Reduced dimensionality offers a crucial information in deciding the type of the quantum ground state in heavy fermion materials. Here we have examined stoichiometric CeCo$_{2}$Ga$_{8}$ compound, which crystallizes in a quasi-one-dimensional crystal structure with Ga-Ce-Co chains along the $c$-axis. The low-temperature behavior of magnetic susceptibility ($χ\sim-\ln T$), heat capacity ($C_p/T\sim-\ln T$), and resistivity ($ρ\sim T^{n}$) firmly confirm the non-Fermi liquid ground state of CeCo$_{2}$Ga$_{8}$. We studied the low-energy spin dynamics of CeCo$_{2}$Ga$_{8}$ compound utilizing zero field (ZF-) and longitudinal field (LF-) muon spin relaxation ($μ$SR) measurements. ZF-$μ$SR measurement reveals the absence of long-range magnetic ordering down to 70 mK, and interestingly below 1 K, the electronic relaxation rate sharply rises, intimating the appearance of low energy quantum spin fluctuations in CeCo$_{2}$Ga$_{8}$.
We report extensive studies on the CeCo$_{1-x}$Fe$_{x}$Ge$_3$ alloys, which show quantum critical point (QCP) due to damping the antiferromagnetic order in CeCoGe$_3$ down to 0 K by doping with the paramagnetic CeFeGe$_3$ compound. The presence of QCP is confirmed by detecting the non-Fermi liquid behavior (NFL) using a wide range of the experimental methods: magnetic susceptibility, specific heat, electrical resistivity, magnetoresistance, and thermoelectric power. In the case of the thermoelectric power we find a clear enhancement of the Seebeck coefficient for $x$ around 0.6, i.e. in the ne…
Dimensionality plays an essential role in determining the anomalous non-Fermi liquid properties in heavy fermion systems. So far most heavy fermion compounds are quasi-two-dimensional or three-dimensional. Here we report the synthesis and systematic investigations of the single crystals of the quasi-one-dimensional Kondo lattice CeCo$_2$Ga$_8$. Resistivity measurements at ambient pressure reveal the onset of coherence at $T^*\approx 20\,$K and non-Fermi liquid behavior with linear temperature dependence over a decade in temperature from 2 K to 0.1 K. The specific heat increases logarithmically…
Structural, magnetic and thermal measurements performed on CeCo{1-x}Fe{x}Si alloys are reported. Three regions can be recognized: i) Co-rich (x < 0.20) with a decreasing long range antiferromagnetic order which vanishes at finite temperature, ii) an intermediate region (0.20 < x < 0.30) showing a broad magnetic anomaly (C_A) in specific heat and iii) the non-magnetic region progressively changing from a non-Fermi-liquid type behavior towards a Fermi liquid one as Fe concentration increases. The C_A anomaly emerges as an incipient contribution above T_N already at x = 0.10, which indicates that…
We report the results of de-Haas-van-Alphen (dHvA) measurements in Cd doped CeCoIn$_5$ and LaCoIn$_5$. Cd doping is known to induce an antiferromagnetic order in the heavy fermion superconductor CeCoIn$_5$, whose effect can be reversed with applied pressure. We find a slight but systematic change of the dHvA frequencies with Cd doping in both compounds, reflecting the chemical potential shift due to the addition of holes. The frequencies and effective masses are close to those found in the nominally pure compounds with similar changes apparent in the Ce and La compounds with Cd substitution. W…
We report detailed very low temperature resistivity measurements on the heavy fermion compounds Ce_{1-x}La_{x}CoIn5 (x=0 and x=0.01), with current applied in two crystallographic directions [100] (basal plane) and [001] (perpendicular to the basal plane) under magnetic field applied in the [001] or [011] direction. We found a Fermi liquid (ρ\propto T^{2}) ground state, in all cases, for fields above the superconducting upper critical field. We discuss the possible location of a field induced quantum critical point with respect to Hc2(0), and compare our measurements with the previous reports i…
The effect of off-plane impurity on superconductivity and non-Fermi-liquid (NFL) behavior in the layered heavy-fermion compound CeCo$_{1-x}$Ni$_x$In$_5$ is investigated by specific heat, magnetization, and electrical resistivity measurements. These measurements reveal that the superconducting (SC) transition temperature T$_c$ monotonically decreases from 2.3 K (x=0) to 0.8 K (x=0.20) with increasing x, and then the SC order disappears above x=0.25. At the same time, the Ni substitution yields the NFL behavior at zero field for x=0.25, characterized by the -ln T divergence in specific heat divi…
We report a detailed and comparative study of the single crystal CeCoInGa$_3$ in both experiment and theory. Resistivity measurements reveal the typical behavior of Kondo lattice with the onset temperature of coherence, $T^*\approx 50\,$K. The magnetic specific heat can be well fitted using a spin-fluctuation model at low temperatures, yielding a large Sommerfeld coefficient, $γ\approx172\,$mJ/mol K$^2$ at 6 K, suggesting that this is a heavy-fermion compound with a pronounced coherence effect. The magnetic susceptibility exhibits a broad field-independent peak at $T_χ$ and shows an obvious an…
We revisited the anisotropy of the heavy-fermion material CeCo$_2$Ga$_8$ by measuring the electrical resistivity and magnetic susceptibility along all the principal $\mathbf{a}$-, $\mathbf{b}$- and $\mathbf{c}$-axes. Resistivity along $\mathbf{c}$-axis ($ρ_c$) shows clear Kondo coherence below about 17 K, while both $ρ_{a}$ and $ρ_{b}$ remain incoherent down to 2 K. The magnetic anisotropy is well understood within the theoretical frame of crystalline electric field effect in combination with magnetic exchange interactions. We found the anisotropy ratio of these magnetic exchange interactions,…
One of the greatest challenges to Landau's Fermi liquid theory - the standard theory of metals - is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic properties are often explained by the presence of a continuous quantum phase transition which happens at a quantum critical point (QCP). A QCP can be revealed by applying pressure, magnetic field, or changing the chemical composition. In the heavy-fermion compound CeCoIn$_5$, the QCP is assumed to play a decisive role in defining the microscopic structure of both n…
The high field superconducting state in CeCoIn5 has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic c-axis close to the upper critical field Hc2 = 4.97 T. At magnetic fields >= 4.8 T the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate sigma reveal paramagnetic spin fluctuations in the field regime from 2 T < H < 4.8 T. In the normal s…
In the tetragonal heavy fermion system CeCoIn5 the unconventional superconducting state is probed by means of muon spin rotation. The pressure dependence (0-1 GPa) of the basal-plane magnetic penetration depth (λ_a), the penetration depth anisotropy (γ=λ_c/λ_a) and the temperature dependence of 1/λ_i^2 (i=a,c) were studied in single crystals. A strong decrease of λ_a with pressure was observed, while γand λ_i^2(0)/λ_i^2(T) are pressure independent. A linear relationship between 1/λ_a^2(270 mK) and Tc was also found. The large decrease of λ_a with pressure is the signature of an increase of the…
The appearance of spin-density-wave (SDW) magnetic order in the low-temperature and high-field corner of the superconducting phase diagram of CeCoIn$_5$ is unique among unconventional superconductors. The nature of this magnetic $Q$ phase is a matter of current debate. Here, we present the thermal conductivity of CeCoIn$_5$ in a rotating magnetic field, which reveals the presence of an additional order inside the $Q$ phase that is intimately intertwined with the superconducting $d$-wave and SDW orders. A discontinuous change of the thermal conductivity within the $Q$ phase, when the magnetic f…
We performed low-temperature de Haas-van Alphen (dHvA) effect measurements on a Ce$_{1-x}$Nd$_x$CoIn$_5$ series, for x = 0.02, 0.05, 0.1, and 1, down to T = 40 mK using torque magnetometry in magnetic felds up to 35 T. Our results indicate that a Fermi-surface (FS) reconstruction occurs from a quasi-two-dimensional (2D) topology for Nd-2% to a rather three-dimensional (3D) for Nd-5%, thus reducing the possibility of perfect FS nesting. The FS evolves further with increasing Nd content with no observed divergence of the effective mass between Nd-2% and 10%, consistent with the crossing of a spi…
In the generic phase diagram of heavy fermion systems, tuning an external parameter such as hydrostatic or chemical pressure modifies the superconducting transition temperature. The superconducting phase forms a dome in the temperature-tuning parameter phase diagram, which is associated with a maximum of the superconducting pairing interaction. Proximity to antiferromagnetism suggests a relation between the disappearance of antiferromagnetic order and superconductivity. We combine muon spin rotation, neutron scattering, and x-ray absorption spectroscopy techniques to gain access to the magneti…
The formation of heavy fermion bands can occur by means of the conversion of a periodic array of local moments into itinerant electrons via the Kondo effect and the huge consequent Fermi-liquid renormalizations. Leggett predicted for liquid $^3$He that Fermi-liquid renormalizations change in the superconducting state, leading to a temperature dependence of the London penetration depth~$Λ$ quite different from that in the BCS theory. Using Leggett's theory, as modified for heavy fermions, it is possible to extract from the measured temperature dependence of $Λ$ in high quality samples both Land…
We report Knight shift experiments on the superconducting heavy electron material CeCoIn$_5$ that allow one to track with some precision the behavior of the heavy electron Kondo liquid in the superconducting state with results in agreement with BCS theory. An analysis of the $^{115}$In nuclear quadrupole resonance (NQR) spin-lattice relaxation rate $T_1^{-1}$ measurements under pressure reveals the presence of 2d magnetic quantum critical fluctuations in the heavy electron component that are a promising candidate for the pairing mechanism in this material. Our results are consistent with an an…
Recent progress in the fabrication techniques of superlattices (SLs) has made it possible to sandwich several-layer-thick block layers (BLs) of heavy-fermion superconductor CeCoIn5 between conventional-metal YbCoIn5 BLs or spin-density-wave-metal CeRhIn5 BLs of a similar thickness. However, the magnetic state in each BL, particularly at the interface, is not yet understood, as experimental techniques applicable to the SL system are limited. Here, we report measurements of 59Co nuclear magnetic resonance, which is a microscopic probe of the magnetic properties inside the target BLs. In the CeCo…
Superconductivity and fractionalized magnetic excitations in CeCoIn5
Oak Ridge National Laboratory（橡树岭国家实验室）；The University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Harvard University（哈佛大学）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）；Department of Physics, Brookhaven National Laboratory（布鲁海文国家实验室物理系）；University of Edinburgh（爱丁堡大学）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Quantum Condensed Matter Division and Shull-Wollan Center, Oak Ridge National Laboratory（橡树岭国家实验室量子凝聚态物质部和舒尔-沃兰中心）
This paper demonstrates the anisotropic response of quantum critical fluctuations with respect to the direction of the magnetic field $B$ in Ni-doped CeCoIn$_5$ by measuring the magnetization $M$ and specific heat $C$. The results show that $M/B$ at $B=0.1\ {\rm T}$ for both the tetragonal $c$ and $a$ directions exhibits $T^{-η}$ dependencies, and that $C/T$ at $B=0$ follows a $-\ln T$ function, which are the characteristics of non-Fermi-liquid (NFL) behaviors. For $B\,||\,c$, both the $M/B\propto T^{-η}$ and $C/T \propto -\ln T$ dependencies change into nearly temperature-constant behaviors b…
Quantum criticality in the normal and superconducting state of the heavy-fermion metal CeCoIn$_5$ is studied by measurements of the magnetic Grüneisen ratio, $Γ_H$, and specific heat in different field orientations and temperatures down to 50 mK. Universal temperature over magnetic field scaling of $Γ_H$ in the normal state indicates a hidden quantum critical point at zero field. Within the superconducting state the quasiparticle entropy at constant temperature increases upon reducing the field towards zero, providing additional evidence for zero-field quantum criticality.
An incommensurate spin density wave ($Q$ phase) confined inside the superconducting state at high basal plane magnetic field is an unique property of the heavy fermion metal CeCoIn$_5$. The neutron scattering experiments and the theoretical studies point out that this state come out from the soft mode condensation of magnetic resonance excitations. We show that the fixation of direction of antiferromagnetic modulations by a magnetic field reported by Gerber et al., Nat. Phys. {\bf 10}, 126 (2014) is explained by spin-orbit coupling. This result, obtained on the basis of quite general phenomeno…
We report on the anisotropic properties of Pauli-limited superconductivity (SC) and antiferromagnetism (AFM) in the solid solutions CeCo(In_{1-x}Zn_x)_5 (x<=0.07). In CeCo(In_{1-x}Zn_x)_5, the SC transition temperature T_c is continuously reduced from 2.3 K (x=0) to ~1.4 K (x=0.07) by doping Zn, and then the AFM order with the transition temperature of T_N~2.2 K develops for x larger than ~0.05. The present thermal, transport and magnetic measurements under magnetic field B reveal that the substitution of Zn for In yields little change of low-temperature upper critical field μ_0H_{c2} for both…
The implications of the spin exciton mechanism are exposed in the context of a Spin Density Wave (SDW) instability occurring inside the superconducting phase of a layered heavy electron compound. In this model a magnetic field serves as a tuning parameter bringing the system to the point where the transverse spin correlations are enhanced due to dx2 -y2 -wave superconductivity and induces an instability to a phase with coexisting superconductivity and SDW order. The model considers electrons in a crystal with antiferromagnetic interactions and provides restrictions on the Fermi surface charact…
We present core level non-resonant inelastic x-ray scattering (NIXS) data of the heavy fermion compounds CeCoIn$_5$ and CeRhIn$_5$ measured at the Ce $N_{4,5}$-edges. The higher than dipole transitions in NIXS allow determining the orientation of the $Γ_7$ crystal-field ground-state orbital within the unit cell. The crystal-field parameters of the Ce$M$In$_5$ compounds and related substitution phase diagrams have been investigated in great detail in the past; however, whether the ground-state wavefunction is the $Γ_7^+$ ($x^2\,-\,y^2$) or $Γ_7^-$ ($xy$ orientation) remained undetermined. We sh…
We demonstrate a close connection between observed field-induced antiferromagnetic (AFM) order and quantum critical fluctuation (QCF) in the Zn7%-doped heavy-fermion superconductor CeCoIn5. Magnetization, specific heat, and electrical resistivity at low temperatures all show the presence of new field-induced AFM order under the magnetic field B of 5-10 T, whose order parameter is clearly distinguished from the low-field AFM phase observed for B < 5 T and the superconducting phase for B < 3 T. The 4f electronic specific heat divided by the temperature, C_e/T, exhibits -lnT dependence at B~10 T …
Incommensurate spin fluctuations in one-dimensional Kondo metal CeCo2Ga8
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Cornell University（康奈尔大学）；Brookhaven National Lab（布鲁克海文国家实验室）；Japan Atomic Energy Agency（日本原子能机构）
Employing the elemental sensitivity of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), we study the valence and magnetic order in the heavy fermion superconductor CeCoIn$_5$. We probe spin population of the f-electrons in Ce and d-electrons in Co as a function of temperature (down to 0.1 K) and magnetic field (up to 6 T). From the XAS we find a pronounced contribution of Ce$^{4+}$ component at low temperature and a clear temperature dependence of the Ce valence below 5 K, suggesting enhanced valence fluctuations, an indication for the presence of a nearby quan…
In this chapter we discuss the physical properties of a particular family of non-centrosymmetric superconductors belonging to the class heavy-fermion compounds. This group includes the ferromagnet UIr and the antiferromagnets CeRhSi3, CeIrSi3, CeCoGe3, CeIrGe3 and CePt3Si, of which all but CePt3Si become superconducting only under pressure. Each of these superconductors has intriguing and interesting properties. We first analyze CePt3Si, then review CeRhSi3, CeIrSi3, CeCoGe3 and CeIrGe3, which are very similar to each other in their magnetic and electrical properties, and finally discuss UIr. …
The Ce compounds CeCoIn$_5$ and CeRhIn$_5$ are ideal model systems to study the competition of antiferromagnetism (AF) and superconductivity (SC). Here we discuss the pressure--temperature and magnetic field phase diagrams of both compounds. In CeRhIn$_5$ the interesting observation is that in zero magnetic field a coexistence AF+SC phase exist inside the AF phase below the critical pressure $p_{\rm c}^\star \approx 2$ GPa. Above $p_{\rm c}^\star$ AF is suppressed in zero field but can be re-induced by applying a magnetic field. The collapse of AF under pressure coincides with the abrupt chang…
We calculate the low temperature one-particle scattering rate and the specific heat in a weakly disordered metal close to a quantum critical point. To lowest order in the fluctuation potential, we obtain typical Fermi-liquid results proportional to T^2 and T respectively, with prefactors which diverge as a power law of the control parameter upon approaching the critical point. The Kadowaki-Woods ratio is shown to be independent of the control parameter only for the case of 3-D FM fluctuations. Our work is relevant for experiments on CeCoIn$_5$ and Sr_3Ru_2O_7.
We report low-temperature specific heat measurements in magnetic fields up to 12 T applied parallel and perpendicular to the tetragonal c-axis of the heavy fermion superconductor Ce$_2$PdIn$_8$. In contrast to its quasi-two-dimensional (2D) relative CeCoIn$_5$, the system displays an almost isotropic upper critical field. While there is no indication for a FFLO phase in Ce$_2$PdIn$_8$, the data suggest a smeared weak first-order superconducting transition close to $H_{c2}\approx 2$ T. The normal state electronic specific heat coefficient displays logarithmically divergent behavior, comparable …
The in-plane electrical resistivity, rho, and thermal conductivity, kappa, of the heavy-fermion superconductor CeIrIn5 were measured down to 40mK in magnetic fields up to 11 T applied along the c axis. For all fields above Hc2=4T of filamentary superconductivity, we find that the ratio of heat and charge conductivities in the T to 0 limit obeys the Wiedemann-Franz law, kappa/T=L0/rho, where L0 = 2.45*10^-8 WOhmK^-2 is the Sommerfeld value of the Lorenz number. The temperature-dependent parts of both the electrical and thermal resistivity,w = T/L0 kappa, follow the functional dependence expecte…
We calculate analytically the low temperature quasi-particle scattering rate, the conductivity, and the specific heat in weakly disordered metals close to a quantum critical point, via the use of a proper fluctuation potential $V(q,ω)$ between the quasi-particles. We obtain typical Fermi liquid results proportional to $T^2$ and $T$ respectively, with prefactors which diverge as power laws of the control parameter $a$ upon approaching the critical point. The Kadowaki-Woods ratio is shown to be independent of $a$ (possibly times a logarithmic dependence on $a$) only for the case of three-dimensi…
