Correlation between the valence state of cerium and the magnetic transition in $\text{Ce}({\text{Ru}}_{1-x}$${\text{Fe}}_x{)}_2{\text{Al}}_{10}$ studied by resonant x-ray emission spectroscopy

The correlation between the $4f$-conduction electron ($c$-$f$) hybridization and the transition temperature $T_0$ into the unconventional antiferromagnetically (AFM) ordered state in $\text{Ce}({\text{Ru}}_{1-x}$${\text{Fe}}_x{)}_2{\text{Al}}_{10}$ has been investigated. The impact of pressure on the crystal structure and the electronic structure has been measured using x-ray diffraction and resonant x-ray emission spectroscopy at the Ce $L_3$ absorption edge in a diamond anvil cell. Our results show that the lattice spacings imply some correlation with the disappearance of $T_0$. Analyses of the measured valence states, however, show only a weak correlation with the corresponding critical disappearance of the AFM order within experimental errors. Our results may be explained by a scenario based on the Kondo-Heisenberg model beyond the conventional Doniach phase diagram.

Figure 1

(a) Change in the orthorhombic lattice parameters of $a$, $b$, and $c$ as a function of $x$ for Ce(${\text{Ru}}_{1-x}$${\text{Fe}}_x$)${}_2$${\text{Al}}_{10}$ ($x=0$ to 1.0) at 300 K. (b) Change in the volume as a function of $x$. Data errors are comparable to the symbol sizes. (c)–(e) Interatomic distance as a function of $x$ for Ce(${\text{Ru}}_{1-x}$${\text{Fe}}_x$)${}_2$${\text{Al}}_{10}$.

Figure 2

(a) $x$ dependence of the PFY-XAS spectra at 20 K for Ce(${\text{Ru}}_{1-x}$${\text{Fe}}_x$)${}_2$${\text{Al}}_{10}$. (b) $x$ dependence of the Ce valence derived from the PFY-XAS spectra. (c) An example of the fit to the PFY-XAS spectra (open circles) measured at 20 K for Ce(${\text{Ru}}_{0.875}$${\text{Fe}}_{0.125}$)${}_2$${\text{Al}}_{10}$. Dotted line is a guide for the eye fitted with linear function. (d) $x$ dependence of the Néel temperature ($T_0$) for ${\text{CeRu}}_2$${\text{Al}}_{10}$. The data in (d) are taken from the results of the susceptibility [20] (closed circle) and $\mu$SR [21] (open square) measured previously.

Figure 3

(a) Pressure dependence of the PFY-XAS spectra at 18 K for ${\text{CeRu}}_2$${\text{Al}}_{10}$. (b) Pressure dependence of the PFY-XAS spectra at 15–18 K for ${\text{CeFe}}_2$${\text{Al}}_{10}$. (c) Pressure dependence of the Ce valence for ${\text{CeRu}}_2$${\text{Al}}_{10}$ and ${\text{CeFe}}_2$${\text{Al}}_{10}$ derived from the fits to the PFY-XAS spectra. Symbols of open and closed squares for ${\text{CeRu}}_2$${\text{Al}}_{10}$ correspond to different series of the measurements. (d) Pressure dependence of the Néel temperature ($T_0$) for ${\text{CeRu}}_2$${\text{Al}}_{10}$ [22].

Figure 4

(a) Conventional Doniach phase diagram. There is a clear separation between the magnetically ordered state and the itinerant Fermi liquid [1]. (b) A phase diagram based on the calculation for the Kondo-Heisenberg lattice at finite temperatures [4].