Hidden order and beyond: an experimental—theoretical overview of the multifaceted behavior of URu2Si2

Mydosh, J. A.; Oppeneer, P. M.; Riseborough, P. S.

doi:10.1088/1361-648X/ab5eba

Title: Hidden order and beyond: an experimental—theoretical overview of the multifaceted behavior of URu₂Si₂

Journal Article · 08 January 2020 · Journal of Physics. Condensed Matter

DOI: https://doi.org/10.1088/1361-648X/ab5eba · OSTI ID:1617899

^[1];

^[2]; Riseborough, P. S. ^[3]

Leiden Univ. (Netherlands); Temple University
Uppsala Univ. (Sweden)
Temple Univ., Philadelphia, PA (United States)

This topical review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu₂Si₂ when tuned with pressure, magnetic field, and substitutions for all three elements. Such 'perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) remains puzzling and non-clarified, and the search continues in 2019 into a fourth decade for its final resolution. We attempt herein to update the present situation of URu₂Si₂ importing the latest experimental results and theoretical proposals. First, let us consider the pristine compound as a function of temperature and report the recent measurements and models relating to its heavy Fermi liquid crossover, its HO and superconductivity (SC). Recent experiments and theories are surmized that address four-fold symmetry breaking (or nematicity), Isingness and unconventional excitation modes. Second, we discuss the pressure dependence of URu₂Si₂ and its transformation to antiferromagnetic long-range order. Next we confront the dramatic high magnetic-field phases requiring fields above 40 T. And finally, we attempt to answer how does random substitutions of other 5f elements for U, and 3d, 4d, and 5d elements for Ru, and even P for Si affect and transform the HO. Commensurately, recent theoretical models are summarized and then related to the intriguing experimental behavior.

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Research Organization:: Temple Univ., Philadelphia, PA (United States)

Sponsoring Organization:: K. and A. Wallenberg Foundation; Swedish National Infrastructure for Computing (SNIC); Swedish Research Council; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: FG02-01ER45872

OSTI ID:: 1617899

Journal Information:: Journal of Physics. Condensed Matter, Journal Name: Journal of Physics. Condensed Matter Journal Issue: 14 Vol. 32; ISSN 0953-8984

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (223)

Superconductivity and magnetic order in a strongly interacting fermi-system: URu2Si2 Schlabitz, W.; Baumann, J.; Pollit, B. Zeitschrift f�r Physik B Condensed Matter, Vol. 62, Issue 2 https://doi.org/10.1007/BF01323427	journal	June 1986
Crystal growth of some rare earth and uranium intermetallics from the melt Menovsky, A.; Franse, J. J. M. Journal of Crystal Growth, Vol. 65, Issue 1-3 https://doi.org/10.1016/0022-0248(83)90062-3	journal	December 1983
Seeded growth in a soft lined crucible: Application to phosphorus doped optical germanium single crystals Azoulay, M.; Gafni, G.; Roth, M. Journal of Crystal Growth, Vol. 79, Issue 1-3 https://doi.org/10.1016/0022-0248(86)90457-4	journal	December 1986
Magnetochemistry and crystal chemistry of ternary actinoidmetal-silicides {Th, U}{Cu, Ru, Os, Ir, Pt}2Si2 Hiebl, K.; Rogl, P. Journal of Nuclear Materials, Vol. 144, Issue 1-2 https://doi.org/10.1016/0022-3115(87)90294-7	journal	January 1987
Structural characterization of new ternary compounds of uranium and cerium Cordier, G.; Czech, E.; Schäfer, H. Journal of the Less Common Metals, Vol. 110, Issue 1-2 https://doi.org/10.1016/0022-5088(85)90340-6	journal	August 1985
Magnetic properties and structural chemistry of ternary silicides (RE, Th, U)Ru2Si2 (RE = RARE EARTH) Hiebl, K.; Horvath, C.; Rogl, P. Journal of Magnetism and Magnetic Materials, Vol. 37, Issue 3 https://doi.org/10.1016/0304-8853(83)90058-6	journal	July 1983
Specific heat and susceptibility of U(Ru1−xRhx)2Si2 Amitsuka, H.; Hyomi, K.; Nishioka, T. Journal of Magnetism and Magnetic Materials, Vol. 76-77 https://doi.org/10.1016/0304-8853(88)90354-X	journal	December 1988
Magnetic phase diagram of the U(Rh1−xRux)Si2 system Burlet, P.; Bourdarot, F.; Quezel, S. Journal of Magnetism and Magnetic Materials, Vol. 108, Issue 1-3 https://doi.org/10.1016/0304-8853(92)91411-L	journal	February 1992
Specific heat of URu2Si2: Effect of pressure and magnetic field on the magnetic and superconducting transitions Fisher, R. A.; Kim, S.; Wu, Y. Physica B: Condensed Matter, Vol. 163, Issue 1-3 https://doi.org/10.1016/0921-4526(90)90229-N	journal	April 1990
Th-doped URu2Si2: influence of “Kondo holes” on coexisting superconductivity and magnetism de la Torre, A. Lopez; Visani, P.; Dalichaouch, Y. Physica B: Condensed Matter, Vol. 179, Issue 3 https://doi.org/10.1016/0921-4526(92)90018-N	journal	July 1992
Low moments in heavy-fermion systems Buyers, W. J. L. Physica B: Condensed Matter, Vol. 223-224 https://doi.org/10.1016/0921-4526(96)00027-0	journal	June 1996
Comparative study of the electronic structure of XRu2Si2: probing the Anderson lattice Denlinger, J. D.; Gweon, G. -H; Allen, J. W. Journal of Electron Spectroscopy and Related Phenomena, Vol. 117-118 https://doi.org/10.1016/S0368-2048(01)00257-2	journal	June 2001
Hidden order and weak antiferromagnetism in URu2Si2 Amitsuka, Hiroshi; Yokoyama, Makoto; Miyazaki, Shikou Physica B: Condensed Matter, Vol. 312-313 https://doi.org/10.1016/S0921-4526(01)01343-6	journal	March 2002
Inhomogeneous magnetism in URu2Si2 studied by muon spin relaxation under high pressure Amitsuka, H.; Tenya, K.; Yokoyama, M. Physica B: Condensed Matter, Vol. 326, Issue 1-4 https://doi.org/10.1016/S0921-4526(02)01654-X	journal	February 2003
Investigation of the crystal structure of URu2Si2 by high-resolution X-ray diffraction Kernavanois, N.; de Réotier, P. Dalmas; Yaouanc, A. Physica B: Condensed Matter, Vol. 259-261 https://doi.org/10.1016/S0921-4526(98)01005-9	journal	January 1999
Non-Fermi-liquid behavior in R1−xUxRu2Si2 (R=Th, Y and La; x⩽0.07) Amitsuka, H.; Kuwahara, K.; Yokoyama, M. Physica B: Condensed Matter, Vol. 281-282 https://doi.org/10.1016/S0921-4526(99)01054-6	journal	June 2000
A model for metastable magnetism in the hidden-order phase of URu 2 Si 2 Boyer, Lance; Yakovenko, Victor M. Annals of Physics, Vol. 388 https://doi.org/10.1016/j.aop.2017.11.024	journal	January 2018
Pressure–temperature phase diagram of the heavy-electron superconductor Amitsuka, H.; Matsuda, K.; Kawasaki, I. Journal of Magnetism and Magnetic Materials, Vol. 310, Issue 2 https://doi.org/10.1016/j.jmmm.2006.10.008	journal	March 2007
Kramers degeneracy in a magnetic field and zeeman spin-orbit coupling in antiferromagnetic conductors Ramazashvili, Revaz Physica B: Condensed Matter, Vol. 404, Issue 3-4 https://doi.org/10.1016/j.physb.2008.11.027	journal	March 2009
Raman active high energy excitations in URu2Si2 Buhot, Jonathan; Gallais, Yann; Cazayous, Maximilien Physica B: Condensed Matter, Vol. 506 https://doi.org/10.1016/j.physb.2016.10.034	journal	February 2017
Thermodynamic evidence for broken fourfold rotational symmetry in the hidden-order phase of URu2Si2 Shibauchi, T.; Matsuda, Y. Physica C: Superconductivity, Vol. 481 https://doi.org/10.1016/j.physc.2012.04.012	journal	November 2012
The Kondo Problem to Heavy Fermions Hewson, Alexander Cyril https://doi.org/10.1017/CBO9780511470752	book	January 1993
Hastatic order in the heavy-fermion compound URu2Si2 Chandra, Premala; Coleman, Piers; Flint, Rebecca Nature, Vol. 493, Issue 7434 https://doi.org/10.1038/nature11820	journal	January 2013
Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ Shekhter, Arkady; Ramshaw, B. J.; Liang, Ruixing Nature, Vol. 498, Issue 7452 https://doi.org/10.1038/nature12165	journal	June 2013
Unfolding the physics of URu2Si2 through silicon to phosphorus substitution Gallagher, A.; Chen, K. -W.; Moir, C. M. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10712	journal	February 2016
Field-induced spin-density wave beyond hidden order in URu2Si2 Knafo, W.; Duc, F.; Bourdarot, F. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13075	journal	October 2016
Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2 Tonegawa, S.; Kasahara, S.; Fukuda, T. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5188	journal	June 2014
Momentum-resolved hidden-order gap reveals symmetry breaking and origin of entropy loss in URu2Si2 Bareille, C.; Boariu, F. L.; Schwab, H. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5326	journal	July 2014
Evidence for a nematic component to the hidden-order parameter in URu2Si2 from differential elastoresistance measurements Riggs, Scott C.; Shapiro, M. C.; Maharaj, Akash V. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7425	journal	March 2015
Hidden order in URu2Si2 originates from Fermi surface gapping induced by dynamic symmetry breaking Elgazzar, S.; Rusz, J.; Amft, M. Nature Materials, Vol. 8, Issue 4 https://doi.org/10.1038/nmat2395	journal	February 2009
Neutron scattering from quantum condensed matter Bramwell, Steven T.; Keimer, Bernhard Nature Materials, Vol. 13, Issue 8 https://doi.org/10.1038/nmat4045	journal	July 2014
Arrested Kondo effect and hidden order in URu2Si2 Haule, Kristjan; Kotliar, Gabriel Nature Physics, Vol. 5, Issue 11 https://doi.org/10.1038/nphys1392	journal	September 2009
Magnetically driven superconductivity in CeCu2Si2 Stockert, O.; Arndt, J.; Faulhaber, E. Nature Physics, Vol. 7, Issue 2 https://doi.org/10.1038/nphys1852	journal	December 2010
Emergent rank-5 nematic order in URu2Si2 Ikeda, Hiroaki; Suzuki, Michi-To; Arita, Ryotaro Nature Physics, Vol. 8, Issue 7 https://doi.org/10.1038/nphys2330	journal	June 2012
Colossal thermomagnetic response in the exotic superconductor URu2Si2 Yamashita, T.; Shimoyama, Y.; Haga, Y. Nature Physics, Vol. 11, Issue 1 https://doi.org/10.1038/nphys3170	journal	December 2014
Gapped itinerant spin excitations account for missing entropy in the hidden-order state of URu2Si2 Wiebe, C. R.; Janik, J. A.; MacDougall, G. J. Nature Physics, Vol. 3, Issue 2 https://doi.org/10.1038/nphys522	journal	January 2007
Unusual magnetic field-dependence of a possible hidden order phase Calegari, Eleonir João; Magalhaes, Sergio Garcia; Riseborough, Peter S. npj Quantum Materials, Vol. 2, Issue 1 https://doi.org/10.1038/s41535-017-0055-2	journal	August 2017
Translational Symmetry Breaking and Gapping of Heavy-Quasiparticle Pocket in URu2Si2 Yoshida, Rikiya; Tsubota, Koji; Ishiga, Toshihiko Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep02750	journal	October 2013
Visualizing the formation of the Kondo lattice and the hidden order in URu2Si2 Aynajian, P.; da Silva Neto, E. H.; Parker, C. V. Proceedings of the National Academy of Sciences, Vol. 107, Issue 23 https://doi.org/10.1073/pnas.1005892107	journal	May 2010
Holes in a Kondo lattice Thompson, J. D. Proceedings of the National Academy of Sciences, Vol. 108, Issue 45 https://doi.org/10.1073/pnas.1115741108	journal	October 2011
Direct bulk-sensitive probe of 5 f symmetry in URu ₂ Si ₂ Sundermann, Martin; Haverkort, Maurits W.; Agrestini, Stefano Proceedings of the National Academy of Sciences, Vol. 113, Issue 49 https://doi.org/10.1073/pnas.1612791113	journal	November 2016
Phase diagram of URu _{2– x} Fe _x Si ₂ in high magnetic fields Ran, Sheng; Jeon, Inho; Pouse, Naveen Proceedings of the National Academy of Sciences, Vol. 114, Issue 37 https://doi.org/10.1073/pnas.1710192114	journal	August 2017
High magnetic field behavior of strongly correlated uranium-based compounds Mydosh, J. A. Advances in Physics, Vol. 66, Issue 4 https://doi.org/10.1080/00018732.2017.1466475	journal	October 2017
Exotic Kondo effects in metals: Magnetic ions in a crystalline electric field and tunnelling centres Cox, D. L.; Zawadowski, A. Advances in Physics, Vol. 47, Issue 5 https://doi.org/10.1080/000187398243500	journal	September 1998
Fermi surface properties and de Haas–van Alphen oscillation in both the normal and superconducting mixed states of URu ₂ Si ₂ Ohkuni, H.; Inada, Y.; Tokiwa, Y. Philosophical Magazine B, Vol. 79, Issue 7 https://doi.org/10.1080/13642819908214859	journal	July 1999
Universality of the Mott–Ioffe–Regel limit in metals Hussey ‖, N. E.; Takenaka, K.; Takagi, H. Philosophical Magazine, Vol. 84, Issue 27 https://doi.org/10.1080/14786430410001716944	journal	September 2004
Itinerant multipolar order in URu ₂ Si ₂ and its signature in magnetic and lattice properties Thalmeier, Peter; Takimoto, Tetsuya; Ikeda, Hiroaki Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2013.861615	journal	November 2013
High purity specimens of URu ₂ Si ₂ produced by a molten metal flux technique Baumbach, R. E.; Fisk, Z.; Ronning, F. Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.895876	journal	April 2014
Optical study of hybridization and hidden order in URu ₂ Si ₂ Hall, J. S.; Timusk, T. Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.899439	journal	April 2014
Magnetic-field-induced chiral hidden order in URu ₂ Si ₂ Kotetes, P.; Aperis, A.; Varelogiannis, G. Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.909614	journal	May 2014
Spin-orbit density wave: a new phase of matter applicable to the hidden order state of URu ₂ Si ₂ Das, Tanmoy Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.916425	journal	May 2014
Hidden order behaviour in URu ₂ Si ₂ (A critical review of the status of hidden order in 2014) Mydosh, J. A.; Oppeneer, P. M. Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.916428	journal	May 2014
Neutron scattering studies on URu ₂ Si ₂ Bourdarot, Frederic; Raymond, Stephane; Regnault, Louis-Pierre Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.935513	journal	July 2014
Photoemission investigations of URu ₂ Si ₂ Durakiewicz, Tomasz Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.937783	journal	July 2014
X-ray backscattering study of crystal lattice distortion in hidden order of URu ₂ Si ₂ Tabata, C.; Inami, T.; Michimura, S. Philosophical Magazine, Vol. 94, Issue 32-33 https://doi.org/10.1080/14786435.2014.952701	journal	September 2014
Intermetallic compounds of rare-earth and 3d transition metals Buschow, K. H. J. Reports on Progress in Physics, Vol. 40, Issue 10 https://doi.org/10.1088/0034-4885/40/10/002	journal	October 1977
Angle-resolved heat capacity of heavy fermion superconductors Sakakibara, Toshiro; Kittaka, Shunichiro; Machida, Kazushige Reports on Progress in Physics, Vol. 79, Issue 9 https://doi.org/10.1088/0034-4885/79/9/094002	journal	August 2016
Temperature dependence of the resistivity due to localized spin fluctuations. II. Coles alloys Rivier, N.; Zlatic, V. Journal of Physics F: Metal Physics, Vol. 2, Issue 5 https://doi.org/10.1088/0305-4608/2/5/003	journal	September 1972
Weak-magnetism phenomena in heavy-fermion superconductors: selected SR studies Amato, A.; Graf, M. J.; Visser, A. de Journal of Physics: Condensed Matter, Vol. 16, Issue 40 https://doi.org/10.1088/0953-8984/16/40/001	journal	September 2004
Itinerant spin excitations near the hidden order transition in URu ₂ Si ₂ Janik, J. A.; Zhou, H. D.; Jo, Y-J Journal of Physics: Condensed Matter, Vol. 21, Issue 19 https://doi.org/10.1088/0953-8984/21/19/192202	journal	April 2009
Symmetry-protected hidden order and magnetic neutron Bragg diffraction by URu ₂ Si ₂ Khalyavin, D. D.; Lovesey, S. W.; Dobrynin, A. N. Journal of Physics: Condensed Matter, Vol. 26, Issue 4 https://doi.org/10.1088/0953-8984/26/4/046003	journal	January 2014
Studies of alloying effects on URu ₂ (Si,X) ₂ ; X=Al or Ge Park, J. -G; Coles, B. R. Journal of Physics: Condensed Matter, Vol. 6, Issue 7 https://doi.org/10.1088/0953-8984/6/7/014	journal	February 1994
Non-trivial magnetic order in URu ₂ Si ₂ ? Mason, T. E.; Buyers, W. J. L.; Petersen, T. Journal of Physics: Condensed Matter, Vol. 7, Issue 26 https://doi.org/10.1088/0953-8984/7/26/014	journal	June 1995
Superconducting gap structure of heavy-Fermion compound URu ₂ Si ₂ determined by angle-resolved thermal conductivity Kasahara, Y.; Shishido, H.; Shibauchi, T. New Journal of Physics, Vol. 11, Issue 5 https://doi.org/10.1088/1367-2630/11/5/055061	journal	May 2009
A Study of Elastic Properties of URu ₂ Si ₂ in Comparison with the Non-5 f Contribution of ThRu ₂ Si ₂ Yanagisawa, T.; Saito, H.; Watanabe, Y. Journal of Physics: Conference Series, Vol. 391 https://doi.org/10.1088/1742-6596/391/1/012079	journal	December 2012
Nodal gap structure of the heavy-fermion superconductor URu ₂ Si ₂ revealed by field-angle-dependent specific-heat measurements Kittaka, Shunichiro; Shimizu, Yusei; Sakakibara, Toshiro Journal of Physics: Conference Series, Vol. 807 https://doi.org/10.1088/1742-6596/807/5/052001	journal	April 2017
Thermal expansion and specific heat of monocrystalline U Ru 2 Si 2 de Visser, A.; Kayzel, F. E.; Menovsky, A. A. Physical Review B, Vol. 34, Issue 11 https://doi.org/10.1103/PhysRevB.34.8168	journal	December 1986
Mixed valence as an almost broken symmetry Coleman, Piers Physical Review B, Vol. 35, Issue 10 https://doi.org/10.1103/PhysRevB.35.5072	journal	April 1987
Crystalline electric field effects in UPt 2 Si 2 and URu 2 Si 2 Nieuwenhuys, G. J. Physical Review B, Vol. 35, Issue 10 https://doi.org/10.1103/PhysRevB.35.5260	journal	April 1987
Hall-effect and resistivity study of the heavy-fermion system URu 2 Si 2 Schoenes, J.; Schönenberger, C.; Franse, J. J. M. Physical Review B, Vol. 35, Issue 10 https://doi.org/10.1103/PhysRevB.35.5375	journal	April 1987
Magnetic excitations and phonon anomalies in U Ru 2 Si 2 Cooper, S. L.; Klein, M. V.; Maple, M. B. Physical Review B, Vol. 36, Issue 10 https://doi.org/10.1103/PhysRevB.36.5743	journal	October 1987
Ferromagnetic instability in the heavy-electron compound URu 2 Si 2 doped with Re or Tc Dalichaouch, Y.; Maple, M. B.; Torikachvili, M. S. Physical Review B, Vol. 39, Issue 4 https://doi.org/10.1103/PhysRevB.39.2423	journal	February 1989
Magnetic excitations in the heavy-fermion superconductor URu 2 Si 2 Broholm, C.; Lin, H.; Matthews, P. T. Physical Review B, Vol. 43, Issue 16 https://doi.org/10.1103/PhysRevB.43.12809	journal	June 1991
Anomalous phase transition in URu 2 Si 2 Agterberg, D. F.; Walker, M. B. Physical Review B, Vol. 50, Issue 1 https://doi.org/10.1103/PhysRevB.50.563	journal	July 1994
Hidden order in URu 2 Si 2 Shah, N.; Chandra, P.; Coleman, P. Physical Review B, Vol. 61, Issue 1 https://doi.org/10.1103/PhysRevB.61.564	journal	January 2000
Gaussian fluctuation corrections to the BCS mean-field gap amplitude at zero temperature Kos, Š.; Millis, A. J.; Larkin, A. I. Physical Review B, Vol. 70, Issue 21 https://doi.org/10.1103/PhysRevB.70.214531	journal	December 2004
Competition between hidden order and antiferromagnetism in URu 2 Si 2 under uniaxial stress studied by neutron scattering Yokoyama, M.; Amitsuka, H.; Tenya, K. Physical Review B, Vol. 72, Issue 21 https://doi.org/10.1103/PhysRevB.72.214419	journal	December 2005
Signature of hidden order in heavy fermion superconductor URu 2 Si 2 : Resonance at the wave vector Q 0 = ( 1,0,0 ) Villaume, A.; Bourdarot, F.; Hassinger, E. Physical Review B, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevB.78.012504	journal	July 2008
Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors Ramazashvili, Revaz Physical Review B, Vol. 79, Issue 18 https://doi.org/10.1103/PhysRevB.79.184432	journal	May 2009
Antiferromagnetic patches and hidden order in URu 2 Si 2 by impurity doping Baek, S. -H.; Graf, M. J.; Balatsky, A. V. Physical Review B, Vol. 81, Issue 13 https://doi.org/10.1103/PhysRevB.81.132404	journal	April 2010
Degree of 5 f electron localization in URu 2 Si 2 : Electron energy-loss spectroscopy and spin-orbit sum rule analysis Jeffries, J. R.; Moore, K. T.; Butch, N. P. Physical Review B, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevB.82.033103	journal	July 2010
Antiferromagnetic critical pressure in URu 2 Si 2 under hydrostatic conditions Butch, Nicholas P.; Jeffries, Jason R.; Chi, Songxue Physical Review B, Vol. 82, Issue 6 https://doi.org/10.1103/PhysRevB.82.060408	journal	August 2010
Electronic structure theory of the hidden-order material URu 2 Si 2 Oppeneer, P. M.; Rusz, J.; Elgazzar, S. Physical Review B, Vol. 82, Issue 20 https://doi.org/10.1103/PhysRevB.82.205103	journal	November 2010
Signature of hidden order and evidence for periodicity modification in URu 2 Si 2 Yoshida, Rikiya; Nakamura, Yoshiaki; Fukui, Masaki Physical Review B, Vol. 82, Issue 20 https://doi.org/10.1103/PhysRevB.82.205108	journal	November 2010
Magnetization, Maxwell’s relations, and the local physics of Th 1 − x U x Ru 2 Si 2 Tóth, Anna; Chandra, Premala; Coleman, Piers Physical Review B, Vol. 82, Issue 23 https://doi.org/10.1103/PhysRevB.82.235116	journal	December 2010
Band structure and Fermi surface of URu 2 Si 2 studied by soft x-ray angle-resolved photoemission spectroscopy Kawasaki, Ikuto; Fujimori, Shin-ichi; Takeda, Yukiharu Physical Review B, Vol. 83, Issue 23 https://doi.org/10.1103/PhysRevB.83.235121	journal	June 2011
5 f delocalization-induced suppression of quadrupolar order in U(Pd 1 − x Pt x ) 3 Walker, H. C.; Le, M. D.; McEwen, K. A. Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235142	journal	December 2011
Spin and orbital hybridization at specifically nested Fermi surfaces in URu 2 Si 2 Oppeneer, P. M.; Elgazzar, S.; Rusz, J. Physical Review B, Vol. 84, Issue 24 https://doi.org/10.1103/PhysRevB.84.241102	journal	December 2011
Phase transition arising from the underscreened Anderson lattice model: A candidate concept for explaining hidden order in URu 2 Si 2 Riseborough, Peter S.; Coqblin, B.; Magalhães, S. G. Physical Review B, Vol. 85, Issue 16 https://doi.org/10.1103/PhysRevB.85.165116	journal	April 2012
Hidden and antiferromagnetic order as a rank-5 superspin in URu 2 Si 2 Rau, Jeffrey G.; Kee, Hae-Young Physical Review B, Vol. 85, Issue 24 https://doi.org/10.1103/PhysRevB.85.245112	journal	June 2012
Neutron scattering study of URu 2 − x Re x Si 2 ( x = 0.10 ): Driving order towards quantum criticality Williams, T. J.; Yamani, Z.; Butch, N. P. Physical Review B, Vol. 86, Issue 23 https://doi.org/10.1103/PhysRevB.86.235104	journal	December 2012
Bulk evidence for a time-reversal symmetry broken superconducting state in URu 2 Si 2 Li, G.; Zhang, Q.; Rhodes, D. Physical Review B, Vol. 88, Issue 13 https://doi.org/10.1103/PhysRevB.88.134517	journal	October 2013
Hybridization-driven orthorhombic lattice instability in URu 2 Si 2 Yanagisawa, T.; Mombetsu, S.; Hidaka, H. Physical Review B, Vol. 88, Issue 19 https://doi.org/10.1103/PhysRevB.88.195150	journal	November 2013
Magnetic field-tuned localization of the 5 f -electrons in URu 2 Si 2 Harrison, N.; Moll, P. J. W.; Sebastian, S. E. Physical Review B, Vol. 88, Issue 24 https://doi.org/10.1103/PhysRevB.88.241108	journal	December 2013
Imprints of spin-orbit density wave in the hidden-order state of URu 2 Si 2 Das, Tanmoy Physical Review B, Vol. 89, Issue 4 https://doi.org/10.1103/PhysRevB.89.045135	journal	January 2014
Strict limit on in-plane ordered magnetic dipole moment in URu 2 Si 2 Ross, K. A.; Harriger, L.; Yamani, Z. Physical Review B, Vol. 89, Issue 15 https://doi.org/10.1103/PhysRevB.89.155122	journal	April 2014
Effective critical and tricritical exponents Riedel, Eberhard K.; Wegner, Franz J. Physical Review B, Vol. 9, Issue 1 https://doi.org/10.1103/PhysRevB.9.294	journal	January 1974
Nuclear-resonance line shapes due to magnetic impurities in metals Walstedt, R. E.; Walker, L. R. Physical Review B, Vol. 9, Issue 11 https://doi.org/10.1103/PhysRevB.9.4857	journal	June 1974
Exceptional Ising magnetic behavior of itinerant spin-polarized carriers in URu 2 Si 2 Werwiński, Mirosław; Rusz, Jan; Mydosh, John A. Physical Review B, Vol. 90, Issue 6 https://doi.org/10.1103/PhysRevB.90.064430	journal	August 2014
Superconductivity from fractionalized excitations in URu 2 Si 2 Hsu, Chen-Hsuan; Chakravarty, Sudip Physical Review B, Vol. 90, Issue 13 https://doi.org/10.1103/PhysRevB.90.134507	journal	October 2014
Multipole order and global/site symmetry in the hidden-order phase of URu 2 Si 2 Suzuki, Michi-To; Ikeda, Hiroaki Physical Review B, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevB.90.184407	journal	November 2014
Giant Nernst and Hall effects due to chiral superconducting fluctuations Sumiyoshi, Hiroaki; Fujimoto, Satoshi Physical Review B, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevB.90.184518	journal	November 2014
Hidden-order symmetry and superconductivity in URu 2 Si 2 investigated by quasiparticle interference Akbari, Alireza; Thalmeier, Peter Physical Review B, Vol. 90, Issue 22 https://doi.org/10.1103/PhysRevB.90.224511	journal	December 2014
Symmetry and correlations underlying hidden order in URu 2 Si 2 Butch, Nicholas P.; Manley, Michael E.; Jeffries, Jason R. Physical Review B, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevB.91.035128	journal	January 2015
Lattice dynamics of the heavy-fermion compound URu 2 Si 2 Buhot, J.; Méasson, M. A.; Gallais, Y. Physical Review B, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevB.91.035129	journal	January 2015
Chemical pressure tuning of URu 2 Si 2 via isoelectronic substitution of Ru with Fe Das, Pinaki; Kanchanavatee, N.; Helton, J. S. Physical Review B, Vol. 91, Issue 8 https://doi.org/10.1103/PhysRevB.91.085122	journal	February 2015
Evidence for broken time-reversal symmetry in the superconducting phase of URu 2 Si 2 Schemm, E. R.; Baumbach, R. E.; Tobash, P. H. Physical Review B, Vol. 91, Issue 14 https://doi.org/10.1103/PhysRevB.91.140506	journal	April 2015
Hastatic order in URu 2 Si 2 : Hybridization with a twist Chandra, Premala; Coleman, Piers; Flint, Rebecca Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/PhysRevB.91.205103	journal	May 2015
Collective spin resonance excitation in the gapped itinerant multipole hidden order phase of URu 2 Si 2 Akbari, Alireza; Thalmeier, Peter Physical Review B, Vol. 92, Issue 9 https://doi.org/10.1103/PhysRevB.92.094512	journal	September 2015
Role of commensurate and incommensurate low-energy excitations in the paramagnetic to hidden-order transition of URu 2 Si 2 Niklowitz, P. G.; Dunsiger, S. R.; Pfleiderer, C. Physical Review B, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevB.92.115116	journal	September 2015
Dilute RKKY model for NMR line broadening in the hidden-order state of URu 2 Si 2 Walstedt, R. E.; Kambe, S.; Tokunaga, Y. Physical Review B, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevB.93.045122	journal	January 2016
Antiferromagnetism and hidden order in isoelectronic doping of URu 2 Si 2 Wilson, M. N.; Williams, T. J.; Cai, Y. -P. Physical Review B, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevB.93.064402	journal	February 2016
Inelastic x-ray scattering measurements of phonon dynamics in URu 2 Si 2 Gardner, D. R.; Bonnoit, C. J.; Chisnell, R. Physical Review B, Vol. 93, Issue 7 https://doi.org/10.1103/PhysRevB.93.075123	journal	February 2016
Probing 5 f -state configurations in URu 2 Si 2 with U L III -edge resonant x-ray emission spectroscopy Booth, C. H.; Medling, S. A.; Tobin, J. G. Physical Review B, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevB.94.045121	journal	July 2016
Evolution of critical pressure with increasing Fe substitution in the heavy-fermion system URu 2 − x Fe x Si 2 Wolowiec, C. T.; Kanchanavatee, N.; Huang, K. Physical Review B, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevB.94.085145	journal	August 2016
Phase diagram and correlation functions of the two-dimensional dissipative quantum XY model Hou, Changtao; Varma, Chandra M. Physical Review B, Vol. 94, Issue 20 https://doi.org/10.1103/PhysRevB.94.201101	journal	November 2016
Detailed optical spectroscopy of hybridization gap and hidden-order transition in high-quality URu 2 Si 2 single crystals Bachar, N.; Stricker, D.; Muleady, S. Physical Review B, Vol. 94, Issue 23 https://doi.org/10.1103/PhysRevB.94.235101	journal	December 2016
Electronic properties of a heavy-fermion U ( Ru 0.92 Rh 0.08 ) 2 Si 2 single crystal Prokeš, K.; Huang, Y. -K.; Reehuis, M. Physical Review B, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevB.95.035138	journal	January 2017
NMR investigation of antiferromagnetism and coherence in URu 2 Si 2 − x P x Shirer, K. R.; Lawson, M.; Kissikov, T. Physical Review B, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevB.95.041107	journal	January 2017
Hidden order signatures in the antiferromagnetic phase of U ( Ru 1 − x Fe x ) 2 Si 2 Williams, T. J.; Aczel, A. A.; Stone, M. B. Physical Review B, Vol. 95, Issue 10 https://doi.org/10.1103/PhysRevB.95.104440	journal	March 2017
Gapped excitations in the high-pressure antiferromagnetic phase of URu 2 Si 2 Williams, T. J.; Barath, H.; Yamani, Z. Physical Review B, Vol. 95, Issue 19 https://doi.org/10.1103/PhysRevB.95.195171	journal	May 2017
Resonant x-ray spectroscopy of uranium intermetallics at the M 4 , 5 edges of uranium Kvashnina, K. O.; Walker, H. C.; Magnani, N. Physical Review B, Vol. 95, Issue 24 https://doi.org/10.1103/PhysRevB.95.245103	journal	June 2017
Role of band filling in tuning the high-field phases of URu 2 Si 2 Wartenbe, M. R.; Chen, K. -W.; Gallagher, A. Physical Review B, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevB.96.085141	journal	August 2017
On the possibility to detect multipolar order in URu 2 Si 2 by the electric quadrupolar transition of resonant elastic x-ray scattering Wang, Y. L.; Fabbris, G.; Meyers, D. Physical Review B, Vol. 96, Issue 8 https://doi.org/10.1103/PhysRevB.96.085146	journal	August 2017
Magnetic structure in a U ( Ru 0.92 Rh 0.08 ) 2 Si 2 single crystal studied by neutron diffraction in static magnetic fields up to 24 T Prokeš, K.; Bartkowiak, M.; Rivin, O. Physical Review B, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevB.96.121117	journal	September 2017
Electronic structure of ThRu 2 Si 2 studied by angle-resolved photoelectron spectroscopy: Elucidating the contribution of U 5 f states in URu 2 Si 2 Fujimori, Shin-ichi; Kobata, Masaaki; Takeda, Yukiharu Physical Review B, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevB.96.125117	journal	September 2017
Measurements of the NMR Knight shift tensor and nonlinear magnetization in URu 2 Si 2 Lawson, M.; Bush, B. T.; Kissikov, T. Physical Review B, Vol. 97, Issue 7 https://doi.org/10.1103/PhysRevB.97.075138	journal	February 2018
Search for multipolar instability in URu 2 Si 2 studied by ultrasonic measurements under pulsed magnetic field Yanagisawa, T.; Mombetsu, S.; Hidaka, H. Physical Review B, Vol. 97, Issue 15 https://doi.org/10.1103/PhysRevB.97.155137	journal	April 2018
Odd-parity electronic multipolar ordering in URu 2 Si 2 : Conclusions from Si and Ru NMR measurements Kambe, S.; Tokunaga, Y.; Sakai, H. Physical Review B, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevB.97.235142	journal	June 2018
Universal 2 Δ max / k B T c scaling decoupled from the electronic coherence in iron-based superconductors Miao, H.; Brito, W. H.; Yin, Z. P. Physical Review B, Vol. 98, Issue 2 https://doi.org/10.1103/PhysRevB.98.020502	journal	July 2018
ARPES/STM study of the surface terminations and 5 f -electron character in URu 2 Si 2 Zhang, W.; Lu, H. Y.; Xie, D. H. Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115121	journal	September 2018
Gaussian fluctuation corrections to a mean-field theory of complex hidden order in URu 2 Si 2 Shen, Pengtao; Dzero, Maxim Physical Review B, Vol. 98, Issue 12 https://doi.org/10.1103/PhysRevB.98.125131	journal	September 2018
Hidden order in URu 2 Si 2 : Symmetry-induced antitoroidal vortices Dmitrienko, Vladimir E.; Chizhikov, Viacheslav A. Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevB.98.165118	journal	October 2018
Pressure-induced rotational symmetry breaking in URu 2 Si 2 Choi, J.; Ivashko, O.; Dennler, N. Physical Review B, Vol. 98, Issue 24 https://doi.org/10.1103/PhysRevB.98.241113	journal	December 2018
Fermi-surface selective determination of the g -factor anisotropy in URu 2 Si 2 Bastien, Gaël; Aoki, Dai; Lapertot, Gérard Physical Review B, Vol. 99, Issue 16 https://doi.org/10.1103/PhysRevB.99.165138	journal	April 2019
Magnetoelastic coupling in URu 2 Si 2 : Probing multipolar correlations in the hidden order state Wartenbe, Mark; Baumbach, Ryan E.; Shekhter, Arkady Physical Review B, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevB.99.235101	journal	June 2019
Instability of the f -electron state in URu 2 Si 2 − x P x probed using high magnetic fields Huang, K.; Chen, K. -W.; Gallagher, A. Physical Review B, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevB.99.235146	journal	June 2019
Field-Angle-Dependent Specific Heat Measurements and Gap Determination of a Heavy Fermion Superconductor URu 2 Si 2 Yano, K.; Sakakibara, T.; Tayama, T. Physical Review Letters, Vol. 100, Issue 1 https://doi.org/10.1103/PhysRevLett.100.017004	journal	January 2008
Kramers Degeneracy in a Magnetic Field and Zeeman Spin-Orbit Coupling in Antiferromagnetic Conductors Ramazashvili, Revaz Physical Review Letters, Vol. 101, Issue 13 https://doi.org/10.1103/PhysRevLett.101.137202	journal	September 2008
Possible Phase Transition Deep Inside the Hidden Order Phase of Ultraclean URu 2 Si 2 Shishido, H.; Hashimoto, K.; Shibauchi, T. Physical Review Letters, Vol. 102, Issue 15 https://doi.org/10.1103/PhysRevLett.102.156403	journal	April 2009
Itinerant Magnetic Multipole Moments of Rank Five as the Hidden Order in URu 2 Si 2 Cricchio, Francesco; Bultmark, Fredrik; Grånäs, Oscar Physical Review Letters, Vol. 103, Issue 10 https://doi.org/10.1103/PhysRevLett.103.107202	journal	September 2009
Chirality Induced Tilted-Hill Giant Nernst Signal Kotetes, P.; Varelogiannis, G. Physical Review Letters, Vol. 104, Issue 10 https://doi.org/10.1103/PhysRevLett.104.106404	journal	March 2010
Parasitic Small-Moment Antiferromagnetism and Nonlinear Coupling of Hidden Order and Antiferromagnetism in URu 2 Si 2 Observed by Larmor Diffraction Niklowitz, P. G.; Pfleiderer, C.; Keller, T. Physical Review Letters, Vol. 104, Issue 10 https://doi.org/10.1103/PhysRevLett.104.106406	journal	March 2010
Similarity of the Fermi Surface in the Hidden Order State and in the Antiferromagnetic State of URu 2 Si 2 Hassinger, E.; Knebel, G.; Matsuda, T. D. Physical Review Letters, Vol. 105, Issue 21 https://doi.org/10.1103/PhysRevLett.105.216409	journal	November 2010
Modulated Spin Liquid: A New Paradigm for URu 2 Si 2 Pépin, C.; Norman, M. R.; Burdin, S. Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.106601	journal	March 2011
Sequential Spin Polarization of the Fermi Surface Pockets in URu 2 Si 2 and Its Implications for the Hidden Order Altarawneh, M. M.; Harrison, N.; Sebastian, S. E. Physical Review Letters, Vol. 106, Issue 14 https://doi.org/10.1103/PhysRevLett.106.146403	journal	April 2011
Spin Nematic State as a Candidate of the Hidden Order Phase of URu 2 Si 2 Fujimoto, Satoshi Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.196407	journal	May 2011
Superconducting Pairs with Extreme Uniaxial Anisotropy in URu 2 Si 2 Altarawneh, M. M.; Harrison, N.; Li, G. Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.066407	journal	February 2012
Cyclotron Resonance in the Hidden-Order Phase of URu 2 Si 2 Tonegawa, S.; Hashimoto, K.; Ikada, K. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.036401	journal	July 2012
Fermi Surface Reconstruction by Dynamic Magnetic Fluctuations Holt, Michael; Oitmaa, Jaan; Chen, Wei Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.037001	journal	July 2012
Hidden Order in URu 2 Si 2 Unveiled Ressouche, E.; Ballou, R.; Bourdarot, F. Physical Review Letters, Vol. 109, Issue 6 https://doi.org/10.1103/PhysRevLett.109.067202	journal	August 2012
Momentum-Resolved Evolution of the Kondo Lattice into “Hidden Order” in URu 2 Si 2 Boariu, F. L.; Bareille, C.; Schwab, H. Physical Review Letters, Vol. 110, Issue 15 https://doi.org/10.1103/PhysRevLett.110.156404	journal	April 2013
Formation of the Coherent Heavy Fermion Liquid at the Hidden Order Transition in URu 2 Si 2 Chatterjee, Shouvik; Trinckauf, Jan; Hänke, Torben Physical Review Letters, Vol. 110, Issue 18 https://doi.org/10.1103/PhysRevLett.110.186401	journal	May 2013
Magnetic Structure of Phase II in U ( Ru 0.96 Rh 0.04 ) 2 Si 2 Determined by Neutron Diffraction under Pulsed High Magnetic Fields Kuwahara, K.; Yoshii, S.; Nojiri, H. Physical Review Letters, Vol. 110, Issue 21 https://doi.org/10.1103/PhysRevLett.110.216406	journal	May 2013
NMR Study of In-Plane Twofold Ordering in URu 2 Si 2 Kambe, S.; Tokunaga, Y.; Sakai, H. Physical Review Letters, Vol. 110, Issue 24 https://doi.org/10.1103/PhysRevLett.110.246406	journal	June 2013
Imaging the Three-Dimensional Fermi-Surface Pairing near the Hidden-Order Transition in URu 2 Si 2 Using Angle-Resolved Photoemission Spectroscopy Meng, Jian-Qiao; Oppeneer, Peter M.; Mydosh, John A. Physical Review Letters, Vol. 111, Issue 12 https://doi.org/10.1103/PhysRevLett.111.127002	journal	September 2013
Symmetry of the Excitations in the Hidden Order State of URu 2 Si 2 Buhot, J.; Méasson, M. -A.; Gallais, Y. Physical Review Letters, Vol. 113, Issue 26 https://doi.org/10.1103/PhysRevLett.113.266405	journal	December 2014
Spectroscopic Determination of the Atomic f -Electron Symmetry Underlying Hidden Order in URu 2 Si 2 Wray, L. Andrew; Denlinger, Jonathan; Huang, Shih-Wen Physical Review Letters, Vol. 114, Issue 23 https://doi.org/10.1103/PhysRevLett.114.236401	journal	June 2015
Thermodynamic Measurement of Angular Anisotropy at the Hidden Order Transition of URu 2 Si 2 Trinh, Jennifer; Brück, Ekkes; Siegrist, Theo Physical Review Letters, Vol. 117, Issue 15 https://doi.org/10.1103/PhysRevLett.117.157201	journal	October 2016
Analogy Between the “Hidden Order” and the Orbital Antiferromagnetism in URu 2 − x Fe x Si 2 Kung, H. -H.; Ran, S.; Kanchanavatee, N. Physical Review Letters, Vol. 117, Issue 22 https://doi.org/10.1103/PhysRevLett.117.227601	journal	November 2016
Evidence for Spin Singlet Pairing with Strong Uniaxial Anisotropy in URu 2 Si 2 Using Nuclear Magnetic Resonance Hattori, T.; Sakai, H.; Tokunaga, Y. Physical Review Letters, Vol. 120, Issue 2 https://doi.org/10.1103/PhysRevLett.120.027001	journal	January 2018
First-Order Phase Transitions in Superconductors and Smectic- A Liquid Crystals Halperin, B. I.; Lubensky, T. C.; Ma, Shang-keng Physical Review Letters, Vol. 32, Issue 6 https://doi.org/10.1103/PhysRevLett.32.292	journal	February 1974
Superconducting and Magnetic Transitions in the Heavy-Fermion System U Ru 2 Si 2 Palstra, T. T. M.; Menovsky, A. A.; Berg, J. van den Physical Review Letters, Vol. 55, Issue 24 https://doi.org/10.1103/PhysRevLett.55.2727	journal	December 1985
Partially gapped Fermi surface in the heavy-electron superconductor URu 2 Si 2 Maple, M. B.; Chen, J. W.; Dalichaouch, Y. Physical Review Letters, Vol. 56, Issue 2 https://doi.org/10.1103/PhysRevLett.56.185	journal	January 1986
Magnetic excitations and ordering in the heavy-electron superconductor URu 2 Si 2 Broholm, C.; Kjems, J. K.; Buyers, W. J. L. Physical Review Letters, Vol. 58, Issue 14 https://doi.org/10.1103/PhysRevLett.58.1467	journal	April 1987
Quadrupolar Kondo effect in uranium heavy-electron materials? Cox, D. L. Physical Review Letters, Vol. 59, Issue 11 https://doi.org/10.1103/PhysRevLett.59.1240	journal	September 1987
Far-Infrared Properties of URu 2 Si 2 Bonn, D. A.; Garrett, J. D.; Timusk, T. Physical Review Letters, Vol. 61, Issue 11 https://doi.org/10.1103/PhysRevLett.61.1305	journal	September 1988
X-ray magnetic scattering in antiferromagnetic URu 2 Si 2 Isaacs, E. D.; McWhan, D. B.; Kleiman, R. N. Physical Review Letters, Vol. 65, Issue 25 https://doi.org/10.1103/PhysRevLett.65.3185	journal	December 1990
Neutron-scattering measurements of long-range antiferromagnetic order in URu 2 Si 2 Mason, T. E.; Gaulin, B. D.; Garrett, J. D. Physical Review Letters, Vol. 65, Issue 25 https://doi.org/10.1103/PhysRevLett.65.3189	journal	December 1990
Nature of the order parameter in the heavy-fermion system URu 2 Si 2 Walker, M. B.; Buyers, W. J. L.; Tun, Z. Physical Review Letters, Vol. 71, Issue 16 https://doi.org/10.1103/PhysRevLett.71.2630	journal	October 1993
Novel Raman-active electronic excitations near the charge-transfer gap in insulating cuprates Liu, Ran; Salamon, D.; Klein, M. V. Physical Review Letters, Vol. 71, Issue 22 https://doi.org/10.1103/PhysRevLett.71.3709	journal	November 1993
Crystal Field Model of the Magnetic Properties of U Ru 2 Si 2 Santini, P.; Amoretti, G. Physical Review Letters, Vol. 73, Issue 7 https://doi.org/10.1103/PhysRevLett.73.1027	journal	August 1994
Effect of Pressure on Tiny Antiferromagnetic Moment in the Heavy-Electron Compound URu 2 Si 2 Amitsuka, H.; Sato, M.; Metoki, N. Physical Review Letters, Vol. 83, Issue 24 https://doi.org/10.1103/PhysRevLett.83.5114	journal	December 1999
Raman Scattering Study of Anomalous Spin, Charge, and Lattice Dynamics in the Charge-Ordered Phase of Bi 1 − x Ca x MnO 3 ( x > 0.5 ) Yoon, S.; Rübhausen, M.; Cooper, S. L. Physical Review Letters, Vol. 85, Issue 15 https://doi.org/10.1103/PhysRevLett.85.3297	journal	October 2000
Spatially Inhomogeneous Development of Antiferromagnetism in URu 2 Si 2 : Evidence from S 29 i NMR under Pressure Matsuda, K.; Kohori, Y.; Kohara, T. Physical Review Letters, Vol. 87, Issue 8 https://doi.org/10.1103/PhysRevLett.87.087203	journal	August 2001
First-Order Superconducting Phase Transition in C e C o I n 5 Bianchi, A.; Movshovich, R.; Oeschler, N. Physical Review Letters, Vol. 89, Issue 13 https://doi.org/10.1103/PhysRevLett.89.137002	journal	September 2002
Non-Fermi-Liquid Behavior within the Ferromagnetic Phase in U R u 2 − x R e x S i 2 Bauer, E. D.; Zapf, V. S.; Ho, P. -C. Physical Review Letters, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevLett.94.046401	journal	February 2005
Exotic Superconducting Properties in the Electron-Hole-Compensated Heavy-Fermion “Semimetal” URu 2 Si 2 Kasahara, Y.; Iwasawa, T.; Shishido, H. Physical Review Letters, Vol. 99, Issue 11 https://doi.org/10.1103/PhysRevLett.99.116402	journal	September 2007
Intertwined Orders in Heavy-Fermion Superconductor CeCoIn 5 Kim, Duk Y.; Lin, Shi-Zeng; Weickert, Franziska Physical Review X, Vol. 6, Issue 4 https://doi.org/10.1103/PhysRevX.6.041059	journal	December 2016
The superconducting phases of UPt 3 Joynt, Robert; Taillefer, Louis Reviews of Modern Physics, Vol. 74, Issue 1 https://doi.org/10.1103/RevModPhys.74.235	journal	March 2002
Superconducting phases of f -electron compounds Pfleiderer, Christian Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/RevModPhys.81.1551	journal	November 2009
Multipolar interactions in f -electron systems: The paradigm of actinide dioxides Santini, Paolo; Carretta, Stefano; Amoretti, Giuseppe Reviews of Modern Physics, Vol. 81, Issue 2 https://doi.org/10.1103/RevModPhys.81.807	journal	June 2009
Colloquium : Hidden order, superconductivity, and magnetism: The unsolved case of URu 2 Si 2 Mydosh, J. A.; Oppeneer, P. M. Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1301	journal	November 2011
Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2 Okazaki, R.; Shibauchi, T.; Shi, H. J. Science, Vol. 331, Issue 6016 https://doi.org/10.1126/science.1197358	journal	January 2011
Chirality density wave of the "hidden order" phase in URu2Si2 Kung, H. - H.; Baumbach, R. E.; Bauer, E. D. Science, Vol. 347, Issue 6228 https://doi.org/10.1126/science.1259729	journal	February 2015
Field-Induced Destruction of Heavy Fermion State in URu ₂ Si ₂ Sugiyama, Kiyohiro; Fuke, Hiroyuki; Kindo, Koichi Journal of the Physical Society of Japan, Vol. 59, Issue 9 https://doi.org/10.1143/JPSJ.59.3331	journal	September 1990
Single Uranium-Site Properties of the Dilute Heavy Electron System U _x Th _{1- x} Ru ₂ Si ₂ ( x ≤0.07) Amitsuka, Hiroshi; Sakakibara, Toshiro Journal of the Physical Society of Japan, Vol. 63, Issue 2 https://doi.org/10.1143/JPSJ.63.736	journal	February 1994
Metamagnetic Transition in a Heavy Fermion Superconductor URu ₂ Si ₂ Sugiyama, Kiyohiro; Nakashima, Miho; Ohkuni, Hitoshi Journal of the Physical Society of Japan, Vol. 68, Issue 10 https://doi.org/10.1143/JPSJ.68.3394	journal	October 1999
Neutron Scattering Study on Competition between Hidden Order and Antiferromagnetism in U(Ru _{1- x} Rh _x ) ₂ Si ₂ ( x ≤0.05) Yokoyama, Makoto; Amitsuka, Hiroshi; Itoh, Seiichiroh Journal of the Physical Society of Japan, Vol. 73, Issue 3 https://doi.org/10.1143/JPSJ.73.545	journal	March 2004
¹⁰¹ Ru NQR and Hidden Order in URu ₂ Si ₂ Saitoh, Satoru; Takagi, Shigeru; Yokoyama, Makoto Journal of the Physical Society of Japan, Vol. 74, Issue 8 https://doi.org/10.1143/JPSJ.74.2209	journal	August 2005
Description of Multipole in f -Electron Systems Kusunose, Hiroaki Journal of the Physical Society of Japan, Vol. 77, Issue 6 https://doi.org/10.1143/JPSJ.77.064710	journal	June 2008
Precise Study of the Resonance at Q ₀ =(1,0,0) in URu ₂ Si ₂ Bourdarot, Frederic; Hassinger, Elena; Raymond, Stephane Journal of the Physical Society of Japan, Vol. 79, Issue 6 https://doi.org/10.1143/JPSJ.79.064719	journal	June 2010
On the Hidden Order in URu ₂ Si ₂ – Antiferro Hexadecapole Order and Its Consequences Kusunose, Hiroaki; Harima, Hisatomo Journal of the Physical Society of Japan, Vol. 80, Issue 8 https://doi.org/10.1143/JPSJ.80.084702	journal	August 2011
Details of Sample Dependence and Transport Properties of URu ₂ Si ₂ D. Matsuda, Tatsuma; Hassinger, Elena; Aoki, Dai Journal of the Physical Society of Japan, Vol. 80, Issue 11 https://doi.org/10.1143/JPSJ.80.114710	journal	November 2011
Magnetic Exciton Mediated Superconductivity in the Hidden-Order Phase of URu ₂ Si ₂ Kusunose, Hiroaki Journal of the Physical Society of Japan, Vol. 81, Issue 2 https://doi.org/10.1143/JPSJ.81.023704	journal	February 2012
High-Field Fermi Surface Properties in the Low-Carrier Heavy-Fermion Compound URu ₂ Si ₂ Aoki, Dai; Knebel, Georg; Sheikin, Ilya Journal of the Physical Society of Japan, Vol. 81, Issue 7 https://doi.org/10.1143/JPSJ.81.074715	journal	July 2012
Symmetry of the Hidden Order in URu ₂ Si ₂ from Nuclear Magnetic Resonance Studies Takagi, Shigeru; Ishihara, Shu; Yokoyama, Makoto Journal of the Physical Society of Japan, Vol. 81, Issue 11 https://doi.org/10.1143/JPSJ.81.114710	journal	November 2012
Super Clean Sample of URu ₂ Si ₂ D. Matsuda, Tatsuma; Aoki, Dai; Ikeda, Shugo Journal of the Physical Society of Japan, Vol. 77, Issue Suppl.A https://doi.org/10.1143/JPSJS.77SA.362	journal	January 2008
Complex Landau-Ginzburg theory of the hidden order in URu ₂ Si ₂ Haule, K.; Kotliar, G. EPL (Europhysics Letters), Vol. 89, Issue 5 https://doi.org/10.1209/0295-5075/89/57006	journal	March 2010
Single Crystal Growth of URu2Si2 by the Modified Bridgman Technique Gallagher, Andrew; Nelson, William; Chen, Kuan Crystals, Vol. 6, Issue 10 https://doi.org/10.3390/cryst6100128	journal	October 2016
Gapped itinerant spin excitations account for missing entropy in the hidden order state of URu$_2$Si$_2$ Wiebe, C. R.; Janik, J. A.; Macdougall, G. J. arXiv https://doi.org/10.48550/arxiv.0710.0896	text	January 2007
Description of Multipole in f-Electron Systems Kusunose, Hiroaki arXiv https://doi.org/10.48550/arxiv.0803.4358	text	January 2008
Superconducting phases of f-electron compounds Pfleiderer, C. arXiv https://doi.org/10.48550/arxiv.0905.2625	text	January 2009
Chirality Induced Tilted-Hill Giant Nernst Signal Kotetes, Panagiotis; Varelogiannis, Georgios arXiv https://doi.org/10.48550/arxiv.0911.2512	text	January 2009
Visualizing the Formation of the Kondo Lattice and the Hidden Order in URu2Si2 Aynajian, Pegor; Neto, Eduardo H. da Silva; Parker, Colin V. arXiv https://doi.org/10.48550/arxiv.1003.5259	text	January 2010
Precise study of the resonance at Q0=(1,0,0) in URu2Si2 Bourdarot, Frederic; Hassinger, Elena; Raymond, Stephane arXiv https://doi.org/10.48550/arxiv.1004.1899	text	January 2010
The modulated spin liquid: a new paradigm for URu$_2$Si$_2$ Pepin, C.; Norman, M. R.; Burdin, S. arXiv https://doi.org/10.48550/arxiv.1010.1237	text	January 2010
Rotational Symmetry Breaking in the Hidden-Order Phase of URu2Si2 Okazaki, R.; Shibauchi, T.; Shi, H. J. arXiv https://doi.org/10.48550/arxiv.1107.5480	text	January 2011
Details of Sample Dependence and Transport Properties of URu2Si2 Matsuda, Tatsuma D.; Hassinger, Elena; Aoki, Dai arXiv https://doi.org/10.48550/arxiv.1109.1953	text	January 2011
Role of commensurate and incommensurate low-energy excitations in the paramagnetic to hidden-order transition of URu$_2$Si$_2$ Niklowitz, P. G.; Dunsiger, S. R.; Pfleiderer, C. arXiv https://doi.org/10.48550/arxiv.1110.5599	text	January 2011
Magnetically driven superconductivity in CeCu2Si2 Stockert, O.; Arndt, J.; Faulhaber, E. arXiv https://doi.org/10.48550/arxiv.1202.4112	text	January 2012
Optical study of hybridization and hidden order in URu$_2$Si$_2$ Hall, J. S.; Timusk, T. arXiv https://doi.org/10.48550/arxiv.1404.7093	text	January 2014
Exceptional Ising Magnetic Behavior of Itinerant Spin-polarized Carriers in URu2Si2 Werwinski, Miroslaw; Rusz, Jan; Mydosh, John A. arXiv https://doi.org/10.48550/arxiv.1405.1631	text	January 2014
A Model for Metastable Magnetism in the Hidden-Order Phase of URu2Si2 Boyer, Lance; Yakovenko, Victor M. arXiv https://doi.org/10.48550/arxiv.1704.06231	text	January 2017
On the possibility to detect multipolar order in URu$_2$Si$_2$ by the electric quadrupolar transition of resonant elastic X-ray scattering Wang, Y. L.; Fabbris, G.; Meyers, D. arXiv https://doi.org/10.48550/arxiv.1708.05307	text	January 2017
Γ ₃ -Type Lattice Instability and the Hidden Order of URu ₂ Si ₂ Yanagisawa, Tatsuya; Mombetsu, Shota; Hidaka, Hiroyuki Journal of the Physical Society of Japan, Vol. 82, Issue 1 https://doi.org/10.7566/JPSJ.82.013601	journal	January 2013
Neutron Scattering Experiments for the Study of In-Plane Ordered Moment in URu ₂ Si ₂ Metoki, Naoto; Sakai, Hironori; Yamamoto, Etsuji Journal of the Physical Society of Japan, Vol. 82, Issue 5 https://doi.org/10.7566/JPSJ.82.055004	journal	May 2013
Magnetic and Electronic Properties of URu ₂ Si ₂ Revealed by Comparison with Nonmagnetic References ThRu ₂ Si ₂ and LaRu ₂ Si ₂ Emi, Naoya; Hamabata, Ryosuke; Nakayama, Daisuke Journal of the Physical Society of Japan, Vol. 84, Issue 6 https://doi.org/10.7566/JPSJ.84.063702	journal	June 2015
Evidence for Chiral d -Wave Superconductivity in URu ₂ Si ₂ from the Field-Angle Variation of Its Specific Heat Kittaka, Shunichiro; Shimizu, Yusei; Sakakibara, Toshiro Journal of the Physical Society of Japan, Vol. 85, Issue 3 https://doi.org/10.7566/JPSJ.85.033704	journal	March 2016
Electronic Structures of Uranium Compounds Studied by Soft X-ray Photoelectron Spectroscopy Fujimori, Shin-ichi; Takeda, Yukiharu; Okane, Tetsuo Journal of the Physical Society of Japan, Vol. 85, Issue 6 https://doi.org/10.7566/JPSJ.85.062001	journal	June 2016
No Detectable Change in In-Plane ²⁹ Si Knight Shift in the Superconducting State of URu ₂ Si ₂ Hattori, Taisuke; Sakai, Hironori; Tokunaga, Yo Journal of the Physical Society of Japan, Vol. 85, Issue 7 https://doi.org/10.7566/JPSJ.85.073711	journal	July 2016
Detection of Magnetic Moment Distribution in URu ₂ Si ₂ Hanzawa, Katsurou Journal of the Physical Society of Japan, Vol. 86, Issue 4 https://doi.org/10.7566/JPSJ.86.044702	journal	April 2017
First-principles Theory of Magnetic Multipoles in Condensed Matter Systems Suzuki, Michi-To; Ikeda, Hiroaki; Oppeneer, Peter M. Journal of the Physical Society of Japan, Vol. 87, Issue 4 https://doi.org/10.7566/JPSJ.87.041008	journal	April 2018

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36 MATERIALS SCIENCE
Isingness
correlated electron system
hidden order
multifaceted phases
unconventional superconductivity

Title: Hidden order and beyond: an experimental—theoretical overview of the multifaceted behavior of URu2Si2

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Title: Hidden order and beyond: an experimental—theoretical overview of the multifaceted behavior of URu₂Si₂