path: root/hidden_order.bib

@article{el-showk_solving_2014,
  title = {Solving the 3d {{Ising Model}} with the {{Conformal Bootstrap II}}. {$\mathsl{c}$}-{{Minimization}} and {{Preise Critial Exponents}}},
  volume = {157},
  issn = {0022-4715, 1572-9613},
  abstract = {We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge \textbackslash{}(c\textbackslash{}) in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several \textbackslash{}(\textbackslash{}mathbb \{Z\}\_2\textbackslash{})-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension \textbackslash{}(\textbackslash{}Delta \_\textbackslash{}sigma = 0.518154(15)\textbackslash{}), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.},
  language = {en},
  number = {4-5},
  journal = {Journal of Statistical Physics},
  doi = {10.1007/s10955-014-1042-7},
  author = {{El-Showk}, Sheer and Paulos, Miguel F. and Poland, David and Rychkov, Slava and {Simmons-Duffin}, David and Vichi, Alessandro},
  month = dec,
  year = {2014},
  keywords = {_tablet},
  pages = {869-914},
  file = {/home/pants/.zotero/data/storage/XB5EWQ28/El-Showk et al. - 2014 - Solving the 3d Ising Model with the Conformal Boot.pdf}
}

@article{guida_critical_1998,
  title = {Critical Exponents of the {{N}}-Vector Model},
  volume = {31},
  issn = {0305-4470},
  abstract = {Recently the series for two renormalization group functions (corresponding to the anomalous dimensions of the fields \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img1.gif] and \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img2.gif] ) of the three-dimensional \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img3.gif] field theory have been extended to next order (seven loops) by Murray and Nickel. We examine the influence of these additional terms on the estimates of critical exponents of the N -vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within the errors of the previous evaluation. Exponents such as \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img4.gif] (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou-Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img5.gif] expansions (order \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img6.gif] ), we have also re-analysed the determination of exponents from the \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img7.gif] -expansion. The conclusion is that the general agreement between \#\#IMG\#\# [http://ej.iop.org/images/0305-4470/31/40/006/img7.gif] -expansion and three-dimensional series has improved with respect to Le Guillou-Zinn-Justin.},
  language = {en},
  number = {40},
  journal = {Journal of Physics A: Mathematical and General},
  doi = {10.1088/0305-4470/31/40/006},
  author = {Guida, R. and {Zinn-Justin}, J.},
  year = {1998},
  keywords = {_tablet},
  pages = {8103},
  file = {/home/pants/.zotero/data/storage/K468APXL/Guida and Zinn-Justin - 1998 - Critical exponents of the N-vector model.pdf}
}

@book{chaikin_principles_2000,
  title = {Principles of {{Condensed Matter Physics}}},
  isbn = {978-1-139-64305-4},
  abstract = {Now in paperback, this book provides an overview of the physics of condensed matter systems. Assuming a familiarity with the basics of quantum mechanics and statistical mechanics, the book establishes a general framework for describing condensed phases of matter, based on symmetries and conservation laws. It explores the role of spatial dimensionality and microscopic interactions in determining the nature of phase transitions, as well as discussing the structure and properties of materials with different symmetries. Particular attention is given to critical phenomena and renormalization group methods. The properties of liquids, liquid crystals, quasicrystals, crystalline solids, magnetically ordered systems and amorphous solids are investigated in terms of their symmetry, generalised rigidity, hydrodynamics and topological defect structure. In addition to serving as a course text, this book is an essential reference for students and researchers in physics, applied physics, chemistry, materials science and engineering, who are interested in modern condensed matter physics.},
  language = {en},
  publisher = {{Cambridge University Press}},
  author = {Chaikin, P. M. and Lubensky, T. C.},
  month = sep,
  year = {2000},
  keywords = {Science / Physics / Condensed Matter,Science / Physics / General,Science / Chemistry / Physical \& Theoretical,Technology \& Engineering / Electronics / General,Technology \& Engineering / Materials Science / General,_tablet},
  file = {/home/pants/.zotero/data/storage/VYB3UA2Z/Chaikin and Lubensky - 2000 - Principles of Condensed Matter Physics.pdf},
  googlebooks = {lAohAwAAQBAJ}
}

@book{landau_theory_1995,
  series = {Landau and {{Lifshitz Course}} of {{Theoretical Physics}}},
  title = {Theory of {{Elasticity}}},
  author = {Landau, Lev Davidovich and Lifshitz, Eugin M and Berestetskii, VB and Pitaevskii, LP},
  year = {1995},
  keywords = {_tablet},
  file = {/home/pants/.zotero/data/storage/AQ7G8AHB/Landau et al. - 1995 - Theory of Elasticity.pdf}
}

@article{fisher_specific_1990,
  title = {Specific Heat of {{URu}}{$_{2}$}{{Si}}{$_2$}: {{Effect}} of Pressure and Magnetic Field on the Magnetic and Superconducting Transitions},
  volume = {163},
  issn = {0921-4526},
  shorttitle = {Specific Heat of {{URu2Si2}}},
  abstract = {Specific heats were measured in the range 0.3 {$\leqslant$}T{$\leqslant$}30 K for 0{$\leqslant$}H{$\leqslant$}7T and P=0, and for H=0 and 0{$\leqslant$}P{$\leqslant$}6.3 kbar. For H=0 and P=0, the measurements were extended to 0.15K. Above the superconducting transition the H=0 and 7T data can be superimposed. For the magnetic transition near T0 = 18K, T0 increased with increasing P accompanied by a broadening and attenuation of the specific heat anomally. The superconducting transition near Tc = 1.5 K was broadened, attenuated and shifted to lower temperatures for both increasing P and H. The superconducting transition is similar to that of UPt3, and both the temperature dependence of the superconducting state specific heat and the derived parameters are consistent with an unconventional polar-type pairing.},
  number = {1},
  journal = {Physica B: Condensed Matter},
  doi = {10.1016/0921-4526(90)90229-n},
  author = {Fisher, R. A. and Kim, S. and Wu, Y. and Phillips, N. E. and McElfresh, M. W. and Torikachvili, M. S. and Maple, M. B.},
  month = apr,
  year = {1990},
  keywords = {_tablet},
  pages = {419-423},
  file = {/home/pants/.zotero/data/storage/HHVDKMSP/Fisher et al. - 1990 - Specific heat of URu₂Si₂ Effect of pressure and m.pdf}
}

@article{hornreich_lifshitz_1980,
  title = {The {{Lifshitz}} Point: {{Phase}} Diagrams and Critical Behavior},
  volume = {15-18},
  issn = {0304-8853},
  shorttitle = {The {{Lifshitz}} Point},
  abstract = {The Lifshitz multicritical point (LP) divides the phase diagram of a magnetic system into paramagnetic, uniform (ferro- or antiferromagnetic) and modulated (spiral or helicoidal) phases, which coexist at the LP. It can occur in a variety of different systems, including magnetic compounds and alloys, liquid crystals, charge-transfer salts, and structurally incommensurate materials. Theoretical studies, including renormalization group, exact spherical model and high temperature series expansion calculations, are reviewed with emphasis on possible experimental (including Monte Carlo) verifications of the theoretical predictions in three and two dimensional systems. Some promising materials for further research are indicated.},
  journal = {Journal of Magnetism and Magnetic Materials},
  doi = {10/ccgt88},
  author = {Hornreich, R. M.},
  month = jan,
  year = {1980},
  keywords = {_tablet},
  pages = {387-392},
  file = {/home/pants/.zotero/data/storage/FQWHY9TF/Hornreich - 1980 - The Lifshitz point Phase diagrams and critical be.pdf}
}

@article{lifshitz_theory_1942-1,
  title = {On the Theory of Phase Transitions of the Second Order {{II}}. {{Phase}} Transitions of the Second Order in Alloys},
  volume = {6},
  journal = {Proceedings of the USSR Academy of Sciences Journal of Physics},
  author = {Lifshitz, EM},
  year = {1942},
  keywords = {⛔ No DOI found,_tablet},
  pages = {251},
  file = {/home/pants/.zotero/data/storage/TAA9G46H/Lifshitz - 1942 - On the theory of phase transitions of the second o.pdf}
}

@article{lifshitz_theory_1942,
  title = {On the Theory of Phase Transitions of the Second Order {{I}}. {{Changes}} of the Elementary Cell of a Crystal in Phase Transitions of the Second Order},
  volume = {6},
  journal = {Proceedings of the USSR Academy of Sciences Journal of Physics},
  author = {Lifshitz, EM},
  year = {1942},
  keywords = {⛔ No DOI found,_tablet},
  pages = {61},
  file = {/home/pants/.zotero/data/storage/D9BYG3FK/Lifshitz - 1942 - On the theory of phase transitions of the second o.pdf}
}

@article{ginzburg_remarks_1961,
  title = {Some {{Remarks}} on {{Phase Transitions}} of the {{Second Kind}} and the {{Microscopic}} Theory of {{Ferroelectric Materials}}},
  volume = {2},
  number = {9},
  journal = {Soviet Physics, Solid State},
  author = {Ginzburg, V. L.},
  year = {1961},
  keywords = {⛔ No DOI found},
  pages = {1824-1834},
  file = {/home/pants/.zotero/data/storage/JVMTIZGB/Ginzburg - 1961 - Some Remarks on Phase Transitions of the Second Ki.pdf}
}

@article{choi_pressure-induced_2018,
  title = {Pressure-Induced Rotational Symmetry Breaking in \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {98},
  abstract = {Phase transitions and symmetry are intimately linked. Melting of ice, for example, restores translation invariance. The mysterious hidden order (HO) phase of URu2Si2 has, despite relentless research efforts, kept its symmetry breaking element intangible. Here, we present a high-resolution x-ray diffraction study of the URu2Si2 crystal structure as a function of hydrostatic pressure. Below a critical pressure threshold pc{$\approx$}3 kbar, no tetragonal lattice symmetry breaking is observed even below the HO transition THO=17.5 K. For p{$>$}pc, however, a pressure-induced rotational symmetry breaking is identified with an onset temperatures TOR{$\sim$}100 K. The emergence of an orthorhombic phase is found and discussed in terms of an electronic nematic order that appears unrelated to the HO, but with possible relevance for the pressure-induced antiferromagnetic (AF) phase. Existing theories describe the HO and AF phases through an adiabatic continuity of a complex order parameter. Since none of these theories predicts a pressure-induced nematic order, our finding adds an additional symmetry breaking element to this long-standing problem.},
  number = {24},
  journal = {Physical Review B},
  doi = {10/gf5c39},
  author = {Choi, J. and Ivashko, O. and Dennler, N. and Aoki, D. and {von Arx}, K. and Gerber, S. and Gutowski, O. and Fischer, M. H. and Strempfer, J. and {v. Zimmermann}, M. and Chang, J.},
  month = dec,
  year = {2018},
  pages = {241113},
  file = {/home/pants/.zotero/data/storage/8IBGVH7U/Choi et al. - 2018 - Pressure-induced rotational symmetry breaking in $.pdf}
}

@article{hassinger_temperature-pressure_2008,
  title = {Temperature-Pressure Phase Diagram of \$\textbackslash{}mathrm\{\vphantom\}{{U}}\vphantom\{\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Ru}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$ from Resistivity Measurements and Ac Calorimetry: {{Hidden}} Order and {{Fermi}}-Surface Nesting},
  volume = {77},
  shorttitle = {Temperature-Pressure Phase Diagram of \$\textbackslash{}mathrm\{\vphantom\}{{U}}\vphantom\{\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Ru}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$ from Resistivity Measurements and Ac Calorimetry},
  abstract = {By performing combined resistivity and calorimetric experiments under pressure, we have determined a precise temperature-pressure (T,P) phase diagram of the heavy fermion compound URu2Si2. It will be compared with previous diagrams determined by elastic neutron diffraction and strain gauge techniques. At first glance, the low-pressure ordered phase referred to as hidden order is dominated by Fermi-surface nesting, which has strong consequences on the localized spin dynamics. The high-pressure phase is dominated by large moment antiferromagnetism (LMAF) coexisting with at least dynamical nesting needed to restore on cooling a local moment behavior. ac calorimetry confirms unambiguously that bulk superconductivity does not coexist with LMAF. URu2Si2 is one of the most spectacular examples of the dual itinerant and local character of uranium-based heavy fermion compounds.},
  number = {11},
  journal = {Physical Review B},
  doi = {10.1103/physrevb.77.115117},
  author = {Hassinger, E. and Knebel, G. and Izawa, K. and Lejay, P. and Salce, B. and Flouquet, J.},
  month = mar,
  year = {2008},
  pages = {115117},
  file = {/home/pants/.zotero/data/storage/U5V8JT6U/Hassinger et al. - 2008 - Temperature-pressure phase diagram of $mathrm U .pdf}
}

@article{kambe_odd-parity_2018,
  title = {Odd-Parity Electronic Multipolar Ordering in \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$: {{Conclusions}} from {{Si}} and {{Ru NMR}} Measurements},
  volume = {97},
  shorttitle = {Odd-Parity Electronic Multipolar Ordering in \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  abstract = {We report 29Si and 101Ru NMR measurements on high-quality, single-crystal URu2Si2 samples with a residual resistivity ratio RRR{$\sim$}70. Our results show that the Si and Ru sites exhibit fourfold electronic symmetry around the c axis in the hidden-order state. A previously observed twofold contribution of Si NMR linewidth is concluded to be due to extrinsic magnetic centers. Since the U and Si sites are aligned along the c axis, we conclude further that the electronic state shows fourfold symmetry around the U site below the hidden-order transition. From this observed local symmetry, possible space groups for the hidden-order state are P4/nnc or I4/m, based on group theoretical considerations. Since the order vector is considered to be Q=(001), the hidden-order state is then found to be P4/nnc with rank 5 odd parity, i.e., electric dotriacontapolar order.},
  number = {23},
  journal = {Physical Review B},
  doi = {10/gf5vbp},
  author = {Kambe, S. and Tokunaga, Y. and Sakai, H. and Hattori, T. and Higa, N. and Matsuda, T. D. and Haga, Y. and Walstedt, R. E. and Harima, H.},
  month = jun,
  year = {2018},
  pages = {235142},
  file = {/home/pants/.zotero/data/storage/UQWWD3SU/Kambe et al. - 2018 - Odd-parity electronic multipolar ordering in $ ma.pdf}
}

@article{haule_arrested_2009,
  title = {Arrested {{Kondo}} Effect and Hidden Order in {{URu}}{\textsubscript{2}}{{Si}}{\textsubscript{2}}},
  volume = {5},
  issn = {1745-2481},
  abstract = {Complex electronic matter shows subtle forms of self-organization, which are almost invisible to the available experimental tools. One prominent example is provided by the heavy-fermion material URu2Si2. At high temperature, the 5f electrons of uranium carry a very large entropy. This entropy is released at 17.5 K by means of a second-order phase transition1 to a state that remains shrouded in mystery, termed a `hidden order' state2. Here, we develop a first-principles theoretical method to analyse the electronic spectrum of correlated materials as a function of the position inside the unit cell of the crystal and use it to identify the low-energy excitations of URu2Si2. We identify the order parameter of the hidden-order state and show that it is intimately connected to magnetism. Below 70 K, the 5f electrons undergo a multichannel Kondo effect, which is `arrested' at low temperature by the crystal-field splitting. At lower temperatures, two broken-symmetry states emerge, characterized by a complex order parameter {$\psi$}. A real {$\psi$} describes the hidden-order phase and an imaginary {$\psi$} corresponds to the large-moment antiferromagnetic phase. Together, they provide a unified picture of the two broken-symmetry phases in this material.},
  language = {en},
  number = {11},
  journal = {Nature Physics},
  doi = {10/fw2wcx},
  author = {Haule, Kristjan and Kotliar, Gabriel},
  month = nov,
  year = {2009},
  pages = {796-799},
  file = {/home/pants/.zotero/data/storage/L3WFEVLT/Haule and Kotliar - 2009 - Arrested Kondo effect and hidden order in URusub.pdf}
}

@article{kusunose_hidden_2011,
  title = {On the {{Hidden Order}} in {{URu2Si2}} \textendash{} {{Antiferro Hexadecapole Order}} and {{Its Consequences}}},
  volume = {80},
  issn = {0031-9015},
  abstract = {An antiferro ordering of an electric hexadecapole moment is discussed as a promising candidate for the long standing mystery of the hidden order phase in URu 2 Si 2 . Based on localized  f -electron picture, we discuss the rationale of the selected multipole and the consequences of the antiferro hexadecapole order of  x y ( x 2 - y 2 ) symmetry. The mean-field solutions and the collective excitations from them explain reasonably significant experimental observations: the strong anisotropy in the magnetic susceptibility, characteristic behavior of pressure versus magnetic field or temperature phase diagrams, disappearance of inelastic neutron-scattering intensity out of the hidden order phase, and insensitiveness of the NQR frequency at Ru-sites upon ordering. A consistency with the strong anisotropy in the magnetic responses excludes all the multipoles in two-dimensional representations, such as ( O y z , O z x ). The expected azimuthal angle dependences of the resonant X-ray scattering amplitude are given. The ( x 2 - y 2 )-type antiferro quadrupole should be induced by an in-plane magnetic field along [110], which is reflected in the thermal expansion and the elastic constant of the transverse ( c 11 - c 12 )/2 mode. The ( x 2 - y 2 )-type [( x y )-type] antiferro quadrupole is also induced by applying the uniaxial stress along [110] direction [[100] direction]. A detection of these induced antiferro quadrupoles under the in-plane magnetic field or the uniaxial stress using the resonant X-ray scattering provides a direct redundant test for the proposed order parameter.},
  number = {8},
  journal = {Journal of the Physical Society of Japan},
  doi = {10/csgkg7},
  author = {Kusunose, Hiroaki and Harima, Hisatomo},
  month = jul,
  year = {2011},
  pages = {084702},
  file = {/home/pants/.zotero/data/storage/VSG5VAMT/Kusunose and Harima - 2011 - On the Hidden Order in URu2Si2 – Antiferro Hexadec.pdf}
}

@article{kung_chirality_2015,
  title = {Chirality Density Wave of the ``Hidden Order'' Phase in {{URu2Si2}}},
  volume = {347},
  copyright = {Copyright \textcopyright{} 2015, American Association for the Advancement of Science},
  issn = {0036-8075, 1095-9203},
  abstract = {Uncovering the symmetry of a hidden order
Cooling matter generally makes it more ordered and may induce dramatic transitions: Think of water becoming ice. With increased order comes loss of symmetry; water in its liquid form will look the same however you rotate it, whereas ice will not. Kung et al. studied the symmetry properties of a mysteriously ordered phase of the material URu2Si2 that appears at 17.5 K. They shone laser light on the crystal and studied the shifts in the frequency of the light. The electron orbitals of the uranium had a handedness to them that alternated between the atomic layers.
Science, this issue p. 1339
A second-order phase transition in a physical system is associated with the emergence of an ``order parameter'' and a spontaneous symmetry breaking. The heavy fermion superconductor URu2Si2 has a ``hidden order'' (HO) phase below the temperature of 17.5 kelvin; the symmetry of the associated order parameter has remained ambiguous. Here we use polarization-resolved Raman spectroscopy to specify the symmetry of the low-energy excitations above and below the HO transition. We determine that the HO parameter breaks local vertical and diagonal reflection symmetries at the uranium sites, resulting in crystal field states with distinct chiral properties, which order to a commensurate chirality density wave ground state.
Raman spectroscopy is used to uncover an unusual ordering in the low-temperature phase of a heavy fermion compound.
Raman spectroscopy is used to uncover an unusual ordering in the low-temperature phase of a heavy fermion compound.},
  language = {en},
  number = {6228},
  journal = {Science},
  doi = {10/f6479q},
  author = {Kung, H.-H. and Baumbach, R. E. and Bauer, E. D. and Thorsm{\o}lle, V. K. and Zhang, W.-L. and Haule, K. and Mydosh, J. A. and Blumberg, G.},
  month = mar,
  year = {2015},
  pages = {1339-1342},
  file = {/home/pants/.zotero/data/storage/E93SDWTG/Kung et al. - 2015 - Chirality density wave of the “hidden order” phase.pdf},
  pmid = {25678557}
}

@article{cricchio_itinerant_2009,
  title = {Itinerant {{Magnetic Multipole Moments}} of {{Rank Five}} as the {{Hidden Order}} in \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {103},
  abstract = {A broken symmetry ground state without any magnetic moments has been calculated by means of the local-density approximation to density functional theory plus a local exchange term, the so-called LDA+U approach, for URu2Si2. The solution is analyzed in terms of a multipole tensor expansion of the itinerant density matrix and is found to be a nontrivial magnetic multipole. Analysis and further calculations show that this type of multipole enters naturally in time reversal breaking in the presence of large effective spin-orbit coupling and coexists with magnetic moments for most magnetic actinides.},
  number = {10},
  journal = {Physical Review Letters},
  doi = {10/csgzd4},
  author = {Cricchio, Francesco and Bultmark, Fredrik and Gr{\aa}n{\"a}s, Oscar and Nordstr{\"o}m, Lars},
  month = sep,
  year = {2009},
  pages = {107202},
  file = {/home/pants/.zotero/data/storage/KAXQ32EJ/Cricchio et al. - 2009 - Itinerant Magnetic Multipole Moments of Rank Five .pdf}
}

@article{ohkawa_quadrupole_1999,
  title = {Quadrupole and Dipole Orders in {{URu2Si2}}},
  volume = {11},
  issn = {0953-8984},
  abstract = {Exotic magnetism below TN17.5 K is studied within the level scheme where the lowest multiplet is a doublet within the 5f2 configuration. Effective g-factors of pseudo-spins with S = \textonehalf, which describe the degree of freedom of the doublet, are highly anisotropic: gx = gy = 0 for the xy-components and gz0 for the z-component. It is proposed that a recently discovered transition of first order at a critical pressure pc1.5 GPa is that between an ordered state of quadrupoles, with order parameter O(x2)-y2 or Oxy, below pc and an ordered state of dipoles, with order parameter Oz, above pc; pseudo-spins are ordered within the xy-plane below pc, and they are along the z-axis above pc. The proposal of this scenario is followed by many predictions. No static magnetic moments exist below pc. The anisotropy of Van Vleck's susceptibility within the xy-plane is of twofold symmetry corresponding to O(x2)-y2 or Oxy. What one observes by means of neutron diffraction and {$\mathrm{\mu}$}SR (muon spin resonance) below pc are dynamically but slowly fluctuating magnetic moments. The softening of magnons occurs with pressures approaching pc below pc. Although static magnetic moments exist above pc, no magnon excitations can be observed there.},
  language = {en},
  number = {46},
  journal = {Journal of Physics: Condensed Matter},
  doi = {10/bcspzg},
  author = {Ohkawa, Fusayoshi J. and Shimizu, Hirofumi},
  month = nov,
  year = {1999},
  pages = {L519--L524},
  file = {/home/pants/.zotero/data/storage/AG7SQ5WT/Ohkawa and Shimizu - 1999 - Quadrupole and dipole orders in URu2Si2.pdf}
}

@article{santini_crystal_1994,
  title = {Crystal {{Field Model}} of the {{Magnetic Properties}} of {{U}}\$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Ru}}\vphantom\{\}\vphantom\{\}\_\{2\}\$\$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {73},
  abstract = {We propose a model based on quadrupolar ordering of localized f electrons to explain the 17.5 K phase transition of URu2Si2. The tiny staggered magnetic moment observed by neutron scattering is interpreted as a weak secondary effect associated to the symmetry-breaking perturbation. The model is able to account for the observed behavior of the linear and nonlinear susceptibilities throughout the transition. A connection with the quadrupolar Kondo theory is proposed.},
  number = {7},
  journal = {Physical Review Letters},
  doi = {10/fn6ntc},
  author = {Santini, P. and Amoretti, G.},
  month = aug,
  year = {1994},
  pages = {1027-1030},
  file = {/home/pants/.zotero/data/storage/2ZPUF4NZ/Santini and Amoretti - 1994 - Crystal Field Model of the Magnetic Properties of .pdf}
}

@article{harima_why_2010,
  title = {Why the {{Hidden Order}} in {{URu2Si2 Is Still Hidden}}\textendash{{One Simple Answer}}},
  volume = {79},
  issn = {0031-9015},
  abstract = {For more than two decades, the nonmagnetic anomaly observed around 17.5 K in URu 2 Si 2 , has been investigated intensively. However, any kind of fingerprint for the lattice anomaly has not been observed in the low-temperature ordered phase. Therefore, the order has been called ``the hidden order''. One simple answer to why the hidden order is still hidden is presented from the space group analysis. The second-order phase transition from  I 4/ m m m  (No.~139) to  P 4 2 / m n m  (No.~136) does not require any kind of lattice distortion in this system and allows the NQR frequency at a Ru site unchanged. It is compatible with  O x y -type antiferro-quadrupole ordering with  Q =(0, 0, 1). The characteristics of the hidden order are discussed based on the local 5  f 2  electron picture.},
  number = {3},
  journal = {Journal of the Physical Society of Japan},
  doi = {10/fgmjmf},
  author = {Harima, Hisatomo and Miyake, Kazumasa and Flouquet, Jacques},
  month = mar,
  year = {2010},
  pages = {033705},
  file = {/home/pants/.zotero/data/storage/2MY7VK9P/Harima et al. - 2010 - Why the Hidden Order in URu2Si2 Is Still Hidden–On.pdf}
}

@article{thalmeier_signatures_2011,
  title = {Signatures of Hidden-Order Symmetry in Torque Oscillations, Elastic Constant Anomalies, and Field-Induced Moments in {{URu}}\$\{\}\_\{2\}\${{Si}}\$\{\}\_\{2\}\$},
  volume = {83},
  abstract = {We discuss the conclusions on the symmetry of hidden order (HO) in URu2Si2 that may be drawn from recent torque experiments in a rotating magnetic field by Okazaki et al. [Science 331, 439 (2011)] (to be published). They are very sensitive to changes in the magnetic susceptibility induced by HO. We show that the observed twofold angular torque oscillations give evidence that HO has degenerate E-type (yz, zx) symmetry where both components are realized. The oscillations have the wrong characteristics or are absent for the one-dimensional (1D) nontrivial representations like quadrupolar B1(x2-y2) and B2(xy) type HO or hexadecapolar A2[xy(x2-y2)] type HO. Therefore, they may be excluded as candidates for HO. We also predict the field-angular variation of possible field-induced Bragg peaks based on the underlying E-type order parameter and discuss the expected elastic constant anomalies.},
  number = {16},
  journal = {Physical Review B},
  doi = {10/bjx43x},
  author = {Thalmeier, Peter and Takimoto, Tetsuya},
  month = apr,
  year = {2011},
  pages = {165110},
  file = {/home/pants/.zotero/data/storage/UD5E2IUD/Thalmeier and Takimoto - 2011 - Signatures of hidden-order symmetry in torque osci.pdf}
}

@article{tonegawa_cyclotron_2012,
  title = {Cyclotron {{Resonance}} in the {{Hidden}}-{{Order Phase}} of \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {109},
  abstract = {We report the first observation of cyclotron resonance in the hidden-order phase of ultraclean URu2Si2 crystals, which allows the full determination of angle-dependent electron-mass structure of the main Fermi-surface sheets. We find an anomalous splitting of the sharpest resonance line under in-plane magnetic-field rotation. This is most naturally explained by the domain formation, which breaks the fourfold rotational symmetry of the underlying tetragonal lattice. The results reveal the emergence of an in-plane mass anisotropy with hot spots along the [110] direction, which can account for the anisotropic in-plane magnetic susceptibility reported recently. This is consistent with the ``nematic'' Fermi liquid state, in which itinerant electrons have unidirectional correlations.},
  number = {3},
  journal = {Physical Review Letters},
  doi = {10/f35jzf},
  author = {Tonegawa, S. and Hashimoto, K. and Ikada, K. and Lin, Y.-H. and Shishido, H. and Haga, Y. and Matsuda, T. D. and Yamamoto, E. and Onuki, Y. and Ikeda, H. and Matsuda, Y. and Shibauchi, T.},
  month = jul,
  year = {2012},
  pages = {036401},
  file = {/home/pants/.zotero/data/storage/MHBZ6QTK/Tonegawa et al. - 2012 - Cyclotron Resonance in the Hidden-Order Phase of $.pdf}
}

@article{rau_hidden_2012,
  title = {Hidden and Antiferromagnetic Order as a Rank-5 Superspin in {{URu}}\$\{\}\_\{2\}\${{Si}}\$\{\}\_\{2\}\$},
  volume = {85},
  abstract = {We propose a candidate for the hidden order in URu2Si2: a rank-5 E type spin-density wave between uranium 5f crystal-field doublets {$\Gamma$}(1)7 and {$\Gamma$}(2)7, breaking time-reversal and lattice tetragonal symmetry in a manner consistent with recent torque measurements [Okazaki et al., Science 331, 439 (2011)]. We argue that coupling of this order parameter to magnetic probes can be hidden by crystal-field effects, while still having significant effects on transport, thermodynamics, and magnetic susceptibilities. In a simple tight-binding model for the heavy quasiparticles, we show the connection between the hidden order and antiferromagnetic phases arises since they form different components of this single rank-5 pseudospin vector. Using a phenomenological theory, we show that the experimental pressure-temperature phase diagram can be qualitatively reproduced by tuning terms which break pseudospin rotational symmetry. As a test of our proposal, we predict the presence of small magnetic moments in the basal plane oriented in the [110] direction ordered at the wave vector (0,0,1).},
  number = {24},
  journal = {Physical Review B},
  doi = {10/gf5vbn},
  author = {Rau, Jeffrey G. and Kee, Hae-Young},
  month = jun,
  year = {2012},
  pages = {245112},
  file = {/home/pants/.zotero/data/storage/6HP8DPHU/Rau and Kee - 2012 - Hidden and antiferromagnetic order as a rank-5 sup.pdf}
}

@article{riggs_evidence_2015,
  title = {Evidence for a Nematic Component to the Hidden-Order Parameter in {{URu}}{\textsubscript{2}}{{Si}}{\textsubscript{2}} from Differential Elastoresistance Measurements},
  volume = {6},
  issn = {2041-1723},
  abstract = {For materials that harbour a continuous phase transition, the susceptibility of the material to various fields can be used to understand the nature of the fluctuating order and hence the nature of the ordered state. Here we use anisotropic biaxial strain to probe the nematic susceptibility of URu2Si2, a heavy fermion material for which the nature of the low temperature `hidden order' state has defied comprehensive understanding for over 30 years. Our measurements reveal that the fluctuating order has a nematic component, confirming reports of twofold anisotropy in the broken symmetry state and strongly constraining theoretical models of the hidden-order phase.},
  language = {en},
  journal = {Nature Communications},
  doi = {10/gf5vbm},
  author = {Riggs, Scott C. and Shapiro, M. C. and Maharaj, Akash V. and Raghu, S. and Bauer, E. D. and Baumbach, R. E. and {Giraldo-Gallo}, P. and Wartenbe, Mark and Fisher, I. R.},
  month = mar,
  year = {2015},
  pages = {6425},
  file = {/home/pants/.zotero/data/storage/MK6ZXXR6/41467_2015_BFncomms7425_MOESM1049_ESM.pdf;/home/pants/.zotero/data/storage/Z57IE8J9/Riggs et al. - 2015 - Evidence for a nematic component to the hidden-ord.pdf}
}

@article{hoshino_resolution_2013,
  title = {Resolution of {{Entropy}} \textbackslash{}(\textbackslash{}ln\textbackslash{}sqrt\{2\}\textbackslash{}) by {{Ordering}} in {{Two}}-{{Channel Kondo Lattice}}},
  volume = {82},
  issn = {0031-9015},
  abstract = {Peculiar property of electronic order is clarified for the two-channel Kondo lattice. With two conduction electrons per site, the order parameter is a composite quantity involving both local and itinerant degrees of freedom. In contrast to the ordinary Kondo lattice, a heavy electron band is absent above the transition temperature, but is rapidly formed below it. The change of entropy associated with the ordering is found to be close to ln2\textendash{$\surd$}ln⁡2\textbackslash{}ln \textbackslash{}sqrt\{2\} per site. This entropy corresponds to the residual entropy in a two-channel Kondo impurity, which has been regarded as due to localized free Majorana particles. The present composite order is interpreted as instability of Majorana particles toward non-Kramers conduction electrons plus heavy fermions that involve localized electrons.},
  number = {4},
  journal = {Journal of the Physical Society of Japan},
  doi = {10/gf5vbk},
  author = {Hoshino, Shintaro and Otsuki, Junya and Kuramoto, Yoshio},
  month = mar,
  year = {2013},
  pages = {044707},
  file = {/home/pants/.zotero/data/storage/TY637XGC/Hoshino et al. - 2013 - Resolution of Entropy (lnsqrt 2 ) by Ordering .pdf}
}

@article{ikeda_theory_1998,
  title = {Theory of {{Unconventional Spin Density Wave}}: {{A Possible Mechanism}} of the {{Micromagnetism}} in {{U}}-Based {{Heavy Fermion Compounds}}},
  volume = {81},
  shorttitle = {Theory of {{Unconventional Spin Density Wave}}},
  abstract = {We propose a novel spin density wave (SDW) state as a possible mechanism of the anomalous antiferromagnetism, the so called micromagnetism, in URu2Si2 below 17.5 K. In this new SDW, the electron-hole pair amplitude changes its sign in the momentum space as in the case of the unconventional superconductivity. It is shown that this state can be realized in an extended Hubbard model within the mean field theory. We also examine some characteristic properties of this SDW to compare with the experimental results. All these properties well explain the unsolved problem of the micromagnetism.},
  number = {17},
  journal = {Physical Review Letters},
  doi = {10/bw6hn5},
  author = {Ikeda, Hiroaki and Ohashi, Yoji},
  month = oct,
  year = {1998},
  pages = {3723-3726},
  file = {/home/pants/.zotero/data/storage/QNE8NK4Q/Ikeda and Ohashi - 1998 - Theory of Unconventional Spin Density Wave A Poss.pdf}
}

@article{chandra_hastatic_2013,
  title = {Hastatic Order in the Heavy-Fermion Compound {{URu}}{\textsubscript{2}}{{Si}}{\textsubscript{2}}},
  volume = {493},
  issn = {1476-4687},
  abstract = {The development of collective long-range order by means of phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry, whereas superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5 kelvin in the heavy-fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such `hastatic' order hybridizes uranium-atom conduction electrons with Ising 5f2 states to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction-electron `sea', a colossal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant, energy-dependent nematicity in the tunnelling density of states.},
  language = {en},
  number = {7434},
  journal = {Nature},
  doi = {10/gf5vbj},
  author = {Chandra, Premala and Coleman, Piers and Flint, Rebecca},
  month = jan,
  year = {2013},
  pages = {621-626},
  file = {/home/pants/.zotero/data/storage/B272KFL9/Chandra et al. - 2013 - Hastatic order in the heavy-fermion compound URus.pdf}
}

@article{ikeda_emergent_2012,
  title = {Emergent Rank-5 Nematic Order in {{URu}}{\textsubscript{2}}{{Si}}{\textsubscript{2}}},
  volume = {8},
  issn = {1745-2481},
  abstract = {Exotic electronic states resulting from entangled spin and orbital degrees of freedom are hallmarks of strongly correlated f-electron systems. A spectacular example is the so-called hidden-order (HO) phase transition1 in the heavy-electron metal URu2Si2, which is characterized by the huge amount of entropy lost at THO=17.5 K (refs 2, 3). However, no evidence of magnetic/structural phase transition has been found below THO so far. The origin of the HO phase transition has been a long-standing mystery in condensed-matter physics. Here, on the basis of a first-principles theoretical approach, we examine the complete set of multipole correlations allowed in this material. The results uncover that the HO parameter is a rank-5 multipole (dotriacontapole) order with nematic E- symmetry, which exhibits staggered pseudospin moments along the [110] direction. This naturally provides comprehensive explanations of all key features in the HO phase including anisotropic magnetic excitations, the nearly degenerate antiferromagnetic-ordered state and spontaneous rotational-symmetry breaking.},
  language = {en},
  number = {7},
  journal = {Nature Physics},
  doi = {10/f34f8m},
  author = {Ikeda, Hiroaki and Suzuki, Michi-To and Arita, Ryotaro and Takimoto, Tetsuya and Shibauchi, Takasada and Matsuda, Yuji},
  month = jul,
  year = {2012},
  pages = {528-533},
  file = {/home/pants/.zotero/data/storage/9NYNGB45/Ikeda et al. - 2012 - Emergent rank-5 nematic order in URusub2subSi.pdf}
}

@article{kiss_group_2005,
  title = {Group Theory and Octupolar Order in \$\textbackslash{}mathrm\{\vphantom\}{{U}}\vphantom\{\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Ru}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {71},
  abstract = {Recent experiments on URu2Si2URu2Si2 show that the low-pressure hidden order is nonmagnetic but it breaks time reversal invariance. Restricting our attention to local order parameters of 5f25f2 shells, we find that the best candidate for hidden order is staggered order of either Tz{$\beta$}T{$\beta$}z or TxyzTxyz octupoles. Group theoretical arguments for the effect of symmetry-lowering perturbations (magnetic field, mechanical stress) predict behavior in good overall agreement with observations. We illustrate our general arguments on the example of a five-state crystal field model which differs in several details from models discussed in the literature. The general appearance of the mean field phase diagram agrees with the experimental results. In particular, we find that (a) at zero magnetic field, there is a first-order phase boundary between octupolar order and large-moment antiferromagnetism with increasing hydrostatic pressure; (b) arbitrarily weak uniaxial pressure induces staggered magnetic moments in the octupolar phase; and (c) a new phase with different symmetry appears at large magnetic fields.},
  number = {5},
  journal = {Physical Review B},
  doi = {10.1103/physrevb.71.054415},
  author = {Kiss, Annam{\'a}ria and Fazekas, Patrik},
  month = feb,
  year = {2005},
  pages = {054415},
  file = {/home/pants/.zotero/data/storage/YTARVDIM/Kiss and Fazekas - 2005 - Group theory and octupolar order in $mathrm U m.pdf}
}

@article{varshni_temperature_1970,
  title = {Temperature {{Dependence}} of the {{Elastic Constants}}},
  volume = {2},
  abstract = {The following two equations are proposed for the temperature dependence of the elastic stiffness constants: cij=c0ij-s(etT-1) and cij=a-bT2(T+c), where c0ij, s, t, a, b, and c are constants. The applicability of these two equations and that of Wachtman's equation is examined for 57 elastic constants of 22 substances. The first equation has a theoretical justification and gives the best over-all results. Neither of the three equations give the theoretically expected T4 dependence at low temperatures, and therefore they are not expected to give very accurate results at very low temperatures ({$\lessequivlnt\Theta$}D50). A new melting criterion is also examined.},
  number = {10},
  journal = {Physical Review B},
  doi = {10.1103/physrevb.2.3952},
  author = {Varshni, Y. P.},
  month = nov,
  year = {1970},
  pages = {3952-3958},
  file = {/home/pants/.zotero/data/storage/QN7TLJV7/Varshni - 1970 - Temperature Dependence of the Elastic Constants.pdf}
}

@article{hornreich_critical_1975,
  title = {Critical {{Behavior}} at the {{Onset}} of \$\textbackslash{}stackrel\{\textbackslash{}ensuremath\{\textbackslash{}rightarrow\}\}\{\textbackslash{}mathrm\{k\}\}\$-{{Space Instability}} on the \$\textbackslash{}ensuremath\{\textbackslash{}lambda\}\$ {{Line}}},
  volume = {35},
  abstract = {We calculate the critical behavior of systems having a multicritical point of a new type, hereafter called a Lifshitz point, which separates ordered phases with \textrightarrowk=0 and \textrightarrowk{$\not =$}0 along the {$\lambda$} line. For anisotropic systems, the correlation function is described in terms of four critical exponents, whereas for isotropic systems two exponents suffice. Critical exponents are calculated using an {$\epsilon$}-type expansion.},
  number = {25},
  journal = {Physical Review Letters},
  doi = {10.1103/PhysRevLett.35.1678},
  author = {Hornreich, R. M. and Luban, Marshall and Shtrikman, S.},
  month = dec,
  year = {1975},
  pages = {1678-1681},
  file = {/home/pants/.zotero/data/storage/GBYIESIW/Hornreich et al_1975_Critical Behavior at the Onset of.pdf;/home/pants/.zotero/data/storage/KBYQHWSH/PhysRevLett.35.html}
}

@article{inoue_high-field_2001,
  series = {Proceedings of the {{Sixth International}}  {{Symposium}} on {{Research}} in {{High Magnetic Fields}}},
  title = {High-Field Magnetization of {{URu2Si2}} under High Pressure},
  volume = {294-295},
  issn = {0921-4526},
  abstract = {The temperature dependence of the magnetic susceptibility and the high-field magnetization up to 55T are measured for URu2Si2 under high pressures up to 1GPa. Both T{$\chi$}max and TN in the susceptibility increase with increasing pressure. The value of the susceptibility below T{$\chi$}max decreases with increasing pressure. The three high-field metamagnetic transitions at Hc1=35.1T, Hc2=36.5T and Hc3=39.6T at ambient pressure, show different pressure-dependent behaviors. The metamagnetic transition at Hc1 broadens but survives and its transition field increases with increasing pressure. However, the transition at Hc2 is smeared out and disappears above 0.4GPa. The transition at Hc3 broadens more clearly than the transition at Hc1. The fact that both T{$\chi$}max and the metamagnetic transition fields increase suggests that the interaction between the f-electrons and the conduction electrons is enhanced by pressure.},
  journal = {Physica B: Condensed Matter},
  doi = {10.1016/S0921-4526(00)00657-8},
  author = {Inoue, T. and Kindo, K. and Okuni, H. and Sugiyama, K. and Haga, Y. and Yamamoto, E. and Kobayashi, T. C. and Uwatoko, Y. and Onuki, Y.},
  month = jan,
  year = {2001},
  keywords = {High pressure,High-field magnetization,Metamagnetic transition,URuSi},
  pages = {271-275},
  file = {/home/pants/.zotero/data/storage/CDTQB6PI/Inoue et al_2001_High-field magnetization of URu2Si2 under high pressure.pdf;/home/pants/.zotero/data/storage/323PS9NS/S0921452600006578.html}
}

@article{shekhter_bounding_2013,
  title = {Bounding the Pseudogap with a Line of Phase Transitions in {{YBa}}{\textsubscript{2}}{{Cu}}{\textsubscript{3}}{{O}}{\textsubscript{6+{\emph{{$\delta$} }}}}},
  volume = {498},
  copyright = {2013 Nature Publishing Group},
  issn = {1476-4687},
  abstract = {Close to optimal doping, the copper oxide superconductors show `strange metal' behaviour1,2, suggestive of strong fluctuations associated with a quantum critical point3,4,5,6. Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting `dome'. The underdoped region of the temperature\textendash{}doping phase diagram from which superconductivity emerges is referred to as the `pseudogap'7,8,9,10,11,12,13 because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa2Cu3O6+{$\delta$} is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behaviour and therefore superconductivity in the copper oxide superconductors.},
  language = {en},
  number = {7452},
  journal = {Nature},
  doi = {10.1038/nature12165},
  author = {Shekhter, Arkady and Ramshaw, B. J. and Liang, Ruixing and Hardy, W. N. and Bonn, D. A. and Balakirev, Fedor F. and McDonald, Ross D. and Betts, Jon B. and Riggs, Scott C. and Migliori, Albert},
  month = jun,
  year = {2013},
  pages = {75-77},
  file = {/home/pants/.zotero/data/storage/Y3X6VXIK/Shekhter et al_2013_Bounding the pseudogap with a line of phase transitions in.pdf;/home/pants/.zotero/data/storage/ZZ3MR77N/nature12165.html}
}

@article{meng_imaging_2013,
  title = {Imaging the {{Three}}-{{Dimensional Fermi}}-{{Surface Pairing}} near the {{Hidden}}-{{Order Transition}} in \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$ {{Using Angle}}-{{Resolved Photoemission Spectroscopy}}},
  volume = {111},
  abstract = {We report angle-resolved photoemission spectroscopy experiments probing deep into the hidden-order state of URu2Si2, utilizing tunable photon energies with sufficient energy and momentum resolution to detect the near Fermi-surface (FS) behavior. Our results reveal (i) the full itinerancy of the 5f electrons, (ii) the crucial three-dimensional k-space nature of the FS and its critical nesting vectors, in good comparison with density-functional theory calculations, and (iii) the existence of hot-spot lines and pairing of states at the FS, leading to FS gapping in the hidden-order phase.},
  number = {12},
  journal = {Physical Review Letters},
  doi = {10.1103/PhysRevLett.111.127002},
  author = {Meng, Jian-Qiao and Oppeneer, Peter M. and Mydosh, John A. and Riseborough, Peter S. and Gofryk, Krzysztof and Joyce, John J. and Bauer, Eric D. and Li, Yinwan and Durakiewicz, Tomasz},
  month = sep,
  year = {2013},
  pages = {127002},
  file = {/home/pants/.zotero/data/storage/EBTUZTN7/Meng et al_2013_Imaging the Three-Dimensional Fermi-Surface Pairing near the Hidden-Order.pdf;/home/pants/.zotero/data/storage/U2Z93ZIJ/PhysRevLett.111.html}
}

@article{chandra_origin_2013,
  title = {Origin of the {{Large Anisotropy}} in The\$\textbackslash{}upchi\${{3Anomaly inURu2Si2}}},
  volume = {449},
  issn = {1742-6596},
  abstract = {Motivated by recent quantum oscillations experiments on U Ru2Si2, we discuss the microscopic origin of the large anisotropy observed many years ago in the anomaly of the nonlinear susceptibility in this same material. We show that the magnitude of this anomaly emerges naturally from hastatic order, a proposal for hidden order that is a two-component spinor arising from the hybridization of a non-Kramers {$\Gamma$}5 doublet with Kramers conduction electrons. A prediction is made for the angular anisotropy of the nonlinear susceptibility anomaly as a test of this proposed order parameter for U Ru2Si2.},
  language = {en},
  journal = {Journal of Physics: Conference Series},
  doi = {10.1088/1742-6596/449/1/012026},
  author = {Chandra, P. and Coleman, P. and Flint, R.},
  month = jul,
  year = {2013},
  pages = {012026},
  file = {/home/pants/.zotero/data/storage/7K2FNND4/Chandra et al. - 2013 - Origin of the Large Anisotropy in the$upchi$3Anom.pdf}
}

@article{garel_commensurability_1976,
  title = {Commensurability Effects on the Critical Behaviour of Systems with Helical Ordering},
  volume = {9},
  issn = {0022-3719},
  abstract = {The critical behaviour of an m-component spin system with helical ordering is studied using the renormalization group method to order epsilon 2 (where epsilon =4-d). For m=1 and 2 the system is equivalent to a 2m-vector model. For m=3 a first-order transition is expected. The effect of the commensurability of the helical structure with the lattice has been considered and is shown in certain situations to change the order of the transition.},
  language = {en},
  number = {10},
  journal = {Journal of Physics C: Solid State Physics},
  doi = {2011031909475300},
  author = {Garel, T. and Pfeuty, P.},
  month = may,
  year = {1976},
  pages = {L245--L249},
  file = {/home/pants/.zotero/data/storage/34KTXA6I/Garel_Pfeuty_1976_Commensurability effects on the critical behaviour of systems with helical.pdf}
}

@article{nicoll_onset_1977,
  title = {Onset of Helical Order},
  volume = {86-88},
  issn = {0378-4363},
  abstract = {Renormalization group methods are used to describe systems which model critical phenomena at the onset of helical order. This onset is marked by a change in the ``bare propagator'' used in perturbation theory from a k2-dependence to a more general form. We consider systems which in the non-helical region exhibit O simultaneously critical phases. Results are given to first order in an {$\epsilon$}-expansion. For the isotropic case of k2L dependence and O = 2, we give {$\eta$} to first order in 1/n for d- {$\leqslant$} d {$\leqslant$} d+ where d+- are upper and lower borderline dimensions.},
  journal = {Physica B+C},
  doi = {10.1016/0378-4363(77)90620-9},
  author = {Nicoll, J. F. and Tuthill, G. F. and Chang, T. S. and Stanley, H. E.},
  month = jan,
  year = {1977},
  pages = {618-620},
  file = {/home/pants/.zotero/data/storage/ZLV5YFH6/Nicoll et al_1977_Onset of helical order.pdf;/home/pants/.zotero/data/storage/84ZZT6CN/0378436377906209.html}
}

@article{nicoll_renormalization_1976,
  title = {Renormalization Group Calculation for Critical Points of Higher Order with General Propagator},
  volume = {58},
  issn = {0375-9601},
  abstract = {We give first order perturbation results for the critical point exponents at order O critical points with anisotropic propagators. The exponent {$\eta$} is calculated to second order for isotropic propagators, and all O; 1/n expansion results are given for O = 2.},
  number = {1},
  journal = {Physics Letters A},
  doi = {10.1016/0375-9601(76)90527-2},
  author = {Nicoll, J. F. and Tuthill, G. F. and Chang, T. S. and Stanley, H. E.},
  month = jul,
  year = {1976},
  pages = {1-2},
  file = {/home/pants/.zotero/data/storage/55AS69UD/Nicoll et al_1976_Renormalization group calculation for critical points of higher order with.pdf;/home/pants/.zotero/data/storage/L6WH4D36/0375960176905272.html}
}

@article{hornreich_exactly_1977,
  title = {Exactly Solvable Model Exhibiting a Multicritical Point},
  volume = {86},
  issn = {0378-4371},
  abstract = {A hypercubic d-dimensional lattice of spins with nearest neighbor ferromagnetic coupling and next nearest neighbor antiferromagnetic coupling along a single axis is studied in the spherical model limit (n\textrightarrow{$\infty$}) and is found to exhibit a multicritical point of the uniaxial Lifshitz type. The shape of the {$\lambda$} line is calculated explicitly in the vicinity of the multicritical point, and analytic expressions are given for the shift exponent {$\psi$}(d) and its amplitudes A{$\pm$}(d). The amplitude A\_(d) changes sign for d = 3.},
  number = {2},
  journal = {Physica A: Statistical Mechanics and its Applications},
  doi = {10.1016/0378-4371(77)90042-5},
  author = {Hornreich, R. M. and Luban, Marshall and Shtrikman, S.},
  month = feb,
  year = {1977},
  pages = {465-470},
  file = {/home/pants/.zotero/data/storage/5MFN7M9Z/Hornreich et al_1977_Exactly solvable model exhibiting a multicritical point.pdf;/home/pants/.zotero/data/storage/CZNV72TI/0378437177900425.html}
}

@article{hornreich_critical_1975-1,
  title = {Critical Exponents at a {{Lifshitz}} Point to {{O}}(1/n)},
  volume = {55},
  issn = {0375-9601},
  abstract = {The critical exponents at a general Lifshitz point are calculated in the spherical model limit, as are those of an isotropic Lifshitz point to O(1/n). These results are in exact agreement in the overlap region with those obtained using an {$\epsilon$}-expansion.},
  number = {5},
  journal = {Physics Letters A},
  doi = {10.1016/0375-9601(75)90465-X},
  author = {Hornreich, R. M. and Luban, M. and Shtrikman, S.},
  month = dec,
  year = {1975},
  pages = {269-270},
  file = {/home/pants/.zotero/data/storage/RED39SK4/Hornreich et al_1975_Critical exponents at a Lifshitz point to O(1-n).pdf;/home/pants/.zotero/data/storage/X8UJ5CHZ/037596017590465X.html}
}

@article{selke_monte_1978,
  title = {Monte Carlo Calculations near a Uniaxial {{Lifshitz}} Point},
  volume = {29},
  issn = {1431-584X},
  abstract = {The Monte Carlo method is applied to a threedimensional Ising model with nearest neighbour ferromagnetic interactions and next nearest neighbour antiferromagnetic interactions along one axis only. Special emphasis is given to the critical behaviour near the Lifshitz point.},
  language = {en},
  number = {2},
  journal = {Zeitschrift f{\"u}r Physik B Condensed Matter},
  doi = {10.1007/BF01313198},
  author = {Selke, Walter},
  month = jun,
  year = {1978},
  keywords = {Complex System,Neural Network,Spectroscopy,State Physics,Monte Carlo Method},
  pages = {133-137},
  file = {/home/pants/.zotero/data/storage/5NRZEWP8/Selke_1978_Monte carlo calculations near a uniaxial Lifshitz point.pdf}
}

@article{harrison_hidden_nodate,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1902.06588},
  title = {Hidden Valence Transition in {{URu2Si2}}?},
  abstract = {The term "hidden order" refers to an as yet unidentified form of broken-symmetry order parameter that is presumed to exist in the strongly correlated electron system URu2Si2 on the basis of the reported similarity of the heat capacity at its phase transition at To\textasciitilde{}17 K to that produced by Bardeen-Cooper-Schrieffer (BCS) mean field theory. Here we show that the phase boundary in URu2Si2 has the elliptical form expected for an entropy-driven phase transition, as has been shown to accompany a change in valence. We show one characteristic feature of such a transition is that the ratio of the critical magnetic field to the critical temperature is defined solely in terms of the effective quasiparticle g-factor, which we find to be in quantitative agreement with prior g-factor measurements. We further find the anomaly in the heat capacity at To to be significantly sharper than a BCS phase transition, and, once quasiparticle excitations across the hybridization gap are taken into consideration, loses its resemblance to a second order phase transition. Our findings imply that a change in valence dominates the thermodynamics of the phase boundary in URu2Si2, and eclipses any significant contribution to the thermodynamics from a hidden order parameter.},
  author = {Harrison, Neil and Jaime, Marcelo},
  keywords = {Condensed Matter - Strongly Correlated Electrons},
  file = {/home/pants/.zotero/data/storage/79NX4WI3/Harrison and Jaime - 2019 - Hidden valence transition in URu2Si2.pdf}
}

@article{ghosh_single-component_nodate,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1903.00552},
  title = {Single-{{Component Order Parameter}} in {{URu}}\$\_2\${{Si}}\$\_2\$ {{Uncovered}} by {{Resonant Ultrasound Spectroscopy}} and {{Machine Learning}}},
  abstract = {URu\$\_2\$Si\$\_2\$ exhibits a clear phase transition at T\$\_\{HO\}= 17.5\textasciitilde\$K to a low-temperature phase known as "hidden order" (HO). Even the most basic information needed to construct a theory of this state---such as the number of components in the order parameter---has been lacking. Here we use resonant ultrasound spectroscopy (RUS) and machine learning to determine that the order parameter of HO is one-dimensional (singlet), ruling out a large class of theories based on two-dimensional (doublet) order parameters. This strict constraint is independent of any microscopic mechanism, and independent of other symmetries that HO may break. Our technique is general for second-order phase transitions, and can discriminate between nematic (singlet) versus loop current (doublet) order in the high-\textbackslash{}Tc cuprates, and conventional (singlet) versus the proposed \$p\_x+ip\_y\$ (doublet) superconductivity in Sr\$\_2\$RuO\$\_4\$. The machine learning framework we develop should be readily adaptable to other spectroscopic techniques where missing resonances confound traditional analysis, such as NMR.},
  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.},
  keywords = {Condensed Matter - Strongly Correlated Electrons,Physics - Data Analysis; Statistics and Probability},
  file = {/home/pants/.zotero/data/storage/XIE9PPL6/Ghosh et al. - 2019 - Single-Component Order Parameter in URu$_2$Si$_2$ .pdf}
}

@article{ramshaw_avoided_2015,
  title = {Avoided Valence Transition in a Plutonium Superconductor},
  volume = {112},
  issn = {0027-8424, 1091-6490},
  abstract = {The d and f electrons in correlated metals are often neither fully localized around their host nuclei nor fully itinerant. This localized/itinerant duality underlies the correlated electronic states of the high-TcTc{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:msub{$><$}mml:mi{$>$}T{$<$}/mml:mi{$><$}mml:mi{$>$}c{$<$}/mml:mi{$><$}/mml:msub{$><$}/mml:mrow{$><$}/mml:math{$>$} cuprate superconductors and the heavy-fermion intermetallics and is nowhere more apparent than in the 5f5f{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:mn{$>$}5{$<$}/mml:mn{$><$}mml:mi{$>$}f{$<$}/mml:mi{$><$}/mml:mrow{$><$}/mml:math{$>$} valence electrons of plutonium. Here, we report the full set of symmetry-resolved elastic moduli of PuCoGa5\textemdash{}the highest TcTc{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:msub{$><$}mml:mi{$>$}T{$<$}/mml:mi{$><$}mml:mi{$>$}c{$<$}/mml:mi{$><$}/mml:msub{$><$}/mml:mrow{$><$}/mml:math{$>$} superconductor of the heavy fermions (TcTc{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:msub{$><$}mml:mi{$>$}T{$<$}/mml:mi{$><$}mml:mi{$>$}c{$<$}/mml:mi{$><$}/mml:msub{$><$}/mml:mrow{$><$}/mml:math{$>$} = 18.5 K)\textemdash{}and find that the bulk modulus softens anomalously over a wide range in temperature above TcTc{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:msub{$><$}mml:mi{$>$}T{$<$}/mml:mi{$><$}mml:mi{$>$}c{$<$}/mml:mi{$><$}/mml:msub{$><$}/mml:mrow{$><$}/mml:math{$>$}. The elastic symmetry channel in which this softening occurs is characteristic of a valence instability\textemdash{}therefore, we identify the elastic softening with fluctuations of the plutonium 5f mixed-valence state. These valence fluctuations disappear when the superconducting gap opens at TcTc{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:msub{$><$}mml:mi{$>$}T{$<$}/mml:mi{$><$}mml:mi{$>$}c{$<$}/mml:mi{$><$}/mml:msub{$><$}/mml:mrow{$><$}/mml:math{$>$}, suggesting that electrons near the Fermi surface play an essential role in the mixed-valence physics of this system and that PuCoGa5 avoids a valence transition by entering the superconducting state. The lack of magnetism in PuCoGa5 has made it difficult to reconcile with most other heavy-fermion superconductors, where superconductivity is generally believed to be mediated by magnetic fluctuations. Our observations suggest that valence fluctuations play a critical role in the unusually high TcTc{$<$}mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"{$><$}mml:mrow{$><$}mml:msub{$><$}mml:mi{$>$}T{$<$}/mml:mi{$><$}mml:mi{$>$}c{$<$}/mml:mi{$><$}/mml:msub{$><$}/mml:mrow{$><$}/mml:math{$>$} of PuCoGa5.},
  language = {en},
  number = {11},
  journal = {Proceedings of the National Academy of Sciences},
  doi = {10.1073/pnas.1421174112},
  author = {Ramshaw, B. J. and Shekhter, Arkady and McDonald, Ross D. and Betts, Jon B. and Mitchell, J. N. and Tobash, P. H. and Mielke, C. H. and Bauer, E. D. and Migliori, Albert},
  month = mar,
  year = {2015},
  keywords = {quantum criticality,heavy fermions,resonant ultrasound spectroscopy,unconventional superconductivity,valence fluctuations},
  pages = {3285-3289},
  file = {/home/pants/.zotero/data/storage/ERT8A25E/Ramshaw et al. - 2015 - Avoided valence transition in a plutonium supercon.pdf},
  pmid = {25737548}
}

@article{luthi_sound_1970,
  title = {Sound {{Propagation}} near the {{Structural Phase Transition}} in {{Strontium Titanate}}},
  volume = {2},
  abstract = {Finite ultrasonic velocity changes at the structural phase transition in SrTi03 are observed for different modes. They are interrelated and correlated by theory. No critical effects are observed.},
  number = {4},
  journal = {Physical Review B},
  doi = {10.1103/PhysRevB.2.1211},
  author = {L{\"u}thi, B. and Moran, T. J.},
  month = aug,
  year = {1970},
  pages = {1211-1214},
  file = {/home/pants/.zotero/data/storage/RQZGTK9L/Lüthi and Moran - 1970 - Sound Propagation near the Structural Phase Transi.pdf}
}

@article{bak_commensurate_1982,
  title = {Commensurate Phases, Incommensurate Phases and the Devil's Staircase},
  volume = {45},
  issn = {0034-4885, 1361-6633},
  number = {6},
  journal = {Reports on Progress in Physics},
  doi = {10.1088/0034-4885/45/6/001},
  author = {Bak, P},
  month = jun,
  year = {1982},
  pages = {587-629},
  file = {/home/pants/.zotero/data/storage/TYKMSDX7/Bak - 1982 - Commensurate phases, incommensurate phases and the.pdf}
}

@article{broholm_magnetic_1991,
  title = {Magnetic Excitations in the Heavy-Fermion Superconductor \$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{URu}}\vphantom\{\}\vphantom\{\}\_\{2\}\$\$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {43},
  abstract = {Antiferromagnetic order and fluctuations in the heavy-fermion superconductor URu2Si2 have been studied by magnetic neutron scattering. Below TN=17.5 K, URu2Si2 is a type-I antiferromagnet with an anomalously small ordered moment of (0.04{$\pm$}0.01){$\mu$}B polarized along the tetragonal c axis. Dispersive resonant excitations exist in the ordered state with a zone-center gap of 0.43 THz. The excitations are polarized along the ordered moment and have a large dipolar matrix element, which suggests that they are coupled transitions between singlet crystal-field-like states. For energy transfer above 3 THz, peaks have not been identified in the magnetic excitation spectra, but instead a continuous spectrum of scattering peaked around the ordering wave vector indicates the presence of overdamped antiferromagnetically correlated spin fluctuations. Upon heating above TN, the resonant excitations abruptly become heavily damped but the magnetic scattering at higher energies does not change at TN. Instead, the disappearance of the antiferromagnetic modulation of the higher-energy scattering coincides with the maximum in the resistivity of URu2Si2.},
  number = {16},
  journal = {Physical Review B},
  doi = {10.1103/PhysRevB.43.12809},
  author = {Broholm, C. and Lin, H. and Matthews, P. T. and Mason, T. E. and Buyers, W. J. L. and Collins, M. F. and Menovsky, A. A. and Mydosh, J. A. and Kjems, J. K.},
  month = jun,
  year = {1991},
  pages = {12809-12822},
  file = {/home/pants/.zotero/data/storage/XSPQ8TDT/Broholm et al_1991_Magnetic excitations in the heavy-fermion superconductor.pdf;/home/pants/.zotero/data/storage/ALCY8T8W/PhysRevB.43.html}
}

@article{wiebe_gapped_2007,
  title = {Gapped Itinerant Spin Excitations Account for Missing Entropy in the Hidden-Order State of {{URu}}{\textsubscript{2}}{{Si}}{\textsubscript{2}}},
  volume = {3},
  copyright = {2007 Nature Publishing Group},
  issn = {1745-2481},
  abstract = {Many correlated electron materials, such as high-temperature superconductors1, geometrically frustrated oxides2 and low-dimensional magnets3,4, are still objects of fruitful study because of the unique properties that arise owing to poorly understood many-body effects. Heavy-fermion metals5\textemdash{}materials that have high effective electron masses due to those effects\textemdash{}represent a class of materials with exotic properties, ranging from unusual magnetism, unconventional superconductivity and `hidden' order parameters6. The heavy-fermion superconductor URu2Si2 has held the attention of physicists for the past two decades owing to the presence of a `hidden-order' phase below 17.5 K. Neutron scattering measurements indicate that the ordered moment is 0.03{$\mu$}B, much too small to account for the large heat-capacity anomaly at 17.5 K. We present recent neutron scattering experiments that unveil a new piece of this puzzle\textemdash{}the spin-excitation spectrum above 17.5 K exhibits well-correlated, itinerant-like spin excitations up to at least 10 meV, emanating from incommensurate wavevectors. The large entropy change associated with the presence of an energy gap in the excitations explains the reduction in the electronic specific heat through the transition.},
  language = {en},
  number = {2},
  journal = {Nature Physics},
  doi = {10.1038/nphys522},
  author = {Wiebe, C. R. and Janik, J. A. and MacDougall, G. J. and Luke, G. M. and Garrett, J. D. and Zhou, H. D. and Jo, Y.-J. and Balicas, L. and Qiu, Y. and Copley, J. R. D. and Yamani, Z. and Buyers, W. J. L.},
  month = feb,
  year = {2007},
  pages = {96-99},
  file = {/home/pants/.zotero/data/storage/H775USBY/Wiebe et al_2007_Gapped itinerant spin excitations account for missing entropy in the.pdf;/home/pants/.zotero/data/storage/NAURLM99/nphys522.html}
}

@article{bourdarot_precise_2010,
  title = {Precise {{Study}} of the {{Resonance}} at {{Q0}}=(1,0,0) in {{URu2Si2}}},
  volume = {79},
  issn = {0031-9015},
  abstract = {New inelastic neutron scattering experiments have been performed on URu 2 Si 2  with special focus on the response at  Q 0 =(1,0,0), which is a clear signature of the hidden order (HO) phase of the compound. With polarized inelastic neutron experiments, it is clearly shown that below the HO temperature ( T 0 =17.8 K) a collective excitation (the magnetic resonance at  E 0  {$\simeq$}1.7 meV) as well as a magnetic continuum co-exist. Careful measurements of the temperature dependence of the resonance lead to the observation that its position shifts abruptly in temperature with an activation law governed by the partial gap opening and that its integrated intensity has a BCS-type temperature dependence. Discussion with respect to recent theoretical development is made.},
  number = {6},
  journal = {Journal of the Physical Society of Japan},
  doi = {10.1143/JPSJ.79.064719},
  author = {Bourdarot, Frederic and Hassinger, Elena and Raymond, Stephane and Aoki, Dai and Taufour, Valentin and Regnault, Louis-Pierre and Flouquet, Jacques},
  month = jun,
  year = {2010},
  pages = {064719},
  file = {/home/pants/.zotero/data/storage/IPNNKJIA/Bourdarot et al_2010_Precise Study of the Resonance at Q0=(1,0,0) in URu2Si2.pdf;/home/pants/.zotero/data/storage/QYBEHN3M/JPSJ.79.html}
}

@article{de_visser_thermal_1986,
  title = {Thermal Expansion and Specific Heat of Monocrystalline {{U}}\$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Ru}}\vphantom\{\}\vphantom\{\}\_\{2\}\$\$\{\textbackslash{}mathrm\{\vphantom{\}\}}{{Si}}\vphantom\{\}\vphantom\{\}\_\{2\}\$},
  volume = {34},
  abstract = {Thermal-expansion and specific-heat measurements have been performed on a monocrystalline sample of URu2Si2 in the temperature region between 1.4 and 100 K. The thermal expansion of this tetragonal compound is strongly anisotropic and exhibits several anomalies in the investigated temperature range. Broad anomalies are centered around 5 and 25 K, whereas sharp peaks in the thermal-expansion coefficients are observed at the transition to the antiferromagnetic state at 17.5 K. The ca ratio exhibits a similar temperature dependence as the susceptibility along the tetragonal axis. The anomaly in the thermal expansion near 25 K suggests the presence of crystal-field effects, in agreement with recent calculations for the magnetic susceptibility at elevated temperatures.},
  number = {11},
  journal = {Physical Review B},
  doi = {10.1103/PhysRevB.34.8168},
  author = {{de Visser}, A. and Kayzel, F. E. and Menovsky, A. A. and Franse, J. J. M. and {van den Berg}, J. and Nieuwenhuys, G. J.},
  month = dec,
  year = {1986},
  pages = {8168-8171},
  file = {/home/pants/.zotero/data/storage/MQ6T7UM5/de Visser et al. - 1986 - Thermal expansion and specific heat of monocrystal.pdf}
}

@article{wolf_elastic_1994,
  title = {Elastic Properties of the Heavy Fermion Superconductor {{URu2Si2}}},
  volume = {94},
  issn = {1573-7357},
  abstract = {Measurements of the elastic constants in the normal and superconducting state on a high quality URu2Si2 single crystal exhibit large anomalies in thec11 mode versus temperature around 30 K andTc. No such anomalies are visible in the c33 mode and in the shear elastic constants. We describe this behaviour with the anisotropic Gr{\"u}neisen parameter coupling. Using the c11 anomaly a B-T phase diagram is determined which clearly shows the single phase bulk properties of superconducting URu2Si2. The magnetic field dependences of the shear waves in the superconducting and normal state can be interpreted quantitatively with a Lorentz force mechanism.},
  language = {en},
  number = {3},
  journal = {Journal of Low Temperature Physics},
  doi = {10.1007/BF00754672},
  author = {Wolf, B. and Sixl, W. and Graf, R. and Finsterbusch, D. and Bruls, G. and L{\"u}thi, B. and Knetsch, E. A. and Menovsky, A. A. and Mydosh, J. A.},
  month = feb,
  year = {1994},
  keywords = {Elastic Constant,Elastic Property,Magnetic Field,Phase Diagram,Shear Wave},
  pages = {307-324},
  file = {/home/pants/.zotero/data/storage/4Q7FILTJ/Wolf et al. - 1994 - Elastic properties of the heavy fermion supercondu.pdf}
}

@article{kuwahara_lattice_1997,
  title = {Lattice {{Instability}} and {{Elastic Response}} in the {{Heavy Electron System URu 2Si}} 2},
  volume = {66},
  issn = {0031-9015},
  abstract = {We have performed thermal expansion and elastic constant  measurements of the heavy electron system URu 2 Si 2 , focusing attention on  the {$\Gamma$} 3 ( x 2 - y 2 ) and {$\Gamma$} 4 ( x y ) symmetry of the tetragonal group  D 4 h . It is  reconfirmed that there is no sizable uniform spontaneous distortion for these  two types of symmetry through the puzzling phase transition at  T 0 =17.5 K.  On the other hand, a weak but significant tendency of softening are found  below about 70 K in the transverse ( c 11 - c 12 )/2 mode. The results strongly  suggest the presence of a lattice instability in the {$\Gamma$} 3  symmetry. From the  results, proposed crystalline-electric-field models are also discussed.},
  number = {10},
  journal = {Journal of the Physical Society of Japan},
  doi = {10.1143/JPSJ.66.3251},
  author = {Kuwahara, Keitaro and Amitsuka, Hiroshi and Sakakibara, Toshiro and Suzuki, Osamu and Nakamura, Shintaro and Goto, Terutaka and Mihalik, Mari{\'a}n and Menovsky, Alois A. and {de Visser}, Anne and Franse, Jaap J. M.},
  month = oct,
  year = {1997},
  pages = {3251-3258},
  file = {/home/pants/.zotero/data/storage/99CG76ZA/Kuwahara et al. - 1997 - Lattice Instability and Elastic Response in the He.pdf}
}

@article{yanagisawa_ultrasonic_2014,
  title = {Ultrasonic Study of the Hidden Order and Heavy-Fermion State in {{URu2Si2}} with Hydrostatic Pressure, {{Rh}}-Doping, and High Magnetic Fields},
  volume = {94},
  issn = {1478-6435},
  abstract = {This paper reports recent progress of ultrasonic measurements on URuSi, including ultrasonic measurements under hydrostatic pressure, in pulsed magnetic fields, and the effect of Rh-substitution. The observed changes of the elastic responses shed light on the orthorhombic-lattice instability with -symmetry existing within the hidden order and the hybridized 5-electron states of URuSi.},
  number = {32-33},
  journal = {Philosophical Magazine},
  doi = {10.1080/14786435.2013.878054},
  author = {Yanagisawa, Tatsuya},
  month = nov,
  year = {2014},
  keywords = {band Jahn–Teller effect,elastic constant,hidden order,hybridization,hydrostatic pressure,lattice instability,pulsed magnetic field,ultrasound,URu2Si2},
  pages = {3775-3788},
  file = {/home/pants/.zotero/data/storage/UJTH89KV/Yanagisawa - 2014 - Ultrasonic study of the hidden order and heavy-fer.pdf}
}