Neutron scattering in the proximate quantum spin liquid α-RuCl3

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Science  09 Jun 2017:
Vol. 356, Issue 6342, pp. 1055-1059
DOI: 10.1126/science.aah6015
  • Fig. 1 Structure and magnetism in single-crystal α-RuCl3.

    (A) Honeycomb lattice of Ru3+ magnetic ions in one plane of α-RuCl3, showing the projections of the three mutually competing Ising bonds corresponding to the Kitaev terms in Eq. 1. (B) The intensity of the magnetic Bragg Peak occurring at the M point of the 2D honeycomb lattice corresponding to a zigzag structure with three-layer stacking [Embedded Image in trigonal or Embedded Image in monoclinic notation]. The single sharp magnetic transition is characteristic of crystals with few or no stacking faults (26). The solid line is a power-law fit yielding TN = 6.96 ± 0.02 K and a critical exponent β = 0.125 ± 0.015, suggesting 2D Ising behavior. Error bars indicate 1 SD, assuming Poisson counting statistics. (Inset) The 490-mg single crystal of α-RuCl3 used for the neutron measurements. [For more sample details, see the materials and methods (27).]

  • Fig. 2 Momentum and temperature dependence of the scattering continuum.

    Neutron scattering measurements using fixed incident energy Ei = 40 meV, projected on the reciprocal honeycomb plane defined by the perpendicular directions (H, H, 0) and (K, –K, 0), integrated over the interval L = [–2.5, 2.5]. Intensities are denoted by color, as indicated in the scale at right. Measurements integrated over the energy range [4.5, 7.5] meV are shown on the top row at temperatures (A) 5 K, (B) 10 K, and (C) 120 K. The corresponding measurements integrated over the interval [7.5, 12.5] meV are shown on the bottom in (D), (E), and (F). The white regions lack detector coverage. See fig. S11 for orientationally averaged data.

  • Fig. 3 Detailed features of the Γ point scattering.

    (A and B) Energy dependence of the scattering at (A) 5 K and (B) 10 K shows a broad peak. The data shown are integrated over constant momentum volumes defined by the following ranges: Embedded Image over the range Embedded Image over the range Embedded Image. The solid lines are visual guides produced by modeling the elastic component as a Gaussian peak and the inelastic features using damped harmonic oscillator (DHO) functions: E, elastic component; S, spin-wave (SW) peaks appearing below TN; C, continuum. Fit parameters and the DHO function are presented in table S1. Error bars indicate 1 SD, assuming Poisson counting statistics. (C) Scattering symmetrized in the (H, H, L) plane and over positive and negative L, integrated over the intervals Embedded Image and E = [4.5, 7.5] meV at T = 10 K. (D) Same scattering, but in the (K, –K, L) plane integrated over ξ = [–0.1, 0.1] and E = [4.5, 7.5] meV. (E) Representative low-energy scattering expected from spin-wave theory (SWT) for a zigzag-ordered phase (25). (F) Scattering at T = 5 K integrated over L = [–2.5, 2.5] and E = [2, 3] meV. The white regions lack detector coverage.

  • Fig. 4 Comparison of the scattering with T = 0 Kitaev model calculations.

    (A) Data at Ei = 40 meV and T = 5 K, integrated over the range E = [4.5, 7.5] meV and L = [–2.5, 2.5] and symmetrized along the (H, H) direction. (B) Expected scattering from an isotropic antiferromagnetic (AF) Kitaev model at an energy E = 1.2Kγ, taking into account the neutron polarization and the spherically approximated Ru3+ form factor. (C) Plot of the nonsymmetrized data (points with error bars) along (H, H, 0) at T = 5 K, integrated over the same L and E intervals as in panel (A), as well as Embedded Image. The solid red line is the calculated scattering for an AF Kitaev model with R = 2, as discussed in the text. The solid purple line represents the corresponding unmodified AF Kitaev model, and the green line denotes the ferromagnetic (FM) Kitaev model. Some of the scattering at larger Q near (H, H) = ±(1, 1) is due to phonons. Error bars indicate 1 SD, assuming Poisson counting statistics.

Supplementary Materials

  • Neutron scattering in the proximate quantum spin liquid α-RuCl3

    Arnab Banerjee, Jiaqiang Yan, Johannes Knolle, Craig A. Bridges, Matthew B. Stone, Mark D. Lumsden, David G. Mandrus, David A. Tennant, Roderich Moessner, Stephen E. Nagler

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S11
    • Table S1
    • References

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