Session Q16: Heavy Fermions - 1-1-5 Systems

Strong magnetic fluctuations in superconducting state of CeCoIn$_5$

We probe the magnetism inside the superconducting state of CeCoIn$_5$ by locally suppressing superconductivity and investigating the underlying normal state through current-voltage measurements under applied pressure and external magnetic field in the mixed state. We observe that the vortex core resistivity increases sharply with decreasing temperature ($T$) for $T < T_c$ and magnetic field. We attribute this result to the presence of critical spin fluctuations near the Neel temperature inside the vortex core. This behavior is greatly suppressed with increasing pressure, due to the suppressed antiferromagnetic order inside the vortex core. Using our experimental results we construct a three-dimensional phase diagram which provides a direct evidence for a quantum critical line inside the superconducting phase. An experimentally obtained explicit equation for the antiferromagnetic boundary inside the superconducting dome shows the close relationship between quantum criticality, antiferromagnetism, and superconductivity.   

Visualizing the Emergence of Heavy Fermions in a Kondo Lattice (Part I)

The interaction between magnetic moments and conduction electrons is at the heart of many phenomena in condensed matter physics, from the Kondo effect in magnetic alloys and nanostructures to superconductivity in strongly correlated systems. We use the scanning tunneling microscope (STM) to detect the emergence of these heavy excitations with lowering of temperature in a prototypical 115 family of Ce-based heavy fermion compounds. Experiments on different atomically terminated layers and their modeling are used to demonstrate the sensitivity of the tunneling process to the composite nature of these heavy quasiparticles, which arise from quantum entanglement of itinerant conduction and $f-$electrons. The momentum space electronic structure of those heavy excitations will be discussed in the next talk by Pegor Aynajian.   

Visualizing the Emergence of Heavy Fermions in a Kondo Lattice (Part II)

The development of low energy fermionic excitations with heavy mass in compounds with $f$-orbitals is one of the key concepts in the physics of correlated electronic states and fundamental to the mechanism of unconventional superconductivity in such systems. We use spectroscopic mapping with the scanning tunneling microscope (STM) to detect the emergence of these heavy excitations in the Ce-115 heavy fermion compounds. Scattering and interference of the heavy quasiparticles is used to resolve their energy-momentum structure and to extract their mass enhancement, which develops near the Fermi energy with decreasing temperature. This work is funded by a DOE-BES grant. Infrastructure at the Princeton Nanoscale Microscopy Laboratory are also supported by grants from NSF-DMR, Keck Foundation, and NSF-MRSEC. PA also acknowledges support of a fellowship through the PCCM funded by NSF MERSEC.   

Scanning tunneling microscopy studies of heavy fermion compound CeCo(In$_{1-x}$Cd$_{x})_{5}$

Heavy fermion materials, such as those forming in actinide- or lanthanide-based compounds, have a rich variety of phases from unconventional superconductivity to antiferromagnetism to possibly exotic and non-Fermi liquid states. Central to all these ground states is the interaction between the magnetic impurities and the conduction electrons. In the Ce-based heavy fermions compounds (e.g. CeCoIn$_{5})$, the ground state can be tuned by doping or isovalent substitution, for example, Cd doping tunes the system toward antiferromagnetism. We present scanning tunneling microscopy/spectroscopy.measurements on the Cd-doped CeCoIn$_{5}$ heavy fermion compounds as a function of temperature. These results will be analyzed within the context of how tunning the chemical structure impacts the formation of heavy electron band and various ground states of this material system.   

Magnetic penetration depth and skin depth study of superconductivity and quantum criticality in Ce$_{1-x}$R$_x$CoIn$_5$ (R=La and Nd)

A heavy fermion superconductor CeCoIn$_5$ shows different responses to Nd- or La- substitutions for Ce, with the former inducing static magnetic order coexisting with superconductivity for some concentrations. To understand the origin of the differences, we studied the temperature and field dependent in-plane magnetic penetration depth, $\lambda(T)$, in single crystals of (Ce,R)CoIn$_5$ (R=La, Nd). Measurements were performed with a tunnel diode resonator down to 50~mK in a dilution refrigerator, in magnetic field up to 14 T parallel to the $c$-axis. These low-temperature and high field measurements allowed for the exploration for the full domain of superconductivity and quantum criticality in the $T-H$ phase diagram. Some previously unreported features were observed and will be discussed from the point of view of measured differential magnetic susceptibility. Combined with the contact-less measurements of resistivity via normal-state skin depth, these measurements bring new insight into the interplay between superconductivity and magnetism as well as field-tuned quantum critical behavior of doped 115 systems.   

Quantum oscillations study of the Fermi-surface evolution in Yb-substituted CeCoIn$_{5}$

We report results of systematic de Haas-van Alphen (dHvA) studies on Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ single crystals with varying Yb concentrations $x$. For a low dilution of $x$ = 0.1, the well-documented Fermi surface and the heavy effective masses of CeCoIn$_{5}$ ($x = 0$) remain nearly unchanged. A clear change of the Fermi-surface topology becomes evident for high Yb concentrations of $x = 0.55$, and above. The effective masses are reduced considerably to values between 0.7 and 2.6 free electron masses. Nevertheless, the superconducting transition temperature $T_c$ and upper critical field $H_{\mathrm{c2}}$ are only weakly suppressed with $x$. The angular-resolved dHvA frequencies for YbCoIn$_{5}$ show a good agreement with our density functional theory band-structure calculation with localized 4$f$ electrons and an Yb valence of 2+, which has been used to constructed the Fermi surface.   

Field induced QCP in Yb-doped CeCoIn$_5$

We performed magnetoresistance and Hall effect measurements on Yb-doped CeCoIn$_5$. The longitudinal resistivity data measured in 14 T show that the onset of coherence in the dilute Kondo lattice remains robust with respect to Yb concentration. In addition, we find that the superconducting transition temperature is weakly suppressed with doping ($x\leq 0.2$). Our analysis of the magnetoresistance data allowed us to identify the magnetic field induced quantum critical point and its evolution upon doping. At high Yb concentrations, our Hall effect data point to a possible valence transition of Yb ions. At small doping, our results provide an insight into the nature of the interplay between quantum criticality, magnetism, and unconventional superconductivity, while the behavior of this system at high doping can be characterized by a subtle interplay between Kondo screening on Ce sites and strong valence fluctuations on Yb sites.   

Effect of local electronic tuning in CeCoIn$_{5}$

The relationship between quantum criticality ($QC$), non-Fermi-liquid ($nFl$) behavior and the emergence of unconventional superconductivity ($SC$) in the vicinity of an antiferromagnetic quantum critical point ($QCP$) is one of the important issues in strongly correlated electron physics. Here we report on the effect of electronic tuning on superconductivity and quantum criticality in CeCoIn$_{5}$ driven by electron (Pt and Sn) and hole doping (Hg). We show that both Pt and Sn doping have similar strong effect on superconductivity and push the system slightly away from the $QCP$. The sub-linear power law exponent, even at a high doping level (where the superconductivity is suppressed) could point to the formation of electronic inhomogeneity. Moreover, hole doping by Hg can tune the system back to the $QCP$ as demonstrated by an increase of $T_{c}$ (and subsequently the onset of AFM), a decrease of the coherence temperature $T^{*}$ and an increase of the power law coefficient $n$ stressing the importance of the interplay of electronic tuning and pair breaking effects.   

Doping effects of CeCo$_{1-x}$Ru$_{x}$In$_{5}$

CeCoIn$_{5}$ lies in close proximity to a QCP which can be tuned with chemical doping, pressure or magnetic field. In this work, single crystals of Ruthenium doped CeCoIn$_{5}$ were prepared by means of self-flux in Indium. The lattice structure of CeCo$_{1-x}$Ru$_{x}$In$_{5}$ was identified as tetragonal by powder XRD with slightly increasing lattice constants. The results of electrical resistivity down to 1.8 K reveals that both coherence (T*) and superconducting transition (Tc) temperatures are decreasing monotonically with increasing Ru doping. Antiferromagnetism is anticipated on the basis of both negative chemical pressure and hole doping. Transport and thermodynamic data will be compared and contrasted with results from Rh and Cd doping.   

Effect of Pressure on Superconductivity and the Kondo-Lattice Coherence Temperature in Ce$_{1-x}R_x$CoIn$_5$ with $R$ = Yb, Y, Gd

Generally, rare-earth substitution for Ce in the heavy fermion superconductor CeCoIn$_5$ suppresses superconductivity rapidly. However, it was recently reported that the correlated electron ground state of Ce$_{1-x}$Yb$_x$CoIn$_5$ is stabilized over an anomalously large range in $x$, perhaps because of cooperative valence fluctuations of the Ce and Yb ions. Motivated by this possibility, we studied the effect of applied pressure on the superconducting critical ($T_c$) and Kondo-lattice coherence ($T^*$) temperatures of Ce$_{1-x}R_x$CoIn$_5$ with $R$ = Yb, Y, and Gd in order to compare the effect of Yb substitution with other magnetic and non-magnetic rare-earth ion substitutions. We performed electrical resistivity measurements under pressures up to a maximum of $\sim$2.3 GPa in a piston-cylinder clamped high pressure cell using a 50:50 mixture of $n$-pentane and isoamyl alcohol for the pressure transmitting medium. It was found that the variations of $T_c$ and $T^*$ in Ce$_{1-x}R_x$CoIn$_5$ under pressure were approximately independent of $R$. This result implies that the effect of pressure is independent of the magnetic configuration of the rare-earth ion being introduced.   

Antiferromagnetic Order in Pauli-Limited Unconventional Superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn5. We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.   

Staggered moments in the vortex cores of CeCoIn$_5$

Our previous nuclear magnetic resonance measurements revealed that magnetic field can induce an exotic superconducting phase, characterized by the presence of strong antiferromagnetic fluctuations. In the low field superconducting state, NMR spectra are determined by the inhomogeneous field distribution of a vortex lattice. In the exotic superconducting phase the NMR spectra broaden well beyond what is expected on the basis of the vortex lattice distribution. Here we explore the possibility that this extra broadening of the NMR spectra arises from the staggered magnetization induced locally around the vortex cores.   

Knight Shift anomaly in anti-ferromagnetic Heavy Fermion, CeRhIn$_{5}$

Since their discovery, the CeMIn$_{5}$ (M=Ir, Rh, Co) class of heavy fermion superconductors has attracted a lot of attention for their unusual properties. These compounds all have a scaling behavior which Nakatsuji et al (NPF) proposed is best explained by a two-fluid model. Below a characteristic temperature T*, the f-moments delocalize and form a coherent state with the conduction electrons, similar to super-fluid $^{4}$He. One of the central questions in the field is which energy scale correlates with the onset of coherence, T$_{Kondo}$ or T$_{RKKY}$. We will present new data on the Knight Shift anomaly in CeRhIn$_{5}$ which allows us to learn about the spin correlations as we approach the coherent state. By comparing the Knight shift anomaly in the three cousin compounds, we can explore how the characteristic energy scales of these materials change as we transition from a superconducting to an anti-ferromagnetic ground state.   

Strong suppression of superconductivity and Kondo coherence by Yb substitution in CeCoIn$_{5}$ epitaxial films

One of the important issues in strongly correlated electron system is the relationship between unconventional superconductivity and quantum criticality. Among them, the heavy-fermion superconductor CeCoIn$_{5}$ is a key material situated near an antiferromagnetic quantum critical point. When rare-earth ions are substituted for Ce, superconductivity and Kondo-lattice coherence are usually suppressed, but it has been recently pointed out from bulk studies that Yb substitution may be distinguished because of its valence instability. Here we report our recent study on Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ epitaxial thin films grown by the molecular beam epitaxy, which have high homogeneity. We find that the superconducting transition temperature is suppressed with increasing x much more rapidly than the previous bulk results, and that the coherence temperature is suppressed concurrently. We also observe a systematic reduction of the low-temperature Hall coefficient magnitude with x, establishing that the antiferromagnetic fluctuations fade even by the Yb substitutions.   

Extremely strong-coupling superconductivity in artificial two-dimensional Kondo lattices

Superconductivity with the strongest electron correlations is realized in heavy-fermion system, where almost all of the compounds have three-dimensional nature. It had remained an unanswered question whether superconductivity would persist on reducing the dimensionality of these materials. We succeeded in observing superconductivity in the system of heavy electrons confined within a two dimensional square lattice of Ce atoms, which was realized by fabricating epitaxial superlattices built of alternating layers of heavy-fermion CeCoIn$_{5}$ and conventional metal YbCoIn$_{5}$[1]. The field-temperature phase diagram of the superlattices exhibits a striking enhancement of the upper critical field relative to the transition temperature. This implies that the force holding together the superconducting electron pairs takes on an extremely strong-coupled nature as a result of two-dimensionalization. [1]Mizukami \textit{et al}., Nature Phys. \textbf{7}, 849 (2011).