Crystal-field and Kondo-scale investigations of $\text{Ce}M{\text{In}}_5$ ($M=\text{Co}$, Ir, and Rh): A combined x-ray absorption and inelastic neutron scattering study

Linear-polarized soft-x-ray absorption (XAS) and inelastic neutron scattering (INS) experiments have been performed on $\text{Ce}M{\text{In}}_5$ with $M=\text{Rh}$, Ir, and Co to determine the crystal-field scheme and characteristic Kondo temperatures $T^{\ast }$ for the hybridization between $4f$ and conduction electrons. The ground-state wave functions are determined from the polarization-dependent soft-XAS data at the cerium $M_{4,5}$ edge and the crystal-field splittings from INS. The characteristic temperature $T^{\ast }$ has been determined from the line widths of the neutron scattering data. We find that the quasielastic linewidths of the superconducting compounds ${\text{CeCoIn}}_5$ and ${\text{CeIrIn}}_5$ are comparable with the low-energy crystal-field splitting.

Figure 1

(Color online) Low temperature $\left(T=20\text{K}\right)$ linear-polarized XAS spectra of ${\text{CeRhIn}}_5$, ${\text{CeIrIn}}_5$, and ${\text{CeCoIn}}_5$ at the ${\text{Ce}}^{3+}$ $M_{4,5}$ edges. The solid lines are the measured data, the dotted ones the simulations as described in the text. The orbitals represent the spatial distribution of the $4f$ wave functions according to the respective ground-state admixtures, $\alpha |\pm 5/2⟩+\beta |\mp 3/2⟩$.

Figure 2

(Color online) Inelastic neutron data at 5 K with 20 meV (a)–(e) and 60 meV (f)–(h) incident energy. The blue triangles represent the total scattering, the black lines the phonon intensities as obtained from a high to low angle scaling. The red circles show the magnetic scattering obtained after phonon correction (see appendix) and the red lines are Lorentzian fits.

Figure 3

(Color online) Left panel: temperature-dependent linear-polarized XAS spectra at the ${\text{Ce}}^{3+}$ $M_5$ edge of ${\text{CeRhIn}}_5$, ${\text{CeIrIn}}_5$, and ${\text{CeCoIn}}_5$. The solid lines correspond to the measured data, the dotted lines to the simulation based on the crystal-field energies from the neutron data, and the ground-state wave functions from the low-temperature XAS data.

Figure 4

(Color online) Isotropic spectra of $\text{Ce}M{\text{In}}_5$ with $M=\text{Rh}$, Ir, and Co, (at 20 K) and of ${\text{CeAu}}_2{\text{Si}}_2$ (at 40 K) for comparison. All spectra were recorded under the same beam line conditions at the NSRRC. In the right panel are blow-up graphs with arrows pointing out the $4f^0$ initial-state contributions.

Figure 5

(Color online) Neutron data with 3.1 meV incident energy. For $T=1.5$ and 8 K the neutron energy loss, for 75 K the neutron energy gain side is shown. The blue triangles (pointing down) are the total scattering of the cerium samples, the orange triangles (pointing up) are the La scattering. The 75 and 8 K data are described with one quasielastic (black) and one inelastic Lorentzian (green) with intensity ratios according to the crystal-field models (see Table ). The red lines reflect the total magnetic scattering.

Figure 6

(Color online) Inelastic neutron scattering data of the nonmagnetic reference compounds ${\text{YCoIn}}_5$ and ${\text{LaIrIn}}_5$. Left: high- and low-angle data at 5 K. Right: 5 K low-angle data shown on an expanded intensity scale and scaled $\left(R=1/8\right)$ high-angle data. Bottom right: the red squares are the same low angle data taken at 280 K. The orange line represents the 5 K data scaled to 250 K with the Bose factor.