Relaxing Kondo-screened Kramers doublets in $\mathrm{CeRhSi}{}_3$

${\mathrm{CeRhSi}}_3$ is a superconductor under pressure coexisting with a weakly antiferromagnetic phase characterized by a Bragg peak at ${\vec{q}}_0=(\sim 0.2,0,0.5)$ [N. Aso et al., J. Magn. Magn. Mater. 310, 602 (2007)]. The compound is also a heavy-fermion material with a large specific heat coefficient $\gamma =110$ mJ ${\mathrm{mol}}^{-1}{\mathrm{K}}^{-2}$ and a high Kondo temperature of $T_K=50$ K, indicating ${\mathrm{CeRhSi}}_3$ is in a strongly Kondo screened state. We apply high-resolution neutron spectroscopy to investigate the magnetic fluctuations in the normal phase, at ambient pressures, and at low temperatures. We measure a commensurate dynamic response centered around the $\vec{Q}=(0,0,2)$ position that gradually evolves to $H\sim 0.2$ with decreasing temperature and/or energy transfers. The response is broadened both in momentum and energy and is not reminiscent of sharp spin wave excitations found in insulating magnets where the electrons are localized. We parametrize the excitation spectrum and temperature dependence using a heuristic model utilizing the random-phase approximation to couple relaxing ${\mathrm{Ce}}^{3+}$ ground-state Kramers doublets with a Kondo-like dynamic response. With a Ruderman-Kittel-Kasuya-Yosida exchange interaction within the $ab$ plane and an increasing single-site susceptibility, we can qualitatively reproduce the neutron spectroscopic results in ${\mathrm{CeRhSi}}_3$ and, namely, the trade-off between scattering at commensurate and incommensurate positions. We suggest that the antiferromagnetic phase in ${\mathrm{CeRhSi}}_3$ is driven by weakly correlated relaxing localized Kramers doublets and that ${\mathrm{CeRhSi}}_3$ at ambient pressures is on the border between a Rudderman-Kittel-Yosida antiferromagnetic state and a Kondo-screened phase where static magnetism is predominately absent.

Figure 1

(a) The $I4mm$ (No. 107) crystal structure of ${\mathrm{CeRhSi}}_3$ and (b) the crystal field scheme discussed in the text using the Stevens parameters extracted by Muro et al. [32].

Figure 2

(a) The rocking curve through the (002) Bragg peak with a full width at half maximum of $4.0^{\circ }$ at room temperature. (b) Heat capacity data as a function of temperature for ${\mathrm{CeRhSi}}_3$, confirming a transition at $\sim 1.8$ K. (c) and (d) The sample mount used for the neutron inelastic scattering studies on ${\mathrm{CeRhSi}}_3$ discussed in the text.

Figure 3

The method used to determine the background. (a) The smoothed intensity. (b) The remaining data after removing the main magnetic signal, Bragg peaks, and central beam. (c) The background signal generated by finding the radial average of (b). (d) The magnetic signal found by removing the background in (c) from the smoothed data in (a).

Figure 4

Constant $E=0.5$ meV slices taken on MACS at (a) $T=0.3$ K, (b) 6 K, and (c) 10 K. Slices along the $(H,0,1.5\pm 0.2)$ direction are shown in (d)–(f). The lines are fits to Gaussians, with (d) illustrating two symmetrically displaced peaks and (e) showing a fit to two peaks and also a single peak. At high temperatures of 10 K in (f), the correlated scattering is well described by a single peak centered at the $H=0$ position.

Figure 5

$T=0.5$ K constant-energy cuts at (a) $E=0.5$ meV, (b) 0.75 meV, and (c) 1.0 meV. The correlated magnetic scattering weakens and also shifts spectral weight to the commensurate position with increasing energy transfer.

Figure 6

A comparison of the magnetic scattering in the (a)–(c) $(H,0,L)$ and (d)–(f) $(H,H,L)$ scattering planes.

Figure 7

Constant $E=0.5$ meV scans at 0 and 6 T taken on the IN12 spectrometer (ILL) with $E_f=3.5$ meV. A temperature-independent background has been subtracted from the data. No strong or significant response of the magnetic fluctuations to field is observed.

Figure 8

(a) The location in $H$ of the maximum scattering intensity as a function of $X_0$ and exchange constant $J$ between different ${\mathrm{Ce}}^{3+}$ ions. (b) A simulated constant $E=0.5$ meV slice taken with large $X_0$ and interlayer correlations $\alpha$. (c) A simulated constant-energy slice with weak $X_0$ and interlayer correlations. The calculations were done with $\mathrm{\Gamma }=0.5$ meV.