Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels

Reig-i-Plessis, D.; Cote, A.; van Geldern, S.; Mayrhofer, R. D.; Aczel, Adam A.; MacDougall, G. J.

doi:10.1103/PhysRevMaterials.3.114408

Title: Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels

Abstract

The symmetry of local moments plays a defining role in the nature of exotic ground states stabilized in frustrated magnetic materials. Here, we present inelastic neutron scattering (INS) measurements of the crystal electric field (CEF) excitations in the family of compounds $Mg R_{2} {Se}_{4}$ $(R ϵ {Ho, Tm, Yb})$ . These compounds form in the spinel structure, with the rare-earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed transitions in the INS spectra to determine the most likely CEF Hamiltonian for each material and comment on the ground-state wavefunctions in the local electron picture. In this way, we experimentally confirm ${MgTm}_{2} {Se}_{4}$ has a nonmagnetic ground state, and ${MgYb}_{2} {Se}_{4}$ has effective $S = \frac{1}{2}$ spins with $g_{∥} = 5.188 (79)$ and $g_{⊥} = 0.923 (85)$ . The spectrum of ${MgHo}_{2} {Se}_{4}$ indicates a ground-state doublet containing Ising spins with $g_{∥} = 2.72 (46)$ , though low-lying CEF levels are also seen at thermally accessible energies $E = 0.591 (36)$ , 0.945(30), and 2.88(7) meV, which can complicate interpretation. These results are used to comment on measured magnetization data of all compounds and are compared to published results on the material ${MgEr}_{2} {Se}_{4}$ .

Authors:

Reig-i-Plessis, D. ^[1]; Cote, A. ^[1]; van Geldern, S. ^[1]; Mayrhofer, R. D. ^[2];

^[3];

^[1]

Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
Univ. of Rochester, NY (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)

Publication Date:: Tue Nov 12 00:00:00 EST 2019

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

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

OSTI Identifier:: 1607070

Grant/Contract Number:: AC05-00OR22725; DMR-1455264-CAR; 1659598

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review Materials

Additional Journal Information:: Journal Volume: 3; Journal Issue: 11; Journal ID: ISSN 2475-9953

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; frustrated magnetism; magnestism

Citation Formats


                    Reig-i-Plessis, D., Cote, A., van Geldern, S., Mayrhofer, R. D., Aczel, Adam A., and MacDougall, G. J. Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevMaterials.3.114408.

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                    Reig-i-Plessis, D., Cote, A., van Geldern, S., Mayrhofer, R. D., Aczel, Adam A., & MacDougall, G. J. Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels.  United States.  https://doi.org/10.1103/PhysRevMaterials.3.114408

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                    Reig-i-Plessis, D., Cote, A., van Geldern, S., Mayrhofer, R. D., Aczel, Adam A., and MacDougall, G. J. Tue .  
"Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels".  United States.  https://doi.org/10.1103/PhysRevMaterials.3.114408.  https://www.osti.gov/servlets/purl/1607070.

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@article{osti_1607070,

  title        = {Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels},

  author       = {Reig-i-Plessis, D. and Cote, A. and van Geldern, S. and Mayrhofer, R. D. and Aczel, Adam A. and MacDougall, G. J.},

  abstractNote = {The symmetry of local moments plays a defining role in the nature of exotic ground states stabilized in frustrated magnetic materials. Here, we present inelastic neutron scattering (INS) measurements of the crystal electric field (CEF) excitations in the family of compounds MgR2Se4 (Rϵ{Ho,Tm,Yb}). These compounds form in the spinel structure, with the rare-earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed transitions in the INS spectra to determine the most likely CEF Hamiltonian for each material and comment on the ground-state wavefunctions in the local electron picture. In this way, we experimentally confirm MgTm2Se4 has a nonmagnetic ground state, and MgYb2Se4 has effective S=12 spins with g∥=5.188(79) and g⊥=0.923(85). The spectrum of MgHo2Se4 indicates a ground-state doublet containing Ising spins with g∥=2.72(46), though low-lying CEF levels are also seen at thermally accessible energies E=0.591(36), 0.945(30), and 2.88(7) meV, which can complicate interpretation. These results are used to comment on measured magnetization data of all compounds and are compared to published results on the material MgEr2Se4.},

  doi          = {10.1103/PhysRevMaterials.3.114408},

  journal      = {Physical Review Materials},

  number       = 11,

  volume       = 3,

  place        = {United States},

  year         = {Tue Nov 12 00:00:00 EST 2019},

  month        = {Tue Nov 12 00:00:00 EST 2019}

}

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Frustrated Quantum Rare-Earth Pyrochlores
journal, March 2019

Rau, Jeffrey G.; Gingras, Michel J. P.
Annual Review of Condensed Matter Physics, Vol. 10, Issue 1
DOI: 10.1146/annurev-conmatphys-022317-110520

Ising Pyrochlore Magnets: Low-Temperature Properties, “Ice Rules,” and Beyond
journal, August 1999

Siddharthan, R.; Shastry, B. S.; Ramirez, A. P.
Physical Review Letters, Vol. 83, Issue 9
DOI: 10.1103/PhysRevLett.83.1854

CdEr2S4: Magnetic and Mössbauer measurements
journal, September 1981

Ben-Dor, L.; Shilo, I.; Felner, I.
Journal of Solid State Chemistry, Vol. 39, Issue 2
DOI: 10.1016/0022-4596(81)90339-X

Sternheimer Shielding-Antishielding; Rare-Earth Ions
journal, March 1973

Gupta, R. P.; Sen, S. K.
Physical Review A, Vol. 7, Issue 3
DOI: 10.1103/PhysRevA.7.850

Quantum spin fluctuations in the spin liquid state of Tb2Ti2O7
text, January 2011

Takatsu, Hiroshi; Kadowaki, Hiroaki; Sato, Taku J.
arXiv
DOI: 10.48550/arxiv.1106.3649

Spin Ice, Fractionalization and Topological Order
text, January 2011

Castelnovo, C.; Moessner, R.; Sondhi, S. L.
arXiv
DOI: 10.48550/arxiv.1112.3793

Magnetic Field Induced Transition in Vanadium Spinels
text, January 2013

Mun, E. D.; Chern, Gia-Wei; Pardo, V.
arXiv
DOI: 10.48550/arxiv.1307.4775

Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice
text, January 2013

Huang, Yi-Ping; Chen, Gang; Hermele, Michael
arXiv
DOI: 10.48550/arxiv.1311.1231

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
text, January 2015

Rau, Jeffrey G.; Petit, Sylvain; Gingras, Michel J. P.
arXiv
DOI: 10.48550/arxiv.1510.04292

Symmetry Enriched U(1) Topological Orders for Dipole-Octupole Doublets on a Pyrochlore Lattice
text, January 2016

Li, Yao Dong; Chen, Gang
arXiv
DOI: 10.48550/arxiv.1607.02287

Effect of Chemical Pressure on the Crystal Electric Field States of Erbium Pyrochlore Magnets
text, January 2017

Gaudet, J.; Hallas, A. M.; Kolesnikov, A. I.
arXiv
DOI: 10.48550/arxiv.1708.01176

Magnets with strong geometric frustration
text, January 2000

Moessner, R.
arXiv
DOI: 10.48550/arxiv.cond-mat/0010301

Ising pyrochlore magnets: Low temperature properties, ice rules and beyond
text, January 1999

Siddharthan, R.; Shastry, B. S.; Ramirez, A. P.
arXiv
DOI: 10.48550/arxiv.cond-mat/9902010

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Title: Neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels

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Citation Formats

Matrix Elements and Operator Equivalents Connected with the Magnetic Properties of Rare Earth Ions journal, March 1952

Evidence for unidimensional low-energy excitations as the origin of persistent spin dynamics in geometrically frustrated magnets journal, March 2015

Spin Ice, Fractionalization, and Topological Order journal, March 2012

Dynamically Induced Frustration as a Route to a Quantum Spin Ice State in Tb 2 Ti 2 O 7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects journal, April 2007

Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra journal, August 2018

Density-functional calculations for rare-earth atoms and ions journal, April 1997

Er 2 Ti 2 O 7 : Evidence of quantum order by disorder in a frustrated antiferromagnet journal, July 2003

Role of the electrostatic model in calculating rare-earth crystal-field parameters journal, July 1998

Collective dynamics in the Heisenberg pyrochlore antiferromagnet Gd 2 Sn 2 O 7 journal, October 2008

Coupling between electronic and lattice degrees of freedom in 4f-electron systems investigated by inelastic neutron scattering journal, February 2003

Experimental Insights into Ground-State Selection of Quantum XY Pyrochlores journal, March 2018

Deviation from the dipole-ice model in the spinel spin-ice candidate MgEr 2 Se 4 journal, April 2019

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

Neutron scattering studies of the cooperative paramagnet pyrochlore Tb 2 Ti 2 O 7 journal, November 2001

Theory of the bound state between phonons and a CEF excitation in CeAl 2 journal, August 1984

Frustrated rare earth magnetism: Spin glasses, spin liquids and spin ices in pyrochlore oxides journal, February 2006

Low-energy electrodynamics of novel spin excitations in the quantum spin ice Yb2Ti2O7 journal, September 2014

Quantum spin fluctuations in the spin-liquid state of Tb 2 Ti 2 O 7 journal, December 2011

Theory of Spin-Orbit Coupling in Atoms. III journal, April 1964

Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore Antiferromagnet Tb 2 Ti 2 O 7 journal, February 1999

Frustrated Magnetism and Cooperative Phase Transitions in Spinels journal, January 2010

Electrical conduction in rare-earth monoselenides and monotellurides and their alloys journal, September 1964

Fluctuations and All-In–All-Out Ordering in Dipole-Octupole Nd 2 Zr 2 O 7 journal, November 2015

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets journal, May 2016

Magnets with strong geometric frustration journal, January 2001

Polarized inelastic neutron scattering of the partially ordered Tb 2 Sn 2 O 7 journal, December 2007

Vindication of Yb 2 Ti 2 O 7 as a Model Exchange Quantum Spin Ice journal, August 2012

Long-range dynamical magnetic order and spin tunneling in the cooperative paramagnetic states of the pyrochlore analogous spinel antiferromagnets CdYb 2 X 4 ( X = S or Se) journal, October 2017

CdEr 2 Se 4 : A New Erbium Spin Ice System in a Spinel Structure journal, June 2010

Magnetic ordering in Gd 2 Sn 2 O 7 : the archetypal Heisenberg pyrochlore antiferromagnet journal, January 2006

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

Crystallographic and Magnetic Studies of Rare Earth Chalcogenide Spinels journal, May 1972

Frustrated magnetism in the Heisenberg pyrochlore antiferromagnets A Yb 2 X 4 ( A = Cd , Mg; X = S , Se) journal, May 2017

Crystal Field Theory Interpretation of the Magnetic Susceptibility of CdYb2Se4 Spinel journal, August 1974

Proprietes magnetiques des oxyseleniures de Gd, Tb, Dy, Ho, Er, Tm et structure magnetique de Ho2O2Se et de Yb2O2Se journal, May 1972

Magnetic properties and crystal field in MgYb2S4 and MgYb2Se4 spinels journal, December 1988

Effect of chemical pressure on the crystal electric field states of erbium pyrochlore magnets journal, January 2018

Magnetic Field Induced Transition in Vanadium Spinels journal, January 2014

Symmetry enriched U(1) topological orders for dipole-octupole doublets on a pyrochlore lattice journal, January 2017

Neutron scattering investigations of the partially ordered pyrochlore Tb 2 Sn 2 O 7 journal, November 2009

Systematic Variation of Quadrupole Crystal-Field Shielding in Rare-Earth Ethyl Sulfates journal, March 1966

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

Crystal growth and optical properties of rare earth sesquiselenides and sesquisulphides — new magneto-optic materials journal, March 1995

Magnetic pyrochlore oxides journal, January 2010

Structure and magnetic properties of sulfides of the type CdRE2S4 and Mg(GdxYb1−x)2S4 journal, November 1980

Phase cubiques type Th 3 P 4 dans les sulfures, les séléniures et les tellurures L 2 X 3 et L 3 X 4 des terres rares, et dans leurs combinaisons ML 2 X 4 avec les sulfures et séléniures MX de calcium, strontium et baryum. Formation et propriétés cristallines journal, July 1965

Dipolar Spin Ice States with a Fast Monopole Hopping Rate in CdEr 2 X 4 ( X = Se , S) journal, March 2018

Quantum Excitations in Quantum Spin Ice journal, October 2011

Magnetic and Orbital Ordering in the Spinel MnV 2 O 4 journal, February 2008

166 Er Mössbauer spectroscopy study of magnetic ordering in a spinel-based potential spin-ice system: CdEr 2 S 4 journal, May 2015

Zero-point entropy in ‘spin ice’ journal, May 1999

Geometrical magnetic frustration in rare-earth chalcogenide spinels journal, August 2005

Magnetic excitations in Tb 2 Sn 2 O 7 and Tb 2 Ti 2 O 7 as measured by inelastic neutron scattering journal, November 2007

Quantum Spin Ices and Topological Phases from Dipolar-Octupolar Doublets on the Pyrochlore Lattice journal, April 2014

Thermodynamic properties of quadrupolar states in the frustrated pyrochlore magnet Tb 2 Ti 2 O 7 journal, April 2017

Orbital Ordering and Magnetic Field Effect in MnV 2 O 4 journal, March 2007

Magnetoelastically induced vibronic bound state in the spin-ice pyrochlore Ho 2 Ti 2 O 7 journal, July 2018

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

Order in the Heisenberg pyrochlore: The magnetic structure of Gd 2 Ti 2 O 7 journal, September 2001

Spin-glass-like behavior in Y2Mo2O7, a concentrated, crystalline system with negligible apparent disorder journal, September 1986

Ordered Spin Ice State and Magnetic Fluctuations in Tb 2 Sn 2 O 7 journal, June 2005

Magnets with strong geometric frustration journal, December 2001

Magnetic ordering in the XY pyrochlore antiferromagnet Er 2 Ti 2 O 7 : a spherical neutron polarimetry study journal, October 2007

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

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

Analysis of the Magnetic Susceptibility of CdYb2 S4 Spinel by Means of the Crystal Field Method journal, September 1975

Jahn–Teller instability in spinel Li–Mn–O journal, September 1999

EasySpin, a comprehensive software package for spectral simulation and analysis in EPR journal, January 2006

Crystal electric field in the R 2 Ti 2 O 7 pyrochlore compounds journal, May 2012

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

Crystal-field states of Pr 3 + in the candidate quantum spin ice Pr 2 Sn 2 O 7 journal, September 2013

Electronic band structure and exchange coupling constants in A Cr 2 X 4 spinels ( A = Zn , Cd, Hg; X = O , S, Se) journal, March 2008

Magnetic susceptibility of Tm2Se3 and CdTm2Se4 compounds journal, January 1977

Frustrated Quantum Rare-Earth Pyrochlores journal, March 2019

Ising Pyrochlore Magnets: Low-Temperature Properties, “Ice Rules,” and Beyond journal, August 1999

Matrix Elements and Operator Equivalents Connected with the Magnetic Properties of Rare Earth Ions
journal, March 1952

Evidence for unidimensional low-energy excitations as the origin of persistent spin dynamics in geometrically frustrated magnets
journal, March 2015

Spin Ice, Fractionalization, and Topological Order
journal, March 2012

Dynamically Induced Frustration as a Route to a Quantum Spin Ice State in ${Tb}_{2} {Ti}_{2} O_{7}$ via Virtual Crystal Field Excitations and Quantum Many-Body Effects
journal, April 2007

Frustration and anisotropic exchange in ytterbium magnets with edge-shared octahedra
journal, August 2018

Density-functional calculations for rare-earth atoms and ions
journal, April 1997

${Er}_{2} {Ti}_{2} O_{7} :$ Evidence of quantum order by disorder in a frustrated antiferromagnet
journal, July 2003

Role of the electrostatic model in calculating rare-earth crystal-field parameters
journal, July 1998

Collective dynamics in the Heisenberg pyrochlore antiferromagnet ${Gd}_{2} {Sn}_{2} O_{7}$
journal, October 2008

Coupling between electronic and lattice degrees of freedom in 4f-electron systems investigated by inelastic neutron scattering
journal, February 2003

Experimental Insights into Ground-State Selection of Quantum XY Pyrochlores
journal, March 2018

Deviation from the dipole-ice model in the spinel spin-ice candidate ${MgEr}_{2} {Se}_{4}$
journal, April 2019

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

Neutron scattering studies of the cooperative paramagnet pyrochlore ${Tb}_{2} {Ti}_{2} O_{7}$
journal, November 2001

Theory of the bound state between phonons and a CEF excitation in CeAl ₂
journal, August 1984

Frustrated rare earth magnetism: Spin glasses, spin liquids and spin ices in pyrochlore oxides
journal, February 2006

Low-energy electrodynamics of novel spin excitations in the quantum spin ice Yb2Ti2O7
journal, September 2014

Quantum spin fluctuations in the spin-liquid state of Tb ₂ Ti ₂ O ₇
journal, December 2011

Theory of Spin-Orbit Coupling in Atoms. III
journal, April 1964

Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore Antiferromagnet ${Tb}_{2} {Ti}_{2} O_{7}$
journal, February 1999

Frustrated Magnetism and Cooperative Phase Transitions in Spinels
journal, January 2010

Electrical conduction in rare-earth monoselenides and monotellurides and their alloys
journal, September 1964

Fluctuations and All-In–All-Out Ordering in Dipole-Octupole ${Nd}_{2} {Zr}_{2} O_{7}$
journal, November 2015

Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
journal, May 2016

Magnets with strong geometric frustration
journal, January 2001

Polarized inelastic neutron scattering of the partially ordered ${Tb}_{2} {Sn}_{2} O_{7}$
journal, December 2007

Vindication of ${Yb}_{2} {Ti}_{2} O_{7}$ as a Model Exchange Quantum Spin Ice
journal, August 2012

Long-range dynamical magnetic order and spin tunneling in the cooperative paramagnetic states of the pyrochlore analogous spinel antiferromagnets ${{CdYb}_{2} X}_{4}$ ( $X = S$ or Se)
journal, October 2017

${CdEr}_{2} {Se}_{4}$ : A New Erbium Spin Ice System in a Spinel Structure
journal, June 2010

Magnetic ordering in Gd ₂ Sn ₂ O ₇ : the archetypal Heisenberg pyrochlore antiferromagnet
journal, January 2006

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

Crystallographic and Magnetic Studies of Rare Earth Chalcogenide Spinels
journal, May 1972

Frustrated magnetism in the Heisenberg pyrochlore antiferromagnets $A {Yb}_{2} X_{4}$ ( $A = Cd$ , Mg; $X = S$ , Se)
journal, May 2017

Crystal Field Theory Interpretation of the Magnetic Susceptibility of CdYb2Se4 Spinel
journal, August 1974

Proprietes magnetiques des oxyseleniures de Gd, Tb, Dy, Ho, Er, Tm et structure magnetique de Ho2O2Se et de Yb2O2Se
journal, May 1972

Magnetic properties and crystal field in MgYb2S4 and MgYb2Se4 spinels
journal, December 1988

Effect of chemical pressure on the crystal electric field states of erbium pyrochlore magnets
journal, January 2018

Magnetic Field Induced Transition in Vanadium Spinels
journal, January 2014

Symmetry enriched U(1) topological orders for dipole-octupole doublets on a pyrochlore lattice
journal, January 2017

Neutron scattering investigations of the partially ordered pyrochlore Tb ₂ Sn ₂ O ₇
journal, November 2009

Systematic Variation of Quadrupole Crystal-Field Shielding in Rare-Earth Ethyl Sulfates
journal, March 1966

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

Crystal growth and optical properties of rare earth sesquiselenides and sesquisulphides — new magneto-optic materials
journal, March 1995

Magnetic pyrochlore oxides
journal, January 2010

Structure and magnetic properties of sulfides of the type CdRE2S4 and Mg(GdxYb1−x)2S4
journal, November 1980

Phase cubiques type Th ₃ P ₄ dans les sulfures, les séléniures et les tellurures L ₂ X ₃ et L ₃ X ₄ des terres rares, et dans leurs combinaisons ML ₂ X ₄ avec les sulfures et séléniures MX de calcium, strontium et baryum. Formation et propriétés cristallines
journal, July 1965

Dipolar Spin Ice States with a Fast Monopole Hopping Rate in ${CdEr}_{2} X_{4}$ ( $X = Se$ , S)
journal, March 2018

Quantum Excitations in Quantum Spin Ice
journal, October 2011

Magnetic and Orbital Ordering in the Spinel ${MnV}_{2} O_{4}$
journal, February 2008

¹⁶⁶ Er Mössbauer spectroscopy study of magnetic ordering in a spinel-based potential spin-ice system: CdEr ₂ S ₄
journal, May 2015

Zero-point entropy in ‘spin ice’
journal, May 1999

Geometrical magnetic frustration in rare-earth chalcogenide spinels
journal, August 2005

Magnetic excitations in ${Tb}_{2} {Sn}_{2} O_{7}$ and ${Tb}_{2} {Ti}_{2} O_{7}$ as measured by inelastic neutron scattering
journal, November 2007

Quantum Spin Ices and Topological Phases from Dipolar-Octupolar Doublets on the Pyrochlore Lattice
journal, April 2014

Thermodynamic properties of quadrupolar states in the frustrated pyrochlore magnet Tb ₂ Ti ₂ O ₇
journal, April 2017

Orbital Ordering and Magnetic Field Effect in ${MnV}_{2} O_{4}$
journal, March 2007

Magnetoelastically induced vibronic bound state in the spin-ice pyrochlore ${Ho}_{2} {Ti}_{2} O_{7}$
journal, July 2018

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

Order in the Heisenberg pyrochlore: The magnetic structure of ${Gd}_{2} {Ti}_{2} O_{7}$
journal, September 2001

Spin-glass-like behavior in Y2Mo2O7, a concentrated, crystalline system with negligible apparent disorder
journal, September 1986

Ordered Spin Ice State and Magnetic Fluctuations in ${Tb}_{2} {Sn}_{2} O_{7}$
journal, June 2005

Magnets with strong geometric frustration
journal, December 2001

Magnetic ordering in the XY pyrochlore antiferromagnet Er ₂ Ti ₂ O ₇ : a spherical neutron polarimetry study
journal, October 2007

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

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

Analysis of the Magnetic Susceptibility of CdYb2 S4 Spinel by Means of the Crystal Field Method
journal, September 1975

Jahn–Teller instability in spinel Li–Mn–O
journal, September 1999

EasySpin, a comprehensive software package for spectral simulation and analysis in EPR
journal, January 2006

Crystal electric field in the R ₂ Ti ₂ O ₇ pyrochlore compounds
journal, May 2012

Candidate Quantum Spin Liquid in the ${Ce}^{3 +}$ Pyrochlore Stannate ${Ce}_{2} {Sn}_{2} O_{7}$
journal, August 2015

Crystal-field states of Pr $^{3 +}$ in the candidate quantum spin ice Pr $_{2}$ Sn $_{2}$ O $_{7}$
journal, September 2013

Electronic band structure and exchange coupling constants in $A {Cr}_{2} X_{4}$ spinels ( $A = Zn$ , Cd, Hg; $X = O$ , S, Se)
journal, March 2008

Magnetic susceptibility of Tm2Se3 and CdTm2Se4 compounds
journal, January 1977

Frustrated Quantum Rare-Earth Pyrochlores
journal, March 2019

Ising Pyrochlore Magnets: Low-Temperature Properties, “Ice Rules,” and Beyond
journal, August 1999

CdEr2S4: Magnetic and Mössbauer measurements
journal, September 1981

Sternheimer Shielding-Antishielding; Rare-Earth Ions
journal, March 1973

Quantum spin fluctuations in the spin liquid state of Tb2Ti2O7
text, January 2011