Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance.

Phases of matter are usually identified through spontaneous symmetry breaking, especially regarding unconventional superconductivity and the interactions from which it originates. In that context, the superconducting state of the quasi-two-dimensional and strongly correlated perovskite Sr2RuO4 is considered to be the only solid-state analogue to the superfluid 3He-A phase1,2, with an odd-parity order parameter that is unidirectional in spin space for all electron momenta and breaks time-reversal symmetry. This characterization was recently called into question by a search for an expected 'split' transition in a Sr2RuO4 crystal under in-plane uniaxial pressure, which failed to find any such evidence; instead, a dramatic rise and a peak in a single-transition temperature were observed3,4. Here we use nuclear magnetic resonance (NMR) spectroscopy of oxygen-17, which is directly sensitive to the order parameter via hyperfine coupling to the electronic spin degrees of freedom, to probe the nature of superconductivity in Sr2RuO4 and its evolution under strain. A reduction of the Knight shift is observed for all strain values and at temperatures below the critical temperature, consistent with a drop in spin polarization in the superconducting state. In unstrained samples, our results contradict a body of previous NMR work reporting no change in the Knight shift5 and the most prevalent theoretical interpretation of the order parameter as a chiral p-wave state. Sr2RuO4 is an extremely clean layered perovskite and its superconductivity emerges from a strongly correlated Fermi liquid, and our work imposes tight constraints on the order parameter symmetry of this archetypal system.

Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5.

Electronic nematic materials are characterized by a lowered symmetry of the electronic system compared to the underlying lattice, in analogy to the directional alignment without translational order in nematic liquid crystals. Such nematic phases appear in the copper- and iron-based high-temperature superconductors, and their role in establishing superconductivity remains an open question. Nematicity may take an active part, cooperating or competing with superconductivity, or may appear accidentally in such systems. Here we present experimental evidence for a phase of fluctuating nematic character in a heavy-fermion superconductor, CeRhIn5 (ref. 5). We observe a magnetic-field-induced state in the vicinity of a field-tuned antiferromagnetic quantum critical point at Hc ≈ 50 tesla. This phase appears above an out-of-plane critical field H* ≈ 28 tesla and is characterized by a substantial in-plane resistivity anisotropy in the presence of a small in-plane field component. The in-plane symmetry breaking has little apparent connection to the underlying lattice, as evidenced by the small magnitude of the magnetostriction anomaly at H*. Furthermore, no anomalies appear in the magnetic torque, suggesting the absence of metamagnetism in this field range. The appearance of nematic behaviour in a prototypical heavy-fermion superconductor highlights the interrelation of nematicity and unconventional superconductivity, suggesting nematicity to be common among correlated materials.

Competing magnetic orders in the superconducting state of heavy-fermion CeRhIn5.

Applied pressure drives the heavy-fermion antiferromagnet CeRhIn5 toward a quantum critical point that becomes hidden by a dome of unconventional superconductivity. Magnetic fields suppress this superconducting dome, unveiling the quantum phase transition of local character. Here, we show that [Formula: see text] magnetic substitution at the Ce site in CeRhIn5, either by Nd or Gd, induces a zero-field magnetic instability inside the superconducting state. This magnetic state not only should have a different ordering vector than the high-field local-moment magnetic state, but it also competes with the latter, suggesting that a spin-density-wave phase is stabilized in zero field by Nd and Gd impurities, similarly to the case of Ce0.95Nd0.05CoIn5 Supported by model calculations, we attribute this spin-density wave instability to a magnetic-impurity-driven condensation of the spin excitons that form inside the unconventional superconducting state.

Enhanced Hybridization Sets the Stage for Electronic Nematicity in CeRhIn_{5}.

High magnetic fields induce a pronounced in-plane electronic anisotropy in the tetragonal antiferromagnetic metal CeRhIn_{5} at H^{*}≳30 T for fields ≃20° off the c axis. Here we investigate the response of the underlying crystal lattice in magnetic fields to 45 T via high-resolution dilatometry. At low fields, a finite magnetic field component in the tetragonal ab plane explicitly breaks the tetragonal (C_{4}) symmetry of the lattice revealing a finite nematic susceptibility. A modest a-axis expansion at H^{*} hence marks the crossover to a fluctuating nematic phase with large nematic susceptibility. Magnetostriction quantum oscillations confirm a Fermi surface change at H^{*} with the emergence of new orbits. By analyzing the field-induced change in the crystal-field ground state, we conclude that the in-plane Ce 4f hybridization is enhanced at H^{*}, in agreement with the in-plane lattice expansion. We argue that the nematic behavior observed in this prototypical heavy-fermion material is of electronic origin, and is driven by the hybridization between 4f and conduction electrons which carries the f-electron anisotropy to the Fermi surface.

From Ising Resonant Fluctuations to Static Uniaxial Order in Antiferromagnetic and Weakly Superconducting CeCo(In_{1-x}Hg_{x})_{5}(x=0.01).

CeCo(In_{0.990}Hg_{0.010})_{5} is a charge doped variant of the d-wave CoCoIn_{5} superconductor with coexistent antiferromagnetic and superconducting transitions occurring at T_{N}=3.4 and T_{c}=1.4 K, respectively. We use neutron diffraction and spectroscopy to show that the magnetic resonant fluctuations present in the parent superconducting phase are replaced by collinear c-axis magnetic order with three-dimensional Ising critical fluctuations. No low-energy transverse spin fluctuations are observable in this doping-induced antiferromagnetic phase and the dynamic resonant spectral weight predominately shifts to the elastic channel. Static (τ>0.2 ns) collinear Ising order is proximate to superconductivity in CeCoIn_{5} and is stabilized through hole doping with Hg.

Avoided valence transition in a plutonium superconductor.

The d and f electrons in correlated metals are often neither fully localized around their host nuclei nor fully itinerant. This localized/itinerant duality underlies the correlated electronic states of the high-Tc cuprate superconductors and the heavy-fermion intermetallics and is nowhere more apparent than in the 5f valence electrons of plutonium. Here, we report the full set of symmetry-resolved elastic moduli of PuCoGa5--the highest Tc superconductor of the heavy fermions (Tc = 18.5 K)--and find that the bulk modulus softens anomalously over a wide range in temperature above Tc. The elastic symmetry channel in which this softening occurs is characteristic of a valence instability--therefore, we identify the elastic softening with fluctuations of the plutonium 5f mixed-valence state. These valence fluctuations disappear when the superconducting gap opens at Tc, suggesting that electrons near the Fermi surface play an essential role in the mixed-valence physics of this system and that PuCoGa5 avoids a valence transition by entering the superconducting state. The lack of magnetism in PuCoGa5 has made it difficult to reconcile with most other heavy-fermion superconductors, where superconductivity is generally believed to be mediated by magnetic fluctuations. Our observations suggest that valence fluctuations play a critical role in the unusually high Tc of PuCoGa5.

Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5.

Conventional, thermally driven continuous phase transitions are described by universal critical behavior that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behavior remain open issues. Here we report measurements of heat capacity and de Haas-van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B0* ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn5 suggest that the Fermi-surface change at B0* is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn5, a significant step toward the derivation of a universal phase diagram for QCPs.

Quantum Critical Scaling in the Disordered Itinerant Ferromagnet UCo_{1-x}Fe_{x}Ge.

The Belitz-Kirkpatrick-Vojta (BKV) theory shows in excellent agreement with experiment that ferromagnetic quantum phase transitions (QPTs) in clean metals are generally first order due to the coupling of the magnetization to electronic soft modes, in contrast to the classical analogue that is an archetypical second-order phase transition. For disordered metals the BKV theory predicts that the second-order nature of the QPT is restored because the electronic soft modes change their nature from ballistic to diffusive. Our low-temperature magnetization study identifies the ferromagnetic QPT in the disordered metal UCo_{1-x}Fe_{x}Ge as the first clear example that exhibits the associated critical exponents predicted by the BKV theory.

Detection of a spin-triplet superconducting phase in oriented polycrystalline U(2)PtC(2) samples using

Nuclear magnetic resonance (NMR) measurements on the ^{195}Pt nucleus in an aligned powder of the moderately heavy-fermion material U_{2}PtC_{2} are consistent with spin-triplet pairing in its superconducting state. Across the superconducting transition temperature and to much lower temperatures, the NMR Knight shift is temperature independent for field both parallel and perpendicular to the tetragonal c axis, expected for triplet equal-spin pairing superconductivity. The NMR spin-lattice relaxation rate 1/T_{1}, in the normal state, exhibits characteristics of ferromagnetic fluctuations, compatible with an enhanced Wilson ratio. In the superconducting state, 1/T_{1} follows a power law with temperature without a coherence peak giving additional support that U_{2}PtC_{2} is an unconventional superconductor. Bulk measurements of the ac susceptibility and resistivity indicate that the upper critical field exceeds the Pauli limiting field for spin-singlet pairing and is near the orbital limiting field, an additional indication for spin-triplet pairing.

Reemergent superconductivity and avoided quantum criticality in Cd-doped CeIrIn(5) under pressure.

We investigated the electrical resistivity and heat capacity of 1% Cd-doped CeIrIn_{5} under hydrostatic pressure up to 2.7 GPa, near where long-range antiferromagnetic order is suppressed and bulk superconductivity suddenly reemerges. The pressure-induced T_{c} is close to that of pristine CeIrIn_{5} at 2.7 GPa, and no signatures of a quantum critical point under pressure support a local origin of the antiferromagnetic moments in Cd-CeIrIn_{5} at ambient pressure. Similarities between superconductors CeIrIn_{5} and CeCoIn_{5} in response to Cd substitutions suggest a common magnetic mechanism.

Multiconfigurational nature of 5f orbitals in uranium and plutonium intermetallics.

Uranium and plutonium's 5f electrons are tenuously poised between strongly bonding with ligand spd-states and residing close to the nucleus. The unusual properties of these elements and their compounds (e.g., the six different allotropes of elemental plutonium) are widely believed to depend on the related attributes of f-orbital occupancy and delocalization for which a quantitative measure is lacking. By employing resonant X-ray emission spectroscopy (RXES) and X-ray absorption near-edge structure (XANES) spectroscopy and making comparisons to specific heat measurements, we demonstrate the presence of multiconfigurational f-orbital states in the actinide elements U and Pu and in a wide range of uranium and plutonium intermetallic compounds. These results provide a robust experimental basis for a new framework toward understanding the strongly-correlated behavior of actinide materials.

Magnitude of the magnetic exchange interaction in the heavy-fermion antiferromagnet CeRhIn5.

We have used high-resolution neutron spectroscopy experiments to determine the complete spin wave spectrum of the heavy-fermion antiferromagnet CeRhIn5. The spin wave dispersion can be quantitatively reproduced with a simple frustrated J1-J2 model that also naturally explains the magnetic spin-spiral ground state of CeRhIn5 and yields a dominant in-plane nearest-neighbor magnetic exchange constant J0=0.74(3) meV. Our results pave the way to a quantitative understanding of the rich low-temperature phase diagram of the prominent CeTIn5 (T=Co, Rh, Ir) class of heavy-fermion materials.

Emergent antiferromagnetism out of the "hidden-order" state in URu2Si2: high magnetic field nuclear magnetic resonance to 40 T.

Very high field (29)Si-NMR measurements using a fully (29)Si-enriched URu(2)Si(2) single crystal were carried out in order to microscopically investigate the "hidden order" (HO) state and adjacent magnetic phases in the high field limit. At the lowest measured temperature of 0.4 K, a clear anomaly reflecting a Fermi surface instability near 22 T inside the HO state is detected by the (29)Si shift, (29)K(c). Moreover, a strong enhancement of (29)K(c) develops near a critical field H(c) ≃ 35.6 T, and the ^{29}Si-NMR signal disappears suddenly at H(c), indicating the total suppression of the HO state. Nevertheless, a weak and shifted (29)Si-NMR signal reappears for fields higher than H(c) at 4.2 K, providing evidence for a magnetic structure within the magnetic phase caused by the Ising-type anisotropy of the uranium ordered moments.

Isotropic quantum scattering and unconventional superconductivity.

Superconductivity without phonons has been proposed for strongly correlated electron materials that are tuned close to a zero-temperature magnetic instability of itinerant charge carriers. Near this boundary, quantum fluctuations of magnetic degrees of freedom assume the role of phonons in conventional superconductors, creating an attractive interaction that 'glues' electrons into superconducting pairs. Here we show that superconductivity can arise from a very different spectrum of fluctuations associated with a local (or Kondo-breakdown) quantum critical point that is revealed in isotropic scattering of charge carriers and a sublinear, temperature-dependent electrical resistivity. At this critical point, accessed by applying pressure to the strongly correlated, local-moment antiferromagnet CeRhIn(5), magnetic and charge fluctuations coexist and produce electronic scattering that is maximal at the optimal pressure for superconductivity. This previously unanticipated source of pairing glue opens possibilities for understanding and discovering new unconventional forms of superconductivity.

Zero-field quantum critical point in CeCoIn5.

Quantum criticality in the normal and superconducting states of the heavy-fermion metal CeCoIn5 is studied by measurements of the magnetic Grüneisen ratio ΓH and specific heat in different field orientations and temperatures down to 50 mK. A universal temperature over magnetic field scaling of ΓH in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state, the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.

Measurement of two low-temperature energy gaps in the electronic structure of antiferromagnetic USb2 using ultrafast optical spectroscopy.

Ultrafast optical spectroscopy is used to study the antiferromagnetic f-electron system USb(2). We observe the opening of two charge gaps at low temperatures (

A microscopic Kondo lattice model for the heavy fermion antiferromagnet CeIn3.

Electrons at the border of localization generate exotic states of matter across all classes of strongly correlated electron materials and many other quantum materials with emergent functionality. Heavy electron metals are a model example, in which magnetic interactions arise from the opposing limits of localized and itinerant electrons. This remarkable duality is intimately related to the emergence of a plethora of novel quantum matter states such as unconventional superconductivity, electronic-nematic states, hidden order and most recently topological states of matter such as topological Kondo insulators and Kondo semimetals and putative chiral superconductors. The outstanding challenge is that the archetypal Kondo lattice model that captures the underlying electronic dichotomy is notoriously difficult to solve for real materials. Here we show, using the prototypical strongly-correlated antiferromagnet CeIn3, that a multi-orbital periodic Anderson model embedded with input from ab initio bandstructure calculations can be reduced to a simple Kondo-Heisenberg model, which captures the magnetic interactions quantitatively. We validate this tractable Hamiltonian via high-resolution neutron spectroscopy that reproduces accurately the magnetic soft modes in CeIn3, which are believed to mediate unconventional superconductivity. Our study paves the way for a quantitative understanding of metallic quantum states such as unconventional superconductivity.

Quasiparticle entropy in the high-field superconducting phase of CeCoIn(5).

The heavy-fermion superconductor CeCoIn(5) displays an additional transition within its superconducting (SC) state, whose nature is characterized by high-precision studies of the isothermal field dependence of the entropy, derived from combined specific heat and magnetocaloric effect measurements at temperatures T≥100 mK and fields H≤12 T aligned along different directions. For any of these conditions, we do not observe an additional entropy contribution upon tuning at constant temperature by magnetic field from the homogeneous SC into the presumed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) SC state. By contrast, for H∥[100] a reduction of entropy was found that quantitatively agrees with the expectation for spin-density-wave order without FFLO superconductivity. Our data exclude the formation of a FFLO state in CeCoIn(5) for out-of-plane field directions, where no spin-density-wave order exists.

Heat-capacity measurements of energy-gap nodes of the heavy-fermion superconductor CeIrIn5 deep inside the pressure-dependent dome structure of its superconducting phase diagram.

We use heat-capacity measurements as a function of field rotation to identify the nodal gap structure of CeIrIn(5) at pressures to 2.05 GPa, deep inside its superconducting dome. A fourfold oscillation in the heat capacity at 0.3 K is observed for all pressures, but with its sign reversed between 1.50 and 0.90 GPa. On the basis of recent theoretical models for the field-angle-dependent specific heat, all data, including the sign reversal, imply a d(x(2)-y(2)) order parameter with nodes along [110], which constrains theoretical models of the pairing mechanism in CeIrIn(5).