One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning

Ghosh, Sayak; Matty, Michael; Baumbach, Ryan; Bauer, Eric D.; Modic, K. A.; Shekhter, Arkady; Mydosh, J. A.; Kim, Eun-Ah; Ramshaw, B. J.

doi:10.1126/sciadv.aaz4074

Title: One-component order parameter in URu₂Si₂ uncovered by resonant ultrasound spectroscopy and machine learning

Abstract

The unusual correlated state that emerges in URu2Si2 below THO = 17.5 K is known as “hidden order” because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are “hidden.” We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across THO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.

Authors:

^[1]; Matty, Michael ^[1];

^[2];

^[3];

^[4];

^[2]; Mydosh, J. A. ^[5];

^[1];

^[1]

Cornell Univ., Ithaca, NY (United States). Lab. of Atomic and Solid State Physics
Florida State Univ., Tallahassee, FL (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Max Planck Inst. for Chemical Physics of Solids, Dresden (Germany)
Leiden Univ. (Netherlands)

Publication Date:: 2020-03-06

Research Org.:: Cornell Univ., Ithaca, NY (United States)

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

OSTI Identifier:: 1626059

Alternate Identifier(s):: OSTI ID: 1733304

Grant/Contract Number:: SC0018946; DMR-1719875; DMR-1539918; DMR-1752784

Resource Type:: Accepted Manuscript

Journal Name:: Science Advances

Additional Journal Information:: Journal Volume: 6; Journal Issue: 10; Journal ID: ISSN 2375-2548

Publisher:: AAAS

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Science & Technology - Other Topics

Citation Formats


                    Ghosh, Sayak, Matty, Michael, Baumbach, Ryan, Bauer, Eric D., Modic, K. A., Shekhter, Arkady, Mydosh, J. A., Kim, Eun-Ah, and Ramshaw, B. J. One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning.  United States: N. p., 2020. 
Web.  doi:10.1126/sciadv.aaz4074.

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                    Ghosh, Sayak, Matty, Michael, Baumbach, Ryan, Bauer, Eric D., Modic, K. A., Shekhter, Arkady, Mydosh, J. A., Kim, Eun-Ah, & Ramshaw, B. J. One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning.  United States.  https://doi.org/10.1126/sciadv.aaz4074

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                    Ghosh, Sayak, Matty, Michael, Baumbach, Ryan, Bauer, Eric D., Modic, K. A., Shekhter, Arkady, Mydosh, J. A., Kim, Eun-Ah, and Ramshaw, B. J. Fri .  
"One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning".  United States.  https://doi.org/10.1126/sciadv.aaz4074.  https://www.osti.gov/servlets/purl/1626059.

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@article{osti_1626059,

  title        = {One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning},

  author       = {Ghosh, Sayak and Matty, Michael and Baumbach, Ryan and Bauer, Eric D. and Modic, K. A. and Shekhter, Arkady and Mydosh, J. A. and Kim, Eun-Ah and Ramshaw, B. J.},

  abstractNote = {The unusual correlated state that emerges in URu2Si2 below THO = 17.5 K is known as “hidden order” because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are “hidden.” We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across THO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.},

  doi          = {10.1126/sciadv.aaz4074},

  journal      = {Science Advances},

  number       = 10,

  volume       = 6,

  place        = {United States},

  year         = {2020},

  month        = {3}

}

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https://doi.org/10.1126/sciadv.aaz4074

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Cited by: 19 works

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Figures / Tables:

Table 1: Proposed OPs of the HO state in URu₂Si₂, classified by their dimensionality and their point group representation. Note that designations such as “hexadecapole” order are only applicable in free space—crystalline electric fields break these large multipoles into the representations listed in this table.

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Title: One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning

Abstract

Citation Formats

Figures / Tables:

Classifying snapshots of the doped Hubbard model with machine learning journal, July 2019

Spin Nematic State as a Candidate of the Hidden Order Phase of URu 2 Si 2 journal, May 2011

Hastatic order in the heavy-fermion compound URu2Si2 journal, January 2013

Odd-parity electronic multipolar ordering in URu 2 Si 2 : Conclusions from Si and Ru NMR measurements journal, June 2018

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ journal, June 2013

Search for multipolar instability in URu 2 Si 2 studied by ultrasonic measurements under pulsed magnetic field journal, April 2018

Ultrasonic study of the hidden order and heavy-fermion state in URu 2 Si 2 with hydrostatic pressure, Rh-doping, and high magnetic fields journal, March 2014

Sr 2 RuO 4 : an electronic analogue of 3 He? journal, November 1995

A Study of Elastic Properties of URu 2 Si 2 in Comparison with the Non-5 f Contribution of ThRu 2 Si 2 journal, December 2012

Hidden and antiferromagnetic order as a rank-5 superspin in URu 2 Si 2 journal, June 2012

Details of Sample Dependence and Transport Properties of URu 2 Si 2 journal, November 2011

Signatures of hidden-order symmetry in torque oscillations, elastic constant anomalies, and field-induced moments in URu 2 Si 2 journal, April 2011

Resonant torsion magnetometry in anisotropic quantum materials journal, September 2018

Identifying quantum phase transitions using artificial neural networks on experimental data journal, July 2019

Probing hidden spin order with interpretable machine learning journal, February 2019

Analogy Between the “Hidden Order” and the Orbital Antiferromagnetism in URu 2 − x Fe x Si 2 journal, November 2016

High purity specimens of URu 2 Si 2 produced by a molten metal flux technique journal, April 2014

Unconventional Strain Dependence of Superconductivity in Spin-Triplet Superconductor Sr 2 RuO 4 journal, April 2002

Colloquium : Hidden order, superconductivity, and magnetism: The unsolved case of URu 2 Si 2 journal, November 2011

Hidden order behaviour in URu 2 Si 2 (A critical review of the status of hidden order in 2014) journal, May 2014

Evidence for a nematic component to the hidden-order parameter in URu2Si2 from differential elastoresistance measurements journal, March 2015

Emergent rank-5 nematic order in URu2Si2 journal, June 2012

Ultrasound propagation in the heavy-fermion superconductors URu2Si2 and CeCu2Si2 journal, April 1994

Machine learning phases of matter journal, February 2017

Longitudinal ultrasound in the heavy electron superconductor URu2Si2 journal, August 1990

Group theory and octupolar order in U Ru 2 Si 2 journal, February 2005

Elastic anomaly in (NH4)2SO4 journal, March 1973

Machine learning in electronic-quantum-matter imaging experiments journal, June 2019

Resolution of Entropy \(\ln\sqrt{2}\) by Ordering in Two-Channel Kondo Lattice journal, April 2013

Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens journal, December 2005

Why the Hidden Order in URu 2 Si 2 Is Still Hidden–One Simple Answer journal, March 2010

On the Hidden Order in URu 2 Si 2 – Antiferro Hexadecapole Order and Its Consequences journal, August 2011

Quadrupole and dipole orders in URu 2 Si 2 journal, November 1999

Sound Propagation near the Structural Phase Transition in Strontium Titanate journal, August 1970

Elastic Constants of Ammonium Chloride near the Lambda Point journal, December 1963

Single Crystal Growth of URu2Si2 by the Modified Bridgman Technique journal, October 2016

Pressure-induced rotational symmetry breaking in URu 2 Si 2 journal, December 2018

Spatially Inhomogeneous Development of Antiferromagnetism in URu 2 Si 2 : Evidence from S 29 i NMR under Pressure journal, August 2001

SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates journal, August 2018

Arrested Kondo effect and hidden order in URu2Si2 journal, September 2009

Cyclotron Resonance in the Hidden-Order Phase of URu 2 Si 2 journal, July 2012

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect journal, April 2000

Symmetry of the Excitations in the Hidden Order State of URu 2 Si 2 journal, December 2014

Ultrasonic Attenuation in URu 2 Si 2 journal, January 1987

Avoided valence transition in a plutonium superconductor journal, March 2015

Landau-Khalatnikov Damping of Ultrasound in Heavy-Fermion Superconductors journal, September 1986

The study of structural phase transitions by means of ultrasonic experiments journal, November 1973

Chirality density wave of the "hidden order" phase in URu2Si2 journal, February 2015

Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2 journal, January 2011

Theory of the coupling of quantum-critical fluctuations to fermions and d -wave superconductivity in cuprates journal, February 2010

Crystal Field Model of the Magnetic Properties of U Ru 2 Si 2 journal, August 1994

Itinerant Magnetic Multipole Moments of Rank Five as the Hidden Order in URu 2 Si 2 journal, September 2009

Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2 journal, June 2014

Title: One-component order parameter in URu₂Si₂ uncovered by resonant ultrasound spectroscopy and machine learning

Classifying snapshots of the doped Hubbard model with machine learning
journal, July 2019

Spin Nematic State as a Candidate of the Hidden Order Phase of ${URu}_{2} {Si}_{2}$
journal, May 2011

Hastatic order in the heavy-fermion compound URu2Si2
journal, January 2013

Odd-parity electronic multipolar ordering in ${URu}_{2} {Si}_{2}$ : Conclusions from Si and Ru NMR measurements
journal, June 2018

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ
journal, June 2013

Search for multipolar instability in ${URu}_{2} {Si}_{2}$ studied by ultrasonic measurements under pulsed magnetic field
journal, April 2018

Ultrasonic study of the hidden order and heavy-fermion state in URu ₂ Si ₂ with hydrostatic pressure, Rh-doping, and high magnetic fields
journal, March 2014

Sr ₂ RuO ₄ : an electronic analogue of ³ He?
journal, November 1995

A Study of Elastic Properties of URu ₂ Si ₂ in Comparison with the Non-5 f Contribution of ThRu ₂ Si ₂
journal, December 2012

Hidden and antiferromagnetic order as a rank-5 superspin in URu $_{2}$ Si $_{2}$
journal, June 2012

Details of Sample Dependence and Transport Properties of URu ₂ Si ₂
journal, November 2011

Signatures of hidden-order symmetry in torque oscillations, elastic constant anomalies, and field-induced moments in URu $_{2}$ Si $_{2}$
journal, April 2011

Resonant torsion magnetometry in anisotropic quantum materials
journal, September 2018

Identifying quantum phase transitions using artificial neural networks on experimental data
journal, July 2019

Probing hidden spin order with interpretable machine learning
journal, February 2019

Analogy Between the “Hidden Order” and the Orbital Antiferromagnetism in ${URu}_{2 - x} {Fe}_{x} {Si}_{2}$
journal, November 2016

High purity specimens of URu ₂ Si ₂ produced by a molten metal flux technique
journal, April 2014

Unconventional Strain Dependence of Superconductivity in Spin-Triplet Superconductor Sr ₂ RuO ₄
journal, April 2002

Colloquium : Hidden order, superconductivity, and magnetism: The unsolved case of ${URu}_{2} {Si}_{2}$
journal, November 2011

Hidden order behaviour in URu ₂ Si ₂ (A critical review of the status of hidden order in 2014)
journal, May 2014

Evidence for a nematic component to the hidden-order parameter in URu2Si2 from differential elastoresistance measurements
journal, March 2015

Emergent rank-5 nematic order in URu2Si2
journal, June 2012

Ultrasound propagation in the heavy-fermion superconductors URu2Si2 and CeCu2Si2
journal, April 1994

Machine learning phases of matter
journal, February 2017

Longitudinal ultrasound in the heavy electron superconductor URu2Si2
journal, August 1990

Group theory and octupolar order in $U {Ru}_{2} {Si}_{2}$
journal, February 2005

Elastic anomaly in (NH4)2SO4
journal, March 1973

Machine learning in electronic-quantum-matter imaging experiments
journal, June 2019

Resolution of Entropy \(\ln\sqrt{2}\) by Ordering in Two-Channel Kondo Lattice
journal, April 2013

Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens
journal, December 2005

Why the Hidden Order in URu ₂ Si ₂ Is Still Hidden–One Simple Answer
journal, March 2010

On the Hidden Order in URu ₂ Si ₂ – Antiferro Hexadecapole Order and Its Consequences
journal, August 2011

Quadrupole and dipole orders in URu ₂ Si ₂
journal, November 1999

Sound Propagation near the Structural Phase Transition in Strontium Titanate
journal, August 1970

Elastic Constants of Ammonium Chloride near the Lambda Point
journal, December 1963

Single Crystal Growth of URu2Si2 by the Modified Bridgman Technique
journal, October 2016

Pressure-induced rotational symmetry breaking in ${URu}_{2} {Si}_{2}$
journal, December 2018

Spatially Inhomogeneous Development of Antiferromagnetism in ${URu}_{2} {Si}_{2}$ : Evidence from ${}^{29}S i$ NMR under Pressure
journal, August 2001

SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates
journal, August 2018

Arrested Kondo effect and hidden order in URu2Si2
journal, September 2009

Cyclotron Resonance in the Hidden-Order Phase of ${URu}_{2} {Si}_{2}$
journal, July 2012

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect
journal, April 2000

Symmetry of the Excitations in the Hidden Order State of ${URu}_{2} {Si}_{2}$
journal, December 2014

Ultrasonic Attenuation in URu ₂ Si ₂
journal, January 1987

Avoided valence transition in a plutonium superconductor
journal, March 2015

Landau-Khalatnikov Damping of Ultrasound in Heavy-Fermion Superconductors
journal, September 1986

The study of structural phase transitions by means of ultrasonic experiments
journal, November 1973

Chirality density wave of the "hidden order" phase in URu2Si2
journal, February 2015

Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2
journal, January 2011

Theory of the coupling of quantum-critical fluctuations to fermions and $d$ -wave superconductivity in cuprates
journal, February 2010

Crystal Field Model of the Magnetic Properties of U ${Ru}_{2}$ ${Si}_{2}$
journal, August 1994

Itinerant Magnetic Multipole Moments of Rank Five as the Hidden Order in ${URu}_{2} {Si}_{2}$
journal, September 2009

Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2
journal, June 2014