skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14

Abstract

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T∗≈0.32  K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T≈0.12  K. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial rolemore » played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.« less

Authors:
ORCiD logo; ; ; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Georgia Institute of Technology, Atlanta, GA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF)
OSTI Identifier:
1668450
Alternate Identifier(s):
OSTI ID: 1673167; OSTI ID: 1798626
Grant/Contract Number:  
SC0018660; AC05-00OR22725; DMR-2003117
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 10 Journal Issue: 3; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Frustrated magnetism; Quantum spin liquid; Kagome lattice; Polycrystalline materials; Spin ice; Mean field theory; Neutron scattering; Random phase approximation; Semiclassical methods; Specific heat measurements; Time-of-flight neutron spectroscopy

Citation Formats

Dun, Zhiling, Bai, Xiaojian, Paddison, Joseph A. M., Hollingworth, Emily, Butch, Nicholas P., Cruz, Clarina D., Stone, Matthew B., Hong, Tao, Demmel, Franz, Mourigal, Martin, and Zhou, Haidong. Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14. United States: N. p., 2020. Web. https://doi.org/10.1103/PhysRevX.10.031069.
Dun, Zhiling, Bai, Xiaojian, Paddison, Joseph A. M., Hollingworth, Emily, Butch, Nicholas P., Cruz, Clarina D., Stone, Matthew B., Hong, Tao, Demmel, Franz, Mourigal, Martin, & Zhou, Haidong. Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14. United States. https://doi.org/10.1103/PhysRevX.10.031069
Dun, Zhiling, Bai, Xiaojian, Paddison, Joseph A. M., Hollingworth, Emily, Butch, Nicholas P., Cruz, Clarina D., Stone, Matthew B., Hong, Tao, Demmel, Franz, Mourigal, Martin, and Zhou, Haidong. Tue . "Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14". United States. https://doi.org/10.1103/PhysRevX.10.031069.
@article{osti_1668450,
title = {Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho 3 Mg 2 Sb 3 O 14},
author = {Dun, Zhiling and Bai, Xiaojian and Paddison, Joseph A. M. and Hollingworth, Emily and Butch, Nicholas P. and Cruz, Clarina D. and Stone, Matthew B. and Hong, Tao and Demmel, Franz and Mourigal, Martin and Zhou, Haidong},
abstractNote = {A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T∗≈0.32  K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T≈0.12  K. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.},
doi = {10.1103/PhysRevX.10.031069},
journal = {Physical Review. X},
number = 3,
volume = 10,
place = {United States},
year = {2020},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevX.10.031069

Figures / Tables:

FIG. 1 FIG. 1: Classical spin fragmentation (CSF) process in a model of dipolar kagome ice displaying emergent-charge order, based on Ref. [39]. The expectation values of spinsmore » $\langle$$σ^z_i$$\rangle$ are represented by black arrows. Each triangle has one spin pointing “in” (toward its center) and two pointing “out” (away from its center), or vice versa. The emergent magnetic charge of a triangle is defined as the number of spins pointing in minus the number pointing out. Positive ($Q_j$ = +) and negative ($Q_j$ = −) emergent charges are represented as red and blue triangles, respectively, and form a staggered arrangement. Three distinct spin configurations are possible for a given emergent charge, which yields a macroscopic number of degenerate spin configurations associated with emergent-charge ordering. Spin fragmentation decomposes each unit length spin into “divergence-full” and “divergence-free” channels (center and right-hand images, respectively). The fragmented spins are shown as orange circles with diameter proportional to the length of the fragmented spin. The green hexagon represents the flipping of six spins around a closed loop: this is the simplest process that connects two distinct spin configurations within the degenerate CSF manifold.« less

Save / Share:

Works referenced in this record:

Relaxation-coupled order-parameter oscillation in a transverse Ising system
journal, February 1988


The Disk Chopper Spectrometer at NIST: a new instrument for quasielastic neutron scattering studies
journal, August 2003


Tunneling-induced restoration of classical degeneracy in quantum kagome ice
journal, April 2019


SEQUOIA: A Newly Operating Chopper Spectrometer at the SNS
journal, November 2010


Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14
journal, December 2016

  • Paddison, Joseph A. M.; Ong, Harapan S.; Hamp, James O.
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms13842

Observation of magnetic fragmentation in spin ice
journal, April 2016

  • Petit, S.; Lhotel, E.; Canals, B.
  • Nature Physics, Vol. 12, Issue 8
  • DOI: 10.1038/nphys3710

Determination of the neutron absorption cross section for hydrogen as a function of wavelength with a pulsed neutron source
journal, April 1987

  • Howard, J. A. K.; Johnson, O.; Schultz, A. J.
  • Journal of Applied Crystallography, Vol. 20, Issue 2
  • DOI: 10.1107/S0021889887087028

Dynamics of the Iongitudinal spin for the three-dimensional, spin-½ Ising model in a transverse field
journal, March 1975


Colorings of odd or even chirality on hexagonal lattices
journal, February 2017


A two-dimensional spin liquid in quantum kagome ice
journal, June 2015

  • Carrasquilla, Juan; Hao, Zhihao; Melko, Roger G.
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8421

Field dependent specific heat study of the dipolar Ising ferromagnet LiHoF4
journal, September 1984

  • Mennenga, G.; de Jongh, L. J.; Huiskamp, W. J.
  • Journal of Magnetism and Magnetic Materials, Vol. 44, Issue 1-2
  • DOI: 10.1016/0304-8853(84)90047-7

Rods of Neutron Scattering Intensity in Yb 2 Ti 2 O 7 : Compelling Evidence for Significant Anisotropic Exchange in a Magnetic Pyrochlore Oxide
journal, May 2011


Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores
journal, April 2014

  • Sala, G.; Gutmann, M. J.; Prabhakaran, D.
  • Nature Materials, Vol. 13, Issue 5
  • DOI: 10.1038/nmat3924

Tetragonal distortion yielding a two-singlet spin liquid in pyrochlore Tb 2 Ti 2 O 7
journal, November 2011


Ising model in a transverse field. I. Basic theory
journal, August 1973


Power-Law Spin Correlations in the Pyrochlore Antiferromagnet Tb 2 Ti 2 O 7
journal, July 2012


Single-ion anisotropy and magnetic field response in the spin-ice materials Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7
journal, October 2015


Nuclear spin ordering observed by neutron diffraction (invited)
journal, April 1985

  • Nicklow, R. M.; Moon, R. M.; Kawarazaki, S.
  • Journal of Applied Physics, Vol. 57, Issue 8
  • DOI: 10.1063/1.334974

Spin Dynamics of a Model Singlet Ground-State System
journal, December 1982


Quantum Ice: A Quantum Monte Carlo Study
journal, February 2012


Acoustic-Phonon Instability and Critical Scattering in Nb 3 Sb
journal, December 1971


Spin liquids in frustrated magnets
journal, March 2010


DAVE: A Comprehensive Software Suite for the Reduction, Visualization, and Analysis of Low Energy Neutron Spectroscopic Data
journal, November 2009

  • Azuah, Richard Tumanjong; Kneller, Larry R.; Qiu, Yiming
  • Journal of Research of the National Institute of Standards and Technology, Vol. 114, Issue 6
  • DOI: 10.6028/jres.114.025

Dipolar-octupolar Ising antiferromagnetism in Sm 2 Ti 2 O 7 : A moment fragmentation candidate
journal, September 2018


Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7
journal, September 2009


Two-Stage Ordering of Spins in Dipolar Spin Ice on the Kagome Lattice
journal, May 2011


Quantum Dimer Model on the Kagome Lattice: Solvable Dimer-Liquid and Ising Gauge Theory
journal, September 2002


Collective Excitations and Magnetic Ordering in Materials with Singlet Crystal-Field Ground State
journal, August 1968


Numerical Evidence of Quantum Melting of Spin Ice: Quantum-to-Classical Crossover
journal, August 2015


Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores
journal, July 2018


Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays
journal, October 2009


Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets
journal, May 2014


Correlated Quantum Tunneling of Monopoles in Spin Ice
journal, August 2019


Geometrical Frustration in the Ferromagnetic Pyrochlore Ho 2 Ti 2 O 7
journal, September 1997


Quantum origins of moment fragmentation in Nd 2 Zr 2 O 7
journal, September 2016


High-temperature dynamics of the Ising model in a transverse field
journal, February 1984


The high-resolution powder diffractometer at the high flux isotope reactor
journal, March 2010


Candidate Quantum Spin Liquid in the Ce 3 + Pyrochlore Stannate Ce 2 Sn 2 O 7
journal, August 2015


Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb 2 Ti 2 O 7 ?
journal, December 2015


Tunnelling and collective excitations in a microscopic model of ferroelectricity
journal, October 1966


Internal Magnetic Field in Rare Earth Metals
journal, September 1961


The nuclear heat capacity of HoF 3
journal, April 1994


Recent advances in magnetic structure determination by neutron powder diffraction
journal, October 1993


Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice
journal, August 2012


Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb 2 Ti 2 O 7 in a Magnetic Field
journal, August 2017


Spin liquid correlations, anisotropic exchange, and symmetry breaking in Tb 2 Ti 2 O 7
journal, November 2012


Treating crystal field parameters in lower than cubic symmetries
journal, January 1984


Observation of Magnetic Monopoles in Spin Ice
journal, October 2009

  • Kadowaki, Hiroaki; Doi, Naohiro; Aoki, Yuji
  • Journal of the Physical Society of Japan, Vol. 78, Issue 10
  • DOI: 10.1143/JPSJ.78.103706

Spin Correlations in Ho 2 Ti 2 O 7 : A Dipolar Spin Ice System
journal, July 2001


Quantum Phase Transition of a Magnet in a Spin Bath
journal, April 2005


Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7
journal, April 2018


Dynamic structure factor of the transverse Ising model
journal, February 1995

  • Florencio, J.; Sen, S.; Cai, Zhi-Xiong
  • Journal of Physics: Condensed Matter, Vol. 7, Issue 7
  • DOI: 10.1088/0953-8984/7/7/017

Structural and magnetic characterization of Ho 3 SbO 7 and Dy 3 SbO 7
journal, December 2001

  • Fennell, T.; Bramwell, S. T.; Green, M. A.
  • Canadian Journal of Physics, Vol. 79, Issue 11-12
  • DOI: 10.1139/p01-106

Magnetic Ground States of the Rare-Earth Tripod Kagome Lattice Mg 2 RE 3 Sb 3 O 14 ( RE = Gd , Dy , Er )
journal, April 2016


Crystal-field parameters of the rare-earth pyrochlores R 2 Ti 2 O 7 ( R = Tb , Dy, and Ho)
journal, July 2016


Candidate quantum spin ice in the pyrochlore Pr 2 Hf 2 O 7
journal, July 2016


Fragmentation in spin ice from magnetic charge injection
journal, August 2017


Coulombic Quantum Liquids in Spin- 1 / 2 Pyrochlores
journal, January 2012


Disorder-Induced Quantum Spin Liquid in Spin Ice Pyrochlores
journal, February 2017


Pyrochlore photons: The U ( 1 ) spin liquid in a S = 1 2 three-dimensional frustrated magnet
journal, February 2004


Theory of the kagome lattice Ising antiferromagnet in weak transverse fields
journal, January 2005


Random-Phase Approximation in the Theory of Superconductivity
journal, December 1958


Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7
journal, September 2009


Dynamic Spin Ice: Pr 2 Sn 2 O 7
journal, November 2008


Quantum Excitations in Quantum Spin Ice
journal, October 2011


Fragmentation of magnetism in artificial kagome dipolar spin ice
journal, May 2016

  • Canals, Benjamin; Chioar, Ioan-Augustin; Nguyen, Van-Dai
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms11446

Calorimetric Investigation of Hyperfine Interactions in Metallic Ho and Tb
journal, January 1969


SIMPRE: A software package to calculate crystal field parameters, energy levels, and magnetic properties on mononuclear lanthanoid complexes based on charge distributions
journal, June 2013

  • Baldoví, José J.; Cardona-Serra, Salvador; Clemente-Juan, Juan M.
  • Journal of Computational Chemistry, Vol. 34, Issue 22
  • DOI: 10.1002/jcc.23341

Dynamical crossover in  hot  spin ice
journal, December 2002

  • Ehlers, G.; Cornelius, A. L.; Orend c., M.
  • Journal of Physics: Condensed Matter, Vol. 15, Issue 2
  • DOI: 10.1088/0953-8984/15/2/102

Atomic structure study of the pyrochlore Y b 2 T i 2 O 7 and its relationship with low-temperature magnetic order
journal, March 2017


Magnetic-Moment Fragmentation and Monopole Crystallization
journal, January 2014


Monte Carlo studies of the dipolar spin ice model
journal, October 2004


Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry
journal, January 2010


Crystal-field interaction in the pyrochlore magnet Ho2Ti2O7
journal, May 2000

  • Rosenkranz, S.; Ramirez, A. P.; Hayashi, A.
  • Journal of Applied Physics, Vol. 87, Issue 9
  • DOI: 10.1063/1.372565

Effect of frustration near the magnetic-nonmagnetic transition
journal, July 1992

  • Núñez Regueiro, M. D.; Lacroix, C.; Ballou, R.
  • Physical Review B, Vol. 46, Issue 2
  • DOI: 10.1103/PhysRevB.46.990

Ising models of quantum frustration
journal, May 2001


Nuclear spin assisted quantum tunnelling of magnetic monopoles in spin ice
journal, April 2019


Ewald summation of electrostatic multipole interactions up to the quadrupolar level
journal, October 2003

  • Aguado, Andrés; Madden, Paul A.
  • The Journal of Chemical Physics, Vol. 119, Issue 14
  • DOI: 10.1063/1.1605941

Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field
journal, May 2000


Order-by-Disorder and Quantum Coulomb Phase in Quantum Square Ice
journal, July 2014


Disorder and Quantum Spin Ice
journal, October 2017


Simulation of Electrostatic Systems in Periodic Boundary Conditions. II. Equivalence of Boundary Conditions
journal, October 1980

  • de Leeuw, S. W.; Perram, J. W.; Smith, E. R.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 1752
  • DOI: 10.1098/rspa.1980.0136

Quantum fluctuations in spin-ice-like Pr2Zr2O7
journal, June 2013

  • Kimura, K.; Nakatsuji, S.; Wen, J-J.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms2914

Disordered Route to the Coulomb Quantum Spin Liquid: Random Transverse Fields on Spin Ice in Pr 2 Zr 2 O 7
journal, March 2017


Spin Ice State in Frustrated Magnetic Pyrochlore Materials
journal, November 2001


Model of localized highly frustrated ferromagnetism:  The kagomé spin ice
journal, October 2002


Magnitude of quantum effects in classical spin ices
journal, October 2015


Tuning the two-step melting of magnetic order in a dipolar kagome spin ice by quantum fluctuations
journal, April 2020


A new approximation for the dynamics of the transverse ising model
journal, March 1980

  • Santos, V. H.; Scherer, C.
  • Zeitschrift f�r Physik B Condensed Matter, Vol. 40, Issue 1-2
  • DOI: 10.1007/BF01295075

Evidence for dynamic kagome ice
journal, September 2018


Magnetic monopoles in spin ice
journal, January 2008

  • Castelnovo, C.; Moessner, R.; Sondhi, S. L.
  • Nature, Vol. 451, Issue 7174
  • DOI: 10.1038/nature06433