29Si NMR and hidden order in URu2Si2

NMR study of in-plane twofold ordering in URu(2)Si(2)

We report (29)Si NMR spectra and Knight shift measurements as a function of applied field orientation in the (001) basal plane of URu(2)Si(2). Observed linewidth oscillations confirm the in-plane twofold ordered domain state observed in recent magnetic susceptibility measurements. Analysis of our linewidth data leads to estimate ∼ 0.4% for the twofold intrinsic (monodomain) susceptibility anisotropy in the basal plane, a value ∼ 15 times smaller than that obtained from recent susceptibility measurements.

Rotational symmetry breaking in the hidden-order phase of URu2Si2

A second-order phase transition is characterized by spontaneous symmetry breaking. The nature of the broken symmetry in the so-called "hidden-order" phase transition in the heavy-fermion compound URu(2)Si(2), at transition temperature T(h) = 17.5 K, has posed a long-standing mystery. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below T(h), which breaks the four-fold rotational symmetry of the tetragonal URu(2)Si(2). Two-fold oscillations in the magnetic torque under in-plane field rotation were sensitively detected in small pure crystals. Our findings suggest that the hidden-order phase is an electronic "nematic" phase, a translationally invariant metallic phase with spontaneous breaking of rotational symmetry.

Hidden octupole order in URu₂Si₂

We propose that the hidden order in URu₂Si₂ is an incommensurate octupole order, which is derived from a spin-1 XXZ model with XX octupole and Z dipole interactions based on the singlet-doublet crystal-field level scheme. The octupole moments break time-reversal invariance and give rise to finite hyperfine fields on the nuclei of the ligand Si and Ru ions. In order for the hyperfine fields to be observed as a nuclear magnetic resonance (NMR) linewidth, the order must be incommensurate, with the ordering vector determined so as to account for the ²⁹Si NMR linewidth data quantitatively.

Helicity order: hidden order parameter in URu2Si2

We propose that the "hidden order parameter" in URu2Si2 is a helicity order that 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, the 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.

High magnetic field studies of the hidden order transition in URu2Si2

We studied in detail the low temperature/high magnetic field phases of URu2Si2 single crystals with specific heat, magnetocaloric effect, and magnetoresistance in magnetic fields up to 45 T. Data obtained down to 0.5 K, and extrapolated to T=0, show a suppression of the hidden-order phase at H0(0)=35.9+/-0.35 T and the appearance of a new phase for magnetic fields in excess of H1(0)=36.1+/-0.35 T observed only at temperatures lower than 6 K. In turn, complete suppression of this high field state is attained at a critical magnetic field H2(0)=39.7+/-0.35 T. No phase transitions are observed above 40 T. We discuss our results in the context of itinerant versus localized f electrons.

Hidden orbital order in the heavy fermion metal URu(2)Si(2)

When matter is cooled from high temperatures, collective instabilities develop among its constituent particles that lead to new kinds of order. An anomaly in the specific heat is a classic signature of this phenomenon. Usually the associated order is easily identified, but sometimes its nature remains elusive. The heavy fermion metal URu(2)Si(2) is one such example, where the order responsible for the sharp specific heat anomaly at T(0) = 17 K has remained unidentified despite more than seventeen years of effort. In URu(2)Si(2), the coexistence of large electron electron repulsion and antiferromagnetic fluctuations leads to an almost incompressible heavy electron fluid, where anisotropically paired quasiparticle states are energetically favoured. Here we develop a proposal for the nature of the hidden order in URu(2)Si(2). We show that incommensurate orbital antiferromagnetism, associated with circulating currents between the uranium ions, can account for the local fields and entropy loss observed at the 17 K transition. We make detailed predictions for the outcome of neutron scattering measurements based on this proposal, so that it can be tested experimentally.