Non-Fermi liquid regimes with and without quantum criticality in Ce1−xYbxCoIn5 Tao Hua,1, Yogesh P. Singha,1, Lei Shub, Marc Janoschekb, Maxim Dzeroa, M. Brian Mapleb,2, and Carmen C. Almasana,2 aDepartment of Physics, Kent State University, Kent, OH 44242; and bDepartment of Physics, University of California at San Diego, La Jolla, CA 92903 Contributed by M. Brian Maple, March 20, 2013 (sent for review September 12, 2012) One of the greatest challenges to Landau’s Fermi liquid theory—the particular, to determine the degree to which quantum criticality standard theory of metals—is presented by complex materials with and SC are coupled to each other. strong electronic correlations. In these materials, non-Fermi liquid To uncover the field-induced QCP and its evolution on Yb transport and thermodynamic properties are often explained by the concentration, we study the magnetic field (H) and temperature presence of a continuous quantum phase transition that happens at (T) dependence of the transverse ðH⊥abÞ in-plane magneto- Δρ⊥=ρ ≡ ½ρ⊥ð Þ − ρ ð Þ=ρ ð Þ ≤ a quantum critical point (QCP). A QCP can be revealed by applying resistivity (MR), a a a H a 0 a 0 , for H 14 T pressure, magnetic field, or changing the chemical composition. In and 2 ≤ T ≤ 70 K. Fig. 1A and its Inset display the field de- the heavy-fermion compound CeCoIn , the QCP is assumed to play Δρ⊥=ρ 5 pendence of a a measured at different temperatures for the a decisive role in defining the microscopic structure of both normal x = 0 and x = 0:40 samples, respectively. We note that the data for and superconducting states. However, the question of whether a these samples fall under two groups: (i) nonmonotonic field de- QCP must be present in the material’s phase diagram to induce non- pendence of MR (main panel) with positive MR at low fields and Fermi liquid behavior and trigger superconductivity remains open. negative quadratic MR at high fields, typical for x ≤ 0:20 and (ii) Here, we show that the full suppression of the field-induced QCP in negative and quadratic MR over the whole measured field range CeCoIn5 by doping with Yb has surprisingly little impact on both (Inset), typical behavior for the high Yb doping ð0:25 ≤ x ≤ 0:65Þ. unconventional superconductivity and non-Fermi liquid behavior. Positive MR in heavy-fermion materials at low fields marks the This implies that the non-Fermi liquid metallic behavior could be departure from the single-ion Kondo behavior and is determined a new state of matter in its own right rather than a consequence by the formation of the coherent Kondo lattice state for systems in of the underlying quantum phase transition. or close to their Fermi liquid ground state (18–23). The maximum in the MR of a Kondo lattice Fermi liquid at a certain field value is Kondo lattice | Kondo breakdown | gyromagnetic factor | a result of the competition between a T-independent residual re- composite pairing sistivity contribution that increases with increasing H,anda T-dependent term that decreases with increasing H (23, 24). Thus, he heavy-fermion material CeCoIn5 is a prototypical system in in conventional Kondo lattice systems, the peak in the field- Twhich strong interactions between conduction and pre- dependent MR moves toward lower H with increasing T because dominantly localized f electrons give rise to a number of remark- a lower field is required to break the Kondo lattice coherence. able physical phenomena (1, 2). Unconventional superconductivity To determine the nature of the positive MR in Ce1−xYbxCoIn5 (SC) emerges in CeCoIn5 out of a metallic state with non-Fermi for x ≤ 0:20, we extract the temperature dependence of the liquid (NFL) properties: linear temperature dependence of re- peak ðHmaxÞ in the field-dependent MR and plot these data in sistivity below 20 K, logarithmic temperature dependence of the Fig. 1B. This figure shows that Hmax vs. T of the x ≤ 0:20 samples Sommerfeld coefficient, and divergence of low-temperature mag- is nonmonotonic, with a maximum around 20 K, and a linear netic susceptibility (3–6). These anomalies disappear beyond behavior at low-T values. The positive MR measured at T > 20 K fi a critical value of the magnetic eld and the system recovers its [for which HmaxðTÞ decreases with increasing T] could reflect the Fermi liquid properties. The crossover from NFL to Fermi liquid presence of the coherent Kondo lattice state at low field values behavior is thought to be governed by a quantum critical point as discussed in the previous paragraph. In contrast, the behavior (QCP), which separates paramagnetic and antiferromagnetic (AFM) below 20 K is strikingly different from what one would expect for phases and is located in the superconducting phase (7, 8). Neu- conventional Kondo lattice systems. The increase of Hmax with tron-scattering studies (9) and more recent measurements of the increasing T at these lower temperatures had previously been vortex-core dissipation through current–voltage characteristics (10) observed in CeCoIn5 and has been attributed to field quenching provide direct evidence for an AFM QCP in CeCoIn5 that could of the AFM spin fluctuations responsible for the NFL behavior fi be accessed by tuning the system via magnetic eld or pressure. (25). Therefore, we conclude that the positive MR measured at Nevertheless, a growing number of f-electron systems do not T < 20 K in Ce1−xYbxCoIn5 with x ≤ 0:20 reflects the dominant conform with this QCP scenario; for example, the NFL behavior role played by the AFM quantum spin fluctuations. and/or SC in some systems occurs in the absence of an obvious An important next goal is to identify the H associated with – QCP QCP (11 14). An intriguing candidate is the alloy Yb-doped these quantum fluctuations. One option is to extrapolate the low CeCoIn that exhibits an unconventional T − x phase diagram 5 temperature linear HmaxðTÞ behavior to T = 0 K and identify without an apparent QCP, whereas the onset of coherence in the this Hmaxð0Þ with HQCP. However, because there is a certain Kondo lattice and the superconducting transition temperature Tc error associated with the determination of Hmax, we adopted are only weakly dependent on Yb concentration and prevail for a more accurate procedure to unambiguously determine HQCP doping up to x = 0:65 (15). However, the presence of a QCP in the parent CeCoIn5 compound and the logarithmic temperature fi dependence of the normal state Sommerfeld coef cient in lightly Author contributions: T.H., Y.P.S., L.S., M.J., M.D., M.B.M., and C.C.A. designed research; doped Ce1−xYbxCoIn5 crystals (16) show that this system is in the T.H., Y.P.S., L.S., M.J., M.D., M.B.M., and C.C.A. performed research; T.H. and Y.P.S. ana- vicinity to a QCP. Therefore, we are presented with the re- lyzed data; and T.H., Y.P.S., L.S., M.J., M.D., M.B.M., and C.C.A. wrote the paper. markable opportunity to elucidate the nature of the NFL be- The authors declare no conflict of interest. havior and unconventional SC in such a system, to search for 1T.H. and Y.P.S. contributed equally to this work. fi possible QCPs, and to determine the speci c role the QCP plays 2To whom correspondence may be addressed: [email protected] or calmasan@kent. in defining the low-temperature properties of this material and, in edu. 7160–7164 | PNAS | April 30, 2013 | vol. 110 | no. 18 www.pnas.org/cgi/doi/10.1073/pnas.1305240110 Downloaded by guest on September 24, 2021 A B The experimental technique used to determine HQCP also per- mits the determination of the gyromagnetic factor g. There is a significant change in the value of the g factor at the QCP. For CeCoIn5, this change is from g ≈ 2:2(g factor of free electrons in a metal) just below HQCP to g ≈ 1:3 just above HQCP. Similarly, for the x = 0:10 sample, the change is from g ≈ 2:5 just below HQCP to g ≈ 1:0 just above HQCP. The experimentally observed changes in the g factor reflect the transformations that the electronic system undergoes with the change in the external magnetic field. There- fore, we conclude that for H < HQCP the conduction electrons are only weakly coupled to the local spins (i.e., there is a small amount of admixture between the f-electron and the conduction-electron states). However, for H > HQCP, given that the values of 1.3 and 1.0 are only slightly larger then the value of g ≈ 0:83 for the crystal field configuration of Ce ions (27), the conduction states are strongly hybridized with the f states because the AFM fluctuations between C the local moments are suppressed, which is reflected in the re- duction in the value of the g factor (28). The change in the value of g at HQCP can be interpreted using the phenomenological theory of “Kondo breakdown” at HQCP (28). Within this theory, the changes in the g factor are governed by the changes in the size of the Fermi surface: larger values of the g factor correspond to a small Fermi surface so that the conduction electrons are effectively decoupled from the localized f states. In the opposite limit of smaller g values, the Fermi surface is large, reflecting the strong coupling between the conduction and f electrons. More importantly, the jump in the A fi Δρ⊥=ρ Fig.