Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6

Fennell, T.; Harris, M. J.; Calder, S.; Ruminy, M.; Boehm, M.; Steffens, P.; Lemée-Cailleau, M. -H.; Zaharko, O.; Cervellino, A.; Bramwell, S. T.

doi:10.1038/s41567-018-0309-3

Title: Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF₆

Abstract

The Coulomb phase is an idealized state of matter whose properties are determined by factors beyond conventional considerations of symmetry, including global topology, conservation laws and emergent order. In theory, Coulomb phases occur in ice-type systems such as water ice and spin ice; in dimer models; and in certain spin liquids. Yet, apart from ice-type systems, more general experimental examples are very scarce. Here we study the partly disordered material CsNiCrF₆ and show that this material is a multiple Coulomb phase with signature correlations in three degrees of freedom: charge configurations, atom displacements and spin configurations. We use neutron and X-ray scattering to separate these correlations and to determine the magnetic excitation spectrum. Our results reveal how the structural and magnetic properties of apparently disordered materials may inherit, and be dictated by, a hidden symmetry—the local gauge symmetry of an underlying Coulomb phase.

Authors:

^[1]; Harris, M. J. ^[2];

^[3]; Ruminy, M. ^[1]; Boehm, M. ^[4]; Steffens, P. ^[4]; Lemée-Cailleau, M. -H. ^[4]; Zaharko, O. ^[1]; Cervellino, A. ^[1]; Bramwell, S. T. ^[5]

Paul Scherrer Inst. (PSI), Villigen (Switzerland)
Univ. of Edinburgh, Scotland (United Kingdom)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Inst. Laue-Langevin (ILL), Grenoble (France)
Univ. College London (UCL), London (United Kingdom)

Publication Date:: Mon Oct 22 00:00:00 EDT 2018

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1506794

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: Nature Physics

Additional Journal Information:: Journal Volume: 15; Journal Issue: 1; Journal ID: ISSN 1745-2473

Publisher:: Nature Publishing Group (NPG)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Fennell, T., Harris, M. J., Calder, S., Ruminy, M., Boehm, M., Steffens, P., Lemée-Cailleau, M. -H., Zaharko, O., Cervellino, A., and Bramwell, S. T. Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6.  United States: N. p., 2018. 
Web.  doi:10.1038/s41567-018-0309-3.

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                    Fennell, T., Harris, M. J., Calder, S., Ruminy, M., Boehm, M., Steffens, P., Lemée-Cailleau, M. -H., Zaharko, O., Cervellino, A., & Bramwell, S. T. Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6.  United States.  https://doi.org/10.1038/s41567-018-0309-3

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                    Fennell, T., Harris, M. J., Calder, S., Ruminy, M., Boehm, M., Steffens, P., Lemée-Cailleau, M. -H., Zaharko, O., Cervellino, A., and Bramwell, S. T. Mon .  
"Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6".  United States.  https://doi.org/10.1038/s41567-018-0309-3.  https://www.osti.gov/servlets/purl/1506794.

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@article{osti_1506794,

  title        = {Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6},

  author       = {Fennell, T. and Harris, M. J. and Calder, S. and Ruminy, M. and Boehm, M. and Steffens, P. and Lemée-Cailleau, M. -H. and Zaharko, O. and Cervellino, A. and Bramwell, S. T.},

  abstractNote = {The Coulomb phase is an idealized state of matter whose properties are determined by factors beyond conventional considerations of symmetry, including global topology, conservation laws and emergent order. In theory, Coulomb phases occur in ice-type systems such as water ice and spin ice; in dimer models; and in certain spin liquids. Yet, apart from ice-type systems, more general experimental examples are very scarce. Here we study the partly disordered material CsNiCrF6 and show that this material is a multiple Coulomb phase with signature correlations in three degrees of freedom: charge configurations, atom displacements and spin configurations. We use neutron and X-ray scattering to separate these correlations and to determine the magnetic excitation spectrum. Our results reveal how the structural and magnetic properties of apparently disordered materials may inherit, and be dictated by, a hidden symmetry—the local gauge symmetry of an underlying Coulomb phase.},

  doi          = {10.1038/s41567-018-0309-3},

  journal      = {Nature Physics},

  number       = 1,

  volume       = 15,

  place        = {United States},

  year         = {Mon Oct 22 00:00:00 EDT 2018},

  month        = {Mon Oct 22 00:00:00 EDT 2018}

}

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https://doi.org/10.1038/s41567-018-0309-3

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Cited by: 12 works

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Fig. 1: Illustration of mappings and structural features of CsNiCrF₆. A: The pyrochlore lattice (medial) consists of corner-sharing tetrahedra, on which a Coulomb phase can be established by ensuring that local degrees of freedom can be represented by a non-divergent field that is derived from lattice fluxes on the diamondmore » lattice (parent) (I). A non-divergent configuration of flux variables (blue arrows) around a diamond lattice point is equivalent to the ice rule for spins in a spin ice (two-in-two-out). Antiferromagnetic pseudo-spins are related to the flux variables and configured two-up-two-down in a Coulomb phase ground state (green and orange arrows). B: Two cations occupying the pyrochlore lattice form a charge ice, with cation configurations directly related to the pseudo-spins (green and orange spheres). C: Vector spins coupled antiferromagnetically on the pyrochlore lattice (i.e. a pyrochlore Heisenberg antiferromagnet) must satisfy the condition that the total magnetization of every tetrahedron is zero (black arrows), which can be ensured if the $S$_x,y,zvector components are each represented by a family of pseudospins that each obey the ice rule (blue, green and orange arrows). D: In the structure of CsNiCrF₆, F^- anions (small blue spheres) are coordinated to two cations. The bond valence sum requirements of the cations can be satisfied by displacing anions shared by a pair of unlike cations towards the cation with larger charge (Cr³⁺). Anions shared between a pair of like cations are not displaced. The edges with non-displaced cations can be identified as a fully packed loop model (FPL) on the diamond lattice, in which loops cover every link of the lattice, every site is visited by exactly two loops, and a given loop is occupied only by one of the cation species (green and orange lines). E: The structure of CsNiCrF₆ is composed of the pyrochlore lattice of cations, coordinated by octahedra of F^-ions. The octahedra share each of their vertices with one other octahedron, forming tetraheda of tilted octahedra. Extended sections of the FPL are shown, but the octahedra are drawn undistorted. F: The structure contains large cages in which the Cs⁺ ions reside. The cage coordination is by 18 F^- ions, forming an octahedron that is truncated and capped with rectangular pyramids.

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Title: Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6

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VIVALDI—A thermal-neutron laue diffractometer for physics, chemistry and materials science journal, January 2002

Magnetic relaxation in rare-earth oxide pyrochlores journal, September 2005

Magnetic excitations in a highly frustrated pyrochlore antiferromagnet journal, July 1995

Properties of a Classical Spin Liquid: The Heisenberg Pyrochlore Antiferromagnet journal, March 1998

Design of crystal-like aperiodic solids with selective disorder–phonon coupling journal, February 2016

Power-law spin correlations in pyrochlore antiferromagnets journal, January 2005

The Materials Science beamline upgrade at the Swiss Light Source journal, July 2013

Ordering and Antiferromagnetism in Ferrites journal, May 1956

Long-Range Order at Low Temperatures in Dipolar Spin Ice journal, July 2001

Amplitude/Higgs Modes in Condensed Matter Physics journal, March 2015

The “Coulomb Phase” in Frustrated Systems journal, August 2010

Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets journal, June 2009

The use of continuous atomic distributions in structural investigations journal, September 1994

LAUEGEN version 6.0 and INTLDM journal, June 1998

Short-range magnetic order in the frustrated pyrochlore antiferromagnet CsNiCrF 6 journal, November 1997

Absence of magnetic long-range order in Y 2 CrSbO 7 : Bond-disorder-induced magnetic frustration in a ferromagnetic pyrochlore journal, September 2017

A short history of SHELX journal, December 2007

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

Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO 4 journal, October 2017

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

Random Tiling and Topological Defects in a Two-Dimensional Molecular Network journal, November 2008

Notizen: Die Struktur einiger Fluoride, Oxide und Oxidfluoride AMe2X6: Der RbNiCrF6-Typ journal, November 1967

Disordered materials studied using neutron polarization analysis on the multi-detector spectrometer, D7 journal, December 2008

Atomic displacements in the charge ice pyrochlore Bi 2 Ti 2 O 6 O ′ studied by neutron total scattering journal, April 2010

Magnetic frustration in the context of pseudo-dipolar ionic disorder journal, January 2012

Empirical Magnetic Structure Solution of Frustrated Spin Systems journal, January 2012

Coulombic charge ice journal, May 2014

Interplay of Superconductivity and Rattling Phenomena in β -Pyrochlore KOs 2 O 6 Studied by Photoemission Spectroscopy journal, September 2007

Interpretation of diffuse X-ray scattering via models of disorder journal, June 1994

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

RbFe 2+ Fe 3 + F 6 : Synthesis, structure, and characterization of a new charge-ordered magnetically frustrated pyrochlore-related mixed-metal fluoride journal, January 2012

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

The crystallography of correlated disorder journal, May 2015

Semiflexible Fully Packed Loop Model and Interacting Rhombus Tilings journal, April 2009

Magnetic monopoles in spin ice journal, January 2008

Crystalline Electric-Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO 4 journal, March 2017

Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites journal, August 2008

Long-Range Order at Low Temperatures in Dipolar Spin Ice text, January 2001

Magnetic Monopoles in Spin Ice journal, January 2008

The semiflexible fully-packed loop model and interacting rhombus tilings text, January 2008

Analysis of a fully packed loop model arising in a magnetic Coulomb phase text, January 2011

Magnetic frustration in the context of pseudo-dipolar ionic disorder preprint, January 2011

Amplitude / Higgs Modes in Condensed Matter Physics text, January 2014

Continuum of quantum fluctuations in a three-dimensional $S\!=\!1$ Heisenberg magnet text, January 2017

Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet text, January 1997

Low-temperature properties of classical, geometrically frustrated antiferromagnets text, January 1998

Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore journal, July 2019

Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore text, January 2019

Title: Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF₆

Anharmonic Magnon Excitations in Noncollinear and Charge-Ordered ${RbFe}^{2 +} {Fe}^{3 +} F_{6}$
journal, August 2018

Continuum of quantum fluctuations in a three-dimensional S = 1 Heisenberg magnet
journal, October 2018

Diffuse Scattering and Defect Structure Simulations
book, July 2008

The recording and analysis of synchrotron X-radiation Laue diffraction photographs
journal, October 1989

A new form of FeF3 with the pyrochlore structure : Soft chemistry synthesis, crystal structure, thermal transitions and structural correlations with the other forms of FeF3
journal, August 1986

The Problem with Determining Atomic Structure at the Nanoscale
journal, April 2007

Quantum spin liquids: a review
journal, November 2016

Low-temperature properties of classical geometrically frustrated antiferromagnets
journal, November 1998

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

Coulomb and Liquid Dimer Models in Three Dimensions
journal, October 2003

Emergent excitations in a geometrically frustrated magnet
journal, August 2002

Analysis of a Fully Packed Loop Model Arising in a Magnetic Coulomb Phase
journal, October 2011

Single-crystal diffraction instrument TriCS at SINQ
journal, March 2000

Recent Developments in the Methods and Applications of the Bond Valence Model
journal, December 2009

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

Dipolar Spin Correlations in Classical Pyrochlore Magnets
journal, October 2004

VIVALDI—A thermal-neutron laue diffractometer for physics, chemistry and materials science
journal, January 2002

Magnetic relaxation in rare-earth oxide pyrochlores
journal, September 2005

Magnetic excitations in a highly frustrated pyrochlore antiferromagnet
journal, July 1995

Properties of a Classical Spin Liquid: The Heisenberg Pyrochlore Antiferromagnet
journal, March 1998

Design of crystal-like aperiodic solids with selective disorder–phonon coupling
journal, February 2016

Power-law spin correlations in pyrochlore antiferromagnets
journal, January 2005

The Materials Science beamline upgrade at the Swiss Light Source
journal, July 2013

Ordering and Antiferromagnetism in Ferrites
journal, May 1956

Long-Range Order at Low Temperatures in Dipolar Spin Ice
journal, July 2001

Amplitude/Higgs Modes in Condensed Matter Physics
journal, March 2015

The “Coulomb Phase” in Frustrated Systems
journal, August 2010

Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
journal, June 2009

The use of continuous atomic distributions in structural investigations
journal, September 1994

LAUEGEN version 6.0 and INTLDM
journal, June 1998

Short-range magnetic order in the frustrated pyrochlore antiferromagnet ${CsNiCrF}_{6}$
journal, November 1997

Absence of magnetic long-range order in $Y_{2} {CrSbO}_{7}$ : Bond-disorder-induced magnetic frustration in a ferromagnetic pyrochlore
journal, September 2017

A short history of SHELX
journal, December 2007

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

Disorder-Induced Mimicry of a Spin Liquid in ${YbMgGaO}_{4}$
journal, October 2017

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

Random Tiling and Topological Defects in a Two-Dimensional Molecular Network
journal, November 2008

Notizen: Die Struktur einiger Fluoride, Oxide und Oxidfluoride AMe2X6: Der RbNiCrF6-Typ
journal, November 1967

Disordered materials studied using neutron polarization analysis on the multi-detector spectrometer, D7
journal, December 2008

Atomic displacements in the charge ice pyrochlore ${Bi}_{2} {Ti}_{2} O_{6} O^{'}$ studied by neutron total scattering
journal, April 2010

Magnetic frustration in the context of pseudo-dipolar ionic disorder
journal, January 2012

Empirical Magnetic Structure Solution of Frustrated Spin Systems
journal, January 2012

Coulombic charge ice
journal, May 2014

Interplay of Superconductivity and Rattling Phenomena in $β$ -Pyrochlore ${KOs}_{2} O_{6}$ Studied by Photoemission Spectroscopy
journal, September 2007

Interpretation of diffuse X-ray scattering via models of disorder
journal, June 1994

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

RbFe ²⁺ Fe ³ ⁺ F ₆ : Synthesis, structure, and characterization of a new charge-ordered magnetically frustrated pyrochlore-related mixed-metal fluoride
journal, January 2012

Geometrical Frustration in the Ferromagnetic Pyrochlore ${Ho}_{2} {Ti}_{2} O_{7}$
journal, September 1997

The crystallography of correlated disorder
journal, May 2015

Semiflexible Fully Packed Loop Model and Interacting Rhombus Tilings
journal, April 2009

Magnetic monopoles in spin ice
journal, January 2008

Crystalline Electric-Field Randomness in the Triangular Lattice Spin-Liquid ${YbMgGaO}_{4}$
journal, March 2017

Breakdown of phonon glass paradigm in La- and Ce-filled Fe4Sb12 skutterudites
journal, August 2008

Long-Range Order at Low Temperatures in Dipolar Spin Ice
text, January 2001

Magnetic Monopoles in Spin Ice
journal, January 2008

The semiflexible fully-packed loop model and interacting rhombus tilings
text, January 2008

Analysis of a fully packed loop model arising in a magnetic Coulomb phase
text, January 2011

Magnetic frustration in the context of pseudo-dipolar ionic disorder
preprint, January 2011

Amplitude / Higgs Modes in Condensed Matter Physics
text, January 2014

Continuum of quantum fluctuations in a three-dimensional $S\!=\!1$ Heisenberg magnet
text, January 2017

Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
text, January 1997

Low-temperature properties of classical, geometrically frustrated antiferromagnets
text, January 1998

Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
journal, July 2019

Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
text, January 2019