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.

Kondo quasiparticle dynamics observed by resonant inelastic x-ray scattering.

Effective models focused on pertinent low-energy degrees of freedom have substantially contributed to our qualitative understanding of quantum materials. An iconic example, the Kondo model, was key to demonstrating that the rich phase diagrams of correlated metals originate from the interplay of localized and itinerant electrons. Modern electronic structure calculations suggest that to achieve quantitative material-specific models, accurate consideration of the crystal field and spin-orbit interactions is imperative. This poses the question of how local high-energy degrees of freedom become incorporated into a collective electronic state. Here, we use resonant inelastic x-ray scattering (RIXS) on CePd3 to clarify the fate of all relevant energy scales. We find that even spin-orbit excited states acquire pronounced momentum-dependence at low temperature-the telltale sign of hybridization with the underlying metallic state. Our results demonstrate how localized electronic degrees of freedom endow correlated metals with new properties, which is critical for a microscopic understanding of superconducting, electronic nematic, and topological states.

Colossal anomalous Nernst effect in a correlated noncentrosymmetric kagome ferromagnet.

The transverse voltage generated by a temperature gradient in a perpendicularly applied magnetic field, termed the Nernst effect, has promise for thermoelectric applications and for probing electronic structure. In magnetic materials, an anomalous Nernst effect (ANE) is possible in a zero magnetic field. We report a colossal ANE in the ferromagnetic metal UCo0.8Ru0.2Al, reaching 23 microvolts per kelvin. Uranium's 5f electrons provide strong electronic correlations that lead to narrow bands, a known route to producing a large thermoelectric response. In addition, uranium's strong spin-orbit coupling produces an intrinsic transverse response in this material due to the Berry curvature associated with the relativistic electronic structure. Theoretical calculations show that in UCo0.8Ru0.2Al at least 148 Weyl nodes, and two nodal lines, exist within 60 millielectron volt of the Fermi level. This work demonstrates that magnetic actinide materials can host strong Nernst and Hall responses due to their combined correlated and topological nature.

Evidence for a pressure-induced antiferromagnetic quantum critical point in intermediate-valence UTe2.

UTe2 is a recently discovered unconventional superconductor that has attracted much interest because of its potentially spin-triplet topological superconductivity. Our ac calorimetry, electrical resistivity, and x-ray absorption study of UTe2 under applied pressure reveals key insights on the superconducting and magnetic states surrounding pressure-induced quantum criticality at P c1 = 1.3 GPa. First, our specific heat data at low pressures, combined with a phenomenological model, show that pressure alters the balance between two closely competing superconducting orders. Second, near 1.5 GPa, we detect two bulk transitions that trigger changes in the resistivity, which are consistent with antiferromagnetic order, rather than ferromagnetism. Third, the emergence of magnetism is accompanied by an increase in valence toward a U4+ (5f 2) state, which indicates that UTe2 exhibits intermediate valence at ambient pressure. Our results suggest that antiferromagnetic fluctuations may play a more substantial role on the superconducting state of UTe2 than previously thought.

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.

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.

Resonant torsion magnetometry in anisotropic quantum materials.

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂2F/∂θ2, the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl3 highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

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.

Quantum limit transport and destruction of the Weyl nodes in TaAs.

Weyl fermions are a recently discovered ingredient for correlated states of electronic matter. A key difficulty has been that real materials also contain non-Weyl quasiparticles, and disentangling the experimental signatures has proven challenging. Here we use magnetic fields up to 95 T to drive the Weyl semimetal TaAs far into its quantum limit, where only the purely chiral 0th Landau levels of the Weyl fermions are occupied. We find the electrical resistivity to be nearly independent of magnetic field up to 50 T: unusual for conventional metals but consistent with the chiral anomaly for Weyl fermions. Above 50 T we observe a two-order-of-magnitude increase in resistivity, indicating that a gap opens in the chiral Landau levels. Above 80 T we observe strong ultrasonic attenuation below 2 K, suggesting a mesoscopically textured state of matter. These results point the way to inducing new correlated states of matter in the quantum limit of Weyl semimetals.

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.

Domain engineering of the metastable domains in the 4f-uniaxial-ferromagnet CeRu2Ga2B.

In search of novel, improved materials for magnetic data storage and spintronic devices, compounds that allow a tailoring of magnetic domain shapes and sizes are essential. Good candidates are materials with intrinsic anisotropies or competing interactions, as they are prone to host various domain phases that can be easily and precisely selected by external tuning parameters such as temperature and magnetic field. Here, we utilize vector magnetic fields to visualize directly the magnetic anisotropy in the uniaxial ferromagnet CeRu2Ga2B. We demonstrate a feasible control both globally and locally of domain shapes and sizes by the external field as well as a smooth transition from single stripe to bubble domains, which opens the door to future applications based on magnetic domain tailoring.

Low temperature magnetic structure of CeRhIn5 by neutron diffraction on absorption-optimized samples.

Two aspects of the ambient pressure magnetic structure of heavy fermion material CeRhIn5 have remained under some debate since its discovery: whether the structure is indeed an incommensurate helix or a spin density wave, and what is the precise magnitude of the ordered magnetic moment. By using a single crystal sample optimized for hot neutrons to minimize neutron absorption by Rh and In, here we report an ordered moment of [Formula: see text]. In addition, by using spherical neutron polarimetry measurements on a similar single crystal sample, we have confirmed the helical nature of the magnetic structure, and identified a single chiral domain.

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.

Anomalous electronic structure and magnetoresistance in TaAs2.

The change in resistance of a material in a magnetic field reflects its electronic state. In metals with weakly- or non-interacting electrons, the resistance typically increases upon the application of a magnetic field. In contrast, negative magnetoresistance may appear under some circumstances, e.g., in metals with anisotropic Fermi surfaces or with spin-disorder scattering and semimetals with Dirac or Weyl electronic structures. Here we show that the non-magnetic semimetal TaAs2 possesses a very large negative magnetoresistance, with an unknown scattering mechanism. Density functional calculations find that TaAs2 is a new topological semimetal [ℤ2 invariant (0;111)] without Dirac dispersion, demonstrating that a negative magnetoresistance in non-magnetic semimetals cannot be attributed uniquely to the Adler-Bell-Jackiw chiral anomaly of bulk Dirac/Weyl fermions.

'Hard' crystalline lattice in the Weyl semimetal NbAs.

We report the effect of hydrostatic pressure on the magnetotransport properties of the Weyl semimetal NbAs. Subtle changes can be seen in the ρ(xx)(T) profiles with pressure up to 2.31 GPa. The Fermi surfaces undergo an anisotropic evolution under pressure: the extremal areas slightly increase in the k(x)-k(y) plane, but decrease in the k(z)-k(y)(k(x)) plane. The topological features of the two pockets observed at atmospheric pressure, however, remain unchanged at 2.31 GPa. No superconductivity can be seen down to 0.3 K for all the pressures measured. By fitting the temperature dependence of specific heat to the Debye model, we obtain a small Sommerfeld coefficient γ(0) = 0.09(1) mJ (mol·K(2))(-1) and a large Debye temperature, Θ(D) = 450(9) K, confirming a 'hard' crystalline lattice that is stable under pressure. We also studied the Kadowaki-Woods ratio of this low-carrier-density massless system, R(KW) = 3.2 × 10(4) µΩ cm mol(2) K(2) J(-2). After accounting for the small carrier density in NbAs, this R(KW) indicates a suppressed transport scattering rate relative to other metals.

Thermal and transport properties of U2Pt(x)Ir(1-x)C2.

We report thermal and transport properties of U2Pt x Ir1-x C2 from which a magnetic phase diagram is obtained. Pure U2IrC2 is an antiferromagnet at 6.5 K, whose Néel temperature initially rises to 13.2 K at x = 0.2 and subsequently is suppressed to zero temperature with increasing Pt content near x = 0.6. Heat capacity divided by temperature at x = 0.6 shows an upturn at low temperature, consistent with the expectations of enhanced quantum fluctuations in the presence of an underlying quantum critical point. The entropy after the phonon contribution has been subtracted has a value of 0.24 Rln2 at the Néel temperature of U2IrC2, revealing an itinerant nature of the 5 f electrons in this compound. On the Pt rich side of the phase diagram, superconductivity is suppressed by x = 0.85. The residual resistivity increases by a factor of 10 from pure Pt (x = 1) to x = 0.85 where superconductivity is suppressed to zero. By comparing the phase diagram of Ir doped U2PtC2 with the phase diagram of pressure tuned and Rh doped U2PtC2 we demonstrate the role of electronic tuning in this system.

Magnetic structure of the antiferromagnetic Kondo lattice compounds CeRhAl4Si2 and CeIrAl4Si2.

We have investigated the magnetic ground state of the antiferromagnetic Kondo-lattice compounds CeMAl4Si2(M = Rh, Ir) using neutron powder diffraction. Although both of these compounds show two magnetic transitions T(N1) and T(N2) in the bulk properties measurements, evidence for magnetic long-range order was only found below the lower transition T(N2). Analysis of the diffraction profiles reveals a commensurate antiferromagnetic structure with a propagation vector k = (0, 0, 1/2). The magnetic moment in the ordered state of CeRhAl4Si2 and CeIrAl4Si2 were determined to be 1.14(2) and 1.41(3) µ(B) Ce(-1), respectively, and are parallel to the crystallographic c-axis in agreement with magnetic susceptibility measurements.

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.