Coexistence of antiferromagnetism and superconductivity near the quantum criticality of the heavy-fermion compound CeRhIn5

Competing Nodal d-Wave Superconductivity and Antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

Robust Fermi-Surface Morphology of CeRhIn_{5} across the Putative Field-Induced Quantum Critical Point

We report a comprehensive de Haas-van Alphen (dHvA) study of the heavy-fermion material CeRhIn_{5} in magnetic fields up to 70 T. Several dHvA frequencies gradually emerge at high fields as a result of magnetic breakdown. Among them is the thermodynamically important β_{1} branch, which has not been observed so far. Comparison of our angle-dependent dHvA spectra with those of the non-4f compound LaRhIn_{5} and with band-structure calculations evidences that the Ce 4f electrons in CeRhIn_{5} remain localized over the whole field range. This rules out any significant Fermi-surface reconstruction, either at the suggested nematic phase transition at B^{*}≈30  T or at the putative quantum critical point at B_{c}≃50  T. Our results rather demonstrate the robustness of the Fermi surface and the localized nature of the 4f electrons inside and outside of the antiferromagnetic phase.

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.

Band Dependent Interlayer f-Electron Hybridization in CeRhIn_{5}

A key issue in heavy fermion research is how subtle changes in the hybridization between the 4f (5f) and conduction electrons can result in fundamentally different ground states. CeRhIn_{5} stands out as a particularly notable example: when replacing Rh with either Co or Ir, antiferromagnetism gives way to superconductivity. In this photoemission study of CeRhIn_{5}, we demonstrate that the use of resonant angle-resolved photoemission spectroscopy with polarized light allows us to extract detailed information on the 4f crystal field states and details on the 4f and conduction electron hybridization, which together determine the ground state. We directly observe weakly dispersive Kondo resonances of f electrons and identify two of the three Ce 4f_{5/2}^{1} crystal-electric-field levels and band-dependent hybridization, which signals that the hybridization occurs primarily between the Ce 4f states in the CeIn_{3} layer and two more three-dimensional bands composed of the Rh 4d and In 5p orbitals in the RhIn_{2} layer. Our results allow us to connect the properties observed at elevated temperatures with the unusual low-temperature properties of this enigmatic heavy fermion compound.

An FBG Optical Approach to Thermal Expansion Measurements under Hydrostatic Pressure

We report on an optical technique for measuring thermal expansion and magnetostriction at cryogenic temperatures and under applied hydrostatic pressures of 2.0 GPa. Optical fiber Bragg gratings inside a clamp-type pressure chamber are used to measure the strain in a millimeter-sized sample of CeRhIn5. We describe the simultaneous measurement of two Bragg gratings in a single optical fiber using an optical sensing instrument capable of resolving changes in length [dL/L=(L−L0)/L0] on the order of 10−7. Our results demonstrate the possibility of performing high-resolution thermal expansion measurements under hydrostatic pressure, a capability previously hindered by the small working volumes typical of pressure cells.

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 Ce_0.95Nd_0.05CoIn₅ 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.

Nuclear magnetic resonance in Kondo lattice systems

Nuclear magnetic resonance has emerged as a vital tool to explore the fundamental physics of Kondo lattice systems. Because nuclear spins experience two different hyperfine couplings to the itinerant conduction electrons and to the local f moments, the Knight shift can probe multiple types of spin correlations that are not accessible via other techniques. The Knight shift provides direct information about the onset of heavy electron coherence and the emergence of the heavy electron fluid.

Tuning the pressure-induced superconductivity in Pd-substituted CeRhIn5

The effect of substituting Rh in CeRh(1-x)Pd(x)In5 with Pd up to x = 0.25 has been studied on single crystals. The crystals have been grown by means of the In self-flux method and characterized by x-ray diffraction and microprobe. The tetragonal HoCoGa5-type of structure and the c/a ratio of the parent compound remains intact by the Pd substitution; the unit cell volume increases by 0.6% with x = 0.25 of Pd. The low-temperature behavior of resistivity was studied also under hydrostatic pressure up to 2.25 GPa. The Pd substitution for Rh affects the magnetic behavior and the maximum value of the superconducting transition temperature measured at pressures above 2 GPa only negligibly. On the other hand, the results provide evidence that superconductivity in CeRh(0.75)Pd(0.25)In5 is induced at significantly lower pressures, i.e. the Pd substitution for Rh shifts the CeRh(1-x)Pd(x)In5 system closer to coexistence of magnetism and superconductivity at ambient pressure.

Emergent states in heavy-electron materials

We obtain the conditions necessary for the emergence of various low-temperature ordered states (local-moment antiferromagnetism, unconventional superconductivity, quantum criticality, and Landau Fermi liquid behavior) in Kondo lattice materials by extending the two-fluid phenomenological theory of heavy-electron behavior to incorporate the concept of hybridization effectiveness. We use this expanded framework to present a new phase diagram and consistent physical explanation and quantitative description of measured emergent behaviors such as the pressure variation of the onset of local-moment antiferromagnetic ordering at T(N), the magnitude of the ordered moment, the growth of superconductivity within that ordered state, the location of a quantum critical point, and of a delocalization line in the pressure/temperature phase diagram at which local moments have disappeared and the heavy-electron Fermi surface has grown to its maximum size. We apply our model to CeRhIn(5) and a number of other heavy-electron materials and find good agreement with experiment.

Anisotropic dependence of superconductivity on uniaxial pressure in CeIrIn5

We measure the effect of uniaxial pressure on the superconducting transition temperature T_{c} in CeIrIn5. We find a linear change in T_{c} with both a-axis and c-axis pressure, with slopes of 56 and -66 mK/kbar, respectively. By comparing results from doping studies and different types of pressure measurements, we separate the influences of hybridization and dimensionality on T_{c}. We find the true geometric influence, for constant hybridization, is partial differentialT_{c}/ partial differential(c/a)=44 K.

Anomalous duality of 4f electrons in filled skutterudite CeOs4Sb12

We study the electronic structure of the filled skutterudite CeOs4Sb12 using photoemission spectroscopy (PES). Soft x-ray excited Ce 3d-4f resonant PES confirms the existence of Ce 4f states at the Fermi level (EF). Temperature dependent high-resolution laser-PES spectra reveal a pseudogap formation around EF, which can be explained in terms of the hybridization gap. Simultaneously, a sharp feature is formed just above EF with decreasing temperature. The heavy-fermion-like specific heat is attributed to the occupation of this feature. The results identify the origin of the anomalous coexistence of heavy-fermion and pseudogap behavior in terms of a symmetry dependent hybridization.

Probing the nodal gap in the pressure-induced heavy fermion superconductor CeRhIn5

We report field-orientation specific heat studies of the pressure-induced heavy-fermion superconductor CeRhIn5. These experiments provide the momentum-dependent superconducting gap function for the first time in any pressure-induced superconductor. In the coexisting phase of superconductivity and antiferromagnetism, field rotation within the Ce-In plane reveals fourfold modulation in the density of states, which favors a d-wave order parameter and constrains a theory of the interplay between superconductivity and magnetism.

Electronic duality in strongly correlated matter

Superconductivity develops from an attractive interaction between itinerant electrons that creates electron pairs, which condense into a macroscopic quantum state-the superconducting state. On the other hand, magnetic order in a metal arises from electrons localized close to the ionic core and whose interaction is mediated by itinerant electrons. The dichotomy between local moment magnetic order and superconductivity raises the question of whether these two states can coexist and involve the same electrons. Here, we show that the single 4f electron of cerium in CeRhIn(5) simultaneously produces magnetism, characteristic of localization, and superconductivity that requires itinerancy. The dual nature of the 4f-electron allows microscopic coexistence of antiferromagnetic order and superconductivity whose competition is tuned by small changes in pressure and magnetic field. Electronic duality contrasts with conventional interpretations of coexisting spin-density magnetism and superconductivity and offers a new avenue for understanding complex states in classes of materials.

Interacting antiferromagnetic droplets in quantum critical CeCoIn5

The heavy fermion superconductor CeCoIn5 can be tuned between superconducting and antiferromagnetic ground states by hole doping with Cd. Nuclear magnetic resonance data indicate that these two orders coexist microscopically with an ordered moment approximately 0.7 microB. As the ground state evolves, there is no change in the low-frequency spin dynamics in the disordered state. These results suggest that the magnetism emerges locally in the vicinity of the Cd dopants.

Superconductivity and magnetic order in CeRhIn5: spectra of coexistence

We discuss the fixed-point Hamiltonian and the spectrum of excitations of a quasi-bidimensional electronic system supporting simultaneously antiferromagnetic ordering and superconductivity. The coexistence of these two order parameters in a single phase is possible because the magnetic order is linked to the formation of a metallic spin density wave, and its order parameter is not associated to a spectral gap but to an energy shift of the paramagnetic bands. This peculiarity entails several distinct features in the phase diagram and the spectral properties of the model, which may have been observed in CeRhIn5. Apart from the coexistence, we find an abrupt suppression of the spin density wave when the superconducting and magnetic ordering temperatures are equal. The divergence of the cyclotron mass extracted from de Haas-van Alphen experiments is also analyzed in the same framework.

Magnetic-field-induced lattice anomaly inside the superconducting state of CeCoIn5: anisotropic evidence of the possible Fulde-Ferrell-Larkin-Ovchinnikov state

We report high magnetic field linear magnetostriction experiments on CeCoIn5 single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field B(c2) that becomes less pronounced as the temperature increases and (ii) a distinctive second orderlike feature observed only along the c axis in the high field (10 T < or approximately B< or = B(c2)) low temperature (T < or approximately 0.35 K) region. This second order transition is observed only when the magnetic field lies within 20 degrees of the ab planes and there is no signature of it above B(c2), which raises questions regarding its interpretation as a field induced magnetically ordered phase. Good agreement with previous results suggests that this anomaly is related to the transition to a possible Fulde-Ferrel-Larkin-Ovchinnikov superconducting state.

Hidden magnetism and quantum criticality in the heavy fermion superconductor CeRhIn5

With only a few exceptions that are well understood, conventional superconductivity does not coexist with long-range magnetic order (for example, ref. 1). Unconventional superconductivity, on the other hand, develops near a phase boundary separating magnetically ordered and magnetically disordered phases. A maximum in the superconducting transition temperature T(c) develops where this boundary extrapolates to zero Kelvin, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity. Invariably, though, unconventional superconductivity masks the magnetic phase boundary when T < T(c), preventing proof of a magnetic quantum-critical point. Here we report specific-heat measurements of the pressure-tuned unconventional superconductor CeRhIn5 in which we find a line of quantum-phase transitions induced inside the superconducting state by an applied magnetic field. This quantum-critical line separates a phase of coexisting antiferromagnetism and superconductivity from a purely unconventional superconducting phase, and terminates at a quantum tetracritical point where the magnetic field completely suppresses superconductivity. The T --> 0 K magnetic field-pressure phase diagram of CeRhIn5 is well described with a theoretical model developed to explain field-induced magnetism in the high-T(c) copper oxides, but in which a clear delineation of quantum-phase boundaries has not been possible. These experiments establish a common relationship among hidden magnetism, quantum criticality and unconventional superconductivity in copper oxides and heavy-electron systems such as CeRhIn5.

Gapless magnetic and quasiparticle excitations due to the coexistence of antiferromagnetism and superconductivity in CeRhIn5: a study of 115In NQR under pressure

We report systematic measurements of ac susceptibility, nuclear-quadrupole-resonance spectrum, and nuclear-spin-lattice-relaxation time (T1) on the pressure (P)-induced heavy-fermion superconductor CeRhIn5. The temperature (T) dependence of 1/T(1) at P=1.6 GPa has revealed that antiferromagnetism (AFM) and superconductivity (SC) coexist microscopically, exhibiting the respective transition at T(N)=2.8 K and T(MF)(c)=0.9 K. It is demonstrated that SC does not yield any trace of gap opening in low-lying excitations below T(onset)(c)=2 K, but T(MF)(c)=0.9 K, followed by a T(1)T=const law. These results point to the unconventional characteristics of SC coexisting with AFM. We highlight that both of the results deserve theoretical work on the gapless nature in the low-lying excitation spectrum due to the coexistence of AFM and SC and the lack of the mean-field regime below T(onset)(c)=2 K.