[[abstract]]Magnetic ordering and Kondo behavior coexist in three (Ce,Al)-based compounds: CeAl2, Ce3Al, and Ce3Al11. A common feature apparently independent of crystal structures also prevails in terms of the size-induced transition between these two magnetic phenomena. As the particle size is reduced to nanoscale, the specific heat anomaly associated with the magnetic ordering diminishes. Although the Kondo temperature also decreases, the entropy associated with Kondo anomaly exhibits a large increase. This results in an enhancement of the Kondo behavior and an increased coefficient γ of the linear term in specific heat. For example, in 80 Å CeAl2 the extrapolated r(0) reaches 9000mJmolCe−1K−2.[[notice]]補正完畢[[booktype]]紙本[[booktype]]電子

Chen, Yih-Sharng

Magnetic ordering and Kondo behavior coexist in three (Ce,Al)-based compounds: CeAl2, Ce3Al, and Ce3Al11. A common feature apparently independent of crystal structures also prevails in terms of the size-induced transition between these two magnetic phenomena. As the particle size is reduced to nanoscale, the specific heat anomaly associated with the magnetic ordering diminishes. Although the Kondo temperature also decreases, the entropy associated with Kondo anomaly exhibits a large increase. This results in an enhancement of the Kondo behavior and an increased coefficient γ of the linear term in specific heat. For example, in 80 Å CeAl2 the extrapolated r(0) reaches 9000mJmolCe−1K−2.補正完畢紙本電子

Tamkang University Institutional Repository

VOLUME 84, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 22 MAY 20004Size-Induced Transition from Magnetic Ordering to Kondo Behavior in (Ce,Al) CompoundsY. Y. Chen,1 Y. D. Yao,1 C. R. Wang,1 W. H. Li,2 C. L. Chang,3 T. K. Lee,1 T. M. Hong,4 J. C. Ho,5 and S. F. Pan11Institute of Physics, Academia Sinica, Taipei, Taiwan, Republic of China2Department of Physics, National Central University, Chung-li, Taiwan, Republic of China3Department of Physics, Tamkang University, Tamsui, Taiwan, Republic of China4Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China5Department of Physics, Wichita State University, Wichita, Kansas 67260(Received 1 September 1999)Magnetic ordering and Kondo behavior coexist in three (Ce,Al)-based compounds: CeAl2, Ce3Al,and Ce3Al11. A common feature apparently independent of crystal structures also prevails in terms ofthe size-induced transition between these two magnetic phenomena. As the particle size is reduced tonanoscale, the specific heat anomaly associated with the magnetic ordering diminishes. Although theKondo temperature also decreases, the entropy associated with Kondo anomaly exhibits a large increase.This results in an enhancement of the Kondo behavior and an increased coefficient g of the linear termin specific heat. For example, in 80 Å CeAl2 the extrapolated r0 reaches 9000 mJ mol Ce21 K22.PACS numbers: 75.30.Mb, 72.15.Qm, 75.40.CxIn Ce32xLaxAl11, Trinkl et al. [1] have shown that thesuppression of magnetic order is accompanied by an en-hancement of the single ion Kondo interaction by La sub-stitution. Since the magnetic order suppression can also beinduced by reducing particle size in, e.g., transition metals[2], it is of great interest to examine further the interplaybetween Kondo interaction and magnetic order through thesize effect. Not surprisingly, point contacts, wires, and thinfilms have been the subject of Kondo effect studies [3–5].However, they have quite different geometry and physi-cal configuration from that of fine particles [6] as focusedupon in the present calorimetric work on CeAl2, Ce3Al,and Ce3Al11.The three (Ce,Al)-based compounds are known to beheavy fermion systems. In its bulk form, CeAl2 has a cubicLaves structure. It undergoes an antiferromagnetic order-ing at TN  3.8 K with g  150 mJ mol Ce21 K22 as thecoefficient of its linear term in specific heat [7]. Ce3Alexhibits a hexagonal Ni3Sn structure, with TN  2.5 Kand g  200 mJ mol Ce21 K22 [8]. In contrast, Ce3Al11having an orthorhombic La3Al11 structure has a ferro-magnetic transition at TC  6.2 K followed by an anti-ferromagnetic order at TN  3.2 K, below which g 120 mJ mol Ce21 K22 [1]. Calorimetrically determinedspecific heat is a thermodynamic quantity providing thebasis of entropy calculation in data analysis. However,one needs to take into consideration the large surface-to-volume ratio for nanoscale particles. This complication iscompounded by the possible alteration of physical proper-ties near the surface [9].To fabricate CeAl2, Ce3Al, or Ce3Al11 particles, thecorresponding bulk compound was first prepared by arcmelting thoroughly mixed constituent elements, Ce(99.9%pure) and Al(99.9999% pure), in argon. Structural con-firmation was made using powder x-ray diffraction. Par-ticle specimens were then fabricated on a liquid-nitrogencold trap by flash evaporation of bulk ingots in a 0.1 torr990 0031-90070084(21)4990(4)$15.00of high-purity helium. According to x-ray diffraction pat-terns for CeAl2, there was no change in structure betweenparticles and parent bulk material, except a slight latticeexpansion (0.37%), some line broadening, and a trace ofCeO2 in nanoparticle specimens. Nevertheless, the charac-teristic reactivity of fine particles, along with the high oxi-dation susceptibility of Ce, could likely lead to a thin layerof CeO2 on the surface. Indeed, a blurred anomaly around2u  28.6± in the diffraction pattern, which correspondsto the main (111) peak of CeO2, suggests the presence ofsuch an impurity, but at a level not exceeding 5%.High resolution transmission electron microscopy(HRTEM) was employed to observe directly the crystallinestructure. An example of the HRTEM images in the pho-tograph attached to Fig. 2 reveals several well-crystallizedparticles having clear lattice arrays of CeAl2. Thestrongest diffraction plane (220) with a lattice spacing of2.85 Å is indicated by a pair of arrows for one sphericalparticle. No abnormal lattice spacing of CeO2 at its rimis noticed. Based on TEM images, an average diameterfor CeAl2 particles was estimated to be 80 Å. Theapproximately spherical shape of these particles makes itstraightforward in calculating the density of states at theFermi level D´F [10]. The same procedures were alsofollowed to characterize bulk and particle specimens ofCe3Al and Ce3Al11. No distinct difference from that ofCeAl2 was observed, except a slightly more CeO2 wasshown in Ce3Al presumably due to its higher Ce content.The average particle sizes of Ce3Al and Ce3Al11 areestimated to be 200 Å and 100 Å, respectively. To helpdelineate different contributions to the total specific heatof CeAl2, isostructural but nonmagnetic LaAl2 in bothbulk and particle forms were also prepared by the samemethod to provide the basic specific heat contributionfrom phonon excitations only.Calorimetric measurements between 0.1 and 50 K wereperformed using a thermal-relaxation microcalorimeter in© 2000 The American Physical SocietyVOLUME 84, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 22 MAY 2000a 3He and a 3He-4He dilution refrigerator [11]. Eachmg-size sample was prepared by lightly pressing fine pow-ders together. It is of interest to note that the surface oxida-tion layer can actually prevent a given particle from makingelectronic contact with its neighbors, thus upholding finitesize effects, if any.The temperature dependence of specific heat for bulkCeAl2 and LaAl2 is shown in Fig. 1 as CT versus T .This format allows entropy determination through a simpleintegration: S RCT  dT . For bulk CeAl2 a well-defined peak reveals the previously known antiferromag-netic ordering at TN  3.8 K. We can account for thespecific heat of bulk CeAl2 by the contributions of the lat-tice phonons Cph, magnetic order Cm, and crystal fieldinduced Schottky anomaly Ccry . Cph is assumed to bethe same as that of the isostructural nonmagnetic com-pound LaAl2 with a Debye temperature QD  325 K.After Cph subtraction the specific heat in the high tem-perature region is fitted well to a Schottky anomaly Ccrywith TCF  110 K. The entropy integrated from the re-mainder Cm saturates to R ln2 at T  17 K as expectedfor the ground state doublet of Ce31 ions (the inset toFig. 1). These results are in good agreement with earlyreports [7,12]. At well below TN , specific heat data arefitted to the equation C  gT 1 aT3, where the T3 termcomes from antiferromagnetic spin waves. The resultingg  150 mJ mol Ce21 K22 is only about one-sixth of thetheoretical g0 value at T  0 based on the equationTK  pR6g0 for the Kondo temperature TK  5 6 Kreported for bulk CeAl2 [7]. According to Fisk et al. [13]the g suppression comes from the partial quenching of theKondo effect by the internal magnetic field generated asmagnetic moments order below TN .FIG. 1. Temperature dependence of specific heat, in terms ofCT versus T , for bulk CeAl2 (closed circles). The phononcontribution Cph is assumed to be the same as that for bulkLaAl2 (open circles, showing a small superconducting-transitionpeak at 3.2 K). The dashed line represents the sum of Cph andCcry (diamonds). Inset: Integrated entropy S RC 2 Cph 2CcryT dT .The specific heat for 80 Å CeAl2 and 80 Å LaAl2 isshown in Fig. 2; no antiferromagnetic transition is presentat 3.8 K in 80 Å CeAl2, except that a minor bump therewith entropy only about 1% of R ln2 might represent asmall number of larger particles in the specimen. Instead,an anomaly at much lower temperatures is believed to bethe Kondo term judging from discussions below. The re-duction of antiferromagnetic transition can be understoodfrom a finite size effect. When the particle diameter be-comes too small, the coherence length of the spin fluc-tuations can reach a point not large enough to sustain atrue phase transition, as observed by Johnson et al. in Tb[14]. In resolving the total specific heat to various com-ponents, the lattice contribution is estimated from mea-surements on 80 Å LaAl2, which yield a QD  212 Kby fitting the specific heat data to the theoretical modelfor a small particle with a free surface [11]. This Debyetemperature is much smaller than that of bulk material, asanticipated for a lattice softening commonly observed infine particles. A crystal field term with TCF  130 K isalso needed to fit the higher temperature data after havingthe lattice phonon subtracted. The nearly 20% higher TCFvalue is presumably a consequence of the larger distanceof Ce31 ions as evidenced by the 0.37% lattice expansionbased on the x-ray diffraction. This is qualitatively consis-tent with earlier pressurized resistivity measurements onCeAl2 by Nicolas-Francillon et al. [12]. Quantitatively,however, the best fit requires only 0.7 mole of the Ce31ions in the compound contributing to this crystal field term.This is corroborated by a complementary SQUID measure-ment. The magnetic susceptibility for 80 Å CeAl2 between7 and 15 K roughly follows the Curie-Weiss law, yield-ing a Curie constant of 0.25 K emu mol Ce21, which isFIG. 2. Temperature dependence of specific heat, in terms ofCT versus T , for 80 Å CeAl2 (closed circles, with the pho-tograph showing an HRTEM image). The phonon contributionCph is assumed to be the same as that for 80 Å LaAl2 (opencircles). The dashed line represents the sum of Cph and Ccry(diamonds). Inset: Lower temperature (C-Cph-Ccry) values be-ing fitted to the Kondo ion (J  12) model with TK  0.65 K.4991VOLUME 84, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 22 MAY 2000equivalent to the bulk value for 0.7 mole of Ce31. Thisconsequence reveals a much larger fraction of Ce ions in80 Å CeAl2 to be tetravalent and hence nonmagnetic. Apreliminary x-ray absorption experiment using synchrotronradiation also found a much larger fraction of Ce14 ions.The major portion of the nonmagnetic Ce ions might berelated then to the appreciable number of surface or outer-shell ions in a particle. For example, with a thickness of0.5a0 (lattice parameter a0  8.09 Å), the surface ions for80 Å CeAl2 would occupy 27% of the total volume.To ascertain that the lower temperature anomaly for80 Å CeAl2 is of the Kondo origin, further calorimetricmeasurements were made in external magnetic fields Hfrom 0.5 up to 7 T. The results with H  2.6 and 6.5 T,respectively, are given in Fig. 3. If the anomaly werecaused by an antiferromagnetic transition as seen in thebulk compound, an applied field would lower the order-ing temperature. Instead, the anomaly actually moves upin temperature as the field increases. The profile of theanomaly and its response to magnetic fields are similar tothe theoretical curves for a bulk Kondo ion (J  12) de-rived by Sacramento [15] for bulk CeAl2, except that thepeak positions occur at slightly higher temperatures. Itneeds to be noted that a reduction factor of 0.7 is appliedto the theoretical curves for the reasons mentioned above.A closer examination of the zero-field data providesmore insight of the heavy fermion behavior of the par-ticles. After having the lattice and Schottky contributionssubtracted at the lowest temperatures, the specific heat dataof 80 Å CeAl2 can be fitted to the Kondo model withJ  12 and TK  0.65 K (see Fig. 2 inset). Again, itsintegrated entropy is only 70% of R ln2. The significantreduction in TK as compared to the bulk value of 5–6 Kcan be attributed only partially to lattice expansion. A rele-vant measure is the Gruneisen parameter for TK [16]:FIG. 3. Comparison for 80 Å CeAl2 between the field-dependent specific heat data (solid symbols) and Kondo modelcalculations with TK  0.65 K (open symbols with lines).Inset: Field dependence of TK from experimental data (solidcircles) and Kondo model (open circles).4992V  2µVTK∂ µdTKdV∂. (1)Taking the value V  30 50 from Panfilov et al. [17]and the magnitude of dVV  0.011 from x-ray diffrac-tion data, the estimated TK for 80 Å CeAl2 would be low-ered to 2–4 K. The major difference to the experimentalresults must be caused, therefore, by the possible particlesize and surface effects on the Kondo temperature. Thereis yet a complete theory about the Kondo effect in nano-particles. Recent works [18,19] on Kondo impurities inthin films and wires indicate that surface-induced aniso-tropy for magnetic ions will influence the Kondo behavior.Kondo scattering depends on positions of the Ce ions fromsurface. Hence the Kondo lattice coherent temperature islikely to be reduced in nanoparticles. Subsequently an-tiferromagnetic transition which occurs below the Kondocoherence temperature is also suppressed. The particle sizeand surface effects may also play a role in the field mea-surement data. The peak temperature Tp of the Kondoanomaly increases from below 0.7 to 4 K as the magneticfield increases from 0 to 7 T. In the presence of magneticfield, the formation of Kondo singlets will be deterred,thus diminishing the heavy fermion characteristics, i.e., thelarge linear temperature coefficient of specific heat. Thisis reflected in the field dependence of the Kondo tempera-ture for JgmBH , TK 0 [20]:T2K H  TK 02 1 JgmBH2, (2)where J and g denote the total angular momentum and theLande g factor of f electrons, respectively, and mB is theBohr magneton. Since TK H  2TpeakH, we extractedTK H from magnetic field data and plotted it as T2K Hversus JgmBH2 in the Fig. 3 inset. For 80 Å CeAl2 theobserved linear dependence of T2K H versus H2 can beconsidered as conforming well with the theoretical Kondomodel, but the enhanced slope or proportionality constant2.3 is much larger than the unity for bulk materials. Thedifferent response of Kondo temperature to magnetic fieldcould then be attributed to the consequence of the sizeeffect in small particles.The most impressive finding of this work is the mag-nitude of the coefficient g of the linear term in specificheat. At zero field, this parameter has already reacheda quite large value of almost 7000 mJ mol Ce21 K22 atT  0.11 K, the lowest temperature of measurements.It is extrapolated to 9000 mJ mol Ce21 K22 at absolutezero, which falls in the highest range ever reported forheavy fermion systems. If there are indeed only 70%of Ce ions responsible for the Kondo effect, one couldeven argue that the effective g0 would be close to13 000 mJ mol Ce21 K22.Similar temperature dependence of specific heat isobtained for the other two (Ce,Al) compounds Ce3Aland Ce3Al11 as shown in Fig. 4. In bulk form, theyexhibit magnetic transitions at the expected orderingVOLUME 84, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S 22 MAY 2000FIG. 4. Temperature dependence of specific heat for (a) bulk(closed circles) and 200 Å Ce3Al (open circles) and (b) bulk(closed circles) and 100 Å Ce3Al11 (open circles).temperature TN or TC . In clear contrast, for 200 Å Ce3Alor 100 Å Ce3Al11 only residue bumps remain at thesetemperatures, indicating the almost total disappearanceof magnetic ordering in these fine particles. Meanwhile,the Kondo anomalies are much enhanced, yieldinglarge g values of 1200 mJ mol Ce21 K22 for Ce3Al and1300 mJ mol Ce21 K22 for Ce3Al11 at 0.5 K.In conclusion, experimental observations in three(Ce,Al) compounds of different crystal structures show ageneral trend of a crossover from magnetic ordering toan enhanced Kondo behavior, possibly a consequence ofparticle size and surface effects. Since the interplay be-tween Kondo interaction and magnetic order through thesize and surface effects is yet to be fully understood, suchrevealing experimental results should lay the groundworkfor a better theoretical development and models screening.We are thankful for the help from HRTEM Lab in Mate-rials Science Center, National Tsing-hua University. Thiswork was supported by the National Council of the Repub-lic of China under Grants No. NSC89-2112-M-001-031and No. NSC89-2112-M-007-025.[1] W. Trinkl, S. Corsepius, and G. R. Stewart, J. AlloysCompd. 46–49, 239 (1996).[2] J. L. Moran-Lopez and J. M. Sanchez, New Trends inMagnetism, Magnetic Materials, and Their Application(Plenum Press, New York, 1994).[3] G. Chen and N. Giordano, Phys. Rev. Lett. 66, 209 (1991).[4] I. K. Yanson, V. V. Fisun, R. Hesper, A. V. Khotkevich,J. M. Krans, J. A. Mydosh, and J. M. van Ruitenbeek, Phys.Rev. Lett. 74, 302 (1995).[5] V. Chandrasekhar, P. Santhanam, N. A. Penebre, R. A.Webb, H. Vloeberghs, C. Van Haesendonck, and Y. Bruyn-seraede, Phys. Rev. Lett. 72, 2053 (1994).[6] G. Bergmann, Phys. Rev. Lett. 67, 2545 (1991).[7] F. Steglich, C. D. Bredl, M. Loewenhaupt, and K. D.Schotte, J. Phys. (Paris), Colloq. 40, C5-301 (1979), andreferences therein.[8] Y. Y. Chen, Y. D. Yao, B. C. Hu, C. H. Jang, J. M. Lawrence,H. Huang, and W. H. Li, Phys. Rev. B 55, 5937 (1997).[9] R. H. Kodama, A. E. Berkowitz, E. J. McNiff, Jr., andS. Foner, Phys. Rev. Lett. 77, 394 (1996).[10] W. P. Halperin, Rev. Mod. Phys. 58, 533 (1986).[11] Y. Y. Chen, Y. D. Yao, S. S. Hsiao, S. U. Jen, B. T. Lin,H. M. Lin, and C. Y. Tung, Phys. Rev. B 52, 9364 (1995).[12] M. Nicolas-Francillon, A. Percheron, J. C. Achard,O. Gorochov, B. Cornut, D. Jerome, and B. Coqblin, SolidState Commun. 11, 845 (1972).[13] Z. Fisk, J. L. Sarrao, J. L. Smith, and J. D. Thompson, Proc.Natl. Acad. Sci. U.S.A. 92, 6663–6667 (1995).[14] D. Johnson, P. Perera, and M. J. O’Shea, J. Appl. Phys. 79,5299 (1996).[15] P. D. Sacramento and P. Schlottmann, Phys. Rev. B 40, 431(1989).[16] J. D. Thompson and J. M. Lawrence, Handb. Phys. Chem.Rare Earths 19, 383 (1994).[17] A. S. Panfilov, I. V. Svechkarev, and E. Fawcett, Int. J. Mod.Phys. 7, 703 (1993).[18] V. M. Fomin, V. N. Gladilin, J. T. Devreese, C. Van Hae-sendonck, and G. Neuttiens, Solid State Commun. 106,293 (1998).[19] O. Ujsaghy and A. Zawadowski, Phys. Rev. B 57, 11 609(1998).[20] T. M. Hong and G. A. Gehring, Phys. Rev. B 46, 231(1992).4993

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Size-Induced Transition from Magnetic Ordering to Kondo Behavior in (Ce,AI) Compounds

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Size-Induced Transition from Magnetic Ordering to Kondo Behavior in (Ce,AI) Compounds

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