Gapped itinerant spin excitations account for missing entropy in the hidden-order state of URu2Si2

Abstract

Many correlated electron materials, such as high-temperature superconductors 1 , geometrically frustrated oxides 2 and lowdimensional magnets 3,4 , are still objects of fruitful study because of the unique properties that arise owing to poorly understood many-body effects. Heavy-fermion metals 5 -materials that have high effective electron masses due to those effects-represent a class of materials with exotic properties, ranging from unusual magnetism, unconventional superconductivity and 'hidden' order parameters 6 . The heavy-fermion superconductor URu 2 Si 2 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 0.03μ 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-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.The central issue in URu 2 Si 2 concerns the identification of the order parameter that explains the reduction in the specific heat coefficient, γ = C/T, and thus the change in entropy, through the transition at 17.5 K (ref. 6). Numerous speculations about the ground state have been advanced, from quadrupolar ordering 7 , to spin-density wave formation 8 , to 'orbital currents' 9 to account for the missing entropy. Here, we present cold-neutron time-offlight spectroscopy results that shed some light on the 'hiddenorder' (HO) in URu 2 Si 2 . We have carried out experiments above and below the ordering temperature to measure how the spin excitations evolve. It is clear from our data that above T 0 the spectrum is dominated by fast, itinerant-like spin excitations emanating from incommensurate wavevectors at positions located 0.4a* from the antiferromagnetic (AF) points. From the group velocity and temperature dependence of these modes, we surmise that these are heavy-quasiparticle excitations that form below the 'coherence temperature' and play a crucial role in the formation of the heavy-fermion and HO states. The gapping of these excitations, which corresponds to a loss of accessible states, accounts for the reduction in γ through the transition at 17.5 K. Figure 1 shows the excitation spectrum of URu 2 Si 2 at 1.5 K in the H00 plane. The characteristic gaps at ∼2 meV at the AF zone centre (1, 0, 0) and ∼4 meV at the incommensurate wavevectors (0.6, 0, 0) and (1.4, 0, 0) have been known for some time 10 . The incommensurate wavevector corresponds to a displacement of ∼0.4a * from the AF zone centres (that is, where h + k + l = an odd integer, and is thus forbidden in the body-centred-cubic chemical structure). A scenario for this modesoftening at the incommensurate positi...

Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2

“…This softening may be due to the incommensurate excitations found by neutron experiments 33 , which may also be related to the high-field incommensurate spin density wave phase identified above the critical field of hidden order 34 . In any case this anomaly does not appear to be closely related to the hidden order, because the (C 11 À C 12 )/2 should be coupled to the orthorhombicity with Immm symmetry (Fig.…”

Optical study of hybridization and hidden order in URu2Si2

“…In many ways, this makes a great deal of sense. The gapping of incommensurate magnetic excitations at the hidden order transition has been shown by neutron scattering [44,45], and these account for much of the entropy lost. Band structure calculations [46,47] have yielded a picture of the Fermi surface with strong nesting in the pressure-induced anti-ferromagnetic state, and quantum oscillation measurements [37] demonstrate that there is no significant Fermi surface restructuring between HO and LM-AFM, which implies that the Fermi surface calculated for the latter state applies equally well to the former.…”

Non-Fermi Liquid Regimes and Superconductivity in the Low Temperature Phase Diagrams of Strongly Correlated d- and f-Electron Materials

“…In addition to the BCS-like specific heat anomaly, there are anomalies in the electrical resistivity, magnetic susceptibility [77][78][79], ultrasound [86], thermal expansion [87], and an increase in lattice thermal conductivity [88]. Additional evidence points to the opening of a large gap in the tunneling spectrum [89], the incommensurate spin excitation spectrum [90], and the crossing of the chemical potential by a heavy electron band [91].…”

“…Given the presence of the two phase transitions, the electronic specific heat C(T ) is also somewhat complicated. It is possible to estimate T -linear Fermi liquid-like γ 0 terms both above (∼150 mJ mol −1 K −2 ) and below (∼60 mJ mol −1 K −2 ) the transition [77,79,90], and the Sommerfeld-Wilson ratio χ 0 /γ 0 is on the order of one. However, below 10 K but above the superconducting anomaly, C/T actually has a negative slope, well-described by logarithmic or weak power-law T -dependence [77].…”