Longitudinal Spin Fluctuations Driving Field-Reinforced Superconductivity in UTe_{2}.

Our measurements of ^{125}Te NMR relaxations reveal an enhancement of electronic spin fluctuations above µ_{0}H^{*}∼15 T, leading to their divergence in the vicinity of the metamagnetic transition at µ_{0}H_{m}≈35 T, below which field-reinforced superconductivity appears when a magnetic field (H) is applied along the crystallographic b axis. The NMR data evidence that these fluctuations are dominantly longitudinal, providing a key to understanding the peculiar superconducting phase diagram in H∥b, where such fluctuations enhance the pairing interactions.

Field Induced Multiple Superconducting Phases in UTe_{2} along Hard Magnetic Axis.

The superconducting (SC) phase diagram in uranium ditelluride is explored under magnetic fields (H) along the hard magnetic b axis using a high-quality single crystal with T_{c}=2.1 K. Simultaneous electrical resistivity and ac magnetic susceptibility measurements discern low- and high-field SC (LFSC and HFSC, respectively) phases with contrasting field-angular dependence. Crystal quality increases the upper critical field of the LFSC phase, but the H^{*} of ∼15 T, at which the HFSC phase appears, is always the same through the various crystals. A phase boundary signature is also observed inside the LFSC phase near H^{*}, indicating an intermediate SC phase characterized by small flux pinning forces.

Effect of uranium deficiency on normal and superconducting properties in unconventional superconductor UTe2.

Single crystals of the unconventional superconductor UTe2have been grown in various conditions which result in different superconducting transition temperature as well as normal state properties. Stoichiometry of the samples has been characterized by the single-crystal x-ray crystallography and electron microprobe analyses. Superconducting samples are nearly stoichiometric within an experimental error of about 1%, while non-superconducting sample significantly deviates from the ideal composition. The superconducting UTe2showed that the large density of states was partially gapped in the normal state, while the non-superconducting sample is characterized by the relatively large electronic specific heat as reported previously.

Thermodynamic Perspective on Field-Induced Behavior of α-RuCl_{3}.

Measurements of the magnetic Grüneisen parameter (Γ_{B}) and specific heat on the Kitaev material candidate α-RuCl_{3} are used to access in-plane field and temperature dependence of the entropy up to 12 T and down to 1 K. No signatures corresponding to phase transitions are detected beyond the boundary of the magnetically ordered region, but only a shoulderlike anomaly in Γ_{B}, involving an entropy increment as small as 10^{-5}Rlog2. These observations put into question the presence of a phase transition between the purported quantum spin liquid and the field-polarized state of α-RuCl_{3}. We show theoretically that at low temperatures Γ_{B} is sensitive to crossings in the lowest excitations within gapped phases, and identify the measured shoulderlike anomaly as being of such origin. Exact diagonalization calculations demonstrate that the shoulderlike anomaly can be reproduced in extended Kitaev models that gain proximity to an additional phase at finite field without entering it. We discuss manifestations of this proximity in other measurements.

Tuning the Pairing Interaction in a d-Wave Superconductor by Paramagnons Injected through Interfaces.

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials. A new approach to this most fundamental and hotly debated issue focuses on the role of interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures. Here we fabricate hybrid superlattices consisting of alternating atomic layers of the heavy-fermion superconductor CeCoIn_{5} and antiferromagnetic (AFM) metal CeRhIn_{5}, in which the AFM order can be suppressed by applying pressure. We find that the superconducting and AFM states coexist in spatially separated layers, but their mutual coupling via the interface significantly modifies the superconducting properties. An analysis of upper critical fields reveals that, upon suppressing the AFM order by applied pressure, the force binding superconducting electron pairs acquires an extreme strong-coupling nature. This demonstrates that superconducting pairing can be tuned nontrivially by magnetic fluctuations (paramagnons) injected through the interface.

Full-Gap Superconductivity Robust against Disorder in Heavy-Fermion CeCu_{2}Si_{2}.

A key aspect of unconventional pairing by the antiferromagnetic spin-fluctuation mechanism is that the superconducting energy gap must have the opposite sign on different parts of the Fermi surface. Recent observations of non-nodal gap structure in the heavy-fermion superconductor CeCu_{2}Si_{2} were then very surprising, given that this material has long been considered a prototypical example of a superconductor where the Cooper pairing is magnetically mediated. Here we present a study of the effect of controlled point defects, introduced by electron irradiation, on the temperature-dependent magnetic penetration depth λ(T) in CeCu_{2}Si_{2}. We find that the fully gapped state is robust against disorder, demonstrating that low-energy bound states, expected for sign-changing gap structures, are not induced by nonmagnetic impurities. This provides bulk evidence for s_{++}-wave superconductivity without sign reversal.

Tuning the Magnetic Quantum Criticality of Artificial Kondo Superlattices CeRhIn_{5}/YbRhIn_{5}.

The effects of reduced dimensions and the interfaces on antiferromagnetic quantum criticality are studied in epitaxial Kondo superlattices, with alternating n layers of heavy-fermion antiferromagnet CeRhIn_{5} and seven layers of normal metal YbRhIn_{5}. As n is reduced, the Kondo coherence temperature is suppressed due to the reduction of effective Kondo screening. The Néel temperature is gradually suppressed as n decreases and the quasiparticle mass is strongly enhanced, implying dimensional control toward a quantum critical point. Magnetotransport measurements reveal that a quantum critical point is reached for the n=3 superlattice by applying small magnetic fields. Remarkably, the anisotropy of the quantum critical field is opposite to the expectations from the magnetic susceptibility in bulk CeRhIn_{5}, suggesting that the Rashba spin-orbit interaction arising from the inversion symmetry breaking at the interface plays a key role for tuning the quantum criticality in the two-dimensional Kondo lattice.

Multiple Metamagnetic Quantum Criticality in Sr_{3}Ru_{2}O_{7}.

Bilayer strontium ruthenate Sr_{3}Ru_{2}O_{7} displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Grüneisen parameter Γ_{H}, which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition, we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition.

Possible observation of highly itinerant quantum magnetic monopoles in the frustrated pyrochlore Yb2Ti2O7.

The low-energy elementary excitations in frustrated quantum magnets have fascinated researchers for decades. In frustrated Ising magnets on a pyrochlore lattice possessing macroscopically degenerate spin-ice ground states, the excitations have been discussed in terms of classical magnetic monopoles, which do not contain quantum fluctuations. Here we report unusual behaviours of magneto-thermal conductivity in the disordered spin-liquid regime of pyrochlore Yb2Ti2O7, which hosts frustrated spin-ice correlations with large quantum fluctuations owing to pseudospin-1/2 of Yb ions. The analysis of the temperature and magnetic field dependencies shows the presence of gapped elementary excitations. We find that the gap energy is largely suppressed from that expected in classical monopoles. Moreover, these excitations propagate a long distance without being scattered, in contrast to the diffusive nature of classical monopoles. These results suggests the emergence of highly itinerant quantum magnetic monopole, which is a heavy quasiparticle that propagates coherently in three-dimensional spin liquids.

Quantum criticality in a metallic spin liquid.

When magnetic order is suppressed by frustrated interactions, spins form a highly correlated fluctuating 'spin liquid' state down to low temperatures. The magnetic order of local moments can also be suppressed when they are fully screened by conduction electrons through the Kondo effect. Thus, the combination of strong geometrical frustration and Kondo screening may lead to novel types of quantum phase transition. We report low-temperature thermodynamic measurements on the frustrated Kondo lattice Pr2Ir2O7, which exhibits a chiral spin liquid state below 1.5 K as a result of the frustrated interaction between Ising 4f local moments and their interplay with Ir conduction electrons. Our results provide a first clear example of zero-field quantum critical scaling that emerges in a spin liquid state of a highly frustrated metal.

Quantum bicriticality in the heavy-fermion metamagnet YbAgGe.

Bicritical points, at which two distinct symmetry-broken phases become simultaneously unstable, are typical for spin-flop metamagnetism. Interestingly, the heavy-fermion compound YbAgGe also possesses such a bicritical point (BCP) with a low temperature T(BCP)≈0.3 K at a magnetic field of µH(BCP)≈4.5 T. In its vicinity, YbAgGe exhibits anomalous behavior that we attribute to the influence of a quantum bicritical point that is close in parameter space yet can be reached by tuning T(BCP) further to zero. Using high-resolution measurements of the magnetocaloric effect, we demonstrate that the magnetic Grüneisen parameter ΓH indeed both changes sign and diverges as required for quantum criticality. Moreover, ΓH displays a characteristic scaling behavior but only on the low-field side H≲H(BCP), indicating a pronounced asymmetry with respect to the critical field. We speculate that the small value of T(BCP) is related to the geometric frustration of the Kondo lattice of YbAgGe.

Anomalous reduction of the Lorenz ratio at the quantum critical point in YbAgGe.

We report measurements of the electrical and thermal transport on the hexagonal heavy-fermion metal YbAgGe for temperatures T ≥ 40 mK and in magnetic fields H∥ab up to 14 T. This distorted kagome-lattice system displays a series of magnetic states and a quantum critical point at H(c) = 4.5 T. The Lorenz ratio L(T)/L0 displays a marked reduction only close to H(c). A T-linear contribution below 120 mK, present at all different fields, allows us to extrapolate the Lorenz ratio towards T = 0. At the critical field this yields L/L0 = 0.92±0.03, suggesting a violation of the Wiedemann-Franz law due to strong inelastic scattering.

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.

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.

High-resolution alternating-field technique to determine the magnetocaloric effect of metals down to very low temperatures.

The magnetocaloric effect or "magnetic Grüneisen ratio" Γ(H)=T(-1)(dT/dH)(S) quantifies the cooling or heating of a material when an applied magnetic field is changed under adiabatic conditions. Recently, this property has attracted considerable interest in the field of quantum criticality. Here, we report the development of a low-frequency alternating-field technique for measurements of the magnetocaloric effect down to very low temperatures, which is an important property for the study of quantum critical points. We focus, in particular, on highly conducting metallic samples and discuss the influence of eddy current heating. By comparison with magnetization and specific heat measurements, we demonstrate that our fast and accurate technique gives quantitatively correct values for the magnetocaloric effect under truly adiabatic conditions.

Superconductivity versus quantum criticality: what can we learn from heavy fermions?

Two quantum critical point (QCP) scenarios are being discussed for different classes of antiferromagnetic (AF) heavy-fermion (HF) systems. In the itinerant one, where AF order is of the spin-density wave (SDW) type, the heavy 'composite' charge carriers keep their integrity at the QCP. The second one implies a breakdown of the Kondo effect and a disintegration of the composite fermions at the AF QCP. We discuss two isostructural compounds as exemplary materials for these two different scenarios: CeCu(2)Si(2) exhibits a three-dimensional (3D) SDW QCP and superconductivity, presumably mediated by SDW fluctuations, as strongly suggested by recent inelastic neutron scattering experiments. In Y bRh(2)Si(2), the AF QCP is found to coincide with a Kondo-destroying one. However, in the latter compound these two QCPs can be detached by varying the average unit-cell volume, e.g. through the application of chemical pressure, as realized by partial substitution of either Ir or Co for Rh. A comparison of CeCu(2)Si(2) and Y bRh(2)Si(2) indicates that the apparent differences in quantum critical behaviour go along with disparate behaviour concerning the (non-) existence of superconductivity (SC). No sign of SC could be detected in Y bRh(2)Si(2) down to mK temperatures. A potential correlation between the specific nature of the QCP and the occurrence of SC, however, requires detailed studies on further quantum critical HF superconductors, e.g. on ß-Y bAlB(4), UBe(13), CeCoIn(5) and CeRhIn(5).

Low-temperature magnetothermal transport investigation of a Ni-based superconductor BaNi2As2: evidence for fully gapped superconductivity.

We have performed low-temperature specific heat and thermal conductivity measurements of the Ni-based superconductor BaNi2As2 (T{c}=0.7 K) in a magnetic field. In a zero field, thermal conductivity shows T-linear behavior in the normal state and exhibits a BCS-like exponential decrease below T{c}. The field dependence of the residual thermal conductivity extrapolated to zero temperature is indicative of a fully gapped superconductor. This conclusion is supported by the analysis of the specific heat data, which are well fit by the BCS temperature dependence from T{c} down to the lowest temperature of 0.1 K.

Divergence of the magnetic Grüneisen ratio at the field-induced quantum critical point in YbRh2Si2.

The heavy-fermion metal YbRh2Si2 is studied by low-temperature magnetization M(T) and specific-heat C(T) measurements at magnetic fields close to the quantum critical point (H_{c}=0.06 T, H perpendicularc). Upon approaching the instability, dM/dT is more singular than C(T), leading to a divergence of the magnetic Grüneisen ratio Gamma_{mag}=-(dM/dT)/C. Within the Fermi-liquid regime, Gamma_{mag}=-G_{r}(H-H_{c};{fit}) with G_{r}=-0.30+/-0.01 and H_{c};{fit}=(0.065+/-0.005) T which is consistent with scaling behavior of the specific-heat coefficient in YbRh2(Si0.95Ge0.05)_{2}. The field dependence of dM/dT indicates an inflection point of the entropy as a function of magnetic field upon passing the line T;{ small star, filled}(H) previously observed in Hall and thermodynamic measurements.

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.

Anisotropic effect of Cd and Hg doping on the Pauli limited superconductor CeCoIn5.

We studied the effect of impurity on the first order superconducting (SC) transition and the high field-low temperature (HFLT) SC state of CeCoIn5 by measuring the specific heat of CeCo(In1-xCdx)_{5} with x=0.0011, 0.0022, and 0.0033 and CeCo(In1-xHgx)_{5} with x=0.000 16, 0.000 32, and 0.000 48 at temperatures down to 0.1 K and fields up to 14 T. Cd substitution rapidly suppresses the crossover temperature T0, where the SC transition changes from second to first order, to T=0 K with x=0.0022 for H parallel[100], while it remains roughly constant up to x=0.0033 for H parallel[001]. The associated anomaly of the proposed FFLO state in Hg-doped samples is washed out by x=0.000 48, while remaining at the same temperature, indicating high sensitivity of that state to impurities. We interpret these results as supporting the nonmagnetic, possibly FFLO, origin of the HFLT state in CeCoIn5.