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Spin fluctuation induced Weyl semimetal state in the paramagnetic phase of EuCd2As2

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Science Advances  12 Jul 2019:
Vol. 5, no. 7, eaaw4718
DOI: 10.1126/sciadv.aaw4718
  • Fig. 1 Slow FM fluctuations in the PM phase of EuCd2As2.

    (A) Temperature dependence of the resistivity. The inset shows the crystal structure of EuCd2As2 in one unit cell. mΩ, milliohm. (B) 3D Brillouin zone (BZ) with high-symmetry points and coordinate axes. The normal directions of cleaved (001) and (101) surfaces are also indicated. (C) Temperature dependence of the magnetic susceptibility with H parallel and perpendicular to the c axis, respectively. emu, electromagnetic unit. (D) Temperature dependence of the inverse susceptibility. (E) ESR spectra at various temperatures in the PM phase. The inset plots temperature dependence of the resonance field HRes. a.u., arbitrary units. (F) Magnetic field dependence of the Hall resistivity at various temperatures under in-plane magnetic fields. (G) μSR spectra at 20 K in zero field (ZF) and longitudinal field (LF) of 7000 Oe, respectively. (H) μSR spectra at three representative temperatures. (I) Temperature dependence of the dynamic muon relaxation rate λZF.

  • Fig. 2 Band splitting in the PM phase of EuCd2As2.

    The ARPES data in (A) to (J) were taken from the cleaved (001) surface, and the data in (K) and (L) were collected from the cleaved (101) surface. (A) ARPES intensity map at EF acquired with photon energy of 70 eV, showing a point-like FS in the kx-ky plane. (B) 3D intensity plot of the ARPES data collected with = 70 eV, showing cone-shaped dispersions in the kx-ky plane. (C) Intensity plot of the ARPES data at EF collected with varying from 30 to 130 eV, showing the FSs in the ky-kz plane. (D) ARPES spectrum image along cut1 in the Γ-A direction, as shown in (C). (E) A detailed view of the band structure along cut0, as shown in (A), collected at T = 11 K. (F and G) Zoomed-in views of the raw ARPES spectra in the box shown in (E) and the corresponding 2D curvature intensity plot, respectively. (H) Intensity plot of the ARPES data at EF collected with varying from 250 to 360 eV, showing the FSs in the ky-kz plane. (I) Curvature intensity plot of the ARPES data along Γ-K [cut2 in (H)] collected at T = 14 K with = 270 eV. (J) The profile of BZs in the plane along normal direction passing through Γ, A, and M points and perpendicular to the (101) surface. (K and L) The ARPES spectrum and corresponding 2D curvature intensity plot along cut3 in (J). The arrows indicate the band splitting.

  • Fig. 3 The band structures in the FM phase and PM phase with FM fluctuations.

    (A) The band structure along high-symmetry lines calculated by using DFT + U, with U = 5 eV. The magnetic moments oriented in the (001) direction. The insets are the zoomed-in views of band dispersions in the vicinity of the EF around the Γ point. (B) In the near EF region, the bands along Γ-A with blue and red colors scaling the components of As 4p and Cd 5s orbitals, respectively. The black circles indicate different Weyl points. (C) Locations of Weyl points (W1 and W2) in the 3D BZ. (D) The same as that in (A), but the electronic structure is a superposition of the energy bands calculated with the magnetic moments in all possible directions to simulate the FM fluctuation. (E) The zoomed-in view of the superposed electronic structure along K-Γ-A in the vicinity of EF, indicating the broadening effect induced by spin fluctuation. Ws and Wf are width of spin splitting and the band broadening induced by the FM fluctuation, respectively. (F) The distribution of Weyl points (W1 and W2) calculated with the magnetic moments oriented in all kinds of typical directions.

  • Fig. 4 The observation of Weyl cones.

    Unless otherwise mentioned, the spectra are collected from the cleaved (101) surface using = 88 eV, and the corresponding momentum cut is indicated with the yellow curve in (A), which almost overlaps with the Γ-A-Γ line. (A) The FS map in the kx-kz plane, collected with in the range of 30 to 160 eV. BS, bulk states. (B) The FS map in the ky-kz plane. (C) The 3D ARPES intensity to show two point-like FSs on Γ-A and the cone-shaped dispersions in the ky-kz plane. WPs, Weyl points. (D and E) The ARPES spectrum and its corresponding curvature intensity plot along Γ-A. To obtain the ARPES spectrum on a straight line located exactly on the Γ-A line, a number of high-resolution ARPES data were collected with photon energies in the vicinity of 88 eV. The arrows indicate the band splitting. (F) The 2D curvature intensity plot of the ARPES spectrum along the yellow curve in (A). An electron CB with band bottom below EF is visible. (G) Schematic of the 3D Weyl cone band structure in the kx-kz (ky-kz) plane. (H and I) Zoomed-in views of the dashed line box in (D); the spectrum was divided by Fermi-Dirac function. In (I), black arrows point to the Weyl points. The tunneling differential conductance (dI/dV) curve from STS measurements is plotted for comparison. (J) STM constant current topographic image obtained from (001) surface of EuCd2As2. (K) The dI/dV spectrum recorded at T = 11 K on the (001) surface. In this figure, the data in (A) to (C) and (F) [(D) to (E) and (H) to (I)] were collected from sample no. 1 (sample no. 2). We note that sample no. 1 is slightly less hole-doped than sample no. 2, which makes the electron band easier to be explored in sample no. 1 in (F).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/7/eaaw4718/DC1

    Spin splitting and band broadening by static disorder with finite correlation length

    Fig. S1. Band splitting in EuCd2Sb2.

    Fig. S2. Temperature effects on the band splitting in EuCd2Sb2.

    Fig. S3. Electronic structure of BaCd2As2.

    Fig. S4. Comparison of band structures below and above Néel temperature.

    Fig. S5. Calculated band structures of EuCd2As2 with magnetic moments oriented along the c axis, as a function of onsite Coulomb interaction U.

    Fig. S6. Calculated band structure of EuCd2As2 along high-symmetry lines, deeply within the PM phase.

    Fig. S7. Band structures with different magnetic backgrounds differing in size of FM clusters.

    Fig. S8. The mean free path as a function of the FM correlation length.

    Table S1. Positions of the Weyl points in EuCd2As2 depending on the spin orientation.

  • Supplementary Materials

    This PDF file includes:

    • Spin splitting and band broadening by static disorder with finite correlation length
    • Fig. S1. Band splitting in EuCd2Sb2.
    • Fig. S2. Temperature effects on the band splitting in EuCd2Sb2.
    • Fig. S3. Electronic structure of BaCd2As2.
    • Fig. S4. Comparison of band structures below and above Néel temperature.
    • Fig. S5. Calculated band structures of EuCd2As2 with magnetic moments oriented along the c axis, as a function of onsite Coulomb interaction U.
    • Fig. S6. Calculated band structure of EuCd2As2 along high-symmetry lines, deeply within the PM phase.
    • Fig. S7. Band structures with different magnetic backgrounds differing in size of FM clusters.
    • Fig. S8. The mean free path as a function of the FM correlation length.
    • Table S1. Positions of the Weyl points in EuCd2As2 depending on the spin orientation.

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