Disorder in quantum critical superconductors

Journal name:
Nature Physics
Year published:
Published online

In four classes of materials—the layered copper oxides, organics, iron pnictides and heavy-fermion compounds—an unconventional superconducting state emerges as a magnetic transition is tuned towards absolute zero temperature, that is, towards a magnetic quantum critical point1 (QCP). In most materials, the QCP is accessed by chemical substitution or applied pressure. CeCoIn5 is one of the few materials that are ‘born’ as a quantum critical superconductor2, 3, 4 and, therefore, offers the opportunity to explore the consequences of chemical disorder. Cadmium-doped crystals of CeCoIn5 are a particularly interesting case where Cd substitution induces long-range magnetic order5, as in Zn-doped copper oxides6, 7. Applied pressure globally suppresses the Cd-induced magnetic order and restores bulk superconductivity. Here we show, however, that local magnetic correlations, whose spatial extent decreases with applied pressure, persist at the extrapolated QCP. The residual droplets of impurity-induced magnetic moments prevent the reappearance of conventional signatures of quantum criticality, but induce a heterogeneous electronic state. These discoveries show that spin droplets can be a source of electronic heterogeneity and emphasize the need for caution when interpreting the effects of tuning a correlated system by chemical substitution.

At a glance


  1. Pressure dependence of the specific heat of 1% Cd-doped CeCoIn5 and CeRhIn5.
    Figure 1: Pressure dependence of the specific heat of 1% Cd-doped CeCoIn5 and CeRhIn5.

    a, Specific heat divided by temperature for 1% Cd-doped CeCoIn5 in zero applied field and at pressures of 0.25 (black symbols), 0.60 (red), 0.98 (blue) and 1.21GPa (orange). b, Specific heat divided by temperature for CeRhIn5 at 1.15 (black), 1.51 (red), 1.71 (blue) and 2.05GPa (orange). In CeRhIn5, the spin entropy of Ce 4f local moments is transferred completely to the superconducting phase when magnetism is suppressed, resulting in a large ΔC/CN>4 at Tc (ref. 18). The qualitative difference between CeRhIn5 and Cd-doped CeCoIn5 exists even though the ordered magnetic moment in both is comparable, ~0.7μB. cf, Dependence on temperature of the specific heat divided by temperature of 1% Cd-doped CeCoIn5 under magnetic fields and pressures. c, 0.25GPa at magnetic fields of 0 (black), 1.0 (red), 3.0 (green), 5.0 (blue) and 9.0T (orange). d, 0.6GPa at magnetic fields of 0 (black), 1.0 (red), 3.0 (blue) and 5.0T (orange). e, 0.98GPa at magnetic fields of 0 (black), 2.0 (red), 4.0 (green), 5.0 (blue) and 5.5T (orange). f, 1.54GPa at magnetic fields of 0 (black), 3.0 (red), 4.0 (green), 5.0 (blue) and 6.0T (orange). Solid and dashed arrows indicate superconducting and antiferromagnetic transition temperatures, respectively. Values of C/T for different pressures were normalized against each other with an assumption that the entropy recovered at 10K is the same for all pressures within each compound. This assumption is proved for Cd-doped CeCoIn5 as a function of Cd content at atmospheric pressure5.

  2. Electrical resistivity of 1% Cd-doped CeCoIn5 under pressure.
    Figure 2: Electrical resistivity of 1% Cd-doped CeCoIn5 under pressure.

    a, Contour map of the electrical resistivity (ρab) within the Ce–In plane plotted in the pressure–temperature plane. Tmax is a temperature where the resistivity reaches a maximum, and T* is the temperature below which the resistivity deviates from a T-linear dependence. An antiferromagnetic state coexists with superconductivity for P<0.5GPa. b, In-plane resistivity ρab as a function of temperature on a semi-logarithmic scale for representative pressures. Arrows mark the evolution of Tmax with pressure. The temperature Tmax at which ρ(T) is a maximum occurs at 34K at ambient pressure and increases linearly with increasing pressure, which is typical of strongly correlated Ce-based materials, such as pure CeCoIn5, and reflects a pressure-induced increase of the hybridization between ligand electrons and the periodic array of Ce 4f-electrons. c, Resistivity, with the residual T=0 value subtracted, divided by temperature, plotted against temperature for representative pressures. T* is marked by arrows.

  3. Spin-lattice relaxation rate of 1% Cd-doped CeCoIn5 under pressure.
    Figure 3: Spin-lattice relaxation rate of 1% Cd-doped CeCoIn5 under pressure.

    a115In NQR spectra of the In(1) site at ambient pressure. 115In NQR spectra of CeCoIn5 and 1% Cd-doped CeCoIn5 are shown in the upper and lower parts of the panel. Indium sites in the unit cell of CeCoIn5 are indicated in the inset. In the Cd-doped crystals, additional peaks B and C appear at higher frequencies, and the original peak A is broadened and moved slightly to higher frequency. b, Dependence on temperature of the spin-lattice relaxation rate 1/T1 of CeCo(In0.99Cd0.01)5. Solid lines are guides to the eyes for pressures of 1 bar (black), 0.36 (red), 0.61 (green), 1.04 (blue) and 1.51 GPa (orange). The overall decrease in 1/T1, even at high temperatures, is found in pristine CeCoIn5 (ref. 26). The inset shows 1/T1 at 4K as a function of pressure. Error bars describe the uncertainty in 1/T1. c, Schematic illustration of the dependence on pressure of the size of magnetic droplets. The Cd atoms that replace In in CeCoIn5 nucleate antiferromagnetic droplets surrounding the Cd site. The average distance between the droplets, which is approximately five lattice spacings at 0.75% Cd doping, is independent of pressure, but their spatial extent shrinks with pressure. For a pressure above Pc1 (the middle panel), the magnetic correlation length becomes shorter than inter-droplet spacing, leading to suppression of the long-ranged antiferromagnetic order. AFM, antiferromagnetic; SC, superconducting.


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Author information

  1. These authors contributed equally to this work

    • S. Seo &
    • Xin Lu


  1. Department of Physics, Sungkyunkwan University, Suwon 440-746, South Korea

    • S. Seo &
    • Tuson Park
  2. Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

    • Xin Lu,
    • J-X. Zhu,
    • R. R. Urbano,
    • E. D. Bauer,
    • V. A. Sidorov &
    • J. D. Thompson
  3. Center for Correlated Matter and Department of Physics, Zhejiang University, Hangzhou 310027, China

    • Xin Lu
  4. Instituto de Fisica ‘Gleb Wataghin’, Universidade Estadual de Campinas-SP, 13083-859, Brazil

    • R. R. Urbano
  5. Department of Physics, University of California, Davis, California 95616, USA

    • N. Curro
  6. Institute for High Pressure Physics, Russian Academy of Sciences, RU-142190 Troitsk, Moscow, Russia

    • V. A. Sidorov
  7. Department of Physics, University of California, Irvine, California 92697, USA

    • L. D. Pham &
    • Z. Fisk


All authors discussed the results and commented on the manuscript. S.S. and X.L. performed the measurements and contributed equally to this work. R.R.U., V.A.S. and N.C. performed and analysed NQR experiments. E.D.B., L.D.P. and Z.F. provided samples, J-X.Z. performed theoretical calculations and T.P. and J.D.T. wrote the manuscript with input from all authors.

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