Crystal-electric-field excitations and spin dynamics in ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ semimetallic chiral-lattice phase

Inelastic neutron scattering experiments have been conducted to investigate the spin dynamics and crystal-electric-field level scheme of the Ce $4f$ electrons in ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$. This compound exhibits a large specific heat at low temperatures and anomalous semimetallic transport in the chiral crystallographic phase below 160 K. Distinctly observed magnetic excitations at approximately 6 and 29 meV are asymmetric in spectral shape and are reproduced by two inequivalent crystal-electric-field splitting schemes, which are deduced from the chiral structure. We have also observed the spin dynamics reflecting antiferromagnetic correlations below 1 meV, which is enhanced with an upturn in the electrical resistivity below 15 K and which yields a low-energy density of state relevant to the large specific heat. We discuss the possibility of a three-dimensional Weyl semimetal state, considering the chiral-lattice symmetry, electronic hybridization, and magnetic correlation.

Figure 1

Schematic of enantiomer of ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ chiral cubic structure in low-temperature ${\mathrm{I}}^{\prime }$ phase [15]. The Sn atoms form the cagelike unit shown by the shaded polyhedra and surround the two inequivalent Ce ions, Ce1 and Ce2, as shown by the green and blue columns, respectively.

Figure 2

Magnetic INS intensity contour map for ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ polycrystalline sample at 6 K. The incident neutron energy is $E_{\mathrm{i}}=42.0$ meV. The data correspond to the spectral difference between the Ce- and La-based compounds.

Figure 3

Blue open circles are magnetic INS spectra for the ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ polycrystalline sample at 6 K by using the $E_{\mathrm{i}}=42.0$ meV setup. These data points shown in (a) and (b) are identical, and they correspond to the spectral differences between the Ce- and La-based compounds. The intensity was evaluated by integration over the scattering-vector-magnitude range of $Q=2.0–3.0{\AA }^{-1}$. Solid squares in (a) are incoherent-scattering intensity of ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ multiplied by 1/200, FWHM of which is 2.31 meV corresponding to the energy resolution. (a) and (b) show the results of model 1 and 2 for the CEF analysis, respectively, as described in detail in the main text. The green dotted and brown broken lines are the fitted spectral components, and the red lines are total.

Figure 4

Magnetic INS spectra for ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ polycrystalline sample at 170 K. The incident neutron energy is $E_{\mathrm{i}}=42.0$ meV. The intensity was evaluated by integration over the scattering-vector-magnitude range of $Q=2.0–3.0{\AA }^{-1}$. All the data sets correspond to the spectral differences between the Ce- and La-based compounds. The red line is the results of the least-squares fitting analysis using the CEF model. The green dotted and brown broken lines are the fitted spectral components, as described in detail in the main text.

Figure 5

Magnetic INS spectra for ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ polycrystalline sample at 6 K. The incident neutron energy is 15.14 meV. The intensity was evaluated by integration over the $Q=1.5–2.0{\AA }^{-1}$ range. The data set corresponds to the spectral difference between the Ce- and La-based compounds.

Figure 6

Magnetic INS spectra for ${\mathrm{Ce}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ polycrystalline sample at 6 and 170 K. The incident neutron energy is 3.13 meV. The intensity was evaluated by integration over the $Q=0.5–1.5{\AA }^{-1}$ range. The data set corresponds to the spectral difference between the Ce- and La-based compounds.

Figure 7

INS spectra for $\mathit{Q}=(1,0,0)$, (1.25, 0, 0), and (1.5, 0, 0) measured at 1.4 and 20 K, indicated by red circles and green diamonds, respectively. The left and right ordinates are for the inelastic response and the incoherent elastic part, respectively. The solid lines on the data points are the fitted results. The INS components for the 1.4-K data are shown by the blue broken lines and black broken lines.

Figure 8

(a) Magnetic excitation peak positions, ${\delta }_n$ $(n=1$ and 2), as functions of the magnitude of the reduced wave vector $\mathit{q}$ along the [1 0 0] direction. The vertical bars on the data points are spectral widths evaluated in the fitting analysis. (b) Temperature dependencies of magnetic excitation intensities at $E=0.25$ and 0.3 meV for $\mathit{Q}=(1,0,0)$ and $(1.5,0,0)$, respectively.