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

Controlling unconventional superconductivity in artificially engineeredf-electron Kondo superlattices

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-T_ccuprates, iron pnictides, and heavy-fermion compounds. Interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures provide a new approach to this most fundamental and hotly debated subject. We have been able to use a recent state-of-the-art molecular-beam-epitaxy technique to fabricate superlattices consisting of different heavy-fermion compounds with atomic thickness. These Kondo superlattices provide a unique opportunity to study the mutual interaction between unconventional superconductivity and magnetic order through the atomic interface. Here, we design and fabricate hybrid Kondo superlattices consisting of alternating layers of superconducting CeCoIn₅withd-wave pairing symmetry and nonmagnetic metal YbCoIn₅or antiferromagnetic heavy fermion metals such as CeRhIn₅and CeIn₃. In these Kondo superlattices, superconducting heavy electrons are confined within the two-dimensional CeCoIn₅block layers and interact with neighboring nonmagnetic or magnetic layers through the interface. Superconductivity is strongly influenced by local inversion symmetry breaking at the interface in CeCoIn₅/YbCoIn₅superlattices. The superconducting and antiferromagnetic states coexist in spatially separated layers in CeCoIn₅/CeRhIn₅and CeCoIn₅/CeIn₃superlattices, but their mutual coupling via the interface significantly modifies the superconducting and magnetic properties. The fabrication of a wide variety of hybrid superlattices paves a new way to study the relationship between unconventional superconductivity and magnetism in strongly correlated materials.

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn_{5} in Rotating Magnetic Field

The d-wave superconductor CeCoIn_{5} has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn_{5}, as the mere existence of an SDW does not necessarily exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn_{5} is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

Hybridization Dynamics in CeCoIn_{5} Revealed by Ultrafast Optical Spectroscopy

We investigate the quasiparticle dynamics in the prototypical heavy fermion CeCoIn_{5} using ultrafast optical pump-probe spectroscopy. Our results indicate that this material system undergoes hybridization fluctuations before the establishment of heavy electron coherence, as the temperature decreases from ∼120  K (T^{†}) to ∼55  K (T^{*}). We reveal that the anomalous coherent phonon softening and damping reduction below T^{*} are directly associated with the emergence of collective hybridization. We also discover a distinct collective mode with an energy of ∼8  meV, which may be experimental evidence of the predicted unconventional density wave. Our findings provide important information for understanding the hybridization dynamics in heavy fermion systems.

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.

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.

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.

Anomalous Change in the de Haas-van Alphen Oscillations of CeCoIn_{5} at Ultralow Temperatures

We perform de Haas-van Alphen (dHvA) measurements of the heavy-fermion superconductor CeCoIn_{5} down to 2 mK above the upper critical field. We find that the dHvA amplitudes show an anomalous suppression, concomitantly with a shift of the dHvA frequency, below the transition temperature T_{n}=20  mK. We suggest that the change is owing to magnetic breakdown caused by a field-induced antiferromagnetic (AFM) state emerging below T_{n}, revealing the origin of the field-induced quantum critical point (QCP) in CeCoIn_{5}. The field dependence of T_{n} is found to be very weak for 7-10 T, implying that an enhancement of AFM order by suppressing the critical spin fluctuations near the AFM QCP competes with the field suppression effect on the AFM phase. We suggest that the appearance of a field-induced AFM phase is a generic feature of unconventional superconductors, which emerge near an AFM QCP, including CeCoIn_{5}, CeRhIn_{5}, and high-T_{c} cuprates.

Distinct domain switching in Nd0.05Ce0.95CoIn5 at low and high fields

Nd_0.05Ce_0.95CoIn₅ features a magnetic field-driven quantum phase transition that separates two antiferromagnetic phases with an identical magnetic structure inside the superconducting condensate. Using neutron diffraction we demonstrate that the population of the two magnetic domains in the two phases is affected differently by the rotation of the magnetic field in the tetragonal basal plane. In the low-field SDW-phase the domain population is only weakly affected while in the high-field Q-phase they undergo a sharp switch for fields around the a-axis. Our results provide evidence that the anisotropic spin susceptibility in both phases arises ultimately from spin-orbit interactions but are qualitatively different in the two phases. This provides evidence that the electronic structure is changed at the quantum phase transition, which yields a modified coupling between magnetism and superconductivity in the Q-phase.

Spin Resonance and Magnetic Order in an Unconventional Superconductor

Unconventional superconductivity in many materials is believed to be mediated by magnetic fluctuations. It is an open question how magnetic order can emerge from a superconducting condensate and how it competes with the magnetic spin resonance in unconventional superconductors. Here we study a model d-wave superconductor that develops spin-density wave order, and find that the spin resonance is unaffected by the onset of static magnetic order. This result suggests a scenario, in which the resonance in Nd_{0.05}Ce_{0.95}CoIn_{5} is a longitudinal mode with fluctuating moments along the ordered magnetic moments.

Anisotropic resonance modes emerging in an antiferromagnetic superconducting state

Two strong arguments in favor of magnetically driven unconventional superconductivity arise from the coexistence and closeness of superconducting and magnetically ordered phases on the one hand, and from the emergence of magnetic spin-resonance modes at the superconducting transition on the other hand. Combining these two arguments one may ask about the nature of superconducting spin-resonance modes occurring in an antiferromagnetic state. This problem can be studied in underdoped BaFe₂ As₂, for which the local coexistence of large moment antiferromagnetism and superconductivity is well established by local probes. However, polarized neutron scattering experiments are required to identify the nature of the resonance modes. In the normal state of Co underdoped BaFe₂ As₂ the antiferromagnetic order results in broad magnetic gaps opening in all three spin directions that are reminiscent of the magnetic response in the parent compound. In the superconducting state two distinct anisotropic resonance excitations emerge, but in contrast to numerous studies on optimum and over-doped BaFe₂ As₂ there is no isotropic resonance excitation. The two anisotropic resonance modes appearing within the antiferromagnetic phase are attributed to a band selective superconducting state, in which longitudinal magnetic excitations are gapped by antiferromagnetic order with sizable moment.

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.

Resonances in the Field-Angle-Resolved Thermal Conductivity of CeCoIn_{5}

The thermal conductivity measurement in a rotating magnetic field is a powerful probe of the structure of the superconducting energy gap. We present high-precision measurements of the low-temperature thermal conductivity in the unconventional heavy-fermion superconductor CeCoIn_{5}, with the heat current J along the nodal [110] direction of its d_{x^{2}-y^{2}} order parameter and the magnetic field up to 7 T rotating in the ab plane. In contrast to the smooth oscillations found previously for J∥[100], we observe a sharp resonancelike peak in the thermal conductivity when the magnetic field is also in the [110] direction, parallel to the heat current. We explain this peak qualitatively via a model of the heat transport in a d-wave superconductor. In addition, we observe two smaller but also very sharp peaks in the thermal conductivity for the field directions at angles Θ≈±33° with respect to J. The origin of the observed resonances at Θ≈±33° at present defies theoretical explanation. The challenge of uncovering their source will dictate exploring theoretically more complex models, which might include, e.g., fine details of the Fermi surface, Andreev bound vortex core states, a secondary superconducting order parameter, and the existence of gaps in spin and charge excitations.

Field-induced magnetic instability within a superconducting condensate

The application of magnetic fields, chemical substitution, or hydrostatic pressure to strongly correlated electron materials can stabilize electronic phases with different organizational principles. We present evidence for a field-induced quantum phase transition, in superconducting Nd_0.05Ce_0.95CoIn₅, that separates two antiferromagnetic phases with identical magnetic symmetry. At zero field, we find a spin-density wave that is suppressed at the critical field μ₀H* = 8 T. For H > H*, a spin-density phase emerges and shares many properties with the Q phase in CeCoIn₅. These results suggest that the magnetic instability is not magnetically driven, and we propose that it is driven by a modification of superconducting condensate at H*.

Exotic magnetic states in Pauli-limited superconductors

Magnetism and superconductivity compete or interact in complex and intricate ways. Here we review the special case where novel magnetic phenomena appear due to superconductivity, but do not exist without it. Such states have recently been identified in unconventional superconductors. They are different from the mere coexistence of magnetic order and superconductivity in conventional superconductors, or from competing magnetic and superconducting phases in many materials. We describe the recent progress in the study of such exotic magnetic phases, and articulate the many open questions in this field.

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.

Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}

The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.