Coexistence of magnetic order and valence fluctuations in the Kondo lattice system ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$

We report on the electronic band structure, structural, magnetic, and thermal properties of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$. Ce $L_{\mathrm{III}}$-edge XAS spectra give direct evidence for an intermediate valence behavior. Thermodynamic measurements reveal magnetic transitions at $T_{\mathrm{N}1}\approx 2.9$ K and $T_{\mathrm{N}2}\approx 2.4$ K. Electrical resistivity shows behavior typical for the Kondo lattices. The coexistence of magnetic order and valence fluctuations in a Kondo lattice system we attribute to a peculiar crystal structure in which Ce ions occupy two distinct lattice sites. Analysis of the structural features of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$, together with results of electronic band structure calculations and thermodynamic and spectroscopic data indicate that at low temperatures only Ce ions from the Ce1 sublattice adopt a stable trivalent electronic configuration and show local magnetic moments that give rise to the magnetic ordering. By contrast, our study suggests that Ce2 ions exhibit a nonmagnetic Kondo-singlet ground state. Furthermore, the valence of Ce2 ions estimated from the Ce $L_{\mathrm{III}}$-edge XAS spectra varies between +3.18 at 6 K and +3.08 at room temperature. Thus our joined experimental and theoretical investigations classify ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ as a multivalent charge-ordered system.

Figure 1

The planar layer in the structure of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ occurring at $x=1/2$. Fragment A: a chain of interconnected Ce atoms (yellow line) and edge sharing tetragons and triangles; fragment B: condensed empty pentagons and octagons of Rh (red) and Sn (black) centered by Ce (grey) atoms.

Figure 2

Near-edge regime of Ce $L_{\mathrm{III}}$ XAS spectra for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$. (a) shows deconvolution of the normalized spectrum recorded at $T=6$ K. The contributions due to $f^1$ and $f^0$ configurations are indicated by beige or grey fields underneath the dashed lines, while the solid black line represents the arctan function that accounts for transitions of $2p_{3/2}$ electrons to the extended conduction states. (b) depicts normalized Ce $L_{\mathrm{III}}$ XAS spectra measured at various temperatures between 6 and 300 K. The changes in intensity of the $f^0$ contribution are enlarged in the upper inset, with the arrow indicating the direction of increasing temperature. The lower inset of (b) displays the calculated changes of Ce valence as a function of temperature. The dashed line is a guide to the eye.

Figure 3

The Ce $3d$ XPS spectra for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ and ${\mathrm{CeRh}}_2{\mathrm{Sn}}_4$. The spin-orbit components $3d_{32}$ and $3d_{52}$ as well as the $f^1$ and $f^2$ contributions are labeled. The deconvolution of the spectrum for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ is shown.

Figure 4

Results of $dc$ magnetization measurements for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$. (a) shows the low-temperature part of the $M\left(T\right)$ measured in magnetic field of 100 Oe. Two distinct changes in slope of the $M\left(T\right)$ curve suggestive of magnetic transitions are indicated. The inset displays the magnetic susceptibility measured in a number of magnetic fields between 100 Oe and 70 kOe and plotted as a function of temperature on a logarithmic scale. (b) depicts the full magnetization loop at $T=1.8$ K. Inset shows values of the remanence magnetization at various temperatures. The dashed lines are guided to the eye.

Figure 5

The dc magnetic susceptibility of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ measured in magnetic fields of 1 kOe (brown circles) and 10 kOe (green circles), together with the fit using Eq. (2) (thick solid red line). The Curie-Weiss-type contribution ${\chi }_{\mathrm{CW}}$ due to Ce1 sublattice and the ${\chi }_{\mathrm{Ce}2}$ term estimated based on calculations of Rajan [54] to account for the magnetic susceptibility originating from Ce2 ions are indicated with black and brown dashed lines, respectively. The solid blue line represents the best fit to the $\chi \left(T\right)$ data at temperatures of 8–85 K by using the modified Curie-Weiss law. The inset shows ${\chi }^{-1}\left(T\right)$ in a magnetic field of 10 kOe (green circles) together with the fit by using the modified Curie-Weiss law that covers the data above $\sim 170$ K (dashed red line).

Figure 6

Low-temperature specific heat of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ shown as $C_{\mathrm{p}}\left(T\right)$ (a) and plotted in a conventional $C_p/T\left(T\right)$ representation (b). The experimental data (black circles) are shown together with results of fits based on the Debye model as described in the text. The magnetic contribution (red solid line) as well as fits based on the Kondo model for $S=1/2$ [59] (blue dots) and simulation of the magnetic specific heat of AFM dimers (black dashed line) are also presented in (a). The inset in (b) depicts the entropy per formula unit of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ calculated from the magnetic specific heat (solid brown line) and based on the sum of the electronic and magnetic specific heat (black solid line). The dashed horizontal line indicates the value of Rln2 expected for one Ce ion, a magnetic doublet ground state.

Figure 7

The electrical resistivity of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ measured on three different polycrystalline blocks normalized to the value of the resistivity at 380 K. The inset shows the $\rho \left(T\right)$ data plotted as a function of temperature on a logarithmic scale.

Figure 8

The total energy-vs-FSM curves derived from FSM calculations for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ within the LSDA approximation assuming either the experimental crystal structure (empty beige circles) or the LDA crystal lattice (filled blue circles). The FSM values represent the total magnetic spin moments per formula unit. The total energy scale was shifted to allow for direct comparison of the curves obtained for the experimental and LDA crystal structures. The calculated values of Ce1 and Ce2 spin moments are shown as black circles and red squares, respectively. For the experimental crystal structure, the symbols are empty, whereas for the LDA crystal lattice they are filled. The dashed lines are guided to the eye. The thin vertical dashed-dotted line separates FSM solutions with negligible spin polarization on Ce2 sites (on the left side) from those with Ce2 spin moment of at least 0.$1{\mu }_{\mathrm{B}}$ (on the right side).

Figure 9

The total and atomic resolved DOSs for ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ calculated within the LDA approximation (a) and using the LSDA+$U$ approach for the Ce $4f$ shell [(b) and (c)] with $U_{\mathrm{eff}}=6$ eV [65] [(b); thin lines with dots in (c)] or $U_{\mathrm{eff}}=3$ eV [(thick solid lines in (c)].

Figure 10

XPS valence-band spectrum of ${\mathrm{Ce}}_2{\mathrm{Rh}}_3{\mathrm{Sn}}_5$ (thin black solid line with dots) in comparison with theoretical spectra calculated based on partial DOSs obtained within the LDA approximation (thick black line) and using the LSDA+$U$ $(U_{\mathrm{eff}}=6$ eV) [65] approach for the Ce $4f$ shell (thick dashed red line). The thin red (grey) solid line shows the sum of partial $\text{Ce}14f$ and $\text{Ce}24f$ contributions. The grey field represents background estimated using the Tougaard algorithm [50].