Neutron scattering and μSR studies on a Kondo lattice heavy fermion CeRuSn3

Kondo lattice heavy fermion system CeRuSn3 exhibits anomalies in magnetic susceptibility and specific heat at a temperature T ≈ 0.6 K (much lower than the average Kondo temperature TK ≈ 3.1 K) which are thought to be related to antiferromagnetic ordering or spin-glass transition. Our muon spin relaxation (μSR) data show no clear evidence of long range magnetic order in CeRuSn3 down to 84 mK. However, it reveals a slowing down of spin fluctuations below 0.6 K, and a glassy spin-dynamics seems more appropriate. The inelastic neutron scattering data reveal broad excitations around 6-8 meV due to the crystal field effect.


Introduction
The heavy-fermion compounds that belong to the large class of strongly correlated electronic systems present very rich physics due to its proximity to a quantum critical point (QCP) and have been a topic of intense research for last few decades [1][2][3][4][5][6]. Ce-based heavy fermion systems present fascinating physics due to the Kondo effect that competes with and becomes comparable to RKKY interaction in the vicinity of a QCP. Kondo lattice-heavy fermion CeRuSn 3 is an interesting example. CeRuSn 3 forms in LaRuSn 3 -type cubic structure (space group P m3n, No. 223) in which Ce atoms occupy two different crystallographic sites, Ru and Sn atoms form trigonal RuSn 6 prisms, and the three-dimensional network of these prisms form cages which are occupied by Ce atoms [7]. An enhanced Sommerfeld coefficient γ together with a logarithmic increase (− ln T behavior) in resistivity ρ with decreasing temperature T reflect the Kondo lattice-heavy fermion behavior in CeRuSn 3 [8,9]. However, both resistivity and Hall effect data reveal an absence of coherence effect which was argued to be due to the possible existence of atomic disorder [8,9]. The dc magnetic susceptibility χ was found to show a large magnitude without any magnetic order above 1.7 K. On the other hand, ac χ(T ) was found to show a sharp anomaly at T ≈ 0.5 K and this was accompanied with a broad peak near 0.5 K in specific heat C p /T versus T which Takayanagi et al. [9] suggested to be related to antiferromagnetic ordering or spin-glass transition.
In this contribution through the χ(T ), M (H), C p (T ), ρ(T, H), muon spin relaxation (µSR) and inelastic neutron scattering (INS) investigations we show that there is no long range magnetic order in CeRuSn 3 and a glassy spin-dynamics is favored. Recently, we found a ferromagnetic cluster spin-glass behavior in isostructural PrRhSn 3 [10] and a complex magnetic ground state in the Kondo lattice heavy fermion system CeRhSn 3 [11].

Experimental
The experimental details of sample synthesis and χ(T ), M (H), C p (T ) and ρ(T, H) measurements can be found in [11]. The muon spin relaxation experiment was performed using MuSR spectrometer at ISIS facility of the Rutherford Appleton Laboratory, Didcot, U.K. For µSR experiment the powdered sample of CeRuSn 3 was mounted on a high purity silver holder using diluted GE varnish that was covered with a thin silver foil. The sample mount was cooled in a dilution refrigerator to achieve the low temperature down to 84 mK. The inelastic neutron scattering experiment was performed with the HET time of flight spectrometer at ISIS. For INS experiment the powdered sample was filled in a thin Al-foil envelop (40 × 40 × 0.5 mm 3 ) and mounted inside a top-loading closed cycle refrigerator (CCR).

Results and Discussion
The χ(T ) of CeRuSn 3 and its inverse χ −1 measured in magnetic field H = 0.5 T are shown in figure 1(a). The zero field cooled (ZFC) and field cooled (FC) low-T χ(T ) shown in inset exhibit an irreversibility that sets in at a temperature slightly above 0.6 K and ZFC χ shows a broad anomaly near 0.6 K. Further we see that the χ attains a value ≈ 0.4 emu/mol which is rather large for a Kondo system, as also reported previously [8,9]. At high-T the χ(T ) follows modified Curie-Weiss behavior The isothermal magnetization M (H) data of CeRuSn 3 measured at selected temperatures of 0.5 K, 1.8 K, 5 K and 10 K are shown in figure 1(b). While at 10 K M is almost linear in H, at 1.8 K the M (H) isotherm shows slight nonlinearity likely due to the presence of short range magnetic correlations. At 0.5 K the nonlinearity is even more pronounced. Further, the M (H) isotherm at 0.5 K shows that the M attains a value of only 0.55 µ B at the highest measured field H = 7 T. This value of M is much lower than the expected saturation value of M s = 2.14 µ B /Ce 3+ . The low value of M at 7 T could be due to the crystal field effect and/or due to the screening of moment by Kondo effect.
The C p (T ) data of CeRuSn 3 measured in H = 0.05 T and 1.0 T for 0.38 K ≤ T ≤ 20 K are shown in figure 2. As shown in figure 2(a) the low-T C p (T ) data (H = 0.05 T) of CeRuSn 3 show a broad hump near 3 K (related to Kondo temperature T K ) and a rapid decrease below 0.6 K. The C p (T ) data when plotted as C p /T versus T as shown in figure 2(b) initially decreases with decreasing T down to about 7 K below which an increase is observed in C p /T with decreasing T until it reaches a maximum near 0.6 K below which C p /T starts decreasing again with decreasing T . The C p (T ) data measured at H = 1.0 T show that the entropy associated with the peak in C p (T )/T is smeared out, and the peak becomes broader, moves towards the higher temperature side and peak height is reduced [inset of figure 2(b)]. The C p (T )/T data could be nicely fitted by C p /T = γ + βT 2 and a fit over 10 K ≤ T ≤ 15 K yielded γ = 212(2) mJ/mol K 2 and β = 1.12(1) mJ/mol K 4 . Since at lower T C p /T shows an increase with decreasing T , γ ≥ 212(2) mJ/mol K 2 and reflects the heavy fermion behavior in CeRuSn 3 . A comparison of γ values of CeRuSn 3 and LaRuSn 3 [γ = 5.0(5) mJ/mol K 2 ] suggests the quasi-particle density of states renormalization factor due to 4f correlations in CeRuSn 3 to be ≈ 42.
The ρ(T ) data of CeRuSn 3 measured in zero field for 2 K ≤ T ≤ 350 K are shown in figure 3. The T dependence of ρ reflects the Kondo lattice behavior. It is seen from figure 3(a) H) is negative up to the measured field of 9 T. The magnitude of MR depends on temperature and decreases with incresing T . At 2.0 K initially the negative MR increases slowly up to 1.2 T, above which there is an increase in slope of ∆ρ(H)/ρ(0) and eventually at 9 T the negative MR is about 7.5 %. At 5 K no change in slope is observed near 1.2 T, thus the change in the slope of MR at 2.0 K seems to be related to the 4 K anomaly in ρ(T ) discussed above. The negative MR in paramagnetic state of CeRuSn 3 can be associated with the freezing out of spin-flip scattering due to Kondo interaction.
The zero field µSR asymmetry spectra at few representative temperatures between 0.2 K and 1.9 K are shown in figure 4. The µSR spectra show weak damping above 1 K and damping becomes stronger with decreasing T and a clear change in muon depolarization rates at T ≤ 0.6 K can be inferred from µSR data in figures 4(a)-(d). The muon initial asymmetry is found to remain nearly constant (irrespective of temperature) down to 84 mK. Further, there is no clear sign of time oscillations of the asymmetry down to the lowest T in the µSR spectra. Both these observations indicate that within the µSR probing time scale CeRuSn 3 does not exhibit a We analyzed the µSR data of CeRuSn 3 taking into account both static and dynamic local fields at muon sites. While the static relaxation dominates at short time, at longer time the relaxation rate probes only the dynamic spin fluctuations. The µSR data of CeRuSn 3 were analysed using the following form of the relaxation function, where A 01 and A 02 are the initial asymmetries of the two components, and λ and σ are the depolarization rates. The first term in equation (1) (called Lorentzian form) accounts for the dynamic magnetic fluctuations, second term (called Gaussian form) accounts for isotropic Gaussian distribution of static fields and the third term is a constant background arising from muons stopping on the silver sample holder. The solid curves in figures 4(a)-(d) show the fits of µSR data by this combination of Lorenztian and Gaussian decays. Our analysis of µSR data reveals that the Gaussian contribution (static fluctuations) becomes sizable below 0.6 K and suggests a slowing down of spin fluctuations. We also carried out analysis of µSR data using Abragam functional form [13] which is applicable in an intermediate fluctuation range regime, i.e. in the limit between the slow (static, τ c σ > 1) and fast (dynamic, τ c σ ≪ 1). The data between 0.084 K and 0.9 K could be fitted very well with this function and we found that τ c σ ∼ 1 at 84 mK, which suggests that magnetic ground state in CeRuSn 3 is not fully static long range ordered, but short range ordered.
The inelastic neutron scattering response for the measurement using neutrons with incident energy E i = 23 meV at 4.5 K is shown in figure 5. A broad excitation centered around 6-8 meV is inferred from the INS data in figure 5 that can be attributed to the crystal electric field (CEF) excitations of the Ce 3+ . As there are two crystallographic Ce sites with cubic and tetragonal symmetries, we expect three CEF excitations (one from cubic and two from tetragonal Ce cites). However we see only a broad excitation near 6-8 meV, which indicates that the excitation from the two Ce sites have a similar energy scale. The analysis of INS data is underway.

Conclusions
The Kondo lattice and heavy fermion behaviors in CeRuSn 3 are confirmed from our C p (T ) and ρ(T ) measurements. Both χ(T ) and C p (T ) reveal the reported anomaly at T ≈ 0.6 K < T K ≈ 3.1 K. Observation of an irreversibility between the ZFC and FC χ(T ) suggests that the anomaly is not related to an antiferromagnetic transition as is also inferred from the µSR data which does not show any spontaneous oscillations down to 84 mK to reveal a long range magnetic order. Short range ordering and glassy spin-dynamics seems apposite in CeRuSn 3 . The INS data show only a broad crystal electric field (CEF) excitation centered around 6-8 meV contrasting the expected three CEF excitations.