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

Two-dimensional heavy fermions in the van der Waals metal CeSiI

Heavy-fermion metals are prototype systems for observing emergent quantum phases driven by electronic interactions1-6. A long-standing aspiration is the dimensional reduction of these materials to exert control over their quantum phases7-11, which remains a significant challenge because traditional intermetallic heavy-fermion compounds have three-dimensional atomic and electronic structures. Here we report comprehensive thermodynamic and spectroscopic evidence of an antiferromagnetically ordered heavy-fermion ground state in CeSiI, an intermetallic comprising two-dimensional (2D) metallic sheets held together by weak interlayer van der Waals (vdW) interactions. Owing to its vdW nature, CeSiI has a quasi-2D electronic structure, and we can control its physical dimension through exfoliation. The emergence of coherent hybridization of f and conduction electrons at low temperature is supported by the temperature evolution of angle-resolved photoemission and scanning tunnelling spectra near the Fermi level and by heat capacity measurements. Electrical transport measurements on few-layer flakes reveal heavy-fermion behaviour and magnetic order down to the ultra-thin regime. Our work establishes CeSiI and related materials as a unique platform for studying dimensionally confined heavy fermions in bulk crystals and employing 2D device fabrication techniques and vdW heterostructures12 to manipulate the interplay between Kondo screening, magnetic order and proximity effects.

Evidence for charge delocalization crossover in the quantum critical superconductor CeRhIn5

The nature of charge degrees-of-freedom distinguishes scenarios for interpreting the character of a second order magnetic transition at zero temperature, that is, a magnetic quantum critical point (QCP). Heavy-fermion systems are prototypes of this paradigm, and in those, the relevant question is where, relative to a magnetic QCP, does the Kondo effect delocalize their f-electron degrees-of-freedom. Herein, we use pressure-dependent Hall measurements to identify a finite-temperature scale Eloc that signals a crossover from f-localized to f-delocalized character. As a function of pressure, Eloc(P) extrapolates smoothly to zero temperature at the antiferromagnetic QCP of CeRhIn5 where its Fermi surface reconstructs, hallmarks of Kondo-breakdown criticality that generates critical magnetic and charge fluctuations. In 4.4% Sn-doped CeRhIn5, however, Eloc(P) extrapolates into its magnetically ordered phase and is decoupled from the pressure-induced magnetic QCP, which implies a spin-density-wave (SDW) type of criticality that produces only critical fluctuations of the SDW order parameter. Our results demonstrate the importance of experimentally determining Eloc to characterize quantum criticality and the associated consequences for understanding the pairing mechanism of superconductivity that reaches a maximum Tc in both materials at their respective magnetic QCP.

Non-monotonic pressure dependence of high-field nematicity and magnetism in CeRhIn5

CeRhIn₅ provides a textbook example of quantum criticality in a heavy fermion system: Pressure suppresses local-moment antiferromagnetic (AFM) order and induces superconductivity in a dome around the associated quantum critical point (QCP) near p_c ≈ 23 kbar. Strong magnetic fields also suppress the AFM order at a field-induced QCP at B_c ≈ 50 T. In its vicinity, a nematic phase at B^* ≈ 28 T characterized by a large in-plane resistivity anisotropy emerges. Here, we directly investigate the interrelation between these phenomena via magnetoresistivity measurements under high pressure. As pressure increases, the nematic transition shifts to higher fields, until it vanishes just below p_c. While pressure suppresses magnetic order in zero field as p_c is approached, we find magnetism to strengthen under strong magnetic fields due to suppression of the Kondo effect. We reveal a strongly non-mean-field-like phase diagram, much richer than the common local-moment description of CeRhIn₅ would suggest.

Multiple quantum critical behaviors exist in the heavy fermion material CeRhIn5, but their interrelation is less studied. Here, Helm et al. investigate the interrelation of two quantum critical points and other relevant orders, revealing a strongly non-mean-field-like phase diagram.

Nature of the spin resonance mode in CeCoIn5

Spin-fluctuation-mediated unconventional superconductivity can emerge at the border of magnetism, featuring a superconducting order parameter that changes sign in momentum space. Detection of such a sign-change is experimentally challenging, since most probes are not phase-sensitive. The observation of a spin resonance mode (SRM) from inelastic neutron scattering is often seen as strong phase-sensitive evidence for a sign-changing superconducting order parameter, by assuming the SRM is a spin-excitonic bound state. Here we show that for the heavy fermion superconductor CeCoIn5, its SRM defies expectations for a spin-excitonic bound state, and is not a manifestation of sign-changing superconductivity. Instead, the SRM in CeCoIn5 likely arises from a reduction of damping to a magnon-like mode in the superconducting state, due to its proximity to magnetic quantum criticality. Our findings emphasize the need for more stringent tests of whether SRMs are spin-excitonic, when using their presence to evidence sign-changing superconductivity.

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.

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 H_c ≈ 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.

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.

Robust upward dispersion of the neutron spin resonance in the heavy fermion superconductor Ce1-xYbxCoIn5

The neutron spin resonance is a collective magnetic excitation that appears in the unconventional copper oxide, iron pnictide and heavy fermion superconductors. Although the resonance is commonly associated with a spin-exciton due to the d(s±)-wave symmetry of the superconducting order parameter, it has also been proposed to be a magnon-like excitation appearing in the superconducting state. Here we use inelastic neutron scattering to demonstrate that the resonance in the heavy fermion superconductor Ce1-xYbxCoIn5 with x=0, 0.05 and 0.3 has a ring-like upward dispersion that is robust against Yb-doping. By comparing our experimental data with a random phase approximation calculation using the electronic structure and the momentum dependence of the -wave superconducting gap determined from scanning tunnelling microscopy (STM) for CeCoIn5, we conclude that the robust upward-dispersing resonance mode in Ce1-xYbxCoIn5 is inconsistent with the downward dispersion predicted within the spin-exciton scenario.

Ising Incommensurate Spin Resonance of CeCoIn5: A Dynamical Precursor of the Q Phase

It is shown through detailed inelastic neutron scattering experiments that the gapped collective magnetic excitation of the unconventional superconductor CeCoIn5, the spin resonance mode, is incommensurate and that the corresponding fluctuations are of an Ising nature. The incommensurate peak position of these fluctuations corresponds to the propagation vector of the adjacent field induced static magnetic ordered phase, the so-called Q phase. Furthermore, the direction of the magnetic moment fluctuations is also the direction of the ordered magnetic moments of the Q phase. Hence, the resonance mode and the Q phase share the same symmetry and this strongly supports a scenario where the static order is realized by a condensation of the magnetic excitation.

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.