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Register a new userHidden and Hastatic Orders in URu2Si2
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The hidden order developing below 17.5K in the heavy fermion material URu2Si2 has eluded identification for over twenty five years. This paper will review the recent theory of ``hastatic order, a novel two-component order parameter capturing the hybridization between half-integer spin (Kramers) conduction electrons and the non-Kramers 5f^2 Ising local moments, as strongly indicated by the observation of Ising quasiparticles in de Haas-van Alphen measurements. Hastatic order differs from conventional magnetism as it is a spinor order that breaks both single and double time-reversal symmetry by mixing states of different Kramers parity. The broken time-reversal symmetry simply explains both the pseudo-Goldstone mode between the hidden order and antiferromagnetic phases and the nematic order seen in torque magnetometry. The spinorial nature of the hybridization also explains how the Kondo effect gives a phase transition, with the hybridization gap turning on at the hidden order transition as seen in scanning tunneling microscopy. Hastatic order also has a number of new predictions: a basal-plane magnetic moment of order .01mu_B, a gap to longitudinal spin fluctuations that vanishes continuously at the first order antiferromagnetic transition and a narrow resonant nematic feature in the scanning tunneling spectra.
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The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded identification. Here we argue that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor hybridization order parameter that breaks double time-reversal symmetry by mixing states of integer and half-integer spin. Such hastatic order (hasta:[Latin]spear) hybridizes Kramers conduction electrons with Ising, non-Kramers 5f2 states of the uranium atoms to produce Ising quasiparticles. The development of a spinorial hybridization at 17.5K accounts for both the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. This paper develops the theory of hastatic order in detail, providing the mathematical development of its key concepts. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states.
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~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.
We present new 29-Si NMR spectra in URu2Si2 for varying temperature T, and external field H. On lowering T, the systematics of the low-field lineshape and width reveal an extra component (lambda) to the linewidth below T_N ~ 17 K not observed previously. We find that lambda is magnetic-field independent and dominates the low-field lineshape for all orientations of H with respect to the tetragonal c axis. The behavior of lambda indicates a direct relationship between the 29-Si spin and the transition at T_N, but it is inconsistent with a coupling of the nuclei to static antiferromagnetic order/disorder of the U-spin magnetization. This leads us to conjecture that lambda is due to a coupling of 29-Si to the systems hidden-order parameter. A possible coupling mechanism involving charge degrees of freedom and indirect nuclear spin/spin interactions is proposed. We also propose further experiments to test for the existence of this coupling mechanism.
By means of neutron scattering we show that the high-temperature precursor to the hidden order state of the heavy fermion superconductor URu$_{2}$Si$_{2}$ exhibits heavily damped incommensurate paramagnons whose strong energy dispersion is very similar to that of the long-lived longitudinal f-spin excitations that appear below T$_{0}$. Since the underlying local f-exchange is preserved we expect only the f-d interactions to change across the phase transition and to cause the paramagnetic damping. The damping exhibits single-ion behavior independent of wave vector and vanishes below the hidden order transition. We suggest that this arises from a transition from valence fluctuations to a hybridized f-d state below T$_{0}$. Here we present evidence that the itinerant excitations, like those in chromium, are due to Fermi surface nesting of hole and electron pockets so that the hidden order phase likely originates from a Fermi-surface instability. We identify wave vectors that span nested regions of a band calculation and that match the neutron spin crossover from incommensurate to commensurate on approach to the hidden order phase.
URu2Si2 is one of the most enigmatic strongly-correlated-electron systems and offers a fertile testing ground for new concepts in condensed matter science. In spite of >30 years of intense research, no consensus on the order parameter of its low-temperature hidden-order phase exists. A strong magnetic field transforms the hidden order into magnetically-ordered phases, whose order parameter has also been defying experimental observation. Here, thanks to an instrumentation breakthrough in high-field neutron scattering, we identify the field-induced phases of URu2Si2 as a spin-density-wave state with wavevector k1 = (0.6 0 0). The transition to the spin-density wave represents a unique touchstone for understanding the hidden-order phase. An intimate relationship between this magnetic structure, the magnetic fluctuations, and the Fermi surface is emphasized, calling for dedicated band structure calculations.
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