Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO4

Pierre Massat; Jiajia Wen; Jack M. Jiang; Alexander T. Hristov; Yaohua Liu; Rebecca W. Smaha; Robert S. Feigelson; Young S. Lee; Rafael M. Fernandes; Ian R. Fisher

doi:10.1073/pnas.2119942119

Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO₄

Pierre Massat, Jiajia Wen, Jack M. Jiang, Alexander T. Hristov, Yaohua Liu, Rebecca W. Smaha, Robert S. Feigelson, Young S. Lee, Rafael M. Fernandes, Ian R. Fisher

Physics and Astronomy (Twin Cities)

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO₄, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4f orbitals of the thulium (Tm³⁺) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO₄ as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

Original language	English (US)
Article number	e2119942119
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	119
Issue number	28
DOIs	https://doi.org/10.1073/pnas.2119942119
State	Published - Jul 12 2022

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS. Heat-capacity and MCE measurements performed at Stanford University were supported by Air Force Office of Scientific Research Award FA9550-20-1-0252. Crystal-growth experiments were supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative Grant GBMF9068. The neutron-scattering activities were supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515. A portion of this research used resources at the Spallation Neutron Source (SNS), a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (ORNL), and resources of the SNS Second Target Station Project. ORNL is managed by UT-Battelle LLC for the DOE’s Office of Science, the single largest supporter of basic research in the physical sciences in the United States. A portion of this research used resources of the Advanced Light Source, a US DOE Office of Science User Facility, under Contract DE-AC02-05CH11231. R.W.S. was supported by NSF Graduate Research Fellowship DGE-1656518. Theory work (R.M.F.) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award DESC0020045. We acknowledge helpful discussions with Yuval Gannot, Marcus Garst, Steve Kivelson, and Indranil Paul. This manuscript has been authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (energy.gov/downloads/doe-public-access-plan).

Funding Information:
Heat-capacity and MCE measurements performed at Stanford University were supported by Air Force Office of Scientific Research Award FA9550-20-1-0252. Crystal-growth experiments were supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative Grant GBMF9068. The neutron-scattering activities were supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515. A portion of this research used resources at the Spallation Neutron Source (SNS), a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (ORNL), and resources of the SNS Second Target Station Project. ORNL is managed by UT-Battelle LLC for the DOE's Office of Science, the single largest supporter of basic research in the physical sciences in the United States. A portion of this research used resources of the Advanced Light Source, a US DOE Office of Science User Facility, under Contract DE-AC02-05CH11231. R.W.S. was supported by NSF Graduate Research Fellowship DGE-1656518. Theory work (R.M.F.) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award DESC0020045. We acknowledge helpful discussions with Yuval Gannot, Marcus Garst, Steve Kivelson, and Indranil Paul. This manuscript has been authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (energy.gov/downloads/doe-public-access-plan).

Publisher Copyright:
Copyright © 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

Keywords

electronic nematicity
magnetocaloric effect
neutron diffraction
quantum criticality
specific heat

Publisher link

10.1073/pnas.2119942119

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Cite this

Massat, P., Wen, J., Jiang, J. M., Hristov, A. T., Liu, Y., Smaha, R. W., Feigelson, R. S., Lee, Y. S., Fernandes, R. M., & Fisher, I. R. (2022). Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO₄. Proceedings of the National Academy of Sciences of the United States of America, 119(28), Article e2119942119. https://doi.org/10.1073/pnas.2119942119

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title = "Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO4",

abstract = "We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO4, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4f orbitals of the thulium (Tm3+) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.",

keywords = "electronic nematicity, magnetocaloric effect, neutron diffraction, quantum criticality, specific heat",

author = "Pierre Massat and Jiajia Wen and Jiang, {Jack M.} and Hristov, {Alexander T.} and Yaohua Liu and Smaha, {Rebecca W.} and Feigelson, {Robert S.} and Lee, {Young S.} and Fernandes, {Rafael M.} and Fisher, {Ian R.}",

note = "Funding Information: ACKNOWLEDGMENTS. Heat-capacity and MCE measurements performed at Stanford University were supported by Air Force Office of Scientific Research Award FA9550-20-1-0252. Crystal-growth experiments were supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative Grant GBMF9068. The neutron-scattering activities were supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515. A portion of this research used resources at the Spallation Neutron Source (SNS), a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (ORNL), and resources of the SNS Second Target Station Project. ORNL is managed by UT-Battelle LLC for the DOE{\textquoteright}s Office of Science, the single largest supporter of basic research in the physical sciences in the United States. A portion of this research used resources of the Advanced Light Source, a US DOE Office of Science User Facility, under Contract DE-AC02-05CH11231. R.W.S. was supported by NSF Graduate Research Fellowship DGE-1656518. Theory work (R.M.F.) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award DESC0020045. We acknowledge helpful discussions with Yuval Gannot, Marcus Garst, Steve Kivelson, and Indranil Paul. This manuscript has been authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (energy.gov/downloads/doe-public-access-plan). Funding Information: Heat-capacity and MCE measurements performed at Stanford University were supported by Air Force Office of Scientific Research Award FA9550-20-1-0252. Crystal-growth experiments were supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative Grant GBMF9068. The neutron-scattering activities were supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515. A portion of this research used resources at the Spallation Neutron Source (SNS), a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (ORNL), and resources of the SNS Second Target Station Project. ORNL is managed by UT-Battelle LLC for the DOE's Office of Science, the single largest supporter of basic research in the physical sciences in the United States. A portion of this research used resources of the Advanced Light Source, a US DOE Office of Science User Facility, under Contract DE-AC02-05CH11231. R.W.S. was supported by NSF Graduate Research Fellowship DGE-1656518. Theory work (R.M.F.) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award DESC0020045. We acknowledge helpful discussions with Yuval Gannot, Marcus Garst, Steve Kivelson, and Indranil Paul. This manuscript has been authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (energy.gov/downloads/doe-public-access-plan). Publisher Copyright: Copyright {\textcopyright} 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).",

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month = jul,

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doi = "10.1073/pnas.2119942119",

language = "English (US)",

volume = "119",

journal = "Proceedings of the National Academy of Sciences of the United States of America",

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TY - JOUR

T1 - Field-tuned ferroquadrupolar quantum phase transition in the insulator TmVO4

AU - Massat, Pierre

AU - Wen, Jiajia

AU - Jiang, Jack M.

AU - Hristov, Alexander T.

AU - Liu, Yaohua

AU - Smaha, Rebecca W.

AU - Feigelson, Robert S.

AU - Lee, Young S.

AU - Fernandes, Rafael M.

AU - Fisher, Ian R.

N1 - Funding Information: ACKNOWLEDGMENTS. Heat-capacity and MCE measurements performed at Stanford University were supported by Air Force Office of Scientific Research Award FA9550-20-1-0252. Crystal-growth experiments were supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative Grant GBMF9068. The neutron-scattering activities were supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515. A portion of this research used resources at the Spallation Neutron Source (SNS), a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (ORNL), and resources of the SNS Second Target Station Project. ORNL is managed by UT-Battelle LLC for the DOE’s Office of Science, the single largest supporter of basic research in the physical sciences in the United States. A portion of this research used resources of the Advanced Light Source, a US DOE Office of Science User Facility, under Contract DE-AC02-05CH11231. R.W.S. was supported by NSF Graduate Research Fellowship DGE-1656518. Theory work (R.M.F.) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award DESC0020045. We acknowledge helpful discussions with Yuval Gannot, Marcus Garst, Steve Kivelson, and Indranil Paul. This manuscript has been authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (energy.gov/downloads/doe-public-access-plan). Funding Information: Heat-capacity and MCE measurements performed at Stanford University were supported by Air Force Office of Scientific Research Award FA9550-20-1-0252. Crystal-growth experiments were supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative Grant GBMF9068. The neutron-scattering activities were supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515. A portion of this research used resources at the Spallation Neutron Source (SNS), a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (ORNL), and resources of the SNS Second Target Station Project. ORNL is managed by UT-Battelle LLC for the DOE's Office of Science, the single largest supporter of basic research in the physical sciences in the United States. A portion of this research used resources of the Advanced Light Source, a US DOE Office of Science User Facility, under Contract DE-AC02-05CH11231. R.W.S. was supported by NSF Graduate Research Fellowship DGE-1656518. Theory work (R.M.F.) was supported by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Award DESC0020045. We acknowledge helpful discussions with Yuval Gannot, Marcus Garst, Steve Kivelson, and Indranil Paul. This manuscript has been authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US DOE. The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (energy.gov/downloads/doe-public-access-plan). Publisher Copyright: Copyright © 2022 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

PY - 2022/7/12

Y1 - 2022/7/12

N2 - We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO4, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4f orbitals of the thulium (Tm3+) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

AB - We report results of low-temperature heat-capacity, magnetocaloric-effect, and neutron-diffraction measurements of TmVO4, an insulator that undergoes a continuous ferroquadrupolar phase transition associated with local partially filled 4f orbitals of the thulium (Tm3+) ions. The ferroquadrupolar transition, a realization of Ising nematicity, can be tuned to a quantum critical point by using a magnetic field oriented along the c axis of the tetragonal crystal lattice, which acts as an effective transverse field for the Ising-nematic order. In small magnetic fields, the thermal phase transition can be well described by using a semiclassical mean-field treatment of the transverse-field Ising model. However, in higher magnetic fields, closer to the field-tuned quantum phase transition, subtle deviations from this semiclassical behavior are observed, which are consistent with expectations of quantum fluctuations. Although the phase transition is driven by the local 4f degrees of freedom, the crystal lattice still plays a crucial role, both in terms of mediating the interactions between the local quadrupoles and in determining the critical scaling exponents, even though the phase transition itself can be described via mean field. In particular, bilinear coupling of the nematic order parameter to acoustic phonons changes the spatial and temporal fluctuations of the former in a fundamental way, resulting in different critical behavior of the nematic transverse-field Ising model, as compared to the usual case of the magnetic transverse-field Ising model. Our results establish TmVO4 as a model material and electronic nematicity as a paradigmatic example for quantum criticality in insulators.

KW - electronic nematicity

KW - magnetocaloric effect

KW - neutron diffraction

KW - quantum criticality

KW - specific heat

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