Weyl–Kondo semimetal behavior in the chiral structure phase of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$

The spin dynamics, crystalline-electric-field (CEF) level scheme, specific heat, and x-ray photoemission spectra (XPS) of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ were investigated, which exhibits anomalous semimetal transport in the chiral crystallographic phase. CEF excitations observed at approximately 7 and 39 meV are consistent with the two inequivalent Ce-ion cites in the chiral structure. Because of broader CEF excitations and a strong $4f^1$ peak at the Fermi level in the Ce $4f$ on-resonance spectrum, the hybridized Ce $4f$ electrons contribute to the semimetal carriers. In addition, the spin fluctuation associated with the Kramers doublet ground state is characterized by the peak located at 0.15 meV. The electronic state involving the spin fluctuation causes the $T^3$ behavior of specific heat below 0.6 K, which is attributed to linear dispersion relations of electrons of the Weyl–Kondo semimetal in the chiral-lattice symmetry.

Figure 1

Schematic of crystal structure of an enantiomer of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ in the chiral ${\mathrm{I}}^{\prime }$ phase [30]. The Sn atoms form the cagelike unit shown by the shaded polyhedra, and the Rh atoms are located between them (red prisms). The two inequivalent Ce ions, Ce1 and Ce2, as shown by the orange and blue circles, respectively. The view was drawn using VESTA [47].

Figure 2

(a) Magnetic $S(Q,E)$ contour map for ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at 1.3 K. The incident neutron energy is $E_{\mathrm{i}}=60.4$ meV. The result was obtained by subtracting the data of the reference material, ${\mathrm{La}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ [33]. (b) Scattering function data of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ ($S_{\mathrm{Ce}}$ with red squares) and ${\mathrm{La}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ ($S_{\mathrm{La}}$ with green triangles) at 1.3 K, which correspond to integration of intensity in the range of $Q=3.0-5.0{\AA }^{-1}$. (c) Magnetic $S\left(E\right)$ at 1.3 K (open symbols) after subtracting the corrected La data from the Ce data. The red solid line is a fitted result of the CEF-excitation calculation with the two inequivalent schemes (a green dotted line for A and a brown broken line for B).

Figure 3

Magnetic $S\left(E\right)$ spectra for ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at 1.3 and 30 K measured using $E_{\mathrm{i}}=8.97$ meV, which were evaluated by intensity integration in the range of $Q=1.5-2.5{\AA }^{-1}$. The data correspond to the spectral difference between the Ce- and La-based compounds [33]. The red solid line is a fitted result of the CEF-excitation analysis with the two inequivalent schemes (green dotted line for A and brown broken line for B) for the $E_{\mathrm{i}}=60.4$ meV data.

Figure 4

(a) Magnetic $S(Q,E)$ contour map for ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ powdered sample at 1.3 K using $E_{\mathrm{i}}=3.44$ meV. The data set corresponds to the spectral difference between the Ce- and La-based compounds [33]. (b) $S\left(E\right)$ data of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ ($S_{\mathrm{Ce}}$ with red circles) and ${\mathrm{La}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ ($S_{\mathrm{La}}$ with green triangles) at 1.3 K obtained by intensity integration in the range of $Q=0.5-1.5{\AA }^{-1}$. (c) $S\left(E\right)$ data at 1.3, 10, and 30 K obtained by intensity integration in the range of $Q=0.5-1.5{\AA }^{-1}$ shown in (a). Each temperature data set is shifted by 0.05 along the ordinate. Solid lines are fitted results based on the dynamical susceptibility ${\chi }_{\mathrm{S}}^{\prime \prime }({\mathit{Q}}_{\mathrm{avr}},E)$.

Figure 5

(a) Triple-axis INS spectra at $\mathit{Q}=(3,0,0)$ of the single crystal sample of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ measured at 1.6 (blue symbols) and 20 K (red symbols). Small symbols near $E=0$ with the right ordinate are elastic scattering to show the energy resolution, and larger symbols are the inelastic part with the left ordinate. (b) Several scans with the fixed energy transfer of 0.25 meV along the symmetrical reciprocal-lattice lines at 1.6, 20, and 40 K. Blue and red open symbols are raw data at 1.6 and 20 K, respectively, and solid symbols shown by black diamonds are intensity difference with respect to the 40-K data. The reciprocal lattice unit is defined as $2\pi /a^{\prime }$ with $a^{\prime }=19.4$ Å for ${\mathrm{I}}^{\prime }$ phase.

Figure 6

Symbols are specific heat divided by temperature ($C_p/T$) under the several magnetic fields. Lines are fitted linear functions ($C_p/T=\gamma +{\beta }^{\prime }{T}^2$) to the low-temperature regions.

Figure 7

(a) XAS spectrum near the Ce $3dj=5/2$ and 3/2 absorption edges of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at 20 K. (b) XPS spectra of ${\mathrm{Ce}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ at 20 K. Red circles and black squares are data obtained at the $3d\text{−}4f$ resonance position [red arrow in (a)] and the off-resonance position [black arrow in (a)], respectively. (c) The XPS data near the Fermi energy.

Figure 8

Temperature dependencies of the fitting parameters for the $E_{\mathrm{i}}=3.44\mathrm{meV}$ data. Spectral magnitude $A$, excitation peak position $E_0$, and spectral width $\mathrm{\Gamma }$.

Figure 9

Fitted parameters $\gamma$ and ${\beta }^{\prime }$ for the electronic $C_p/T$ shown in Fig. 6 as functions of the applied magnetic fields.