange interactions. The methods of group theory (symmetry) are used to completely block-diagonalize the Hamiltonian, yielding precise details about symmetry of the eigenstates, in particular those components which arespin icestates, in order to evaluate the spin ice density at finite temperature. At low enough temperatures, a 'perturbed' spin ice phase, where the '2-in-2-out' ice rule is largely obeyed, is clearly outlined within the four parameter space of the general model of exchange interactions. The quantum spin ice phase is expected to exist within these boundaries.
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Affiliation(s)
- C Wei
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's A1B 3X7, Newfoundland & Labrador, Canada
| | - S H Curnoe
- Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John's A1B 3X7, Newfoundland & Labrador, Canada
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2
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Legros A, Zhang SS, Bai X, Zhang H, Dun Z, Phelan WA, Batista CD, Mourigal M, Armitage NP. Observation of 4- and 6-Magnon Bound States in the Spin-Anisotropic Frustrated Antiferromagnet FeI_{2}. PHYSICAL REVIEW LETTERS 2021; 127:267201. [PMID: 35029479 DOI: 10.1103/physrevlett.127.267201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 11/12/2021] [Indexed: 06/14/2023]
Abstract
We observe a wealth of multimagnon bound states in the strongly anisotropic spin-1 triangular antiferromagnet FeI_{2} using time-domain terahertz spectroscopy. These unconventional excitations can arise in ordered magnets due to attractive magnon-magnon interactions and alter their properties. We analyze the energy-magnetic field spectrum via an exact diagonalization method for a dilute gas of interacting magnons and detect up to 4- and 6-magnon bound states, hybridized with single magnons. This zoo of tunable interacting quasiparticles provides a unique platform to study decay and renormalization, reminiscent of the few-body problems found in cold-atom, nuclear, and particle physics.
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Affiliation(s)
- Anaëlle Legros
- The Institute for Quantum Matter and the Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Shang-Shun Zhang
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Xiaojian Bai
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Hao Zhang
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Zhiling Dun
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - W Adam Phelan
- PARADIM, Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Cristian D Batista
- Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Martin Mourigal
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - N P Armitage
- The Institute for Quantum Matter and the Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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3
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Two-dimensional magnetic monopole gas in an oxide heterostructure. Nat Commun 2020; 11:1341. [PMID: 32165628 PMCID: PMC7067881 DOI: 10.1038/s41467-020-15213-z] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2019] [Accepted: 02/18/2020] [Indexed: 11/19/2022] Open
Abstract
Magnetic monopoles have been proposed as emergent quasiparticles in pyrochlore spin ice compounds. However, unlike semiconductors and two-dimensional electron gases where the charge degree of freedom can be actively controlled by chemical doping, interface modulation, and electrostatic gating, there is as of yet no analogue of these effects for emergent magnetic monopoles. To date, all experimental investigations have been limited to large ensembles comprised of equal numbers of monopoles and antimonopoles in bulk crystals. To address these issues, we propose the formation of a two-dimensional magnetic monopole gas (2DMG) with a net magnetic charge, confined at the interface between a spin ice and an isostructural antiferromagnetic pyrochlore iridate and whose monopole density can be controlled by an external field. Our proposal is based on Monte Carlo simulations of the thermodynamic and transport properties. This proposed 2DMG should enable experiments and devices which can be performed on magnetic monopoles, akin to two-dimensional electron gases in semiconductor heterostructures. Heterostructure interfaces have physical properties distinct from bulk materials, providing the basis for many electronic devices. Miao et al. propose a spin ice heterostructure that can host a two-dimensional gas of emergent magnetic monopoles with a net magnetic charge.
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Morampudi SC, Wilczek F, Laumann CR. Spectroscopy of Spinons in Coulomb Quantum Spin Liquids. PHYSICAL REVIEW LETTERS 2020; 124:097204. [PMID: 32202892 DOI: 10.1103/physrevlett.124.097204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Revised: 12/06/2019] [Accepted: 02/20/2020] [Indexed: 06/10/2023]
Abstract
We calculate the effect of the emergent photon on threshold production of spinons in U(1) Coulomb spin liquids such as quantum spin ice. The emergent Coulomb interaction modifies the threshold production cross-section dramatically, changing the weak turn-on expected from the density of states to an abrupt onset reflecting the basic coupling parameters. The slow photon typical in existing lattice models and materials suppresses the intensity at finite momentum and allows profuse Cerenkov radiation beyond a critical momentum. These features are broadly consistent with recent numerical and experimental results.
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Affiliation(s)
| | - Frank Wilczek
- Center for Theoretical Physics, MIT, Cambridge Massachusetts 02139, USA
- T. D. Lee Institute, Shanghai 200240, China
- Wilczek Quantum Center, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Department of Physics, Stockholm University, Stockholm 114 19, Sweden
- Department of Physics and Origins Project, Arizona State University, Tempe Arizona 25287, USA
| | - Chris R Laumann
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Chauhan P, Mahmood F, Changlani HJ, Koohpayeh SM, Armitage NP. Tunable Magnon Interactions in a Ferromagnetic Spin-1 Chain. PHYSICAL REVIEW LETTERS 2020; 124:037203. [PMID: 32031844 DOI: 10.1103/physrevlett.124.037203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 10/07/2019] [Indexed: 06/10/2023]
Abstract
NiNb_{2}O_{6} is an almost ideal realization of a 1D spin-1 ferromagnetic Heisenberg chain compound with weak unidirectional anisotropy. Using time-domain THz spectroscopy, we measure the low-energy electrodynamic response of NiNb_{2}O_{6} as a function of temperature and external magnetic field. At low temperatures, we find a magnonlike spin excitation, which corresponds to the lowest energy excitation at q∼0. At higher temperatures, we unexpectedly observe a temperature-dependent renormalization of the spin-excitation energy, which has a strong dependence on field direction. Using theoretical arguments, exact diagonalizations, and finite temperature dynamical Lanczos calculations, we construct a picture of magnon-magnon interactions that naturally explains the observed renormalization. We show how magnetic field strength and direction may be used to directly tune the sign of the magnon-magnon interaction. This unique scenario is a consequence of the spin-1 nature and has no analog in the more widely studied spin-1/2 systems.
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Affiliation(s)
- Prashant Chauhan
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Fahad Mahmood
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Hitesh J Changlani
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
- Department of Physics, Florida State University, Tallahassee, Florida 32306, USA
- National High Magnetic Field Laboratory, Tallahassee, Florida 32304, USA
| | - S M Koohpayeh
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - N P Armitage
- The Institute for Quantum Matter, Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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Chern LE, Kim YB. Magnetic Order with Fractionalized Excitations in Pyrochlore Magnets with Strong Spin-Orbit Coupling. Sci Rep 2019; 9:10974. [PMID: 31358857 PMCID: PMC6662772 DOI: 10.1038/s41598-019-47517-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2019] [Accepted: 07/18/2019] [Indexed: 11/26/2022] Open
Abstract
A recent inelastic neutron scattering experiment on the pyrochlore magnet Yb2Ti2O7 uncovers an unusual scattering continuum in the spin excitation spectrum despite the splayed ferromagnetic order in the ground state. While there exist well defined spin wave excitations at high magnetic fields, the one magnon modes and the two magnon continuum start to strongly overlap upon decreasing the field, and eventually they become the scattering continuum at zero field. Motivated by these observations, we investigate the possible emergence of a magnetically ordered ground state with fractionalized excitations in the spin model with the exchange parameters determined from two previous experiments. Using the fermionic parton mean field theory, we show that the magnetically ordered state with fractionalized excitations can arise as a stable mean field ground state in the presence of sufficiently strong quantum fluctuations. The spin excitation spectrum in such a ground state is computed and shown to have the scattering continuum. Upon increasing the field, the fractionalized magnetically ordered state is suppressed, and is eventually replaced by the conventional magnetically ordered phase at high fields, which is consistent with the experimental data. We discuss further implications of these results to the experiments and possible improvements on the theoretical analysis.
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Affiliation(s)
- Li Ern Chern
- Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, Canada.
| | - Yong Baek Kim
- Department of Physics, 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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7
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Luo ZX, Lake E, Mei JW, Starykh OA. Spinon Magnetic Resonance of Quantum Spin Liquids. PHYSICAL REVIEW LETTERS 2018; 120:037204. [PMID: 29400534 DOI: 10.1103/physrevlett.120.037204] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Indexed: 06/07/2023]
Abstract
We describe electron spin resonance in a quantum spin liquid with significant spin-orbit coupling. We find that the resonance directly probes spinon continuum, which makes it an efficient and informative probe of exotic excitations of the spin liquid. Specifically, we consider spinon resonance of three different spinon mean-field Hamiltonians, obtained with the help of projective symmetry group analysis, which model a putative quantum spin liquid state of the triangular rare-earth antiferromagnet YbMgGaO_{4}. The band of absorption is found to be very broad and exhibit strong van Hove singularities of single spinon spectrum as well as pronounced polarization dependence.
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Affiliation(s)
- Zhu-Xi Luo
- Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
| | - Ethan Lake
- Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
| | - Jia-Wei Mei
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
| | - Oleg A Starykh
- Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
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Little A, Wu L, Lampen-Kelley P, Banerjee A, Patankar S, Rees D, Bridges CA, Yan JQ, Mandrus D, Nagler SE, Orenstein J. Antiferromagnetic Resonance and Terahertz Continuum in α-RuCl_{3}. PHYSICAL REVIEW LETTERS 2017; 119:227201. [PMID: 29286790 DOI: 10.1103/physrevlett.119.227201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2017] [Indexed: 06/07/2023]
Abstract
We report measurements of optical absorption in the zigzag antiferromagnet α-RuCl_{3} as a function of temperature T, magnetic field B, and photon energy ℏω in the range ∼0.3-8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at B=0 that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of B, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.
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Affiliation(s)
- A Little
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Liang Wu
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - P Lampen-Kelley
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - A Banerjee
- Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
| | - S Patankar
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - D Rees
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - C A Bridges
- Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
| | - J-Q Yan
- Material Sciences and Technology Division, Oak Ridge National Laboratory, Oak Ridge,Tennessee 37830, USA
| | - D Mandrus
- Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - S E Nagler
- Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
- Bredesen Center, University of Tennessee, Knoxville, Tennessee 37966, USA
| | - J Orenstein
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Thompson JD, McClarty PA, Prabhakaran D, Cabrera I, Guidi T, Coldea R. Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb_{2}Ti_{2}O_{7} in a Magnetic Field. PHYSICAL REVIEW LETTERS 2017; 119:057203. [PMID: 28949704 DOI: 10.1103/physrevlett.119.057203] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2017] [Indexed: 06/07/2023]
Abstract
The frustrated pyrochlore magnet Yb_{2}Ti_{2}O_{7} has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.
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Affiliation(s)
- J D Thompson
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - P A McClarty
- ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, United Kingdom
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - D Prabhakaran
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - I Cabrera
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - T Guidi
- ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, United Kingdom
| | - R Coldea
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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10
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Savary L, Balents L. Quantum spin liquids: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:016502. [PMID: 27823986 DOI: 10.1088/0034-4885/80/1/016502] [Citation(s) in RCA: 296] [Impact Index Per Article: 42.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.
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Affiliation(s)
- Lucile Savary
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Jaubert LDC, Benton O, Rau JG, Oitmaa J, Singh RRP, Shannon N, Gingras MJP. Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)? PHYSICAL REVIEW LETTERS 2015; 115:267208. [PMID: 26765024 DOI: 10.1103/physrevlett.115.267208] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2015] [Indexed: 06/05/2023]
Abstract
If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.
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Affiliation(s)
- L D C Jaubert
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Owen Benton
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Jeffrey G Rau
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
| | - J Oitmaa
- School of Physics, The University of New South Wales, Sydney 2052, Australia
| | - R R P Singh
- Department of Physics, University of California, Davis, California 95616, USA
| | - Nic Shannon
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Michel 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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