PHYSICAL REVIEW B VOLUME 36, NUMBER 16 1 DECEMBER 1987

Neutron scattering measurements of spin Auctuations in the heavy-fermion system Upt,

A. I. Goldman and G. ShiraneBrookhaUen National Laboratory, Upton, New York 11 793

G. AeppliAT& T Bell Laboratories, Murray Hill, New Jersey 07974

E. Bucher and J. HufnaglUniuersity of Konstanz, D 7750 K-onstanz, Federal Republic of Germany

(Received 20 May 1987)

We report the results of both polarized and unpolarized neutron scattering measurements onsingle-crystal specimens of the heavy-fermion system UPt3. At low temperatures (T & 30 K), andfor the energy scales probed in these measurements (Ace=6 —8 meV), there is antiferromagneticshort-range order between nearest-neighbor uranium-ion moments located in adjacent basal planes.Such order implies that next-nearest neighbors, located within the same basal plane, are correlatedferromagnetically. As the temperature is raised above 18 K, where the bulk in-plane susceptibilityhas a maximum, the antiferromagnetic correlations between nearest neighbors disappear. Howev-er, the ferromagnetic correlations in the basal plane do not vanish until T ~ 150 K.

I. INTRODUCTION

The heavy-fermion system (HFS) UPt3 remains thesubject of intense theoretical and experimental interest.While much of this attention has focused on the pairingmechanism responsible for superconductivity in this sys-tem (T, =0.5 K), many issues regarding the low temper-ature normal state description of UPt3, and HFS in gen-eral, remain unresolved. What characterizes the"coherent" regime that is signaled by a striking decreasein the resistivity, ' anomalies in the Hall effect, and thedecrease in the in-plane bulk susceptibility at low tem-perature? It now seems clear that the coherent state inHFS such as UPt3 and CeCus (Ref. 4) is one of thefeatures which distinguishes the HFS from systems ofnoninteracting Kondo impurities, in terms of whichmany of the higher-temperature phenomena observed inthese materials may be described. In addition, thereseems to be a delicate balance between the interactionsin HFS which, at low temperature, lead to a rich varietyof ground states (e.g. , superconductivity, magnetic order-ing, paramagnetism). A microscopic description of thenature of the interactions in the low-temperature regimehas obvious importance, and may be realized throughmagnetic neutron scattering measurements.

Polarized neutron scattering measurements of the spinfluctuation spectrum of polycrystalline UPt3 have beenreported by Aeppli et al. As shown in Fig. 1, the ener-gy scan at a constant momentum transfer of 2 A re-

0

veals a quasielastic response, S(Q, co), with a characteris-tic energy of order 10 meV. However, since the mea-surement was performed on a powder, only Brillouinzone averaged information could be obtained. Details ofthe Q dependence of the spin fluctuations require the useof single-crystal samples.

UP t& powderI I

T = 1.3K

400—ED~ 300—

) 200—M

I

100—

o g=2A~ 0=2.6A

40' —80' —80' —80'—E& = 42 meV

I

-8I

16 24hcu (meV)

I

32I

40 48

FKJ. l. Constant Q spectra obtained using polarized neu-trons. Dashed and solid lines are fits to the data using aLorentzian profile (after Aeppli et al. , Ref. 5).

In this paper we discuss the results of both polarizedand unpolarized neutron scattering measurements onsingle-crystal specimens of UPt3. Some of the resultshave been communicated earlier. ' Specifically, we havefound that the low-temperature coherent state of UPt3 ischaracterized by antiferromagnetic correlations betweeneach U ion and its six nearest neighbors. Concommi-tantly, the correlations between the uranium ions andtheir next nearest neighbors (which are located in thesame basal plane) are ferromagnetic. The in-plane,next-nearest-neighbor ferromagnetic correlations persistto temperatures in excess of 150 K, while the antiferro-magnetic spin fluctuations are only well developed below18 K, the temperature at which a peak is observed in thebulk susceptibility measurements.

36 8523 1987 The American Physical Society

8524 C7OLDMAN, SHIRANE, AEPPLI, BUCHER, AND HUFNAGL 36

II. EXPERIMENTAL DETAILS A. Unpolarized beam measurements

O

OCh 3~ &(~)

0I (~)

0

I0

I

Qo

0

0

I0

I

Qs

n42 3

(O, O, QE ) (UNITS OF c )A

)i c

UPt3 crystallizes in the DO &9 hexagonal structure(space group P63lmmc), with two uranium sites in theunit cell as shown in Fig. 2 (a =5.752 A; c =4.889 A).Two cylindrical single crystals, 3 cm long by 0.5 cm indiameter, were cut from the same Czochralski-grownboule and mounted over each other with their c * and a *

axes aligned. The relative angular displacement betweenthe axes of the two crystals was approximately 0.5'. Fig-ure 2 also displays the region of reciprocal space probedin the measurements we report here, as well as the al-lowed nuclear Bragg peaks. The wave vector of all mea-surements will be given in reciprocal lattice units(Q, , O, Q, ), with Q in units of a*=1.25 A ', and Q, inunits of c*=1.28 A

The sample was enclosed in a sealed aluminum can,backfilled with helium to ensure good thermal transfer,and attached to the cold finger of either a He-flow cryo-stat for measurements above 4.2 K, or a pumped He cry-ostat for measurements at 1.2 K. Control at low tem-peratures was to better that +0.2 K. Both polarizedand unpolarized neutron scattering measurements wereperformed at the Brookhaven High Flux Beam Reactor.

Unpolarized neutron scat tering measurements weremade on a triple-axis spectrometer using a pyrolyticgraphite (PG) (002) monochromator and analyzer, and aPG filter after the sample to eliminate the higher har-monic content of the scattered beam. Both energy scansat fixed momentum transfer, and Q scans at fixed energytransfer were performed at a fixed final neutron energyof 14.7 meV, and collimations of 40'-40'-40'-40' or 40'-40'-40'-80', numbers which refer to the horizontal col-limations of the beam between the reactor and mono-chromator, monochromator and sample, sample andanalyzer, and analyzer and detector respectively. Theenergy resolution [full width at half maximum (FWHM)]was approximately 0.8 meV and 1.0 meV for the twoconfigurations, respectively.

In addition to the magnetic scattering of interest here,single- and multiphonon processes contribute to thespectra at finite energy transfer. In the unpolarized neu-tron measurements, both the magnetic and nuclear con-tributions are observed, and must be separated. Thesingle-phonon scat tering processes are easily dis-tinguished since they yield sharp peaks at well-definedvalues of Q and energy transfer (A'ci) for our essentiallysingle-crystal sample. On the other hand, multiphononscattering contributes a diff'use background which isdifficult to separate, in a quantitative fashion, from thediff'use magnetic scattering. However, we remind thereader that the intensity of magnetic scattering decreaseswith increasing momentum transfer as the magneticform factor squared [f (Q)], while the multiphononcross section increases with Q ", where n is the order ofthe process (e.g. , Q for two-phonon scattering).

Most of the measurements which we discuss here weremade with unpolarized neutrons since the higher avail-able flux at the sample position, as compared to ourpolarized-beam measurements, allows superior countrates and finer energy resolution. It is important,though, to confirm the basic results with polarized-beamtechniques which more directly discriminate betweenmagnetic and nuclear scattering.

B. Polarized-beam measurements

Ab

FIG. 2. Upper: Region of the (Q„,O, Q, ) plane in reciprocalspace probed in this investigation. Solid circles representreciprocal-lattice points where nuclear peaks are observed.Open circles and numbers depict positions and relative intensi-ties of antiferromagnetic scattering as described in text.Lower: Unit cell for UPt3 with the positions of uranium ions

Polarized neutron scattering measurements were madeon a modified triple-axis spectrometer using verticallymagnetized Heusler CuzMnA1 (111) transmission crystalsas monochromator and analyzer, magnetic guide fieldsto maintain the polarization of the neutrons, and a flip-ping coil between the sample and analyzer. A smallmagnetic field at the sample position was used to orientthe neutron polarization either along the scattering vec-tor (HF) or perpendicular to the scattering plane (VF) inthis region. The overall flipping ratio of the instrument,which measures the contamination of spin-flip {magnetic)by non-spin-flip {nuclear j scattering was about 15 forboth HF and VF. With the flipper activated, in the ideallimit of an infinite flipping ratio, only spin-flip (magnetic)scattering is detected. The difference in intensity mea-sured in the HF and VF configurations is generally takenin order to further reduce the nuclear scattering contam-

36 NEUTRON SCATTERING MEASUREMENTS OF SPIN. . . 8525

ination due to the finite flipping ratio, and to eliminatethe incoherent nuclear spin scattering contributions.Most data were taken at a fixed final energy of 41 meVand collimations of 40'-80'-80'-130', providing an energyresolution (FWHM) of about 9 meV at fico =0.

III. RESULTS AND ANALYSIS

A. Q dependence of S(Q, c0)

To explore the Q dependence of S(Q, co), we have per-formed a series of scans at a constant energy transfer of8 meV, along several directions using unpolarized neu-trons. This choice of energy transfer was motivated bythe observation that the magnetic scattering shown inFig. 1 peaks in this region. Consider first the longitudi-nal scan (O,O, Q, ) displayed in Fig. 3.

The sharp maxima at Q, =1.76 and 2.24 correspondto a pair of longitudinal acoustic phonons which are ex-pected at this wave vector and energy transfer. ' Theunderlying diffuse scattering clearly peaks at Q, =1 and3, with a minimum at Q, =2. As Fig. 2(b) shows, nu-clear Bragg reflections are found at wave vectors Q, =2n[along (O,O, Q, )] where the scattering from the two urani-um atoms in the unit cell are in phase. Maxima in thediffuse scattering at Q, =2n +1 may be obtained fromshort-range antiferromagnetic correlations between theuranium atoms with a propagation vector along c *.

The ratio of the diffuse scattering in the maxima, aftersubtracting a Q-independent background measured atfico= —4 meV, is I(0,0, 1)/I(0, 0, 3)=1.8. While the de-crease in intensity, as Q, increases, is in qualitativeagreement with that expected from the U 5f form fac-tor, recent induced moment measurements by Stassiset al. " on UPt3, indicate that f (001)/f (003) =2.7,somewhat greater than our determination. As we de-scribe below, there is a significant multiphonon contam-ination which most probably accounts for this discrepan-cy.

Scans transverse to the (O,O, Q, ) direction were takenalong (Q„,0, 1.05) and (Q, 0, 2.05) at 8-meV neutron en-ergy loss as shown in Fig. 4. The scan along(Q„,0, 1.05) clearly exhibits a maximum in the diffusescattering at Q =0, while the spectrum at Q =1.5 issomewhat obscured by several phonon peaks. The pres-ence of significant multiphonon contamination is sig-naled by a striking increase in the scattered intensity atlarge momentum transfer. The solid line beneath thesedata shows the expected Q dependence that resultsfrom two-phonon scattering processes, and adequatelydescribes the intensity variation at large momentumtransfers where the magnetic contribution is small.

The presence of a peak in the diffuse scattering alongthe a direction indicates that, in addition to the antifer-romagnetic correlations between neighboring sheets ofuranium atoms along c ', magnetic correlations mustalso exist between the U atoms within the same plane.In fact, the scan taken along (Q, 0, 2.05) reveals a max-imum at Q =+1. Because the diffuse scattering peaksonly at integer-order reciprocal-lattice vectors, the "unitcell" for the magnetic short-range order is identical tothe nuclear unit cell. Then, since there are only two Uions per nuclear unit cell, the correlations between next-nearest-neighbor ions —located in the same basalplane —must be ferromagnetic. The presence of antifer-romagnetic correlations within the plane would give riseto maxima at half-integer values of Q„.

The relative magnitudes of the structure factor, calcu-lated for the simple magnetic order where each U ion isantiparallel to its six nearest neighbors are shown next tothe open circles in Fig. 2. A strong modulation of thediffuse scattering should be observed at (001) and (102)in agreement with the trends seen in Figs. 3 and 4. Atthe same time, a minimum in the diffuse scattering is ob-served at (0,0,2).

In light of the seemingly significant multiphonon con-

150--

—IOO—I—

WI—

50—

flue = 8meV

Ef = l4.7meV

40 -40 -40'-40'

200—

I I

I

II

I I

I I

ko' 'go

I 00,——

I

CC

IOO—

0 plo 300

V)

IJJ 200—Z

40- 40- 40 —80 UPt3Ef =14.7 meV

(o)( Q „,0, I.05)

T= I.2 K

4~ = 8meV

(b)( Q„,O, 2.05 )

I I I

0 I 2 3Q„( RECIPROCAL LATTICE UNITS )

I

I.O 2.0(O, O, Qz)

3.0 4.0

FICx. 3. Constant-E scan along (O,O, Q, ). Solid triangles indi-cate the background level measured on the energy gain side.Lines are guides to the eye.

FICx. 4. Constant-E scans: (a) Along (Q„,0, 1.05); the solidline through the data is a guide to the eye. Solid curve belowthe data shows the Q' dependence of two-phonon scatteringcontribution. (b) Along (Q„,0,2.05); the solid line is a guide tothe eye. Dashed lines indicate the positions of intense phononpeaks.

8526 GOLDMAN, SHIRANE, AEPPLI, BUCHER, AND HUFNAGL 36

I I

UPt~POLAR I Z E D BEAM

I 200—f

40'- 80- 80 —l30

T = 4.5K/~=6 meV

a6 500—6)CU

UPt~

E f= I 4.7 meV o 400—

40 —40 —40-40

Wee = 6 meV~ Q = (0, 0, 1.05)~ Q = (0.5, 0, ~.05)

c I P00EOcO

800cO

600

I

400

C: hew = 8 meVE 600—

C

g 500—

M

~ 300—I I

50 ]00TEMPERATURE (K )

=4.5K

1 50

200— (0~ 400 —600

I

-p4I

—0.2I I

0 0.2(Ox, o, i.05)

I

0.4 —500ilII

FICx. 5. Constant-E scan along (Q„,0, 1.05) using polarizedneutrons.

T = 200 K

—400

tamination of our unpolarized-beam measurements, it isimportant to verify the magnetic character of the oscilla-tions in the diffuse scattering with polarized neutrons.The polarized-beam data taken along (Q„,0, 1) areshown in Fig. 5, and should be compared with the unpo-larized neutron data in Fig. 4(a). A maximum in themagnetic scattering at (0,0, 1) is observed in agreementwith the unpolarized beam data.

B. Temperature dependence of the magnetic correlations

Having established the existence of correlated spinfluctuations at low temperature, we proceed with adescription of their temperature dependence. Figure 6displays a constant energy scan taken along (Q„,0, 1.05)with unpolarized neutrons at two temperatures. The fer-romagnetic correlations observed at low temperaturedisappear upon warming to, at most, 200 K. The insetof Fig. 6 provides greater detail of the temperaturedependence. These data were taken at the peak of theobserved scattering (0,0, 1.05), and at the minimum at(0.5,0, 1.05). There is a rather sharp drop in the diifusepeak intensity between 5 and 30 K, while above 30 K,the peak intensity decreases in a more gentle fashion. Awell defined maximum along (Q, O, 1.05) is still ob-served well above 100 K, indicating that the ferromag-netic correlations within a given basal plane persistabove this temperature.

In contrast we find that the antiferromagnetic correla-tions between nearest-neighbor uranium atoms disappearupon warming to, approximately 30 K. Figure 7 showsa series of unpolarized beam constant-Q scans taken atseveral temperatures at (0,0, 1.05) and (0,0,2), the max-imum and minimum in the diffuse scattering along c',respectively. At 4.2 K there is a substantial difference in

I I

—0.5 0 0.5( QX, O, l.05) ( RECIPROCAL LATTICE UNITS )

FIG. 6. Constant-E scan along (Q„,0, 1.05) at 4.5 and 200 Kusing unpolarized neutrons. Inset: Temperature dependenceof diffuse scattering at (0,0, 1.05) and (0.5,0,1.05).

the magnitude of the scattering at these two points,beyond that anticipated from the magnetic-form-factorQ dependence. As the temperature is increased, thedifference becomes less pronounced until, at 30 K, thetwo spectra are roughly the same. Since the scatteringvector in these measurements is directed along the c*direction, we measure the component of the susceptibili-ty in the basal (ab) plane. In order to make contactwith the bulk susceptibility measurements, the data inFig. 7 must be converted to the absolute units ofemu/mole U. The magnetic scattering cross section permagnetic ion may be expressed as'

d 0dA dc'

where the symbols have their usual meanings; S(Q, co) isthe dynamical structure factor which is related to theimaginary part of the susceptibility by

S(Q, cu) =[1—exp(fico/ks T)] 'g"(Q, co) .

Aeppli et al. have already shown that the imaginarypart of the susceptibility, X"(Q,co), is well described forthis system by

36 NEUTRON SCATTERING MEASUREMENTS OF SPIN. . . 8527

UP't3

Ef = l4,7 rneV

40-40-40-40o (o,o, l.os)~ (0,0, 2)

—60

ID

OE

E4)

DO

XAJ

12

4— 2If(0,0,2)1 Xb

(a) T=4.2K

(b) T= IOK

—20

—0C:

E

60 I

40

M

20 ~~

Here, Xo(Q) is the real part of the susceptibility, whichwe wish to compare with the bulk measurements, andtriI (Q) is an energy scale which characterizes the relaxa-tion of the spin fluctuations at wave vector Q.

Equation (1), folded with the resolution function of thespectrometer was fitted to the data of Fig. 7 aftercorrecting for the higher-order contamination of the in-cident beam, ' and subtraction of an energy independentbackground determined from data points on the energygain (fico & 0) side of the spectra. Both I (Q) andXo(Q)f (Q) are adjustable parameters in the fits, whichare shown as the dashed and solid lines in Fig. 7.At low temperature, k T && Ace, the quantity[1—exp(A'ni/k~T)] '=1, and the spectrum is charac-terized by scattering which peaks at the quasielastichalf-width fico=fiI (Q). As k&T is raised beyond triI (Q)the scattering becomes more symmetric about Ace=0.

I 200—

I

UPt3POLAR IZED BEAM

Ef = 41 meV40'- 80'- 80'—I 50'

I

%~ = 6 meV~ (0,0, 1)x (0,0, 2)

The data at 1.2 K for (0,0, 1.05) exhibit a clear maximumat a fitted value )ril (0, 0, 1.05)=5.0+0.2 meV(kit Ts„——58+2 K), smaller than that ( —10 meV) foundfrom the powder averaged data previously obtained byAeppli et al. The energy scale determined from fits tothe other, higher-temperature data in Fig. 7 is approxi-mately the same.

To express Xof (Q) in absolute units, the fitted valueswere normalized to the cross section of a longitudinalacoustic phonon at Q=(0, 0, 1.9) using the method ofSteinsvoll et al. ' The inset of Fig. 7 shows graf (Q) cal-culated from the constant-energy scans at (0,0, 1.05) and(0,0,2) along with the bulk in-plane susceptibility data ofFrings and Franse multiplied by f (0,0, 2). There isvery good agreement between the susceptibility mea-sured at (0,0,2) and X„„,~ given the possible systematic er-rors involved in both the conversion to absolute units,and the neglect of multiphonon contamination. In par-ticular, we point out that the decrease in the in-planebulk susceptibility observed at low temperatures isreflected in the neutron measurements at (0,0,2). Theonset of antiferromagnetic spin fluctuations along c', be-tween the planes of U atoms is evidenced by the increasein the sublattice susceptibility measured at (0,0, 1.05) atlow temperature. Therefore, the previously unexplainedmaximum in gb„,„at Tz ——18 K originates from the onsetof these antiferromagnetic correlations.

Figure 8 displays the temperature dependence of thediffuse scattering at (0,0, 1) and (0,0,2) measured with po-larized neutrons. As anticipated from our unpolarized-beam measurements, a pronouned difference in the mag-netic scatterings appears below 30 K, while the intensityat these two points is roughly the same at higher tem-peratures.

I I I

IO 20r (K)

I

-5I

5F ~(rneV)

IO

—60

—20

II

1000 —Qil

c 800—

600 —-I

400—

FIG. 7. Spectra for Q =(0,0, 2) and (0,0, 1.05) at 4.2, 10, and30 K. Solid-dashed lines are derived from fits described intext. Constant backgrounds of 6 and 7.5 counts/min were sub-tracted from the (0,0,2) and (0,0, 1.05) data, respectively. Inset:Temperature dependence of the zero-frequency magnetic sus-ceptibility extracted from measurements at (0,0, 1.05) and (0,0,2)compared with corrected bulk susceptibility. The solid line is aguide to the eye (after Aeppli et al. , Ref. 5).

I

20I

40I

60T(K)

80 100

FIG. 8. Temperature dependence of the diffuse magneticscattering at (0,0, 1) and (0,0,2) measured with polarized neu-trons.

8528 GOLDMAN, SHIRANE, AEPPLI, BUCHER, AND HUFNAGL 36

IV. DISCUSSION

The observation of well-developed magnetic correla-tions at low temperature in UPt3 provides important in-formation concerning the interactions which character-ize the coherent state of this HFS. First we note that asthe temperature is decreased this system appears to ap-proach a magnetically ordered ground state. Recently ithas been discovered' ' that the addition of only a fewpercent Th for U or Pd for Pt does produce antiferro-magnetic ordering. In fact, the magnetic structures ofUi Th Pt3 and U(Pti Pd )3 are identical's with anordered moment well below the effective moment calcu-lated from the high-temperature susceptibility, an obser-vation' not uncommon in magnetically ordered HFS.More surprisingly, the magnetic structure of these dopedsystems, characterized by antiferromagnetic ordering inthe basal planes which doubles the unit cell along a'and ferromagnetic order along c*, bears little resem-blance to the description of the correlations observedhere at this energy scale in pure UPt3. Further investi-gation of both the consequences of impurities in UPt3,and the magnetic correlations in pure UPt3 at lower en-ergies is clearly necessary.

The tendency toward antiferromagnetic spin fluctua-tions in highly correlated electron systems has been dis-cussed by several workers. In particular, it seems that inthe limit of large intrasite repulsion, both the single-bandHubbard model and the Anderson lattice model yieldantiferromagnetic interactions between nearest-neighborantiparallel spins. ' ' In addition, the Monte Carlosimulations of Hirsch, as well as the theoretical treat-ments of Beal-Monod et al. and Miyake et al. haveshown that antiferromagnetic spin fluctuations suppressboth isotropic-singlet and anisotropic-triplet pairingmechanisms for superconductivity, while they enhanceanisotropic-singlet pairing. This result was obtained forsimple (Bravais lattice-based) systems in which the wavevector describing the maximum in the effective interac-tion [J(q) in Ref. 23 or the wave vector of the magneticinstability in Ref. 22] is found at a zone boundary. Wenote that UPt3 presents a somewhat more complicatedproblem since, as we have shown, the maxima in the sus-ceptibility are found at zone centers [the two U atomsper unit cell conspire to eliminate nuclear scattering at(001) and (003)]. A further complication is that the fer-romagnetic next-nearest-neighbor coupling found athigher temperatures may survive even at low tempera-tures where the antiferromagnetic nearest neighbor cou-pling apparently dominates. It is not yet clear how thesepoints modify the arguments which favor anisotropic-singlet pairing. However, while these neutron scatteringmeasurements alone do not provide unambiguous proofof anisotropic-singlet pairing in UPt3, taken togetherwith recent group-theoretical and transport measure-ments, ' they represent strong evidence in favor of this

pairing.In a similar vein, the observation of antiferromagnetic

spin fluctuations in UPt3 contradicts the comparisonoften made between this HFS and the nearly ferromag-netic Fermi liquid He. The analogy arises largely fromthe T ln(T/Ts„) contribution to the specific heats ofboth UPt3 and He at low temperature. First of all, wenote that the energy scale of the spin fluctuations iriI (Q)remains essentially constant across the Brillouin zone,whereas for a single-component weakly interacting Fer-mi liquid AI (Q)~0 as Q approaches a Brillouin-zonecenter. The spin-fluctuation temperature, TsF =60 K,derived from fits to the specific-heat data, agrees quitewell with the energy scale of the spin fluctuations deter-mined from our fits in Fig. 7. It has been pointed outthat the T ln(T/TsF) contribution is actually a quitegeneral feature of all normal Fermi liquids, and does notdepend upon the presence of ferromagnetic interactions.However, as discussed by Moriya, this contribution hasnot been observed in the specific heat of nearly antiferro-magnetic metals.

It is useful to consider our results in the context ofother uranium intermetallic compounds recently re-viewed by Buyers and Lander. In particular, althoughnot a heavy-fermion system in the sense of UPt3 orUBe, 3, UA12 also exhibits spin fluctuation effects thathave been associated with strong ferromagnetic correla-tions, such as a T ln(T/TsF) contribution to the low-temperature specific heat. However, no direct evidencefor ferromagnetic spin fluctuations from neutron scatter-ing has yet been presented.

In conclusion, we have presented evidence from bothpolarized and unpolarized neutron scattering measure-ments that the low-temperature coherent state in UPt3 ischaracterized by antiferromagnetic correlations betweensheets of nearest-neighbor U ions along the c axis, andferromagnetic correlations between the next-nearest-neighbor U ions within the same sheet. While the fer-romagnetic correlations persist to temperatures some-what greater than 100 K, the antiferromagnetic spinfluctuations are found at temperatures below 30 K, andaccount for the decrease in the measured bulk suscepti-bility below 18 K. Further studies of the spin fluctua-tions in UPt3, extending to temperatures below the su-perconducting transition, are anticipated.

ACKNO% LEDGMENTS

We thank E. Abrahams, B. Batlogg, D. J. Bishop, V.J. Emery, Z. Fisk, J. Kjems, K. Levin, A. Millis, K. Mi-yake, D. Osheroff; D. Pines, A. P. Ramirez, T. M. Rice,S. M. Shapiro, C. Stassis, C. Varma, and C. Vettier forvery useful discussions. Work at Brookhaven was sup-ported by the Division of Materials Science, U.S.Department of Energy, under Contract No. DE-AC02-76CH00016.

36 NEUTRON SCATTERING MEASUREMENTS OF SPIN. . . 8529

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