Six closely related YbT2Zn20 (T � Fe, Co, Ru, Rh, Os,Ir) heavy fermion compounds with large localmoment degeneracyM. S. Torikachvili*†, S. Jia*, E. D. Mun*, S. T. Hannahs‡, R. C. Black§, W. K. Neils§, Dinesh Martien§, S. L. Bud’ko*,and P. C. Canfield*¶

*Ames Laboratory, U.S. Department of Energy, and Department of Physics and Astronomy, Iowa State University, Ames, IA 50011; †Department of Physics,San Diego State University, San Diego, CA 92182; ‡National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, FL 32310; and§Quantum Design, Inc., 6325 Lusk Boulevard, San Diego, CA 92121

Communicated by Zachary Fisk, University of California, Irvine, CA, March 26, 2007 (received for review February 21, 2007)

Heavy fermion compounds represent one of the most stronglycorrelated forms of electronic matter and give rise to low temper-ature states that range from small moment ordering to exoticsuperconductivity, both of which are often in close proximity toquantum critical points. These strong electronic correlations areassociated with the transfer of entropy from the local momentdegrees of freedom to the conduction electrons, and, as such, areintimately related to the low temperature degeneracy of the(originally) moment bearing ion. Here we report the discovery ofsix closely related Yb-based heavy fermion compounds, YbT2Zn20,that are members of the larger family of dilute rare earth bearingcompounds: RT2Zn20 (T � Fe, Co, Ru, Rh, Os, Ir). This discoverydoubles the total number of Yb-based heavy fermion materials.Given these compounds’ dilute nature, systematic changes in Tonly weakly perturb the Yb site and allow for insight into theeffects of degeneracy on the thermodynamic and transport prop-erties of these model correlated electron systems.

correlated electron � intermetallic compound

Heavy fermion compounds have been recognized as one ofthe premier examples of strongly correlated electron be-

havior for several decades. Ce- and U-based heavy fermioncompounds have been well studied, and in recent years a smallnumber of Yb-based heavy fermions have been identified as well(1–3). Unfortunately, in part due to the somewhat unpredictablenature of 4f ion hybridization with the conduction electrons, ithas been difficult to find closely related (e.g., structurally) heavyfermion compounds, other than of the ThCr2Si2 structure,especially Yb-based ones, that allow for systematic studies of theYb ion degeneracy. Part of this difficulty is associated with thefact that the 4f hybridization depends so strongly on the localenvironment of the rare earth ion.

Dilute, rare earth (R) bearing, intermetallic compounds areordered materials with �5 atomic percent rare earth fullyoccupying a unique crystallographic site. Such materials offerthe possibility of investigating the interaction between conduc-tion electrons and 4f electrons in fully ordered compounds forrelatively low concentrations of rare earths. For the case of R �Yb or Ce, these materials offer the possibility of preserving lowtemperature, coherent effects while more closely approximatingthe single ion Kondo impurity limit. A very promising exampleof such compounds is derived from the family of RT2Zn20 (4)(T � transition metal), which has recently been shown to allowfor the tuning of the nonmagnetic R � Y and Lu members toexceedingly close to the Stoner limit as well as allowing for thestudy of the effects of such a highly polarizable background onlocal moment magnetic ordering for R � Gd (5).

DiscoveryHere, we present thermodynamic and transport data on sixstrongly correlated Yb-based intermetallic compounds found in

the RT2Zn20 family for T � Fe, Co, Ru, Rh, Os, and Ir,effectively doubling the number of known Yb-based heavyfermions (compounds with linear coefficient of specific heat, �,�400 mJ/mol K2; ref. 1). The RT2Zn20 compounds crystallize inthe cubic CeCr2Al20 (Fd3�m space group) structure (6, 7). Due tothe relatively low concentration of rare earth, as well as transitionmetal, in these compounds, the four nearest neighbors as well asthe 12 next-nearest neighbors of the rare earth ion are Zn atoms.The rare earth ion is coordinated by a 16-atom Frank–Kasperpolyhedron and has a cubic point symmetry. This near sphericaldistribution of neighboring Zn atoms gives rise to the possibilityof relatively low crystal-electric-field (CEF) split levels and alsopromises a large degree of similarity between this isostructuralgroup of Yb-based heavy fermions. These compounds, then, notonly greatly expand the number of known Yb-based heavyfermions, but, as will be shown below, also provide a route tostudying how the degeneracy of the Yb ion at Kondo tempera-ture, TK, effects the low temperature-correlated state.

Thermodynamic and transport data taken on the six YbT2Zn20compounds are presented in Figs. 1–3 and are summarized inTable 1. Whereas the temperature-dependent magnetic suscep-tibility, electrical resistivity, and specific heat for T � Fe, Ru, Rh,Os, and Ir are qualitatively similar, YbCo2Zn20 is, at first glance,somewhat different. Most conspicuously, instead of manifestinga clear loss of local moment behavior at low temperature (8), thetemperature-dependent susceptibility continues to be Curie–Weiss-like down to 2 K (Fig. 1a Inset).

Focusing initially on the five, apparently similar, YbT2Zn20compounds (T � Fe, Ru, Rh, Os, Ir), Fig. 1 a and b demonstratesthat each of these compounds appears to be an excellent exampleof a Yb-based heavy fermion with electronic specific heat, �,values ranging between 500 and 800 mJ/mole K2. [The modestrise in the �C(T)/T data below 2 K is most probably associatedwith a nuclear Schottky anomaly and, for this work, is simplyignored. This assumption is further supported by the data andanalysis presented in Fig. 5 below.] The low temperature mag-netic susceptibility correlates well with the electronic specificheat values leading to the Wilson ratio (1, 2) for these fivecompounds having values of 1.1 and 1.3 (see Table 1). Thetemperature-dependent electrical resistivity data (Fig. 2) forthese five compounds are also remarkably similar at high tem-perature and manifest clear T2 temperature dependencies atlow temperatures (see Inset). Although resistivity data weretaken down to 20 mK, no indications of either magnetic order

Author contributions: S.L.B. and P.C.C. designed research; M.S.T., S.J., S.T.H., R.C.B., W.K.N.,D.M., and S.L.B. performed research; S.J. contributed new reagents/analytic tools; M.S.T.,S.J., E.D.M., and S.L.B. analyzed data; and S.L.B. and P.C.C. wrote the paper.

The authors declare no conflict of interest.

¶To whom correspondence should be addressed. E-mail: canfield@ameslab.gov.

© 2007 by The National Academy of Sciences of the USA

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or superconductivity were found for any of the YbT2Zn20

compounds.The thermodynamic and transport properties of YbCo2Zn20

are somewhat different from the other five compounds.YbCo2Zn20 does not manifest the clear loss of local momentbehavior, �1.8 K, in the susceptibility data (see Fig. 1a Inset) andthe electrical resistivity and the specific heat only manifestFermi-liquid-like behavior for T � 0.2 K (Fig. 3). Although thehigher temperature electrical resistivity of YbCo2Zn20 is similar

to the other five YbT2Zn20 compounds, it manifests a muchclearer example of a resistance minimum and lower temperaturecoherence peak.

AnalysisSome of the salient parameters extracted from these data aresummarized in Table 1 and the coefficient of the T2 resistivity (A)is plotted as a function of the linear coefficient of the specificheat (�) in a Kadowaki–Woods (KW) (8–10) type plot (Fig. 4).Perhaps the most noteworthy point that becomes clear from thispresentation of the data is that, whereas there is relatively littlevariation in the low temperature thermodynamic properties, orWilson ratio, associated with the T � Fe, Ru, Rh, Os, Ircompounds, there is an order of magnitude variation in the valueof the coefficient of the T2 resistivity, A. This gives rise to avertical spread of the KW data points.

Recent theoretical work (11, 19, 20) has generalized the ideaof a fixed KW ratio to one that can vary by over an order ofmagnitude, depending upon the value of the degeneracy of theYb ion when it hybridizes. Fig. 4 shows, as solid lines, the fourdegeneracies possible for the Kramers, Yb3� ion. The YbT2Zn20data indicate that for T � Fe, Ru the Yb ion has a significantlylarger degeneracy upon entering the Kondo-screened state thanit does for the T � Rh, Os, Ir compounds. The data point for

Fig. 1. Low temperature thermodynamic properties of YbT2Zn20 compounds(T � Fe, Ru, Rh, Os, Ir). (a) Magnetic susceptibility (H � 0.1 T) . (Inset) Temperature-dependent inverse susceptibility for YbCo2Zn20 and YbOs2Zn20. (b) Low temper-ature-specific heat, C, divided by temperature, as a function of T2.

Table 1. Summary of structural, thermodynamic, and transport data on YbT2Zn20 compounds (T � Fe, Co, Ru, Rh, Os, Ir)

T a, Å �, K�eff,�B

�0,10 � 3 cm3

mole

�max,10 � 3 cm3

mole

T�max,K

�0,�� cm A,

�� cmK2 RRR

�,mJ

mol K2 WR

KWR,�� cm mole2 K2

mJ2 NTK,K

Fe 14.062 �22.6 4.5 58.0 65.1 14.0 2.1 5.4 10�2

(T � 11 K)31.2 520 1.2 2.0 10�7 8 33

Co 14.005 �4.3 4.3 415.1 21 165(T � 0.2 K)

2.8 7,900 27 10�7 4 1.5

Ru 14.193 �15.5 4.5 58.9 65.4 13.5 5.3 6.8 10�2

(T � 11 K)10.9 580 1.1 2.0 10�7 8 30

Rh 14.150 �15.9 4.4 77.7 82.4 5.3 5.6 54 10�2

(T � 6 K)11.8 740 1.3 10.1 10�7 4 16

Os 14.205 �19.18 4.5 60.0 60.7 11.5 17 53 10�2

(T � 1 K)4.4 580 1.1 15 10�7 4 20

Ir 14.165 �23.8 4.4 55.9 56.3 6.5 8.8 33 10�2

(T � 5 K)8.9 540 1.2 11 10�7 4 21

Shown are cubic lattice parameter, a; paramagnetic Curie–Weiss temperature, , and effective moment, �eff, obtained from fit to inverse susceptibilitybetween �100 and 300 K (after substraction data from the nonmagnetic analogues, LuT2Zn20); low temperature magnetic susceptibility, �0 taken at 1.8 K;magnetic susceptibility at the maximum, �max and corresponding temperature, T�max; residual resistivity, �0, taken at T �20 mK; coefficient of the T2 resistivity,A (with range of fit given below); residual resistivity ratio, RRR; linear coefficient of the specific heat, �; Wilson ratio, WR; Kadowaki–Woods ratio, KWR;degeneracy, N; and estimated Kondo temperature, TK.

Fig. 2. Temperature-dependent electrical resistivity of YbT2Zn20 compounds(T � Fe, Co, Ru, Rh, Os, Ir). (Inset) Low temperature electrical resistivity as afunction of T2 for T � Fe, Ru, Rh, Os, Ir; note separate axes for T � Os on topand right.

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YbCo2Zn20 approaches the far extreme of the KW plot, beingnear to the point associated with the exceptionally heavy fer-mion, YbBiPt (12, 13).

As mentioned above, the sole Yb site is one of cubic pointsymmetry and is surrounded only by Zn in a shell of very highcoordination number. Based on these facts, it is anticipated thatthe Yb ion’s Hund’s rule, ground state multiplet will split into aquartet and two doublet states with a small total splitting. If,indeed, the difference between YbFe2Zn20 and YbRu2Zn20 onone hand and YbRh2Zn20, YbOs2Zn20 and YbIr2Zn20 on theother is the degree to which the Hund’s rule ground statedegeneracy has been lifted by crystalline electric field splittingbefore the Kondo screening takes place, then there should besome indication of this in other data as well. If, as Tsujii et al.suggest (11), the ratio of TK to TCEF is of primary concern, thenan examination of Fig. 1a in the light of the Coqblin–Schrieffermodel (refs. 8 and 21, specifically figure 1 of ref. 8) indicates thatthe larger the ratio of the maximum susceptibility to the lowtemperature susceptibility, the larger is the degeneracy thatremains in the Yb system at TK. The ratios of the maximumsusceptibility to the low temperature susceptibility for T � Feand Ru are 1.12 and 1.11, respectively, whereas the ratios for T �Rh, Os, and Ir are 1.06, 1.01, and 1.01, respectively. These valuesare consistent with a difference in degeneracy of at least �N �2 (see Fig. 4).

This analysis can be made even more thoroughly by perform-ing a fit (8) to the magnetic component of the specific heat overa wide temperature range. This is shown in Fig. 5a forYbFe2Zn20, the compound with the largest degeneracy inferred

from the KW plot (Fig. 4) as well as from the above analysis. Thedata are best fit (and very well fit) by the J � 7/2 (N � 8) curve.These data are particularly compelling because the height of theanomaly is not an adjustable parameter once N is chosen. Thisanalysis further confirms the degeneracy inferred from Fig. 4 andconfirms that the low temperature, greatly enhanced, electronicspecific heat is due to Kondo screening of the large N, Yb ion.Fig. 5a Inset shows the magnetic entropy as a function oftemperature. By 60 K, it rises past the J � 5/2 value. The fact thatit does not reach the Rln8 anticipated is most likely due to (i)difficulties in accurately modeling the nonmagnetic contributionwith LuFe2Zn20 at high temperatures and (ii) difficulties asso-ciated with taking the difference between two large, comparablevalues, as well as the fact that by 60 K a recovery of the full Rln8is not expected (see fit to J � 7/2 in Fig. 5a).

Fig. 5b presents similar data from YbRh2Zn20, one of thecompounds that the KW analysis predicts to have a lowerdegeneracy. The maximum in the magnetic specific heat datafalls between the J � 3/2 and J � 5/2 values, indicating that theCEF splitting scheme will not allow the very simple type ofanalysis on which refs. 8 and 21 are premised: i.e., one that hasthe CEF levels either at T �� TK or T �� TK. These data can bewell fit, though, by the addition of a Schottky anomaly associatedwith a T � TK CEF level. The low temperature part of the specificheat data can be well fit by assuming that a quadruplet is Kondo

Fig. 3. Low temperature electrical resistivity and C/T of YbCo2Zn20 as afunction of T2.

Fig. 4. Log–log plot of A versus � (Kadowaki–Woods plot) of six newYbT2Zn20 heavy fermion compounds (T � Fe, Co, Ru, Rh, Os, Ir) shown withrepresentative data from ref. 11 as well as data for YbBiPt (12, 13), YbNi2B2C(14), YbPtIn (15), YbAgGe (16), YbNiSi3 (17), and YbIr2Si2 (18). The solid lines fordegeneracies N � 2, 4, 6, and 8 are taken from ref. 11.

a

b

Fig. 5. Coqblin–Schrieffer analysis of magnetic specific heat data fromYbFe2Zn20 (a) and YbRh2Zn20 (b) after subtraction data from the nonmagneticanalogues, LuFe2Zn20 and LuFe2Rh20, respectively. Data are shown as opensymbols and best fits to J � 1/2, 3/2, 5/2, and 7/2 using formalism described inref. 8 are shown in black, red, green, and blue lines, respectively. TK valuesfrom these fits are �37 K and �15 for YbFe2Zn20 and YbRh2Zn20, respectively.For YbRh2Zn20, the Schottky contribution (�E1 � 40 K) is shown as a dashed redline; the sum of Schottky and Rajan (J � 3/2) terms is shown as a solid black line.

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screened and that there is a doublet CEF level located at 40 K.The sum of the Kondo screened quadruplet and the Schottkyanomaly associated with the 40 K doublet are shown as the solidline. Taken together, Figs. 4 and 5 indicate that the largeelectronic specific heat values shown in Fig. 1 are due to Kondoscreening and that the degeneracies for the YbT2Zn20 com-pounds are most probably N � 8 for T � Fe, Ru and N � 4 forT � Os, Co, Rh, Ir.

Given the above analyses, Figs. 4 and 5 can be used to inferapproximate degeneracies for the Yb ion in these YbT2Zn20compounds (see Table 1). We can then infer a value of TK byusing TK � (RlnN)/� (22) or by using TK � (N � 1)�2RwN/3N�(where wN is a multiplicative factor that is a function of N asdiscussed in ref. 21). These expressions produce TK values thatare within 5% of each other for 2 � N � 8. It should also be notedthat the TK value estimated by this method is close to that foundby fitting the whole Cp curve (see Fig. 5). As could be anticipated,TK values for T � Fe and Ru are indeed larger than those foundfor T � Rh, Os, Ir.

Given that our earlier work on the RT2Zn20 families has shownthat T � Fe and Ru compounds manifest anomalously hightemperature, local moment ordering due to the fact that the Yand Lu host materials are close to the Stoner limit (5), it isnoteworthy that for the YbT2Zn20 materials it is the T � Fe andRu compounds that appear to be significantly different from theT � Rh, Os, and Ir compounds. Although we currently do nothave enough data to conclude that this Stoner enhancement ofthe host material (if it even persists in the Yb based members)is responsible for the higher TK/TCEF ratio, such an enhancementcertainly could be responsible for increased TK values. Thisquestion is the focus of an ongoing dilution study.

Although at first glance the data for YbCo2Zn20 appear to bedifferent from that of the other members of this family, at lowenough temperatures, it too appears to enter into a Fermi liquidground state and, as shown in Fig. 4, has an intermediate N value,similar to YbOs2Zn20. YbCo2Zn20 has a substantially lower TK,and may be closer to a quantum critical point (QCP) than theother, T � Fe, Ru, Rh, Os, Ir members of the family: i.e., smallperturbations to YbCo2Zn20 may lead to the onset of magneticorder, giving rise to a T � 0 phase transition controlled by anonthermal (magnetic field, pressure, doping) tuning parameter.If YbCo2Zn20 is simply closer to a QCP, then, given that the unitcell dimensions for YbCo2Zn20 are the smallest of the family, thiswould imply that applications of modest pressure to othermembers of the YbT2Zn20 family may lead to several newYb-based compounds for the study of quantum criticality.

MethodsSingle crystalline samples of YbT2Zn20 were grown out of excessZn using standard solution growth techniques (23). Initial ratiosof starting elements (Yb:T:Zn) were 2:4:94 (T � Fe, Co), 2:2:96(T � Ru, Rh), 1:0.5:98.5 (T � Os), and 0.75:1.5:97.75 (T � Ir).Crystals were grown by slowly cooling the melt between 1150°Cand 600°C over �100 h. To reduce the amount of Zn transportedto the top of the growth ampoule, all growths were sealed under�1/3 atmosphere of high purity Ar and were also slightlyelevated from the hearth plate so as to ensure that the top of theampoule was slightly hotter than the bottom. Residual Zn fluxwas etched from the surface of the crystals using diluted HCl (0.5volume percent, T � Fe, Co) or acetic acid (1 volume percent,T � Ru, Rh, Os, Ir). As can be seen in Fig. 1, there is virtuallyno low-temperature Curie tail observed in any of the T � Fe, Ru,Rh, Os, Ir compounds, indicating little, or no local-moment-bearing impurities.

Magnetization measurements were performed for T � 1.8 Kin a Quantum Design MPMS unit with the applied magnetic fieldalong the (111) crystallographic direction. Specific heat andtransport measurements for T � 0.4 K were performed in aQuantum Design PPMS system. Specific heat, C(T), data for 50mK � T � 2 K were taken on YbCo2Zn20 in a dilutionrefrigerator insert for the Quantum Design PPMS system.Whereas all RT2Zn20 (R � Yb, Lu, Y; T � Fe, Co, Ru, Rh, Os,Ir) had D values near 255 K, the linear component of the C(T)was low (50 mJ/mol K2 or less) (5) for the Lu- and Y-analoguesand greatly enhanced for the Yb-bearing materials. Transportdata were taken for T down to 20 mK at the National HighMagnetic Field Laboratory using an Oxford dilution refrigera-tor. Powder x-ray diffraction measurements were performed ona Rigaku Miniflex unit. The YbT2Zn20 (T � Fe, Co, Ru, and Rh)compounds had diffraction patterns and lattice parameters thatagreed well with the data for the RT2Zn20 series presented in ref.4. Although there are no prior reports on the ROs2Zn20 andRIr2Zn20 series, the diffraction patterns for YbOs2Zn20 andYbIr2Zn20 were easily indexed to the RT2Zn20 structure type.Room temperature unit cell parameters are given in Table 1.

P.C.C. and S.L.B. thank L. McArthur for having introduced them tosome of the finer points of QD options and D. Hall for critical advice.Ames Laboratory is operated for the U.S. Department of Energy by IowaState University under Contract DE-AC02-07CH11358. This work wassupported by the Director for Energy Research, Office of Basic EnergySciences and National Science Foundation Grant DMR-0306165 (toM.S.T.). Work at the National High Magnetic Field Laboratory wasperformed under the auspices of the National Science Foundation, U.S.Department of Energy, and the State of Florida.

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