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Quantum criticality in the spin-1/2 Heisenberg chain system copper pyrazine dinitrate

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Science Advances  22 Dec 2017:
Vol. 3, no. 12, eaao3773
DOI: 10.1126/sciadv.aao3773
  • Fig. 1 Phase diagram of CuPzN with a field-induced quantum critical point.

    The color code reflects the measured specific heat C(H,T), and symbols indicate the positions of various thermodynamic signatures that obey the quantum critical scaling T ~ |HHc|νz, with νz = 1 and μ0Hc = 13.9 T. Also shown is the basic structure of the Cu2+ spin chains with S = 1/2 that are exchange-coupled via pyrazine rings C4H4N2.

  • Fig. 2 Thermodynamic quantities of the Heisenberg spin chain compound CuPzN.

    (A) Thermal expansion α, (B) magnetostriction λ, (C) magnetic moment m per spin and susceptibility χ = ∂m/∂(μ0H) (insets), (D and E) molar specific heat C as a function of temperature and magnetic field, respectively, and (F) the field derivative of the molar entropy ∂S/∂H. In (D) and (E), the data for increasing field and temperature are offset with respect to each other by 1 and 0.1 J mol−1 K−1, respectively. Symbols are experimental data, and solid lines are fits obtained via the Bethe-Ansatz solution of the Heisenberg spin chain model, with the parameter set J/kB = 10.6 K, Embedded Image, and gb = 2.27. For α and C, field-independent phononic background contributions are included, which are calculated by the Debye formula and become relevant above 5 K [see dashed lines in (A) and (D)]. For C, an additional contribution Cnuc from the nuclear spins of copper becomes relevant at lowest temperatures and high fields. For T = 0.3 K, the calculated Cnuc is shown by the dotted line in (E), whereas the bare Heisenberg contribution C1D is displayed by the dashed line and the sum of both (solid line) reproduces the experimental data. The corresponding nuclear contribution ∂Snuc/∂H is negligibly small as shown by the dotted line in (F).

  • Fig. 3 Quantum critical scaling of thermodynamic quantities close to the critical field Hc.

    Noncritical background contributions due to phonons and/or nuclear spins have been subtracted. Multiplication by Embedded Image and plotting versus the scaling parameter Embedded Image cause a collapse of (A) C1D/T, (B) α1D, (C) χ1D, and (D) λ1D toward critical scaling functions (solid black lines), which are derived from f0(x) of Eq. 2; symbol colors indicate different temperatures from 0.3 (blue) to 2.0 K (red). The corresponding Bethe-Ansatz results calculated for T = 2 K are shown as red dashed lines in (A) to (D) and, in addition, for T = 0.25 K as blue dashed lines in (C) and (D). The importance of corrections to scaling increases from (A) to (D), spoiling a complete scaling collapse. (E) The experimentally obtained magnetic field–dependent Grüneisen parameter ΓH,1D (symbols) is perfectly described by its critical behavior (solid lines) given by Eq. 3. The dashed lines show the universal divergences of Eq. 3 in the zero-temperature limit, and the inset compares the corresponding k/T divergence at H = Hc with the experimental data (symbols). (F) The pressure-dependent Grüneisen parameter Γp,1D is, according to Eq. 4, proportional to ΓH,1D, and consequently, both Grüneisen parameters collapse on the very same scaling function Φ(x) of Eq. 3, as shown in (G) and (H).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/eaao3773/DC1

    section S1. Magnetocaloric effect

    section S2. Deviations of C around 2.5 K

    section S3. Nuclear contributions

    section S4. Quantum critical theory and corrections to scaling

    fig. S1. Magnetocaloric effect measurement.

    fig. S2. Theoretical prediction for the scaling of quantum critical thermodynamics in CuPzN.

    fig. S3. Deviations from critical scaling.

    References (3639)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Magnetocaloric effect
    • section S2. Deviations of C around 2.5 K
    • section S3. Nuclear contributions
    • section S4. Quantum critical theory and corrections to scaling
    • fig. S1. Magnetocaloric effect measurement.
    • fig. S2. Theoretical prediction for the scaling of quantum critical thermodynamics in CuPzN.
    • fig. S3. Deviations from critical scaling.
    • References (36–39)

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