PHYSICAL REVIE% 8 VOLUME 37, NUMBER 13

Gd interactions in (Ce,Gd) Al3

A. S. Edelstein, R. L. Holtz, D. J. Gillespie, M. Rubinstein, and J. TysonNava/ Research Laboratory, Washington, D.C. 20375

R. A. Fisher and Normal E. Phillipshfaterials and Chemical Sciences DivisionL, awrence Berkeley Laboratory, Berkeley, California 94720

(Received 11 December 1987)

The susceptibility of Cei-~6d~A13 for 0.08 ~ x ~ 0.9 has an anomaly which resembles that as-sociated with a spin-glass transition. For x greater than the percolation threshold concentrationfor antiferromagnetism at x =0.5, the size of the susceptibility anomaly decreases t~o orders ofmagnitude and a resistivity anomaly appears.

When Gd is added to a nonmagnetic host such as La-Au or Ag, the Gd moments interact via the Ruderman-Kittel-Kasuya- Yoshida (RKKY) interaction. Becausethe sign of thts interaction oscillates as a function of thescpsratloll bctwccll the Inolncllts, ally Gd Illolncllt III gcll-eral has both ferromagnetic and antiferromagnetic ex-change interactions with its neighboring Gd atoms. Thesecompeting interactions can give rise to a spin-glass transi-tion.

Here we discuss adding Gd to a special kind of magnet-ic host, a heavy-fermion (HF) systemz CCAlq. The origi-nal motivation of an earher studyI of CCI-,Gd„Alp wasan interest in determining whether replacing Ce with Gdadded ferromagnetic interactions that might sN'ect themagnetostriction. Here we report some of our susceptibil-ity, resistivity, magnetization, and specific-heat measure-ments on this system for 0.08» x» 0.9 which show thatthe interactions between the Gd moments are surprisinglystrong in this host. Further, we have observed several new

phenomena connected with heavy fermions, spin glasses,and percolation.

Because the host is unusual it is worthwhile to briefiydescribe its properties. At high temperatures the Ceatoms in CCAlq are magnetic and have approximately theexpected Hund's-rule moment. At low temperatures thesystem goes into a Kondo singlet ground state. It is lessclear how the Gd moments will interact in this host. For0.08» x» 0.9, we observe susceptibility anomalies (seeFig. I) which resemble spin-glass transitions. For x» 0.50, these anomaltes are cusps while for x 0.635 snd0.77 we only observed step increases. We denote the tem-perature at which these anomalies occur as T~. The phenomena due to the interacting Gd moments occur in twoCOIPOSlf 106 rRQgeS.

(I) For 0.05»x»0.4 and T 2 K, the spontaneousmagnetization M, is approximately 10% of the value pos-sible from just the Gd moments (see Fig. 2), i.e., thisproperty scales with x. For x» 0.23, the system is still aHF system as determined by specific-heat measurements.

(2) For x&0.4, the amplttude of the susceptibilitymaximum peaks as one approaches (from below) the per-colation threshold for antiferromagnetism at x=—x, =0.5.For x 0.5, M, is approximately 40% of the value possiblefrom just the Gd moments (see Fig. 2). For x & x„T

does not change abruptly but the amplitude of the suscep-tibility at the maxima decreases by more than two ordersof magnitude (see inset of Fig. 1). A resistivity anomalyoccurs at T for x&x, but not for x(x,. l The Ceatoms are apparently responsible for the high values of Tand the strong Gd-Gd interactions in this host. Thesevalues, approximately 100 K for x ~0.5, are surprisinglyhigh since the ordering temperatures" of all the rare-earth trialuminides are less that 25 K. An indication thatboth the Ce and Gd are necessary for the high values ofT is provided by the facts that no spin-glass transitionwas found' in (La,CC)Alq and in our measurements onLal —,Gd„Alq with x 0.2, 0.4, 0.6, and 0.8 for5» T»300K.

We investigated arc-melted, polycrystalhne samples'that had been annealed for two weeks st 980'C. X-raydiffraction analysis shows that the lattice parameters ofthis system, which has the hexagonal DOI9 structure(space group P6$IIImc), varied approximately linearly as

0.05-

0.04-

E0.03-

EI0.02-

02 04 06 08 10

77, x20

0.01-

%50 200 250

FIG. l. X of Cei-~6d~hl3 vs T. The values for x 0.635 and0.7'7 have been multiplied by a factor of 20. The arrows indicatethe antiferromagnetic transition in the x 0.635 and 0.77 sam-ples. The peak in X~ for x 0.9 is 2% above the background.The inset shows the logarithm (base 10) of the susceptibilitymaxima (in emu/g) at T vs x.

BRIEF REPORTS

60

50-+

0.50, T=2.0 K

++

+~+

30-Q)

20

10

'0 2 6 8H (T)

FIG. 2. Magnetization M at lwv temperatures vs 6eld 8 forx 0.40, 0.50, and 0.635.

a function of Gd concentration. Because of the inherentdifFiculty of preparing single-phase samples, we presentthe following evidence that the transition at T is due tothe (Ce,Gd)A13 phase.

(1) Evidence agmnsi the dialuminide phase being re-spoan'ble. A few samples which exhibited two transitionshad one at T and the other at the Curie temperature'4 of(Ce,Gd)A12, the dialuminide phase. The magnitude ofthe susceptibility at T correlated with the amount of tri-aluminide and inversely correlated with the amount of di-aluminide as determined by x-ray diffraction. Less care-ful annealing caused the transition at T to disappear butnot the dialuminide transition. None of our conclusionsdepend upon data taken on these samples exhibiting twotransitions.

(2) Evidence against the 3:ll phase being responsibleNo transition was observed at T in (Ceo.55Gdv. 45)3Alii.The drastic change we observe for x & 0.5 is not connect-ed with the disappearance of the 3:11phase since we havefound that this phase persists up to at least 65 at. % Gd.

(3) Evidence against either the dialuminide or the 3:llphase being responsible. It is dif5cult to understand howthe presence of the dialuminide or the 3:11 phase couldgive rise the appearance of a resistivity anomaly for x)x, but not for x & x,.

The susceptibility measurements were made in lowfields (three to several tens of Oe) using superconductingquantum interference device (SQUID) magnetometry.Most measurements were performed with increasing tem-perature after the sample had been cooled in the lowestavailable field, 1-5 Oe. Figure 1 is a plot of the suscepti-bility X vs T for several samples. One sees that forx~0.50 there is a cusp, which resembles that at thefreezing temperature of a spin glass, ' at the temperatureT . Additional support for associating T with a spin-glass transition temperature at low Gd concentrations, isgiven by other observations on the x 0.08 sample. (1)We observed ' the usual difference between initial coolingin "zero" field or in a field. (2) After cooling in "zero"field and then applying a 6eld we observed a slow smallupward drift in the susceptibihty. Further, comparison of

the specific heat C for x 0.08 with that for CeA13 on anexpanded scale shows the existence of a broad shouldernear 8 K, consistent with a spin-glass transition at T~11 K.

Fitting the inverse susceptibility data above T for allthe samples other than x 0.50 to a Curies-Weiss formT—8, one obtains a very small value for the intercept 8(8« T ). This is the usual behavior of a spin-glass sys-tem. For x 0.50, 8 is large and positive. This is con-sistent with considerable ferromagnetic coupling.

The amplitude of the susceptibility anomalies shown in

Fig. 1 is a strong function of x. This is illustrated moreclearly in the inset of Fig. 1 where we plot the logarithmof the susceptibility maximum at T as a function of x.The amplitude of the susceptibility at T~ decreases twoorders of magnitude between x 0.5 and 0.56. We nowshow that this decrease correlates with the onset of anti-ferromagnetism.

For x 0.635, 0.77, and 0.90 (not shown), in additionto the anomaly at T~, there is also a low-temperatureanomaly'5 below 20 K (shown by an arrow). We associ-ate the latter with an antiferromagnetic transition becauseof the following. (1) GdA13 is an antiferromagnet" with

T~ 17 K. (2) The specific heat of Ceo 236do 77A13 showscharacteristics of an antiferromagnetic transition. '

There is a cusp at 13.7 K, and for 0.32~ T~ 1.0 K,C 20.5T+98T3 (mJ/molK). The T3 coefficient is ap-proximately 100 times greater than a typical lattice con-tribution and is of the form expected for antiferromagnet-ic spin %'aves.

Measurements of the low-temperature magnetizationM shown in part in Fig. 2, provide further evidence thatthe magnetic character of the system changes for x & 0.5.(Measurements of M for x 0.05 and 0.20 are omittedfor clarity. ) For x ~ 0.50 and T(T, a linear extrapola-tion of the high-field part of M gives a finite I 0 inter-cept M, . For x~0.40, M, ~x. For x 0.5, M, is ap-proximately four times larger than for x 0.4. Apparent-ly M, increases at a faster rate between 0.4 and 0.5. Thisresult suggests that the fraction of spins that are correlat-ed increases as x approaches 0.5 from below. By contrast,no portion of M saturates at low fields for x 0.635. Forx 0.635, M~H up to our highest fields, 8 T. '7 Such alinear field dependence is associated with antiferromag-netic interactions. These data suggest that ferromagneticinteractions dominate for x 0.5 and antiferromagneticinteractions dominate for x ~ 0.635.

Specific-heat measurements' have determined therange in x for which the system exhibits HF behavior.The T 0 intercepts of C/T, y, are 1.20, 1.24, 0.41, 0.048,and 0.021 J/molK for x 0, 0.08, 0.23, 0.50, and 0.77,respectively. Using Stewart's criterion Cei —«Gd«A13 is aHF system for x ~ 0.23.

As one would expect the HF contribution to y, yHF, isreduced by dilution since yHFO:(1 —x)//T». In addition,the presence of a spin-glass state would give rise to twocompeting effects. The low-temperature portion of thespin-glass speci6c-heat anomaly increases y, but the HFcontribution to y is decreased by the effective internal6eld of the spin-glass state. To be more quantitativeabout this we employ a type of resonant level model

QRIEF REPORTS

(RLM) to interpret the specific heat of the x 0.23 sam-

ple. Previously we applied 's a RLM, which included thecrystal-field contribution, to CeA13. We now also includethe distribution of an effective internal field H,rr of aspin-glass state. Is We assume the following. (1) The Ceatoms give rise to a Lorentzian density of states peakwhich, in zero field, is centered at the Fermi energy. Wetake for the width of the Lorentzian the same value as weused's for CeAlq, 4.5 K (the Kondo temperature Tx ofCeA13), (2) A magnetic field (either applied or internal)rigidly shifts the up and down spina density of states in

different directions relative to the Fermi energy. (3) Thevalues of H, tr in the c-axis direction have a Gaussian prob-ability distribution centered at Ho. The component ofH,rr perpendicular to the c axis is taken to be zero becauseits contribution is small. 's We have chosen p v x 2 ps,Ho 6 T and considered two values for the Gaussian"shalf width, 2 and 6 T.

Experimental and calculated values of C/T for x 0.23are shown in Fig. 3. The curves of the calculated valueshave the correct general shape at high temperatures butdo not reproduce the large decrease that occurs below

1 K. This decrease may be due to spin fluctuations.Doniach2o has shown that spin4ensity-wave fluctuationscan be the source of the peak in C/T of CeA13 and it wasdemonstrated that a temperatureMependent width in theRLM can also be used to obtain this temperature depen-dence. ~' To not introduce additional parameters in thepresent calculation, we have used a temperature-inde-pendent width.

The values calculated above represent only the heavy-fermion contribution to C/T. One should add to thesevalues the contribution from the low-temperature portionof the spin-glass specific-heat anomaly. This contributionis of the form for ysoT for T« T~. Using our specific-heat data for the x 0.08 sample, we estimate @so-0.08J/mol K . One can also use the model to show that there

is a @so contribution to C/T by assuming the H,g acts onthe Gd moments. Unfortunately the values one calculatesfor yao are very sensitive to the choice of the width of theGaussian.

Using ou«ata we have constructed the tentative phasediagram shown In Fig. 4. Sotne of the boundaries are notclearly delineated either because there is not a sharp tran-sition or because of insufllcient data. We have arbitrarilytaken the temperature on the HF "boundary" as thehighest temperature for which the experimental values ofC/T are greater than 0.40 J/mol K2. The value on the an-tiferromagnetic boundary for GdAlq was taken from Ref.11, but also corresponds to that derived from our mea-surement of C. Except for these cases, the values plottedin Fig. 4 are the temperatures of the susceptibility maxi-ma or, if there is no maximum, a temperature just belowthe step increase in the susceptibility. Our susceptibilitydata permit us to determine that 0.5&x, &0.635. Thefact that we were able to qualitatively fit the specific-heatdata for x 0.23 by incorporating an effective field of aspin-glass state suggests that the HF state and the spin-

glass state may coexist at low temperatures.Though the values of T appear to lie near a smooth

curve, which does not change slope at x„our data indicatethat there is at least a change in the character of the tran-sition at x,. For x & x, there is a decrease in the suscepti-bility anomaly, the appearance of the resistivity anomalyat T, and the qualitative change in the magnetization.We wish to emphasize that the state below T at high Gdconcentrations may be quite different from the usualspin-glass state. Nevertheless, because we have no evi-dence that it is different and for want of a better name, wewill call the state for both x ~ x, and x & x, a spin-glass-like state.

Let us summarize our results. We have correlated thelarge decrease in the high-temperature susceptibility max-imum, the qualitative change in M, and the appearance of

(Ce,od)AI ~

08 .

0.60E

0.4 o o 0

60SGL

)00

0 0.6

FIG. 3. Comparison of experimental and calculated values ofC/T vs T for Ceo.TIGds. s3Ais. The two curves are the values calculated from the model for Ho 6 T for a half-vridth at halfmaximum of 6 T (curve labeled a) and for a half-width at halfmaximum of 2 T (curve labeled b).

FIG. 4. Tentative phase diagram. The symbols AF, HF, P,and SGL represent the antiferromagnetic, heavy-fermion, para-magnetic, and spin-glass-like phases, respectively. The dashedcurve representing a transition from a paramagnetic state into aspin-glass-like state curves dowvn at large x since T has to go tozero at x 1.

BRIEF REPORTS

a resistivity anomaly with the onset of antiferromagnetismat x,. Both the distribution of the interactions and thechange in topology at x, probably play a role. The in-

crease in M, between x 0.4 and 0.5 suggests that thefraction of the Gd atoms participating in the spin-glass-like transition increases rapidly as one approachesx, ~0.5 from below. For x &x, ferromagnetic interac-tions appear to dominate, while for x & x, antiferromag-netic interactions appear to dominate even at tempera-tures as high as 100 K. (M~0 for x 0.635 even nearT and a linear field dependence is suggestive of antifer-romagnetic interactions. ) Nearly all the spins, includingthe Ce, may become correlated for x & x,. This is sug-

gested by two facts: (1) the curvature exhibited by themagnetization of CeA13 as a function of field at low tem-

peratures, and (2) M~Hforx 0.635 at T 2.0K.The high values of T relative to the ordering tempera-

ture of other rarewarth trialuminides, and the absence ofa spin-glass-like transition in the isostructural series(La,Gd)A13, point to the important role of the Ce

I,t0818.The large y values observed in HF systems are thought

to be an indication of many-body peaks (one for each spindirection) in the density of states at the Fermi energy.Such peaks played a central role in both the model used'to fit CeA13 data and the generalized model employedhere to interpret the specific-heat data for x 0.23. Thegeneralized model incorporates an internal field of thespin-glass state which acts on the peaks in the density ofstates in this HF system. Thus our work provides some in-

sight into both spin-glass and HF systems.

We wish to thank Professor Chia-Ling Chien for thehospita]ity extended to us during our measurements atJohns Hopkins University. The work at Berkeley was sup-

ported by the Director, OSce of Energy Research, Officeof Basic Energy Sciences, Materials Sciences Division ofthe U.S. Department of Energy under Contract No. DE-AC03-76SF00098.

Deceased.iReviewed by K. Moorjani and J. M. D. Coey, Magnetic

Glasses (Elaevier, Amsterdam, 1985).%'e adept the somewhat arbitrary dejnition of a heavy-fermion

system as one for which the T~ 0 ratio of the speci5c heat Cto the temperature T is greater than 0.400 J/molK . For re-views of such systems, see 6.R. Stewart, Rev. Mod. Phys. 56,755 (1984), and Z. Fisk, H. R. Ott, T. M. Rice, and J. L.Smith, Nature 320, 124 (1986).

3A. S. Edelstein and N. C. Loon, J. Appl. Phys. 55, 1984(1984).

4K. Andres, J. E. Graebner, and H. R. Ott, Phys. Rev. Lett. 35,1779 (1975).

5A. S. Edelstein, C. J. Tranchita, O. D. McMasters, and K. A.Gschneidner, Jx., Solid State Commun. 15, 81 (1974).

C. D. Sredl, S. Horn, F. Steglich, 8. Luthi, and R. M. Martin,Phys. Rev. Lett. 52, 1982 (1984).

76. E. Srodale, R. A. Fisher, C. M. Lisse, N. E. Phillips, andA. S. Edelstein, J. Magn. Magn. Mater. 54-57, 416 (1986).

86. E. Srodale, R. A. Fisher, N. E. Phillips, J. Flouquet, andC. Marcenat, J. Maga. Magn. Mater. 54-57, 419 (1986).

~6. E. Srodale, R. A. Fisher, Norman E. Philhps, and

J. Flouquet, Phys. Rev. Lett. 56, 390 (1986).'OA. S. Edelstein, R. L. Holtz, D. J. Gillespie, R. A. Fisher, and

N. E. Phillips, J. Magn. Maga. Mater. 63-64, 335 (1987)."K.H. J. Buschow and J. F. Fast, Z. Phys. Chem. 50, 1 (1966).i2R. E. Majewski, A. S. Edelstein, and A. E. D~ight, Solid State

Commun. 31, 315 (1979).i3Some samples did not show a spin-glass-like transition. There

were difhculties or deviations in our sample-making procedurefor those samples. A similar sensitivity to sample quality wasobserved in the magnetic ordering of the heavy-fermion com-pound U2Zn&v [J.O. Willis, Z. Fisk, G. R. Stewart, aud H. R.Ott, J. Msgn. Magn. Mater. 54-57, 395 (1986)].

~4N. Iwata, H. Fujii, and T. Okamoto, J. Maga. Magn. Mater.46, 312 (1985).

' Po-zen %ong, S. von Molnar, T. T. M. Palstra, J. A. Mydosh,H. Yoshizawa, S. M. Shapiro, and A. Ito [Phys. Rev. Lett. 55,2043 (1985)1 have reported the coexistence of spin-glass aud

antiferromagnetic states in Fee.ggMg0. 4gC12.

A similar T contribution was observed for antiferromagnetic

U2Zn|7 [H. R. Ott, H. Rudigier, P. Delsing, and Z. Fisk,Phys. Rev. Lett. 52, 1551 (1984); H. R. Ott, H. Rudigier,Z. Flsk, and J. L. Smith, J. AppL Phys. 57, 3044 (1985)].

'7Comparison of the low-field results (Fig. 1) with the slope ofM (Fig. 2) shows there may be 30% increase in Z for H (0.1

T.~SA. S. Edelstein, 6. E. Srodale, R. A. Fisher, Carey M. Lisse,

and Norman E. Phillips, Solid State Commun. %, 271(1985);57, i(E) (1986).

i~Since CeA13 does not magnetically order, there is no motiva-

tion for applying this eNective-f][eld model to CeAl3. The ex-planation of Bredl et al. (Ref. 6) for the peak in C/T ofCeAl3, based on the concept of coherence, should not apply toa disordered system like Ceo.77GdQ. 23A13.

2 S. Douiach, Phys. Rev. B 35, 1814 (1987).2 Since the width in the RLM can be viewed as proportional to

the reciprocal spin self-correlation lifetime, spin fluctuationsincrease the width. Spin fluctuations give rise to a tempera-ture dependence for the relaxation rate [C. Broholm, J. K.Kjems, 6. Aeppli, Z. Fisk, J. L. Smith, S. M. Shapiro,G. Shirane, and H. R. Ott, Phys. Rev. Lett. 58, 917 (1987)]of the order parameter of the HF system U2Zn&7 above theNeel temperature which is similar to the one postulated in

Ref. 7.22Though one might be tempted to attribute the high values of

T to a density-of-states e6'ect in HF systems there is experi-mental [F. Gandra, S. Schultz, S. B. Oseroff, Z. Fisk, aud

J. L. Smith, Phys. Rev. Lett. 55, 2719 (1985)]and theoretical[C. M. Varma, Phys. Rev. Lett. 55, 2723 (1985)] work which

indicates that the RKKY interactions are not enhanced in HFsystems.