Determination of the dynamic Young's modulus of quantum materials in piezoactuator-driven uniaxial pressure cells using a low-frequency AC method.

We report on a new technique for measuring the dynamic Young's modulus, E, of quantum materials at low temperatures as a function of static tuning strain, ϵ, in piezoactuator-driven pressure cells. In addition to a static tuning of stress and strain, we apply a small-amplitude, finite-frequency AC (1 Hz ≲ ω ≲ 1000 Hz) uniaxial stress, σac, to the sample and measure the resulting AC strain, ϵac, using a capacitive sensor to obtain the associated modulus E. We demonstrate the performance of the new technique through proof-of-principle experiments on the unconventional superconductor Sr2RuO4, which is known for its rich temperature-strain phase diagram. In particular, we show that the magnitude of E, measured using this AC technique at low frequencies, exhibits a pronounced nonlinear elasticity, which is in very good agreement with previous Young's modulus measurements on Sr2RuO4 under [1 0 0] strain using a DC method [Noad et al., Science 382, 447-450 (2023)]. By combining the new AC Young's modulus measurements with AC elastocaloric measurements in a single measurement, we demonstrate that these AC techniques are powerful in detecting small anomalies in the elastic properties of quantum materials. Finally, using the case of Sr2RuO4 as an example, we demonstrate how the imaginary component of the modulus can provide additional information about the nature of ordered phases.

In-Plane Magnetic Penetration Depth in Sr_{2}RuO_{4}: Muon-Spin Rotation and Relaxation Study.

We report on measurements of the in-plane magnetic penetration depth (λ_{ab}) in single crystals of Sr_{2}RuO_{4} down to ≃0.015 K by means of muon-spin rotation-relaxation. The linear temperature dependence of λ_{ab}^{-2} for T≲0.7 K suggests the presence of nodes in the superconducting gap. This statement is further substantiated by observation of the Volovik effect, i.e., the reduction of λ_{ab}^{-2} as a function of the applied magnetic field. The experimental zero-field and zero-temperature value of λ_{ab}=124(3) nm agrees with λ_{ab}≃130 nm, calculated based on results of electronic structure measurements reported in A. Tamai et al. [High-resolution photoemission on Sr_{2}RuO_{4} reveals correlation-enhanced effective spin-orbit coupling and dominantly local self-energies, Phys. Rev. X 9, 021048 (2019)PRXHAE2160-330810.1103/PhysRevX.9.021048]. Our analysis reveals that a simple nodal superconducting energy gap, described by the lowest possible harmonic of a gap function, does not capture the dependence of λ_{ab}^{-2} on T, so the higher angular harmonics of the energy gap function need to be introduced.

Probing Momentum-Dependent Scattering in Uniaxially Stressed Sr_{2}RuO_{4} through the Hall Effect.

The largest Fermi surface sheet of the correlated metal Sr_{2}RuO_{4} can be driven through a Lifshitz transition between an electronlike and an open geometry by uniaxial stress applied along the [100] lattice direction. Here, we investigate the effect of this transition on the longitudinal resistivity ρ_{xx} and the Hall coefficient R_{H}. ρ_{xx}(T), when Sr_{2}RuO_{4} is tuned to this transition, is found to have a T^{2}logT form, as expected for a Fermi liquid tuned to a Lifshitz transition. R_{H} is found to become more negative as the Fermi surface transitions from an electronlike to an open geometry, opposite to general expectations from this change in topology. The magnitude of the change in R_{H} implies that scattering changes throughout the Brillouin zone, not just at the point in k space where the transition occurs. In a model of orbital-dependent scattering, the electron-electron scattering rate on sections of Fermi surface with xy orbital weight is found to decrease dramatically.

Hierarchy of Lifshitz Transitions in the Surface Electronic Structure of Sr_{2}RuO_{4} under Uniaxial Compression.

We report the evolution of the electronic structure at the surface of the layered perovskite Sr_{2}RuO_{4} under large in-plane uniaxial compression, leading to anisotropic B_{1g} strains of ϵ_{xx}-ϵ_{yy}=-0.9±0.1%. From angle-resolved photoemission, we show how this drives a sequence of Lifshitz transitions, reshaping the low-energy electronic structure and the rich spectrum of van Hove singularities that the surface layer of Sr_{2}RuO_{4} hosts. From comparison to tight-binding modeling, we find that the strain is accommodated predominantly by bond-length changes rather than modifications of octahedral tilt and rotation angles. Our study sheds new light on the nature of structural distortions at oxide surfaces, and how targeted control of these can be used to tune density of state singularities to the Fermi level, in turn paving the way to the possible realization of rich collective states at the Sr_{2}RuO_{4} surface.

Observation of a robust and active catalyst for hydrogen evolution under high current densities.

Despite the fruitful achievements in the development of hydrogen production catalysts with record-breaking performances, there is still a lack of durable catalysts that could work under large current densities (>1000 mA cm-2). Here, we investigated the catalytic behaviors of Sr2RuO4 bulk single crystals. This crystal has demonstrated remarkable activities under the current density of 1000 mA cm-2, which require overpotentials of 182 and 278 mV in 0.5 M H2SO4 and 1 M KOH electrolytes, respectively. These materials are stable for 56 days of continuous testing at a high current density of above 1000 mA cm-2 and then under operating temperatures of 70 °C. The in-situ formation of ferromagnetic Ru clusters at the crystal surface is observed, endowing the single-crystal catalyst with low charge transfer resistance and high wettability for rapid gas bubble removal. These experiments exemplify the potential of designing HER catalysts that work under industrial-scale current density.

The superconductivity of Sr2RuO4 under c-axis uniaxial stress.

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr2RuO4 can be tuned through a single Van Hove point, resulting in strong enhancement of both Tc and Hc2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr2RuO4. Hc2 increases, as expected for increasing density of states, but unexpectedly Tc falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr2RuO4.

Elastocaloric determination of the phase diagram of Sr2RuO4.

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning2,3, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr2RuO4 (refs. 4-9). Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr2RuO4.

Non-Fermi liquid behavior below the Néel temperature in the frustrated heavy fermion magnet UAu2.

The term Fermi liquid is almost synonymous with the metallic state. The association is known to break down at quantum critical points (QCPs), but these require precise values of tuning parameters, such as pressure and applied magnetic field, to exactly suppress a continuous phase transition temperature to the absolute zero. Three-dimensional non-Fermi liquid states, apart from superconductivity, that are unshackled from a QCP are much rarer and are not currently well understood. Here, we report that the triangular lattice system uranium diauride (UAu2) forms such a state with a non-Fermi liquid low-temperature heat capacity [Formula: see text] and electrical resistivity [Formula: see text] far below its Néel temperature. The magnetic order itself has a novel structure and is accompanied by weak charge modulation that is not simply due to magnetostriction. The charge modulation continues to grow in amplitude with decreasing temperature, suggesting that charge degrees of freedom play an important role in the non-Fermi liquid behavior. In contrast with QCPs, the heat capacity and resistivity we find are unusually resilient in magnetic field. Our results suggest that a combination of magnetic frustration and Kondo physics may result in the emergence of this novel state.

Evidence for even parity unconventional superconductivity in Sr2RuO4.

Unambiguous identification of the superconducting order parameter symmetry in [Formula: see text] has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

High-sensitivity heat-capacity measurements on Sr2RuO4 under uniaxial pressure.

A key question regarding the unconventional superconductivity of [Formula: see text] remains whether the order parameter is single- or two-component. Under a hypothesis of two-component superconductivity, uniaxial pressure is expected to lift their degeneracy, resulting in a split transition. The most direct and fundamental probe of a split transition is heat capacity. Here, we report measurement of heat capacity of samples subject to large and highly homogeneous uniaxial pressure. We place an upper limit on the heat-capacity signature of any second transition of a few percent of that of the primary superconducting transition. The normalized jump in heat capacity, [Formula: see text], grows smoothly as a function of uniaxial pressure, favoring order parameters which are allowed to maximize in the same part of the Brillouin zone as the well-studied van Hove singularity. Thanks to the high precision of our measurements, these findings place stringent constraints on theories of the superconductivity of [Formula: see text].

Electronically driven spin-reorientation transition of the correlated polar metal Ca3Ru2O7.

The interplay between spin-orbit coupling and structural inversion symmetry breaking in solids has generated much interest due to the nontrivial spin and magnetic textures which can result. Such studies are typically focused on systems where large atomic number elements lead to strong spin-orbit coupling, in turn rendering electronic correlations weak. In contrast, here we investigate the temperature-dependent electronic structure of [Formula: see text], a [Formula: see text] oxide metal for which both correlations and spin-orbit coupling are pronounced and in which octahedral tilts and rotations combine to mediate both global and local inversion symmetry-breaking polar distortions. Our angle-resolved photoemission measurements reveal the destruction of a large hole-like Fermi surface upon cooling through a coupled structural and spin-reorientation transition at 48 K, accompanied by a sudden onset of quasiparticle coherence. We demonstrate how these result from band hybridization mediated by a hidden Rashba-type spin-orbit coupling. This is enabled by the bulk structural distortions and unlocked when the spin reorients perpendicular to the local symmetry-breaking potential at the Ru sites. We argue that the electronic energy gain associated with the band hybridization is actually the key driver for the phase transition, reflecting a delicate interplay between spin-orbit coupling and strong electronic correlations and revealing a route to control magnetic ordering in solids.

High pressure synthesis of late rare earth RFeAs(O,F) superconductors; R = Tb and Dy.

New TbFeAs(O,F) and DyFeAs(O,F) superconductors with critical temperatures T(c) = 46 and 45 K and very high critical fields, >or=100 T, have been prepared at 1100-1150 degrees C and 10-12 GPa, demonstrating that high pressure may be used to synthesise late rare earth derivatives of the recently reported RFeAs(O,F) (R = La-Nd, Sm, Gd) high temperature superconductors.