Evolution of a magnetic order in the quasi-kagome lattice system CeRh1–xPdxSn (x ≤ 0.75)

The equiatomic compound CeRhSn with a quasi-kagome lattice of Ce atoms displays a non-Fermi liquid behavior at low temperatures. We have studied how the ground state changes with the substitution of Pd for Rh in CeRh1–xPdxSn (0 ≤ x ≤ 0.75) by measuring the specific heat C, magnetic susceptibility χ, and magnetization M. With increasing x, the lattice parameters a and c increase by 1.6%, the paramagnetic Curie temperature in χ(T) changes from –112 K to 16 K, and M(B = 5 T) at T = 1.8 K increases from 0.05μB/Ce to 1.4μB/Ce. A long-range magnetic order manifests in sharp peaks in C at 0.7, 1.0 and 1.5 K for x = 0.4, 0.5 and 0.65, respectively. An antiferromagnetic order for x = 0.75 is indicated by the observations of peaks in both χ(T) and C(T) at around 3.0 K and metamagnetic behavior in M(B) at B = 2 T. Our results point out that the doping of 4d electrons in the non-Fermi liquid system CeRhSn destroys the coherence of the quasi-kagome lattice and weakens the hybridization between the 4f state and conduction bands, leading to the evolution of antiferromagnetic order.


Introduction
Quantum phase transitions in the 4f electron systems have fascinated physicists for decades because they involve competition and/or coexistence of magnetic order, non-Fermi liquid (NFL) state, and unconventional superconductivity [1,2]. Conventional quantum criticality at zero temperature can be reached by tuning the coupling between the 4f electron and conduction electrons governing the competition between RKKY-interaction and Kondo effect, well known as the Doniach phase diagram [3]. The ordinary ways to tune the balance of the two interactions are through chemical composition, pressure, and magnetic field, leading from a magnetically ordered state to a paramagnetic one [4]. Recently, a kagome lattice of 4f elements with antiferromagnetic nearest neighbor interaction due to the triangular-like geometry is reported to induce an unconventional quantum critical point [5][6][7][8][9][10][11][12]. In this system the competition occurs between a spin liquid state and a Kondo singlet state, which is caused by the interplay among the RKKY-interaction, Kondo effect, and magnetic frustration [13,14]. Hence, a long-range order can be induced by either destruction of symmetry of frustrated structure or breakdown of Kondo screening behavior.
CePdAl has a quasi-kagome lattice of Ce ions in the hexagonal ZrNiAl-type structure [5,15,16]. Within a single quasi-kagome layer, only two thirds of Ce moments participating in the antiferromagnetic (AFM) long-range order occurring at TN = 2.7 K, while the others remain paramagnetic [6]. By doping with Ni for Pd, the AFM order in CePd1-xNixAl is completely suppressed at x = 0.144. The frustrated Ce moments give rise to a two dimensional quantum critical point (QCP) [9]. The ratio |θp|/TN, where p is the paramagnetic Curie temperature in the magnetic susceptibility χ, increases with x as the Kondo effect surpasses the RKKY-interaction. Another example with QCP is the isostructural alloy system CeRh1-xPdxIn, in which a mixed valence state changes to an AFM heavy fermion state [12]. Then, an AFM order appears for x = 0.8 at TN = 0.65 K which rises to 1.7 K for x = 1. Thereby, the increase in the 4d-electron number deepens the 4f level from the Fermi level suppressing the hybridization between 4f states of Ce and 4d states.
In the isostructural compound CeRhSn, layers composed of Ce and Rh1 atoms alternate along the c axis with layers composed of Rh2 and Sn atoms as shown in insert of Figure 1 [11]. Nearest neighbors for the Ce atom are four Rh2 atoms and the second nearest neighbor is one Rh1 atom. This structural aspect suggested that the Ce 4f state is strongly hybridized with the 4d band derived mainly from the Rh2 atoms, leading to the valence-fluctuating state with a high Kondo temperature TK  200 K. Below 7 K, however, NFL behavior appear: χ(T) shows a power-law behavior, ρ(T) decreases with ( ≤ 1.5), and the specific heat divided by temperature C/T shows an upturn and saturation to a large value of 200 mJ/K 2 mol. These evident NFL behaviors are thought to be manifestation of the frustration of Ce moments which hinders the long-range order and leads to a QCP. Furthermore, a zero-field QCP in CeRhSn has been indicated by the measurements of C, uniaxial thermal expansion, and magnetic Grüneisen parameter [17]. The anisotropy of thermal expansion displaying the critical behavior only along the a axis is in support of the fact that the quantum criticality is driven by geometrical frustration in the quasi-kagome lattice.
Recently, it has been reported that the alloy CeRh1-xPdxSn maintains the ZrNiAl-type structure up to x = 0.8 [18]. In the whole range, no magnetic order was found down to 2.5 K in the measurements of χ(T). We expected that the destruction of the local symmetry of the frustrated structure should induce a magnetic order. Therefore, we have studied the magnetic properties down to 0.4 K in this work.

Experiment
Polycrystalline samples with initial compositions of CeRh1-XPdXSn (X = 0, 0.2, 0.3, 0.4, 0.5, 0.7, 0.8) were prepared by arc-melting appropriate amounts of constituent elements Ce (99.9%), Rh (99.9%), Pd (99.99%) and Sn (99.999%) under a pure argon atmosphere. In order to improve the homogeneity, these samples were turned over after melting and remelted for several times, and were subsequently annealed at 900℃ for 6 days in evacuated quartz ampoules. Total weight loss after preparation was not above 1%. The samples were characterized by powder X-ray diffraction and wavelength dispersive electron-probe microanalysis (EPMA). Lattice parameters of the ZrNiAl-type structure were calculated by least-square refinements of the XRD patterns. The metallographic examination showed that the polycrystalline samples are composed of grains preferentially oriented along the c axis, which is perpendicular to the bottom of the ingot. For the measurements of χ(T) and magnetization M(B), the magnetic field was applied along the preferentially oriented c axis of the samples which were cut perpendicularly to the bottom. The measurements were performed in the temperature range from 1.8 to 300 K with a Quantum Design MPMS. The specific heat was measured on 10 mg samples from 0.4 to 20 K by the relaxation method in a Quantum Design PPMS.

Chemical and structural properties
The results of EPMA are consistent with the nominal composition for X ≤ 0.5. However, with increasing X, the quantity of impure phase Ce(Rh1-XPdX)2Sn2 increased. The real compositions of Pd, x, in CeRh1-xPdxSn phase were found to be 0.65 and 0.75 for X = 0.7 and 0. 8 lattice parameters a and c of CeRhSn agree with the reported values [18]. As shown in Figure 1, the a parameter linearly increases as x increases from 0 to 0.75, while the x dependence of the c parameter deviates upward from the Vegard's law, in consistent with the previous report [18]. This deviation hints a change in the 4f state from the valence fluctuating state to the localized state, which is consistent with the results of magnetic susceptibility and magnetization as will be shown in the next subsections. The expansion along the c axis enlarges the distance between Ce and Rh2 out of basal plane, which may decrease the overlap of wave functions between the 4f electron and the 4d electron. Nevertheless, local extension in the basal plane may break the symmetry of the quasi-kagome lattice of Ce atoms. Figure 2 shows the inverse susceptibility as a function of temperature for CeRh1-xPdxSn (x ≤ 0.75) measured in a magnetic field of 1 T. The solid lines at T ˃ 100 K represent the Curie-Weiss fit with χ = C/ (T  θp) + χ0, where the last term represents the temperature independent contribution. For x = 0, the large negative value of paramagnetic Curie temperature θp = 112 K and effective magnetic moment   With the increase in x to 0.2, the value of |θp| decreases to 13 K. This decreasing trend in |θp| suggests that the hybridization is weakened as |θp|/2 is a measure of TK [19]. The sign of θp becomes positive for x  0.65, which can be attributed either to the crystal field effect on nearly trivalent Ce ions or possible ferromagnetic interaction due to the increase in the Fermi wave vector. For x ≥ 0.65, μeff increases to 2.50μB/Ce, which value is close to 2.54μB expected for a free Ce +3 ion. As shown in the inset of Figure 2, the data of χ(T) for x = 0.75 exhibits an obvious maximum at around 3 K, suggesting an antiferromagnetic order. The magnetization curves M(B) measured in fields up to 5 T at T = 1.8 K are shown in Figure 3.

Specific heat
The data of specific heat C between 0.4 K and 20 K are plotted as C/T vs logT in Figure 4. For x = 0, C/T linearly increases on cooling below 7 K and saturates to a value γ = 290 mJ/K 2 mol, in agreement with the behaviour reported for a single crystal [11]. For x = 0.2 and 0.3, pronounced upturns suggest the approach to a QCP. For x ≥ 0.4, the C/T data exhibit peaks, whose temperatures are taken as TN. The TN increases from 0.7 K for x = 0.4 to 1.5 K for x = 0.65, indicating the enhancement of AF  interaction and/or growth of magnetic moments. For x = 0.75, two maxima are found at 1.2 K and 3 K. The latter one is identified as TN because it agrees with the maximum temperature in χ(T). It is noted that the peaks in the C/T data broaden with increasing x from 0.4 to 0.75. The magnetic structure in this system should be further studied by the neutron diffraction experiment.
In order to obtain the magnetic entropy S(T), specific data of CeRh1-xPdxSn for 0 ≤ x ≤ 0.3 and 0.4 ≤ x ≤ 0.75 were extrapolated, respectively, with the equations / = + 2 + 2 ln [20] and / = + 2 + 2 −Δ/ [ 21]. The data of isostructural LaRhSn were used as the phonon contribution. The temperature dependences of S(T) are plotted in Figure 5. The S(T) curves for x = 0.65 and 0.75 are saturated to Rln2 at 20 K, confirming the doublet ground state under the crystal field. The TK was estimated by the relationship S(TK) = 0.65Rln2, which was given for a Kondo impurity [22,23]. The values of TK as a function of x are shown in insert. The TK decreases rapidly from 16 K for x = 0.2 to 5 K for x = 0.4, indicating the strong suppression of Kondo effect.

Conclusions
We have reported a set of measurements on X-ray diffraction, magnetic susceptibility, magnetization, and specific heat for CeRh1-xPdxSn series in which the Ce atoms form a quasi-kagome lattice. With increasing x up to 0.75, which is the limit for the ZrNiAl-type structure, lattice parameters a and c increase by 1.6%. The 4f state of Ce ion changes from a valence fluctuating state to a stable trivalent state with a doublet ground state. Importantly, the specific data show apparent maximum in C/T for x ≥ 0.4. The spin-flop behaviour in the magnetization curve and the peak in χ(T) for x = 0.75 supports the AFM ordered state. The AFM order may be induced by the combination of two mechanisms. On one hand, the increasing c axis parameter and additional 4d electrons weaken the hybridization between 4f orbitals of Ce and 4d orbitals of Rh2. As a result, the magnetic moment is increased and thus the RKKY interaction is enhanced. On the other hand, local extension in the basal plane near the Pd atoms may break the symmetry of the quasi-kagome lattice of Ce atoms, then the frustrated Ce moments have the chance to be coupled antiparallel. In any case, we have found that the NFL state of CeRhSn is easily transformed to an AFM ordered state. For the study of quantum phase transition, the system CeRh1-xPdxSn deserves to be further studied by neutron scattering and μSR experiments.