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Modulated Spin Liquid and Magnetic Order from a Kondo-Heisenberg model applied to $URu_{2}Si_{2}$  [PDF]
X. Montiel,S. Burdin,C. Pépin,A. Ferraz
Physics , 2013, DOI: 10.1103/PhysRevB.90.045125
Abstract: Within the framework of the Kondo-Heisenberg model, we analyse the effect of charge fluctuation on the modulated spin liquid (MSL) and antiferromagnetic (AF) orders which were established in a previous publication. We discuss the emergence of two quantum critical lines separating the coexisting Kondo-MSL and Kondo-MSL-AF phases. The various order parameters of the system possess a characteristic signature observable on the electronic band structure of each of the phases. We calculate that the MSL order is indeed a possible explanation of the hidden order phase of $URu_{2}Si_{2}$ heavy fermion compound. Our model produces results in qualitative agreement with the experimental (T,P) phase diagram and the two gap openings in the system and quantitative agreement with the entropy and Sommerfeld coefficient evolution.
The modulated spin liquid: a new paradigm for URu$_2$Si$_2$  [PDF]
C. Pepin,M. R. Norman,S. Burdin,A. Ferraz
Physics , 2010, DOI: 10.1103/PhysRevLett.106.106601
Abstract: We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks $Z_4$ symmetry, as recently seen in the hidden order phase of URu$_2$Si$_2$. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.
Photoemission Imaging of 3D Fermi Surface Pairing at the Hidden Order Transition in URu2Si2  [PDF]
Jian-Qiao Meng,Peter M. Oppeneer,John A. Mydosh,Peter S. Riseborough,Krzysztof Gofryk,John J. Joyce,Eric D. Bauer,Yinwan Li,Tomasz Durakiewicz
Physics , 2013, DOI: 10.1103/PhysRevLett.111.127002
Abstract: We report angle-resolved photoemission spectroscopy (ARPES) experiments probing deep into the hidden order (HO) 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 (3D) 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 HO phase.
Double-stage continuous-discontinuous superconducting phase transition in the Pauli paramagnetic limit of a 3D superconductor: the URu$%_{2}$Si$_{2}$ case  [PDF]
V. Zhuravlev,T. Maniv
Physics , 2009, DOI: 10.1140/epjb/e2010-00012-y
Abstract: The sharp suppression of the de-Haas van-Alphen oscillations observed in the mixed superconducting (SC) state of the heavy fermion compound URu$_{2}$Si$% _{2}$ is shown to confirm a theoretical prediction of a narrow double-stage SC phase transition, smeared by fluctuations, in a 3D paramagnetically-limitted superconductor. The predicted scenario of a second order transition to a nonuniform (FFLO) state followed by a first order transition to a uniform SC state, obtained by using a non-perturbative approach, is also found to be consistent with recent thermal conductivity measurements performed on this material.
Hybridization wave as the 'Hidden Order' in URu$_2$Si$_2$  [PDF]
Y. Dubi,Alexander V. Balatsky
Physics , 2010, DOI: 10.1103/PhysRevLett.106.086401
Abstract: A phenomenological model for the 'hidden order' transition in the heavy Fermion material URu$_2$Si$_2$ is introduced. The 'hidden order' is identified as an incommensurate, momentum-carrying hybridization between the light hole band and the heavy electron band. This modulated hybridization appears after a Fano hybridization at higher temperatures takes place. We focus on the hybridization wave as the order parameter in URu$_2$Si$_2$ and possibly other materials with similar band structures. The model is qualitatively consistent with numerous experimental results obtained from e.g. neutron scattering and scanning tunneling microscopy. Specifically, we find a gap-like feature in the density of states and the appearance of features at an incommensurate vector $Q^*\sim 0.6 \pi/a_0$. Finally, the model allows us to make various predictions which are amenable to current experiments.
Electrodynamics of the antiferromagnetic phase in URu$_2$Si$_2$  [PDF]
Jesse S. Hall,M. Rahimi Movassagh,M. N. Wilson,G. M. Luke,N. Kanchanavatee,K. Huang,M. Janoschek,M. B. Maple,T. Timusk
Physics , 2015, DOI: 10.1103/PhysRevB.92.195111
Abstract: We present data on the optical conductivity of URu$_{2-x}$(Fe,Os)$_{x}$Si$_{2}$. While the parent material URu$_2$Si$_2$ enters the enigmatic hidden order phase below 17.5 K, an antiferromagnetic phase is induced by the substitution of Fe or Os onto the Ru sites. We find that both the HO and the AFM phases exhibit an identical gap structure that is characterized by a loss of conductivity below the gap energy with spectral weight transferred to a narrow frequency region just above the gap, the typical optical signature of a density wave. The AFM phase is marked by strong increases in both transition temperature and the energy of the gap associated with the transition. In the normal phase just above the transition the optical scattering rate varies as $\omega^2$. We find that in both the HO and the AFM phases, our data are consistent with elastic resonant scattering of a Fermi liquid. This indicates that the appearance of a coherent state is a necessary condition for either ordered phase to emerge. Our measurements favor models in which the HO and the AFM phases are driven by the common physics of a nesting-induced density-wave-gap.
Anisotropic inelastic scattering and its interplay with superconductivity in URu$_{2}$Si$_{2}$  [PDF]
Zengwei Zhu,Elena Hassinger,Zhu'an Xu,Dai Aoki,Jacques Flouquet,Kamran Behnia
Physics , 2009, DOI: 10.1103/PhysRevB.80.172501
Abstract: In contrast to almost all anisotropic superconductors, the upper critical field of URu$_{2}$Si$_{2}$ is larger when the field is oriented along the less conducting direction. We present a study of resistivity and Seebeck coefficient extended down to sub-Kelvin temperature range uncovering a singular case of anisotropy. When the current is injected along the c-axis URu$_{2}$Si$_{2}$ behaves as a low-density Fermi liquid. When it flows along the a-axis, even in presence of a large field, resistivity remains T-linear down to T$_{c}$ and the Seebeck coefficient undergoes a sign change at very low temperatures. We conclude that the characteristic energy scale is anisotropic and vanishingly small in the basal plane.
Inelastic contribution of the resistivity in the hidden order in URu2Si2  [PDF]
E Hassinger,T D Matsuda,G Knebel,V Taufour,D Aoki,J Flouquet
Physics , 2010, DOI: 10.1088/1742-6596/273/1/012031
Abstract: In the hidden order of URu2Si2 the resistivity at very low temperature shows no T^2 behavior above the transition to superconductivity. However, when entering the antiferromagnetic phase, the Fermi liquid behavior is recovered. We discuss the change of the inelastic term when entering the AF phase with pressure considering the temperature dependence of the Grueneisen parameter at ambient pressure and the influence of superconductivity by an extrapolation of high field data.
Helicity Order: Hidden Order Parameter in URu$_2$Si$_2$  [PDF]
C. M. Varma,Lijun Zhu
Physics , 2005, DOI: 10.1103/PhysRevLett.96.036405
Abstract: We propose that the "hidden order parameter" in URu$_2$Si$_2$ is a helicity order which must arise, if the Pomeranchuk criteria for the spin-antisymmetric Landau parameters with respect to the stability of a Fermi liquid state are violated. In a simple model, we calculate the specific heat, linear and nonlinear magnetic susceptibilities and the change of transition temperature in a magnetic field with such an order parameter, and obtain quantitative agreement with experiments in terms of two parameters extracted from the data. The peculiar temperature dependence of the NMR linewidth and the nature of the loss of excitations in the ordered phase seen by neutron scattering are also explained and experiments are suggested to directly confirm the proposed order parameter.
Optical study of hybridization and hidden order in URu$_2$Si$_2$  [PDF]
J. S. Hall,T. Timusk
Physics , 2014, DOI: 10.1080/14786435.2014.899439
Abstract: We summarize existing optical data of URu$_2$Si$_2$ to clarify the nature of the hidden order transition in this heavy fermion metal. Hybridization develops between 50 K and 17.5 K, and a coherent Drude peak emerges which mirrors the changes in the dc resistivity. The Drude weight indicates that there is little change in the effective mass of these carriers in this temperature range. In addition, there is a flat background conductivity that develops a partial hybridization gap at 10 meV as the temperature is lowered, shifting spectral weight to higher frequencies above 300 meV. Below 30 K the carriers become increasingly coherent and Fermi-liquid-like as the hidden order transition is approached. The hidden order state in URu$_2$Si$_2$ is characterized by multiple anisotropic gaps. The gap parameter $\Delta_a=3.2$ meV in the {\it ab}-plane. In the {\it c}-direction, there are two distinct gaps with magnitudes of $\Delta_{c1}=2.7$ meV and $\Delta_{c2}=1.8$ meV. These observations are in good agreement with other spectroscopic measurements. Overall, the spectrum can be fit by a Dynes-type density of states model to extract values of the hidden order gap. The transfer of spectral weight strongly resembles what one sees in density wave transitions.
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