Research ArticleCONDENSED MATTER PHYSICS

Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa2Cu3Oy

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Science Advances  05 Jan 2018:
Vol. 4, no. 1, eaao5235
DOI: 10.1126/sciadv.aao5235
  • Fig. 1 Dependence of the LF exponential relaxation rate λLF(HL) on LF HL in YBa2Cu3Oy.

    (A) y = 6.72, T = 80 K. (B) y = 6.77, T = 85 K. (C) y = 6.83, T = 93 K. Curves: Fits of Eq. 1 to the data. A fit for y = 6.72 using Eq. 1 with τc fixed at one order larger than the optimal fit result [τc = 5 (2) ns] is plotted in (A) (dashed curve) for comparison of fit quality.

  • Fig. 2 Temperature dependence of the dynamic muon relaxation rate λ in YBa2Cu3Oy.

    (A) y = 6.72, LF HL = 0. (B) y = 6.72, μ0HL = 4 mT. (C) y = 6.77, μ0HL = 4 mT, (D) y = 6.95, HL = 0. The pseudogap onset temperature T* is shown for each doping.

  • Fig. 3 Phase diagram of pseudogap and charge-density-wave/charge inhomogeneity onset temperatures in YBa2Cu3Oy.

    Red diamonds: Temperatures Tmag of maxima in μSR exponential relaxation rates (Fig. 2). Open green squares: Pseudogap temperatures T* from polarized neutron diffraction (5, 6). Open blue triangles: T* from THz birefringence (7). Pink pentagons: T* from resonant ultrasound (33). Orange circles: T* from second harmonic generation (8). Green stars: T* from magnetic torque (9). Magenta left triangles: Charge-density-wave (CDW) onset temperatures TCDW from NMR (20). Filled blue triangle: TCDW from nuclear quadrupole resonance (NQR) (43). Black squares: TCDW from Hall effect (53). Blue circle: TCDW from high-energy x-ray diffraction (54). Black circles: Onset of “charge inhomogeneity” (CDW or lattice change) from μSR experiments (14). Gray points: Superconducting transition temperatures. Inset: Doping dependences of the square root Embedded Image of the polarized neutron diffraction cross section (37) and the rms magnitude Embedded Image of the fluctuating local field (Table 1).

  • Fig. 4 Characterization data from YBa2Cu3Oy single crystals.

    (A) Magnetization of YBa2Cu3Oy, y = 6.72, 6.77, 6.83, and 6.95, showing sharp superconducting transitions. (B) Temperature dependence of electrical resistivity ρab for y = 6.77 showing a deviation from linearity. (C) Temperature dependence of the deviation Δρab from linear resistivity for y = 6.77. The deviation sets in below T* = 156 K, which is consistent with reported results (50).

  • Table 1 Correlation times τc and rms muon local fields Embedded Image from muon spin relaxation rates in YBa2Cu3Oy.
    yTemperature (K)τc(ns)Embedded Image (mT)
    6.72805(2)0.92(19)
    6.778510(3)0.87(10)
    6.839325(10)0.37(6)
  • Table 2 IRSDs of Embedded Image and relaxation rate maxima near Tmag from muon spin relaxation rates in YBa2Cu3Oy.
    yEmbedded ImageRelaxation rate maxima (Fig. 2)
    IRSDHL (mT)No. of pointsIRSD
    6.724.8074.5
    6.724113.8
    6.778.74155.2
    6.836.2
    6.95063.9
    Cumulative11.78.8

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/1/eaao5235/DC1

    section S1. Muon relaxation functions

    section S2. Control experiments

    section S3. Temperature dependence of static Gaussian KT relaxation rate ΔZF(T)

    section S4. Muon hopping, superconductivity

    section S5. Superconducting fluctuations

    section S6. High-temperature relaxation

    fig. S1. ZF relaxation of the muon asymmetry Aμ(t) in YBa2Cu3O6.72.

    fig. S2. Time evolution of the positron count rate asymmetry Aμ at various temperatures and fields in single-crystal YBa2Cu3Oy.

    fig. S3. LF muon spin relaxation rates in silver samples.

    fig. S4. Fits of representative ZF-μSR spectra from YBa2Cu3O6.95 for ΔZF fixed and free.

    fig. S5. Temperature dependence of ZF exponential damping rate λZF and static Gaussian KT rate ΔZF for YBa2Cu3O6.95.

    fig. S6. Damped dynamic Gaussian KT fit of ZF data from YBa2Cu3O6.72.

    References (5558)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Muon relaxation functions
    • section S2. Control experiments
    • section S3. Temperature dependence of static Gaussian KT relaxation rate ΔZF(T)
    • section S4. Muon hopping, superconductivity
    • section S5. Superconducting fluctuations
    • section S6. High-temperature relaxation
    • fig. S1. ZF relaxation of the muon asymmetry Aμ(t) in YBa2Cu3O6.72.
    • fig. S2. Time evolution of the positron count rate asymmetry Aμ at various temperatures and fields in single-crystal YBa2Cu3Oy.
    • fig. S3. LF muon spin relaxation rates in silver samples.
    • fig. S4. Fits of representative ZF-μSR spectra from YBa2Cu3O6.95 for ΔZF fixed and free.
    • fig. S5. Temperature dependence of ZF exponential damping rate λZF and static Gaussian KT rate ΔZF for YBa2Cu3O6.95.
    • fig. S6. Damped dynamic Gaussian KT fit of ZF data from YBa2Cu3O6.72.
    • References (55–58)

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