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Journal of Magnetism and Magnetic Materials 311 (2007) 614–617

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Observation of the non-Fermi-liquid behavior in the evolution fromheavy-fermion to valence-fluctuation behavior in Ce(Pt1�xRhx)Si2 series

J.J. Lua,�, M.K. Leeb, Y.M. Luc, L.Y. Jangd

aNano-Technology R&D Center, Kun Shan University, YungKang 710, TaiwanbDepartment of Physics, National Cheng Kung University, Tainan 700, Taiwan

cGraduate Institute of Electro-Optical and Materials Science, National Formosa University, Huwei, Yunlin, Taiwan, ROCdNational Synchrotron Radiation Research Center, Hsinchu, Taiwan, ROC

Received 5 June 2006; received in revised form 21 July 2006

Available online 11 September 2006

Abstract

We report the results of electrical resistivity, magnetic susceptibility, heat-capacity, and Ce-LIII-edge X-ray absorption spectrum (XAS)

measurements for a solid solution series Ce(Pt1�xRhx)Si2 (x ¼ 0, 0.2, 0.4, 0.6, 0.8, 1.0). The results reveal that CePtSi2 is an

antiferromagnetic heavy-fermion compound with TN � 1:5K. As Rh content increases, the Kondo effect gradually dominates over the

magnetic ordering and drives the system towards an intermediate-valence (IV) regime with nearly quenched magnetism. Besides, we also

observed non-Fermi-liquid behaviors in CePt0.4Rh0.6Si2. These results indicate that at x � 0:6, the system is located in the vicinity of a

quantum critical point of the evolution.

r 2006 Elsevier B.V. All rights reserved.

PACS: 75.10 Nr; 71.27.+a; 71.20.Hr

Keywords: Kondo lattice; Non-Fermi-liquid; Quantum critical point

1. Introduction

It is well known that the properties of Ce alloys aregoverned by the competition between RKKY interactionand Kondo effect. The former tends to result in a state ofmagnetic order with localized moments. On the other hand,the latter is likely to lead to an itinerant state with weakmagnetism. For decades, intensive studies on the conse-quence of the interplay between these two interactions havebeen performed in various solid solutions [1–4]. Intheoretical aspect, by using a one-dimensional ‘‘Kondonecklace model’’, Doniach [5] first provided a heuristicpicture about this competition and suggested that theantiferromagnetic ordering temperature (TN) would passthrough a maximum and tend to zero, via a second-orderphase transition, at a quantum critical point (QCP). A

- see front matter r 2006 Elsevier B.V. All rights reserved.

/j.jmmm.2006.08.019

onding author. Tel.: +886 6 2727175x376;

2050509.

ddress: jjlu@mail.ksu.edu.tw (J.J. Lu).

QCP is a zero-temperature instability between two phases.Close to a QCP, the phase transition at zero temperature isnot driven by thermal fluctuation, but rather by quantumfluctuation, which can mediate singular interactionsbetween quasi-particles and provide singular Fermi-liquid(or non-Fermi-liquid (NFL)) behavior around the QCP.The NFL are referred to the metals or solid solutions whichare found to display physical properties at low tempera-tures fundamentally different from the Fermi-liquid theory.The theoretical ideas of the breakdown of the LandauFermi liquids and the fundamental characteristics of theNFL were discussed and categorized in the reviews ofVarma et al. [6] and Coleman et al. [7,8].According to Doniach’s theory [5], for a weak J (Kondo

coupling), the RKKY interaction prevails to form anantiferromagnetic ground state. Either by doping orpressure, a system can be brought to a QCP, at whichpoint the Kondo coupling increases to a critical value Jc.For systems with J4Jc, the Kondo effect dominates, andthe systems turn out to be non-magnetic. Particular

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Table 1

The lattice constants, g-values and valences of Ce(Pt1�xRhx)Si2

x a (A) b (A) c (A) g (mJ/molK2) v

0 4.28(8) 16.86(2) 4.24(8) 395.1(2) 3.01(5)

0.2 4.29(1) 16.85(3) 4.23(7) 267.6(3) 3.02(1)

0.4 4.29(6) 16.82(1) 4.23(4) 211.5(3) 3.02(8)

0.6 4.29(8) 16.78(3) 4.22(6) 145.6(5) 3.03(4)

0.8 4.30(5) 16.75(1) 4.22(0) 75.2(4) 3.06(3)

1.0 4.31(0) 16.74(3) 4.21(6) 46.2(8) 3.07(8)

Fig. 1. The normalized electrical resistivity curves (offset) of the

Ce(Pt1�xRhx)Si2 series between 0.5 and 300K. The inset shows the

electrical resistivity curve of CePt0.4Rh0.6Si2 between 0.5 and 20K.

J.J. Lu et al. / Journal of Magnetism and Magnetic Materials 311 (2007) 614–617 615

interests have focused on the region near a QCP withJ � Jc. A compound with proper magnitude of J willexhibit the so-called NFL behaviors, such asr / T1þ�ð0o�o0:6Þ, w�1ðTÞ / Taðao1Þ, C=T / � log T

in the vicinity of a QCP [7–14].In order to investigate the interplay between RKKY and

Kondo interactions, as well as the roles of NFL behaviornear a QCP, we chose an isostructrual compound seriesCe(Pt1�xRhx)Si2 (x ¼ 0, 0.2, 0.4, 0.6, 0.8, 1.0). Thesecompounds, crystallizing in the orthorhombic CeNiSi2-type structure, exhibit many attractive behaviors, such asCePtSi2 was found to be an antiferromagnetic heavy-fermion (AHF) compound with TN � 1:5K [15]; whileCeRhSi2 was reported to be a valence fluctuationcompound [16]. Therefore, by a progressive substitutionof Rh for Pt, the Ce(Pt1�xRhx)Si2 series can offer anexcellent opportunity to investigate not only the effectivesuppression of the long-range magnetic order by theKondo interaction, but also the quantum critical behaviorsin the vicinity of a QCP.

2. Experimental details

The samples of Ce(Pt1�xRhx)Si2 were synthesized by arc-melting appropriate mixtures of the constituent elements ofat least 99.99% purity under highly purified argon gas atone atmosphere. The arc-melted ingots were then sealed inevacuated quarts tubes and annealed at 1050 1C for 5 days.

The electrical resistivities and specific-heat measure-ments were carried out in the cryostat of a QuantumDesign physical property measurement system (PPMS).Below 1.8K (down to 0.5K), the electrical resistivity andspecific-heat measurements were performed in a continu-ously circulating 3He/4He dilution refrigerator system(Quantum Design, Model P8500) in the PPMS.

The DC magnetic properties were measured by aSQUID magnetometer by zero-field cooled (ZFC) method.It was achieved by cooling the sample to 1.7K, thenapplying a DC magnetic field at 1.7K. We then warmed upthe sample while measuring DC susceptibility in theconstant field.

The valences of Ce ions were determined at the NationalSynchrotron Radiation Research Center (NSRRC,Hsinchu, Taiwan, ROC). Data were obtained by measur-ing the transmission Ce LIII-edge absorption spectrathrough 4 layers of powder spread onto the Scotch tape.All the samples were ground into fine powder to avoidthickness effect. XAS measurements at low temperatureswere carried out using a closed cycle cryogenic system.

3. Results and discussions

A microcomputer controlled powder diffractometer(Rigaku, D/MAX-2500) with Cu-Ka radiation(l ¼ 1:54056 A), was used to examine the purities of allsamples in the range of 201p2yp801. The XRD resultsindicate that all of the samples are essentially single phase

with orthorhombic CeNiSi2-type crystal structure. Thelattice parameters, which were obtained by using the least-square-fitting method, are listed in Table 1. The latticeparameters of CeRhSi2 and CePtSi2 are broadly consistentwith the previous reports [16,17].Fig. 1 displays temperature dependence of normalized

electrical resistances (r(T)/r(300K)) of the samples. ForPt-rich compounds, the r(T) curves show basically a denseKondo system behavior. The r(T) curve of CePtSi2 exhibitsa broad maximum at �30K, followed by a steep dropbelow 6K. The broad maximum is likely to stem from theKondo scattering between the low-lying crystal field (CF)excited states; whereas the steep decrease below 6K mayoriginate from the onset of the Kondo coherent state. ForxX0:8, the r(T) curves show a broad maximum at highertemperatures and exhibit a quadratic dependence at lowtemperatures, revealing the characteristic feature for avalence fluctuation compound with Fermi-liquid groundstate. The position of the broad maximum can be taken asa measure of the Kondo temperature TK, which is thecharacteristic temperature of single-ion Kondo effect.From Fig. 1, one can see that the broad maxima movetowards higher temperatures as x increases. The shift in TK

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Fig. 3. Molar susceptibility w(T) of (a) CeRhSi2, and (b) CePtSi2 in 100Oe

field between 1.7 and 300K. The inset shows w�1(T) curve of

CePt0.4Rh0.6Si2 between 1.7 and 40K.

J.J. Lu et al. / Journal of Magnetism and Magnetic Materials 311 (2007) 614–617616

can be ascribed to the enhancement of the Kondo effect byincreasing the Rh content.

The r(T) curve of CePt0.4Rh0.6Si2 (x ¼ 0:6) between 0.5and 20K, is depicted in the inset of Fig. 1. The resistivitydrops on cooling and exhibits a power law dependence(r / T1:2) below 16K. Such a behavior in resistivity isoften found in a material in the vicinity of a QCP [7–14].

The heat-capacity results of the series are plotted inFig. 2. For x ¼ 0, a pronounced peak near 1.5K isobserved, which was attributed to an antiferromagneticphase transition by Geigel et al. [15]. For CePt0.8Rh0.2Si2,an anomaly is found at �0.6K, which is also likelyassociated with an antiferromagnetic ordering. Withfurther increase in Rh contents, the compounds do notexhibit any feature attributed to a magnetic phasetransition above 0.5K. However, a small bump near 6Kwas observed in all compounds. The little bumps arepresumably due to small amounts of Ce2O3 phase, oftenreported in the literatures of Ce compounds [3,15,18,19].The g-values (electronic specific heat coefficient), which areobtained by fitting the C/T vs. T2 curves, are listed in Table1. The g-value of CePtSi2 is 395.1(2)mJ/molK2, which istypical for a heavy fermion (HF) compound. For CeRhSi2,the g-value is about 46.2(8)mJ/molK2. This g-value is notlarge enough to classify CeRhSi2 as an HF material. On theother hand, it is a typical value of an IV compound[3,20,21]. From Table 1, while increasing the Rh content, atendency towards decreasing g-values is obvious. Weattribute it to the enhancement of c-f hybridization(hybridization between conduction bands and 4f states),stemming from Kondo effect dominating over RKKYinteraction when substituting Rh for Pt.

The temperature dependence of molar magnetic suscept-ibility of CeRhSi2 and CePtSi2 in 100Oe is plotted inFig. 3. The w(T) curve of CeRhSi2 (x ¼ 1:0) shows a broadmaximum around 90K, and exhibits a wðTÞ ¼ w0ð1þ aT2Þ

behavior at low temperatures. Such a feature in suscept-

Fig. 2. The C(T) curves of Ce(Pt1�xRhx)Si2 series between 0.5 and 15K.

ibility is often observed in a valence fluctuation system witha Fermi-liquid ground state [20,22,23]. For CePtSi2(x ¼ 0), the w(T) increases rapidly at low temperatures,presumably due to the antiferromagnetic ordering found inthe heat-capacity measurement. However, the temperaturesof our magnetic susceptibility measurements are not lowenough to observe the peak of the antiferromagnetic phasetransition. The susceptibility of CePtSi2 follows theCurie–Weiss law above T�80K, and the effective momentdeduced from paramagnetic region is 2.62 mB per ceriumion, which is close to Ce3+ free ion in 2F5/2 state. Whileincreasing x, a tendency towards decreasing in magneticsusceptibility is apparent, indicating the enhancement ofquenched magnetism as Rh content increases. The insetdisplays the inverse molar susceptibility w�1(T) ofCePt0.4Rh0.6Si2 between 1.7 and 40K. The w�1(T) curveexhibits a power-law dependence (w�1ðTÞ ¼ wð0Þ�1 þ ATa,with a ¼ 0:337) below 30K. Such a power-law behavior inmagnetic susceptibility, often reported for the systems neara QCP [10–13], is one of the characteristic features of NFLbehaviors.X-ray absorption spectroscopy (XAS) is a useful tool to

identify a valence fluctuation system. The Ce LIII-edgespectrum consists of a superposition of two integral valenceedges (Ce3+ and Ce4+). By fitting the spectrum with thespectral weight of the two valence edges, we are able todetermine the Ce valence. The details of the fittingprocedure have been discussed elsewhere [2,3]. The CeLIII-edge spectra of Ce(Pt1�xRhx)Si2 at T ¼ 15K aredisplayed in Fig. 4. The calculated valence (n) of Ce inCeRhSi2 is 3.07(8), which is a typical value for a Ce IVsystem. As for CePtSi2, the valence of Ce is nearly trivalent(3.015), indicating a localized nature of a Ce3+ ion in this

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Fig. 4. Ce LIII-edge XAS of Ce(Pt1�xRhx)Si2 series at T ¼ 15K.

J.J. Lu et al. / Journal of Magnetism and Magnetic Materials 311 (2007) 614–617 617

compound. The result is also consistent with the effectivemoment obtained from the magnetic susceptibility mea-surement of CePtSi2. The valences of Ce are also listed inTable 1. From Table 1, a tendency of increase in n towardsthe Rh-rich end is obvious. The increase in Ce valence canbe attributed to the enhancement of c-f hybridization as Rhcontent increases, hence offering a direct evidence for theevolution.

4. Conclusions

To study the competition between RKKY and Kondointeractions, as well as the physical properties near a QCP,a solid solution series Ce(Pt1�xRhx)Si2 has been synthe-sized and examined by the X-ray diffraction, electricalresistivity, DC magnetic susceptibility, heat capacitymeasurements and the core-level XAS. The results revealthat for Pt-rich end, the RKKY interaction between localmoments prevails to lead to an AHF behavior. As Rhcontent increases, the antiferromagnetism is graduallysuppressed by the enhanced Kondo interaction, whicheventually drives the series to an intermediate-valence (IV)regime. In other words, the magnetism of local momentsystems will vanish once the Kondo interaction (J)becomes large enough to dominate over RKKY interac-tion. While in the region with critical Kondo interaction,singular interactions between quasi-particles will greatly

modify the physical properties of the system, and give riseto non-Fermi liquid behavior.In this work, the evolution was verified by electrical

resistivity, heat capacity, and magnetic susceptibilitymeasurements, as well as the Ce LIII-edge XAS. Inaddition, non-Fermi liquid behaviors were observed inCePt0.4Rh0.6Si2, indicating that x � 0:6 is in the vicinity ofthe QCP of the transition.

Acknowledgements

This work was supported by the National SynchrotronRadiation Research Center of ROC and National ScienceCouncil of the Republic of China under contract no. NCS-93-2116-E-168-006.

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