Experimental results for the susceptibility, specific heat, 4f occupation
number, Hall effect and magnetoresistance for single crystals of YbAl$_{3}$
show that, in addition to the Kondo energy scale $k_{B}T_{K}$ $% \sim $ 670K,
there is a low temperature scale $T_{coh}<50$K for the onset of coherence.
Furthermore the crossover from the low temperature Fermi liquid regime to the
high temperature local moment regime is slower than predicted by the Anderson
impurity model. These effects may reflect the behavior of the Anderson Lattice
in the limit of low conduction electron density.Comment: Ten pages, including three figure

A. C. Hewson

A. H. Lacerda

A. Hasegawa

A. Hiess

A. J. Millis

A. L. Cornelius

A. N. Tahvildar-Zadeh

B. Bucher

B. C. Webb

C. H. Booth

E. Cattaneo

G. H. Kwei

J. D. Thompson

J. L. Sarrao

J. M. Lawrence

L. Degiorgi

M. F. Hundley

M. H. Jung

N. E. Bickers

P. G. Pagliuso

P. S. Riseborough

S. Burdin

T. Ebihara

English

arXiv

Crossref

Physical Review Letters

German

Two Energy Scales and Slow Crossover in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>YbAl</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We present results for YbAl{sub 3} which show that the susceptibility {chi}(T), 4f occupation number n{sub f}(T) and the entropy S(T) exhibit a slow crossover between the Fermi liquid and local moment regimes. In addition both {chi}(T) and the linear specific heat coefficient {gamma} = C/T exhibit low temperature peaks that imply that in addition to the Kondo scale (T{sub K} {approx} 500K) there is a second low temperature scale (T{sub coh} {approx} 50K) for the onset of coherence. We discuss these results in the context of Nozieres' exhaustion in the Anderson lattice

Lawrence, J. M.

Ebihara, T.

Riseborough, P. S.

Booth, C. H.

Pagliuso, P. G.

Sarrao, J. L.

Thompson, J. D.

UNT (University of North Texas) Digital Library

Two energy scales and slow crossover in YbAl3

Cornelius, A. L.

Hundley, M. F.

Jung, M. H.

Lacerda, A. H.

Kwei, G. H.

Ebihara, Takao

20273162

737db612-083a-4638-b5a9-00d636c36b85

Shizuoka University REpository

Two Energy Scales and Slow Crossover in YbAl3言語: en出版者: American Physical Society公開日: 2008-02-25キーワード (Ja): キーワード (En): 作成者: Cornelius, A. L., Ebihara, Takao, Lawrence, J. M.,Riseborough, P. S., Booth, C. H., Hundley, M. F.,Pagliuso, P. G., Sarrao, J. L., Thompson, J. D., Jung, M.H., Lacerda, A. H., Kwei, G. H.メールアドレス: 所属: メタデータhttp://hdl.handle.net/10297/579URLVOLUME 88, NUMBER 11 P H Y S I C A L R E V I E W L E T T E R S 18 MARCH 2002Two Energy Scales and Slow Crossover in YbAl3A. L. Cornelius,1 J. M. Lawrence,2,* T. Ebihara,3 P. S. Riseborough,4 C. H. Booth,5 M. F. Hundley,6 P. G. Pagliuso,6J. L. Sarrao,6 J. D. Thompson,6 M. H. Jung,7 A. H. Lacerda,7 and G. H. Kwei81University of Nevada, Las Vegas, Nevada 891542University of California, Irvine, California 926973Shizuoka University, Shizuoka 422-8529, Japan4Temple University, Philadelphia, Pennsylvania 191225Lawrence Berkeley National Laboratory, Berkeley, California 947206Los Alamos National Laboratory, Los Alamos, New Mexico 875457National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 875458Lawrence Livermore National Laboratory, Livermore, California 94551(Received 31 July 2001; revised manuscript received 30 January 2002; published 4 March 2002)Experimental results for the susceptibility, magnetization, specific heat, 4f occupation number, Halleffect, and magnetoresistance for single crystals of the intermediate valence (IV) compound YbAl3show that, in addition to the Kondo temperature scale TK  670 K, there is a low temperature scaleTcoh  30 40 K for the onset of Fermi liquid coherence. Furthermore, the crossover from the lowtemperature Fermi liquid regime to the high temperature local moment regime is slower than predictedby the Anderson impurity model. We suggest that these effects are generic for IV compounds and wediscuss them in terms of the theory of the Anderson lattice.DOI: 10.1103/PhysRevLett.88.117201 PACS numbers: 75.30.Mb, 71.27.+a, 71.28.+d, 75.20.HrThe low temperature transport behavior of periodic in-termediate valent (IV) and heavy fermion (HF) compounds[1] is fundamentally different from that expected for theAnderson impurity model (AIM), in that it manifests van-ishing resistivity (Bloch’s law) and an optical conductivity[2] appropriate for renormalized band behavior. Similarly,the 4f electrons have a coherent effect on the Fermi sur-face, as seen in de Haas van Alphen (dHvA) measurements[3]. However, the temperature dependence of the suscep-tibility, specific heat and 4f occupation number, and theenergy dependence of the dynamic susceptibility show be-havior that is qualitatively very similar to the predictions ofthe AIM [4,5]. Essentially this is because these propertiesare dominated by spin/valence fluctuations that are highlylocal and which exhibit a Lorentzian power spectrum [6]consistent with the AIM.In this paper we report data for the IV compound YbAl3and show that these latter properties can differ in at leasttwo ways from the predictions of the AIM. First, thecrossover from low temperature Fermi liquid behavior tohigh temperature local moment behavior is slower (i.e.,more gradual) than predicted for the AIM. Second, anoma-lies (relative to the AIM) in the magnetization, suscep-tibility, specific heat, and magnetotransport occur below30–40 K, which is the temperature scale Tcoh for the on-set of coherent Fermi liquid T 2 behavior in the resistivity.We then argue that the existence of a slow crossover and alow temperature scale that is an order of magnitude smallerthan the AIM Kondo temperature (Tcoh ø TK ) may begeneric features of IV compounds and we discuss themin terms of the theory of the Anderson lattice.The samples were single crystals of YbAl3 and LuAl3grown by the “self-flux” method in excess Al. The suscep-117201-1 0031-90070288(11)117201(4)$20.00tibility was measured using a SQUID magnetometer andthe specific heat was measured via a relaxation technique.The Hall coefficient was measured in a magnetic field of1 T using an ac resistance bridge. The high field magneti-zation and the magnetoresistance were measured at the LosAlamos Pulsed Field Facility of the National High Mag-netic Field Laboratory. The 4f occupation number nf Twas determined from the Yb L3 x-ray absorption near-edgestructure, measured at the Stanford Synchrotron RadiationLaboratory (SSRL); the details of the experiment and theanalysis were similar to those discussed earlier [7]. In par-ticular, the Lu L3 near-edge structure measured for LuAl3was used as a standard.In Fig. 1 we plot the susceptibility xT and the linearcoefficient of the 4f specific heat, where gm  CmT andCm  CYbAl3 2 CLuAl3. (For LuAl3 at low tem-peratures, C  gT 1 bT3 with g  4 mJmol K2 andb  1.15 3 1024 Jmol K4, which implies a Debye tem-perature QD  257 K.) The broad peaks near 100 K aretypical of Yb IV compounds with TK greater than 500 K(see Fig. 4). However, the low temperature specific heatcoefficient displays an upturn below 30 K which saturatesat T  0. In addition, the susceptibility increases below40 K to a peak at 15 K. This was reported earlier by Hiesset al. [8] who raised the possibility that it might representan extrinsic effect due to antiferromagnetic short range or-dering of Yb31 impurities. Our argument against this isthat the quality of our samples, as measured by the resid-ual resistivity (0.5mV cm), is sufficiently high that dHvAsignals are well resolved [9]; the presence of Yb31 impuri-ties should lead to a large residual resistivity. Furthermore,we find that as the residual resistivity increases, the T  0specific heat maximum decreases and a Curie tail grows© 2002 The American Physical Society 117201-1VOLUME 88, NUMBER 11 P H Y S I C A L R E V I E W L E T T E R S 18 MARCH 2002FIG. 1. (a) The magnetic susceptibility xT  and (b) the mag-netic contribution to the specific heat coefficient CmT forYbAl3. The insets exhibit the low temperature behavior; a smallCurie tail has been subtracted from the data in the inset for xT .in the susceptibility. Hence we associate the low tempera-ture anomalies in susceptibility and specific heat with thepurest samples, and assert that they are intrinsic. Theseanomalies are the basic evidence for the existence of a lowtemperature scale, Tcoh  30 40 K. The inset of Fig. 3shows that a T 2 behavior of the resistivity sets in below30 K, which makes it clear that Tcoh is the temperaturescale for the onset of coherent Fermi liquid behavior.In Fig. 2a we plot the magnetization versus applied mag-netic field at low and high temperature; the solid lines arelinear fits to the data. The difference between the linear fitsand the data is shown in the inset. At 250 K the magnetiza-tion is linear in field up to 60 T; at 4 K the data is linear upto 40 T, above which there is a clear change in slope. Weplot the slope xH for low and high field versus tempera-ture in Fig. 2b. The low field results compare well with thesusceptibility measured for B  1 T in the SQUID mag-netometer, showing a maximum near 125 K and a secondmaximum near T  0. In the high field data, the low tem-perature maximum is absent and the data exhibit the quali-tative features expected for an Anderson impurity (see,e.g., Fig. 4b). Clearly, the low temperature susceptibil-ity anomaly is suppressed by magnetic fields greater thanB  40 T. Since mBB is of the same order as kBTcoh,this effect gives strong confirming evidence for the exis-tence of a new low energy scale kBTcoh  3 4 meV whichis an order of magnitude smaller than the AIM Kondoscale.117201-2(a)(b)FIG. 2. (a) The magnetization MH versus the magnetic fieldat 4 and 250 K; the solid lines are linear fits to the data inthe field range 10 , B , 35 T. Inset: The difference DMbetween the data and the linear fits. (b) The susceptibility xTmeasured at both low (10 , B , 35 T) and high (47 , B ,57 T) magnetic field. The dashed line is data taken at B  1 T.Anomalies can also be seen in the magnetotransport(Fig. 3). The Hall coefficient of LuAl3 is temperature in-dependent, as is typical of a metal. The high temperatureHall coefficient of YbAl3 varies with temperature in a man-ner suggestive of scattering from Yb moments (althoughthe data cannot be fit well with the standard skew scat-tering formula [10]). Near 50 K the derivative dRHdTof the Hall coefficient changes sign. The magnetoresis-tance (Fig. 3b, inset) follows a B2 law above 50 K andthe magnitude is approximately the same for field paralleland transverse to the current. Below 50 K, the magneto-resistance becomes more nearly linear and the transversemagnetoresistance becomes substantially larger (DRR 0.75) than the parallel magnetoresistance (DRR  0.35)at 2 K. In Fig. 3b we plot DRR versus Br0 wherer0  R150KRT; this tests Kohler’s rule, i.e., that atany temperature DRR  AfBr0 depends only on theproduct Br0. The data violate this rule essentially becauseA varies with T , increasing by a factor of almost 1.5 be-tween 40 and 80 K; this crossover is seen most clearly inthe data measured as a function of temperature at a fixedfield 17.5 T. These magnetotransport anomalies suggest117201-2VOLUME 88, NUMBER 11 P H Y S I C A L R E V I E W L E T T E R S 18 MARCH 2002FIG. 3. (a) The Hall coefficient of YbAl3 (closed circles)and LuAl3 (open circles) versus temperature. Inset: the resis-tivity plotted versus the square of the temperature. (b) Inset:The transverse magnetoresistance DR  RH , T  2 R0, Tversus magnetic field for four temperatures. Main panel:The relative magnetoresistance DRR versus Br0 wherer0  R150 KRT.that the anomalies in x and CT may be associated withan alteration of the Fermi surface.To demonstrate that the crossover from Fermi liquidbehavior to local moment behavior is slower than pre-dicted by the AIM we proceed as in our recent paperon YbXCu4 [5]. The calculations were performed usingthe noncrossing approximation (NCA); the values of theAIM parameters are given in Fig. 4. It is clear from Fig. 4that the susceptibility, 4f occupation number, and 4f en-tropy Sm RdT CmT all qualitatively follow the pre-dictions of the AIM. The calculated coefficient of specificheat (g  47.8 mJmol K2) is within 20% of the measuredvalue (gm  40.65 mJmol K2). Indeed the data even arein accord with the prediction that the entropy SmT ap-proaches the high temperature limit faster than the effectivemoment TxCJ which in turn evolves more rapidly thannf T (see Fig. 4). Nevertheless, it is also clear that theexperimental data for these quantities approach the hightemperature limit considerably more slowly than predictedby the AIM theory.117201-3FIG. 4. (a) The 4f entropy Sm , (b) the susceptibility xT (solid symbols), and the effective moment TxCJ (open sym-bols) where CJ is the J  72 Curie constant and (c) the 4foccupation number nf T  for YbAl3. The symbols are the ex-perimental data and the solid lines are the predictions of theAnderson impurity model (AIM) calculated in the NCA withinput parameters as given in the figure.Thus we have demonstrated the existence of a newlow energy scale for YbAl3 and we have shown that thecrossover to local moment behavior is slower than expectedbased on the Anderson impurity model. We believe thatthese effects are generic to IV compounds. We have re-cently shown [5] that a slow crossover exists in a numberof YbXCu4 IV compounds. A number of years ago wegave evidence [11] for a small coherence scale in the IVcompound CePd3 based on a low temperature peak in thesusceptibility and the extreme sensitivity of the transportbehavior to Kondo hole impurities below 50 K. A lowtemperature anomaly in the Hall coefficient of several Cecompounds also has been observed [10]. Optical conduc-tivity measurements [2,12,13] showed that the temperaturescale for these effects is the same as for the renormalizationof the effective mass and the onset of the hybridization gap.Hence the anomalies appear to be associated with the on-set of the fully renormalized coherent Fermi liquid groundstate. Measurement of the infrared optical conductivity isa key future experiment for YbAl3.An open issue is the condition under which these anoma-lies occur. One possibility is low background conductionelectron density. In CePd3 the carrier density is less than0.1atom [2]. For YbXCu4 we found [5] that the slow117201-3VOLUME 88, NUMBER 11 P H Y S I C A L R E V I E W L E T T E R S 18 MARCH 2002crossover did not correlate either with the degree of mixedvalence or with the Kondo temperature, but it did corre-late with a low background conduction electron densityas calculated from the Hall coefficient of LuXCu4 in aone-band approximation. Using a similar approximationwe deduce from the Hall coefficient of LuAl3 (Fig. 3a)that nc  0.5atom. This is as low as in those YbXCu4compounds where strong deviations from the AIM areobserved.Indeed, recent theoretical work [14,15] on the Andersonlattice predicts both a slow crossover and a low tempera-ture coherence scale in the limit of low conduction elec-tron density. However, the theoretical work to date hasbeen performed only in the Kondo limit. We have exam-ined the extension of the slave boson mean field theory forthe Anderson lattice to the case nf , 1 and nc , 1 rele-vant to YbAl3, where nf is the number of holes in the2J 1 1 fold degenerate f level. Following Millis andLee [16], we define the Kondo temperature kBTK as theenergy of the renormalized f level relative to the Fermienergy. The coherence scale is defined as the renormal-ized (quasiparticle) T  0 bandwidth which for a back-ground conduction band density of states r is given bykBTcoh  rṼ 2 where Ṽ is the renormalized hybridizationṼ p1 2 nf V . In the limit rṼ 2 ø ncnf2J 1 12we find that TcohTK  nf2J 1 1 independent of nc.For YbAl3 this means that Tcoh should be an order ofmagnitude smaller than TK , in qualitative agreement withthe data.In any case we assert that the two energy scales and slowcrossover predicted by recent theory are features of ourdata, that they are generic for IV compounds, and that theseeffects show some correlation with a standard measure ofthe conduction electron density.Work at UNLV was supported by a DOE EPSCoR-State/National Laboratory Partnership Award No. DE-FG02-00ER45835. Work at UC Irvine was supported byUCDRD funds provided by the University of Californiafor the conduct of discretionary research by the LosAlamos National Laboratory and by the UC/LANLPersonnel Assignment Program. T. E. acknowledges thesupport of the Japanese Ministry of Education. Work atPolytechnic was supported by DOE FG02ER84-45127.Work at Lawrence Berkeley National Laboratory wassupported by DOE Contract No. DE-AC03-76SF00098.117201-4Work at Los Alamos was performed under the auspicesof the DOE. The x-ray absorption experiments wereperformed at SSRL, which is operated by the DOE/OBES.*Electronic address: jmlawren@uci.edu[1] A. C. Hewson, The Kondo Problem to Heavy Fermions(Cambridge University Press, Cambridge, United King-dom, 1993), p. 315.[2] B. C. Webb, A. J. Sievers, and T. Mihalisin, Phys. Rev. Lett.57, 1951 (1986).[3] A. Hasegawa and H. Yamagami, Prog. Theor. Phys. Suppl.108, 27 (1992).[4] N. E. Bickers, D. L. Cox, and J. W. Wilkins, Phys. Rev. B36, 2036 (1987).[5] J. M. Lawrence, P. S. Riseborough, C. H. Booth, J. L.Sarrao, J. D. Thompson, and R. Osborn, Phys. Rev. B 63,054427 (2001).[6] J. M. Lawrence, S. M. Shapiro, J. L. Sarrao, and Z. Fisk,Phys. Rev. B 55, 14 467 (1997); J. M. Lawrence, R. Osborn,J. L. Sarrao, and Z. Fisk, Phys. Rev. B 59, 1134 (1999).[7] J. L. Sarrao, C. D. Immer, Z. Fisk, C. H. Booth, E. Figueroa,J. M. Lawrence, R. Modler, A. L. Cornelius, M. F. Hundley,G. H. Kwei, J. D. Thompson, and F. Bridges, Phys. Rev. B59, 6855 (1999).[8] A. Hiess, J. X. Boucherle, F. Givord, J. Schweizer,E. Lelièvre-Berna, F. Tasset, B. Gillon, and P. C. Canfield,J. Phys. Condens. Matter 12, 829 (2000).[9] T. Ebihara, Y. Inada, M. Murakawa, S. Uji, C. Terakura,T. Terashima, E. Yamamoto, Y. Haga, Y. Onuki, andH. Harima, J. Phys. Soc. Jpn. 69, 895 (2000).[10] E. Cattaneo, Z. Phys. B 64, 305 (1986); 64, 317 (1986).[11] J. M. Lawrence, Y.-Y. Chen, and J. D. Thompson, in Theo-retical and Experimental Aspects of Valence Fluctuationsand Heavy Fermions, edited by L. C. Gupta and S. Malik(Plenum Press, New York, 1987), p. 169.[12] B. Bucher, Z. Schlesinger, D. Mandrus, Z. Fisk, J. Sarrao,J. F. DiTusa, C. Oglesby, G. Aeppli, and E. Bucher, Phys.Rev. B 53, R2948 (1996).[13] L. Degiorgi, F. B. B. Anders, and G. Grüner, Eur. Phys.J. B 19, 167 (2001).[14] A. N. Tahvildar-Zadeh, M. Jarrell, and J. K. Freericks,Phys. Rev. B 55, R3332 (1997); Phys. Rev. Lett. 80, 5168(1998).[15] S. Burdin, A. Georges, and D. R. Grempel, Phys. Rev. Lett.85, 1048 (2000).[16] A. J. Millis and P. A. Lee, Phys. Rev. B 35, 3394 (1987).117201-4

Two Energy Scales and Slow Crossover in YbAl3

Cornelius A. L.

Ebihara Takao

Lawrence J. M.

Riseborough P. S.

Booth C. H.

Hundley M. F.

Pagliuso P. G.

Sarrao J. L.

Thompson J. D.

Jung M. H.

Lacerda A. H.

Kwei G. H.

We present results for YbAl$_3$ which show that the susceptibility  $\chi(T)$, 4f occupation number $n_f(T)$ and the entropy $S(T)$ exhibit a  slow crossover between the Fermi liquid and local moment regimes. In addition  both $\chi(T)$ and the linear specific heat coefficient $\gamma = C/T$ exhibit  low temperature peaks that imply that in addition to the Kondo scale ($T_K$  $\approx $ 500K) there is a second low temperature scale ($T_coh$ ^M$\approx  $ 50K) for the onset of coherence. We discuss these results in the context of  Nozieres' exhaustion in the Anderson lattice

Two energy scales and slow crossover in YbAl3

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