Research ArticlePHYSICS

Quantum valence criticality in a correlated metal

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Science Advances  23 Feb 2018:
Vol. 4, no. 2, eaao3547
DOI: 10.1126/sciadv.aao3547
  • Fig. 1 Phase diagram of the emergent electronic phases of α-YbAlB4 with Fe doping.

    (A) Phase diagram of temperature (vertical axis) versus Fe concentration x (horizontal axis) for α-YbAl1−xFexB4 with the contour plot map of the power law exponent α = ∂ln(ρa(T) − ρa(0))/∂lnT of the a axis resistivity. TN denotes the AF Néel point determined by magnetization (closed circles), specific heat (closed squares), and resistivity (closed triangles). The broken vertical line indicates the critical concentration xc = 1.4% for the valence crossover and the first-order AF transition. (B) Doping dependence of the Yb valence estimated from hard x-ray photoemission spectroscopy (HAXPES) at 20 K (left axis) and doping dependence of the unit cell volume measured by powder x-ray diffraction at 273, 175, and 17 K (right axis). (C) HAXPES spectra of Yb 3d5/2 core level in YbAl1−xFexB4 with x = 1.3 and 4.2% (top) and the difference of these spectra from x = 1.3 to 4.2% (bottom). (D) Schematic phase diagram for the valence QC mechanism, which is shown as a function of temperature T, magnetic field B, and the chemical pressure P for an Yb-based system (8). Valence crossover (blue) and the AF order (green) are both shown. Valence crossover (magenta) and first-order valence transition (FOVT) (red) surface are virtually drawn below 0 K. Valence crossover surface (blue) evolves into a phase boundary due to a virtual FOVT in the negative temperature. The critical end line at the border between FOVT and the crossover surface touches 0 K, forming a quantum critical point (QCP). a.u. arbitrary units.

  • Fig. 2 Doping dependence of the thermodynamic properties of α-YbAl1−xFexB4.

    (A) T dependence of the c axis component of the DC susceptibility M/B for α-YbAl1−xFexB4 with various x and the nonmagnetic analog α-LuAl1−xFexB4. Both zero-field-cooling (ZFC) (open symbols) and field-cooling (FC) (closed symbols) sequences were used. (B) Temperature dependence of the 4f electronic contribution to the specific heat divided by T, C4f/T, which is obtained after subtracting the nonmagnetic contribution estimated using the specific heat of α-LuAlB4 (see the Supplementary Materials for details).

  • Fig. 3 Zero-field QC and its field suppression at xc = 1.4% in α-YbAl1−xFexB4.

    (A) Scaling observed for the magnetization M in the T < 2 K and B < 50 mT. The data can be fitted to the scaling function φ(t) = Λt(A + t2)n with t = T/B, a form chosen to satisfy the appropriate limiting behaviors in the FL regime (24). The solid line is the fitted data for β-YbAlB4 (24). The inset is the T dependence of the DC susceptibility M/B for xc in α-YbAl1−xFexB4 under various fields (solid line). Data at x = 4.2% under B = 3.5 T are also shown (broken line). (B) Contour plot of the power law exponent α = ∂ln(ρ(T) − ρ(0))/∂lnT of the a axis resistivity ρa(T) in the B-T phase diagram of α-YbAl1−xFexB4 at xc.

  • Fig. 4 Field-induced QC of the antiferromagnetism in α-YbAl1−xFexB4 (x = 4.2%).

    (A) Field-temperature phase diagram of the antiferromagnetism. Contour plot of the power law exponent α = ∂ln(ρ(T) − ρ(0))/∂lnT of the a axis resistivity ρa(T) in the B-T phase diagram of α-YbAl1−xFexB4 (x = 4.2%). The Néel points determined by the specific heat C (circles), magnetization M (diamonds), and the resistivity ρ (squares) measurements are shown. (B) T dependence of the DC susceptibility M/B under various fields close to the transition field BN. Both ZFC (open symbols) and FC (closed symbols) sequences were used. (C) Magnetization curve measured at T = 80 mK (right axis) and its field derivative ∂M/∂B (left axis). The broken line is calculated from scaling Eq. 1 using the parameters determined for the fitting to the data of α-YbAl1−xFexB4 at xc = 1.4%. Note that, here, the critical field Bc is shifted from zero field to BN ~ 3.5 T. (D) Magnetization divided by the magnetic field M/B at T = 80 mK as a function of B. The red arrow indicates BN = 3.5 T, where M/B starts to be suppressed with decreasing B. Consistently, the DC susceptibility exhibits bifurcation between FC and ZFC below BN, as shown in (B).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/2/eaao3547/DC1

    Supplementary text

    fig. S1. Yb 3d and Al 1s core level spectrum of α-YbAlB4.

    fig. S2. Yb 3d core level fitting for HAXPES data.

    fig. S3. Temperature dependence of the magnetic susceptibility obtained under a field of 0.1 T along the c axis for x = 0, 1.0, 1.4, and 1.7% and along the ab plane for x = 0 and 4.2%.

    fig. S4. Temperature dependence of the inverse magnetic susceptibility obtained under a field of 0.1 T along the c axis for x = 0, 1.0, 1.4, 1.7, and 4.2%.

    fig. S5. Fe density dependence of the lattice constant and its relation to the Yb valence change.

    fig. S6. Normalized powder x-ray diffraction data at around 400 peak for α-YbAl1−xFexB4 (x = 0.5, 1.3, 1.4, 1.7, and 2.2%), where the intensity and the scattering angle 2θ are normalized by those values at the main peak.

    fig. S7. Electron diffraction patterns of x = 0 for [001] direction at 300 and 14 K (top) and for [010] direction at 300 and 13 K (bottom).

    fig. S8. Electron diffraction patterns of x = 4.2% for [001] direction at 300 and 14 K (top) and for [3-10] direction at 300 and 13 K (bottom).

    fig. S9. The temperature dependence of the specific heat C divided by temperature T obtained at x = 0 and 1.4%.

    fig. S10. Anomalous power law temperature dependence of the a-axis resistivity at the zero-field quantum valence criticality and the field-induced antiferromagnetic instability.

    References (4149)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Yb 3d and Al 1s core level spectrum of α-YbAlB4.
    • fig. S2. Yb 3d core level fitting for HAXPES data.
    • fig. S3. Temperature dependence of the magnetic susceptibility obtained under a field of 0.1 T along the c axis for x = 0, 1.0, 1.4, and 1.7% and along the ab plane for x = 0 and 4.2%.
    • fig. S4. Temperature dependence of the inverse magnetic susceptibility obtained under a field of 0.1 T along the c axis for x = 0, 1.0, 1.4, 1.7, and 4.2%.
    • fig. S5. Fe density dependence of the lattice constant and its relation to the Yb valence change.
    • fig. S6. Normalized powder x-ray diffraction data at around 400 peak for α-YbAl1−xFexB4 (x = 0.5, 1.3, 1.4, 1.7, and 2.2%), where the intensity and the scattering angle 2θ are normalized by those values at the main peak.
    • fig. S7. Electron diffraction patterns of x = 0 for 001 direction at 300 and 14 K
      (top) and for 010 direction at 300 and 13 K (bottom).
    • fig. S8. Electron diffraction patterns of x = 4.2% for 001 direction at 300 and 14 K (top) and for 3-10 direction at 300 and 13 K (bottom).
    • fig. S9. The temperature dependence of the specific heat C divided by temperature T obtained at x = 0 and 1.4%.
    • fig. S10. Anomalous power law temperature dependence of the a-axis resistivity at the zero-field quantum valence criticality and the field-induced antiferromagnetic instability.
    • References (41–49)

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