Research ArticlePHYSICS

Novel excitations near quantum criticality in geometrically frustrated antiferromagnet CsFeCl3

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Science Advances  18 Oct 2019:
Vol. 5, no. 10, eaaw5639
DOI: 10.1126/sciadv.aaw5639
  • Fig. 1 Spin S = 1 easy-plane antiferromagnet.

    (A) Schematic diagram of the S = 1 easy-plane antiferromagnet. In the ordered state, the doublet excited states ∣±1〉 splits into ∣L〉 and ∣T〉. Here, the former and latter have longitudinal and transverse fluctuations, respectively. (B) Crystal structure of CsFeCl3 with the space group P63/mmc (30). Magnetic Fe2+ ions having pseudospin S = 1 form one-dimensional chains along the crystallographic c axis, and the chains form the triangular lattice in the ab plane. Red and blue lines indicate the intrachain interaction Jc and interchain/intratriangle interaction Jab, respectively.

  • Fig. 2 Inelastic neutron scattering spectra.

    The spectra obtained at a chopper spectrometer under (A) 0.0 GPa at 6 K, (B) 0.3 GPa at 2.7 K, and (C) 1.4 GPa at 0.9 K sliced by the energy transfer − wave vector (ħω − q) plane for q = ( − k, 2k, 0). The yellow circles, squares, and red diamonds are the peak positions of the excitations obtained from the constant-q scans using a triple-axis spectrometer. The solid yellow curves are the dispersions calculated by ESW. Calculated neutron cross section by the ESW under (D) 0.0 GPa, (E) 0.3 GPa, (F) 1.4 GPa, and (G) 4.0 GPa at 0 K. Calculated neutron cross section in the absence of the cross term in Eq. 2 under (H) 4.0 GPa and (I) 1.4 GPa at 0 K. The black and red solid curves in (F) to (I) are gapless and gapped modes, respectively. More detailed pressure dependence of the calculated spectra is shown in fig. S3.

  • Fig. 3 Detailed structure of INS spectra.

    (A) Constant-q scans at (−k, 2k, 0) under 1.4 GPa measured at a triple-axis spectrometer. Blue and red curves are the fitting results by Lorentzians convoluted by the instrumental resolution function. Green dashed bars indicate the experimental resolution. (B) Pressure evolutions of the constant-q scans at (−1/3, 2/3, 0) obtained at a triple-axis spectrometer. The black dashed curve is a Gaussian function of the incoherent scattering at 1.4 GPa with the full width at half maximum of 0.17 meV. (C) Phase diagram of the pressure-induced QPT in CsFeCl3, which is obtained from energy gaps Δ and transition temperatures TN (21). Red and blue curves are guides for eyes. (D) Pressure dependence of the excitation energies at (−1/3, 2/3, 0) calculated by the ESW. Above 0.9 GPa, the blue and red curves are the excitations of gapless and gapped modes, respectively; the circles are peak energies evaluated from the constant-q scans.

  • Fig. 4 Role of the LT-hybridization term.

    (A) Relation between the global xyz coordinate and the crystallographic axes. (B) Relationship between the global xyz coordinate and the local ηζξ coordinate. ϕ is the angle of the local magnetic moment measured from the x axis. η axis (ζ axis) is taken parallel (perpendicular) to the moment in the ab plane. (C) Schematic of transition from ∣T〉 state to ∣L〉 state via the intersite interaction. Mi represents the magnetic moment at the i site.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/10/eaaw5639/DC1

    Section S1. Supplementary information on experimental methods

    Section S2. Energy scheme of Fe2+ ion in CsFeCl3

    Section S3. ESW theory for triangular antiferromagnet

    Section S4. Detailed data analysis for triple-axis spectrometer

    Fig. S1. Method of background subtraction for INS spectra.

    Fig. S2. Energy scheme of Fe2+ ion in CsFeCl3.

    Fig. S3. Schematic of hopping and pair creation processes.

    Fig. S4. Calculated INS spectra at various pressures.

    Fig. S5. Data analysis for triple-axis spectrometer.

    Table S1. Summary of experimental setups used for INS measurements under pressures.

    Table S2. Summary of parameters obtained from the refinement on the constant q scans [q = (k, 2k, 0)] at 1.4 GPa by Lorentzians convoluted by the experimental resolution functions.

    References (3137)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Supplementary information on experimental methods
    • Section S2. Energy scheme of Fe2+ ion in CsFeCl3
    • Section S3. ESW theory for triangular antiferromagnet
    • Section S4. Detailed data analysis for triple-axis spectrometer
    • Fig. S1. Method of background subtraction for INS spectra.
    • Fig. S2. Energy scheme of Fe2+ ion in CsFeCl3.
    • Fig. S3. Schematic of hopping and pair creation processes.
    • Fig. S4. Calculated INS spectra at various pressures.
    • Fig. S5. Data analysis for triple-axis spectrometer.
    • Table S1. Summary of experimental setups used for INS measurements under pressures.
    • Table S2. Summary of parameters obtained from the refinement on the constant q scans q = (k, 2k, 0) at 1.4 GPa by Lorentzians convoluted by the experimental resolution functions.
    • References (3137)

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