Exchange field effect in the crystal-field ground state of $\mathrm{Ce}M{\mathrm{Al}}_4{\mathrm{Si}}_2$

The crystal-field ground-state wave functions of the tetragonal, magnetically ordering Kondo lattice materials $\mathrm{Ce}M{\mathrm{Al}}_4{\mathrm{Si}}_2$ $(M=\text{Rh}$, Ir, and Pt) are determined with low-temperature linearly polarized soft-x-ray absorption spectroscopy, and estimates for the crystal-field splittings are given from the temperature evolution of the linear dichroism. Values for the dominant exchange field in the magnetically ordered phases can be obtained from fitting the influence of magnetic order on the linear dichroism. The direction of the required exchange field is $\parallel c$ for the antiferromagnetic Rh and Ir compounds, with the corresponding strength of the order of ${\lambda }_{\text{ex}}\approx 6\text{meV}$ (65 K). Furthermore, the presence of Kondo screening in the Rh and Ir compound is demonstrated on the basis of the absorption due to $f^0$ in the initial state.

Figure 1

Experimental low-temperature $(T=20$ K) linearly polarized soft-x-ray data of ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$ (left), ${\mathrm{CeIrAl}}_4{\mathrm{Si}}_2$ (middle), and ${\mathrm{CePtAl}}_4{\mathrm{Si}}_2$ (right) at the Ce $M_{4,5}$ absorption edge. At the top of each panel the experimental data are shown, and in the middle the simulations are shown. The green circles and black lines at the bottom represent the corresponding experimental and simulated linear dichroism, respectively, and the corresponding spatial distributions of the $4f$ electrons are included as insets. The black arrows indicate the position of absorption due to $f^0$ in the initial state.

Figure 2

Temperature-dependent (20–300 K) linear dichroism of the ${\mathrm{Ce}}^{3+}{M}_{4,5}$ edge of ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$ (left panel) and ${\mathrm{CePtAl}}_4{\mathrm{Si}}_2$ (right panel). The experimental data are shown in the upper part of each panel, and the best-fitting simulation of the LD spectra are given in the lower part. The sequence of crystal-field states is shown as an inset.

Figure 3

Influence of the exchange field on the LD intensity. (a) Experimental LD spectra at 4 and 20 K and simulations with exchange field for ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$. $H_{\mathrm{ex}}\parallel [0,0,1]\cong 6$ meV are used in the simulations for ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$. (b) Experimental LD spectra at 4 and 20 K for ${\mathrm{CePtAl}}_4{\mathrm{Si}}_2$. (c) Temperature-dependent LD intensity, with and without exchange field, for ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$. The LD intensity is modified at $T<20$ K when an exchange field is considered. (d) Temperature-dependent LD intensity of ${\mathrm{CePtAl}}_4{\mathrm{Si}}_2$ can be well-fitted at $T<20$ K without the exchange field.

Figure 4

Impact of an exchange field on the CEF ground state. For ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$ the Zeeman splitting of the ground-state doublet amounts to 0.3 meV, when an exchange field $H_{\mathrm{ex}}\parallel [0,0,1]\cong 6$ meV is active at 4 K. The $J_z=|\pm 5/2\rangle$ contribution is enhanced in the lower singlet with respect to $H_{\mathrm{ex}}=0$.

Figure 5

${\chi }^{-1}$ of ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$ and ${\mathrm{CePtAl}}_4{\mathrm{Si}}_2$, compared to the results from CEF. At high temperature, the magnetic anisotropy can be reproduced from the CEF-only calculation, however a better description requires additional anisotropic molecular fields $\lambda$ along the hard axis, which are ${\lambda }_{ab}=-60$ and ${\lambda }_c=-80$ mol f.u./emu for ${\mathrm{CeRhAl}}_4{\mathrm{Si}}_2$ and ${\mathrm{CePtAl}}_4{\mathrm{Si}}_2$, respectively.

Figure 6

(a) Isotropic spectra of $\mathrm{Ce}M{\mathrm{Al}}_4{\mathrm{Si}}_2$ for the absorption due to $f^0$ in the ground state and (b) $M=\text{Rh}$ $f^0$ spectral weight for all temperatures. The isotropic spectra are constructed from the polarized data and normalized to the total $(f^1$ and $f^0)$ integrated absorption intensity.