Superconductivity of heavy-electron uranium compounds

PhysicaC 153-155 (1988) 1728-1733 North-Holland, Pansterdam

SUPERCONDUCTIVITY

OF HEAVY-ELECTRON

URANIUM COMPOUNDS

Z. F i s k ~', H. B o r g e s , M. M c E l f r e s h , J . L . S m i t h , J . D . T h o m p s o n " , H.R. O t t +, G. A e p p l i E. B u c h e r * * , S . E . L a m b e r t ++ , M.B. Maple ++ , C. B r o h o l m * * * , and J . K . Kjems*** *Los Alamos National Laboratory, Los Alamos, NM 87545, USA, +Eidgen6ssische Technische Hochschule, HSnggerberg, 8093 Z~rich, Switzerland, ""AT&T Bell Laboratories, Murray Hill, NJ 07974,USA, ++University of California at San Diego, La Jolla, CA 92093, USA, """Ris~ National Laboratory, DK-4000 Roskilde, Denmark

The current understanding of the superconductivity of heavy-electron uranium compounds is reviewed. Both the pairing and the mechanism appear to have been established as unusual in UPt 3 and UBe13. Small-moment magnetic ordering is now known to coexist with superconductivity in URu2Si 2 and UPtq. The understanding of the properties of UBe13 may be viewed as the central probIem in heavyelegtron physics.

1.

INTRODUCTION The r e c e n t d e v e l o p m e n t s i n t h e f i e l d o f superconductivity are focussing renewed attention on n o v e l m e c h a n i s m s a n d a n i s o t r o p i c pairings, a situation s i m i l a r to t h a t w h i c h attended the developments in heavy-electron materials. T h e r e a p p e a r t o be a number o f similarities between the physics of the c u p r a t e s and t h a t of the h e a v y - e l e c t r o n superconductors, as well as significant differences. Both are highly correlated electronic systems with strong magnetic interactions. T h e r e i s no e v i d e n c e a s y e t to suggest that the mechanism for superconductivity is similar. But h e a v y - e l e c t r o n superconductivity has served as a very fertile ground for investigating non-phonon mechanisms a n d h i g h e r a n g u l a r momentum p a i r i n g s , and t h i s e x p e r i e n c e h a s much t o t e l l u s . We r e v i e w h e r e the status of the understanding of superconductivity in u r a n i u m h e a v y - e l e c t r o n compounds. 2.

THE HEAVY-ELECTRON NORMAL STATE A useful qualitative viewpoint for thinking about heavy-electron systems is provided by the Kondo effect. All known heavy-electron materials possess f-electrons which are behaving magnetically like local moments at high (room) temperature. The conduction electrons in these materials compensate the local moments as T ~ 0 K, the high temperature entropy of the spin system smoothly transferring to the conduction electron system. In this extreme view, the local f-moments make the conduction electron heavy. If the temperature scale over which this happens is T K, we estimate the low temperature electronic specific heat 7 ~ (klnD)/T K per f-moment, where D is the degeneracy

of the f-moment,

0921-4534/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

B l o c h ' s T h e o r e m w i l l a p p l y t o t h e low temperature electronic s t a t e of the a t o m i c a l l y ordered lattice of f - a t o m s , a s t a t e which s h o u l d b e d e s c r i b a b l e a s some k i n d o f c o r r e l a t e d Fermi l i q u i d . The l a r g e e l e c t r i c a l resistivity due t o t h e s i n g l e i o n - t y p e Kondo scattering i s o b s e r v e d t o be l o s t b e l o w a t e m p e r a t u r e g e n e r a l l y r e f e r r e d to a s the c o h e r e n c e t e m p e r a t u r e , T~. A rapid change in the Hall constant with temperature also accompanies the development of coherence. It is an unsolved problem of theory to describe the development of coherence. RKKY-type magnetic interactions between f-moments can both modify T K and lead to competing magnetically ordered ground states. One way to think about the effect of magnetic order on a heavy electron state is in terms of the internal field produced. The local magnetic field at an f-site due to the long range magnetic order will partially quench the Kondo compensation there. In this view, the loss of below a magnetic transition is due to loss of mass. 3.

URANIUMCOMPOUNDS The p i o n e e r i n g w o r k o f S t e g l i c h e s t a b l i s h i n g the b u l k n a t u r e of the s u p e r c o n ductivity o f CeCu2Si2 f o c u s s e d a t t e n t i o n on f-electron materials with large w's, corr e s p o n d i n g t o e f f e c t i v e m a s s e s some two o r d e r s of magnitude l a r g e r than the e l e c t r o n mass. A strong parallel between the properties o f Ce and U i n t e r m e t a l l i c s has been found to exist. There are, however, enough differences of d e t a i l b e t w e e n t h e p h y s i c s o f Ce a n d U materials t o make i t d e s i r a b l e to t r e a t o n l y U-compounds h e r e .

Z. Fisk et al.

10000

i

f

F

ItJll

I

I

~

I

1Ill11

t

I

I

/ Heavy-electron uranium compounds

1729

I

~11

I

400

~" 1000 ~ &

~

07.6

LJPt3 300

E 0

:=L

0 U6Fe /,

lo-4

a-U

O-

........

10-a

,

UPt 3

200

U 6 Fe

U2 PtC2

.....

lo-2

lo-~

X (0) (emu/mole .f .atom) UBe

100

FIGURE 1. Ln v v e r s u s gn K ( f o r T ~ 0 K) p l o t t e d f o r Uranium s u p e r c o n d u c t o r s . The l i n e i s t h e f r e e e l e c t r o n S o m m e r f e l d r e l a t i o n b e t w e e n v a n d ~.

There are only a small number of superconductors containing U (Table). A convenient way to present these materials is in a ~-v plot, Fig. i. We see that these superconductors are found over the entire range of w-values known for U-compounds. We point out that the two heavy-electron superconductors UPt a and UBe13 very nearly obey the Sommerfeld relation b e t w e e n K a n d v. We d i s c u s s t h e l o w - v s e t o f m a t e r i a l s first. E l e m e n t a l U i s b e l i e v e d n o t t o be a superconductor at ambient pressure (1). The pressure induced superconductivity o f ~-U p e a k s n e a r 2 K a t 10 k b a r . Neutron scattering experiments have found that a charge density wave d e v e l o p s b e l o w a b o u t 40 K i n a - U , a n d i t is plausible t h a t t h e p r e s s u r e e f f e c t on T i s c due t o s u p p r e s s i o n o f t h e c h a r g e d e n s i t y wave with pressure. The s t a b i l i z e d v allotrope of U h a s a l s o b e e n r e p o r t e d t o be s u p e r c o n d u c t i n g (2). The i n t e r e s t i n g s e t o f compounds UeX (X = Mn, Fe, Co a n d N i ) h a v e v ' s i n t h e n e i g h b o r h o o d o f 25 m J / m o l e U-K2 ( 3 ) . T is highest for c UeFe, 3 . 9 K. The c l o s e U-U s p a c i n g s i n t h e s e t e t r a g o n a l m a t e r i a l s make i t l i k e l y t h a t s t r o n g l y h y b r i d i z e d f - b a n d s e x i s t a t the Fermi level. This separates the physics of these materials from direct overlap with that of the much i a r g e r - v m a t e r i a l s , although it is clear that important correlation effects are present here. No o n e a p p e a r s t o h a v e b e e n a b l e t o prepare single crystals of these easily oxidized, periteetieally forming materials.

Nb 3 Sn

100

200

300

T(K)

FIGURE 2 Temperature d e p e n d e n c e o f the electrical resistivity of various superconductors. YBa2CuO7 d a t a f r o m ( 2 2 ) , NbaSn f r o m ( 2 3 ) , U6Fe f r o m ( 2 4 ) , a n d URu2Si2 ( 2 5 ) . Other data from references in text.

The tetragonal U2PtC 2 has a v = 75 mJ/mole U-K 2 and T = 1.5 K (4). The anomalous, c

bulging shape of the electrical resistivity (Fig. 2), coupled with the substantial v, place this material in the transitional region between light- and heavy-electron behavior. There has been little work on this material, and no single crystal data exist. Considerably more attention has been given to URu2Si2. This material crystallizes in the tetragonal structure found for CeCuzSi2, and large single crystals have been produced by several groups. Both the normal state resistivity, most markedly in the basal plane, and the Hall constant decrease strongly in the vicinity of 50 K, (5). The Cr-like K has been correspond

suggesting resistance

that T ~ ~ 50 K anomaly at T N = 17

found by neutron diffraction to 0.02 ~B/U simple antiferro-

magnetic order, the moments to the c-axis (6). At T N,

to

aligning parallel v is extrapolated

to

Z. Fisk et al. /Heavy-electron uranium compounds

1730

be 180 m J / m o l e U-K 2. This is approximately the v a l u e t h a t i s found f o r a l a r g e number of U-intermetallics w h i c h u n d e r g o no low t e m p e r a ture phase transitions. The r e m a r k a b l e f e a t u r e o f U R u 2 S i 2 i s t h e s u b s e q u e n t d e v e l o p m e n t o£ superconductivity b e l o w 1 . 2 K. At t h i s t e m p e r a t u r e n = 75 m J / m o l e U-K 2. At t h e superconducting transition, AC/vT = 1 . 3 , c s o m e w h a t r e d u c e d f r o m t h e BCS weak c o u p l i n g value. There is still a l o t t o be u n d e r s t o o d about URu2Si 2 . Many o£ t h e s i n g l e c r y s t a l e x p e r i m e n t s p e r f o r m e d on UBet3 a n d UPt3 h a v e n o t b e e n c a r r i e d o u t , a n d t h e s e c o u l d go a l o n g way t o w a r d s h e l p i n g s u c h a n u n d e r s t a n d i n g . For example, from thermodynamic data it appears that the commensurate magnetic transition at 17 K o p e n s a g a p a c r o s s ~70% o f t h e F e r m i surface, a surprisingly large fraction in view o f t h e a n o m a l o u s l y s m a l l o r d e r e d moment. T h i s makes t h e t r a n s i t i o n , incidentally, quite different from the magnetic transitions seen in most heavy-electron U-compounds, where it is more likely that the effective mass changes below T N, rather than the Fermi surface area. The idea, then, is that the superconductivity occurs on what remains of the Fermi surface. T h i s , a g a i n , makes U R u 2 S i 2 a p p e a r v e r y d i f f e r ent from the heavier electron U-superconductors. It is likely that the real order parameter here has not been found. 4.

UPt 3

UPt3 c r y s t a l l i z e s i n t h e same h e x a g o n a l s t r u c t u r e a s CeAI3, t h e f i r s t identified h e a v y - e l e c t r o n compound. A wealth of data e x i s t s on s i n g l e c r y s t a l s o f t h i s compound, a n d t h e r e i s now some c o n c e n s u s t h a t t h i s i s a n anisotropic superconductor with a magnetic pairing mechanism. UPt3 h a s a s t r o n g l y b u l g e d , v e r y a n i s o tropic electrical resistivity, much l i k e t h a t o f a n A-15 t r a n s i t i o n metal superconductor (Fig. 2). The H a l l c o n s t a n t s h o w s a r a p i d change in the vicinity o f 20 K, i n d i c a t i n g that T ~ ~ 20 K ( 7 ) . The a l s o a n i s o t r o p i c m a g n e t i c susceptibility p e a k s a t 17 K i n t h e b a s a l p l a n e , a f e a t u r e w h i c h a p p e a r s t o be r e l a t e d [from neutron experiments (8)] to the development o f s t r o n g a n t i f e r r o m a g n e t i c correlations, and p r e s u m a b l y , c o h e r e n c e , de H a a s - v a n A l p h e n work h a s a l s o been r e p o r t e d , f i n d i n g m a s s e s a s h i g h a s 120 m ( 9 ) . This is a lower limit, set e by e xpe r i m e n t a l c o n s traints, on t h e l a r g e s t m a s s on t h e F e r m i s u r f a c e . The l o w - t e m p e r a t u r e s p e c i f i c h e a t s h o w s w h a t was b e l i e v e d t o b e e v i d e n c e f o r s p i n fluctuations b u t i s now i n t e r p r e t e d i n a more g e n e r a l Fermi l i q u i d context. ~ = 450 m J / m o l e U-K2,

and the anomaly a t T

c

i s hC/wT

C

~ 0.8.

T h i s g a v e r i s e t o t h e now dead s u g g e s t i o n the superconductivity was not bulk.

that

An earmark of anisotropic superconductivity is the presence of power laws in T below T in various properties as T + O K arising from nodesCof the superconducting gap on the Fermi surface. In UPt3, a T 2 dependence was found in both the specific heat (I0) and c-axis ultrasonic attenuation below T (11). Additional evidence c for an anisotropic superconducting state comes from anisotropy of sound propagation in the basal plane, depending on polarization of the sound (12), and tunneling experiments which find no gap in the basal plane (13), but a gap perpendicular to the plane. All these contribute to the idea that UPt 3 is a polar superconductor with a line of nodes of the gap perpendicular to the hexagonal c-axis. Recent evidence supporting a magnetic p a i r i n g m e c h a n i s m h a s come f r o m n e u t r o n measurements. These experiments have, firstly, f o u n d a s m a l l moment o r d e r i n g o£ 0 . 0 2 PB/U a t 5 K i n p u r e UPt3 ( 1 4 ) . T h i s i s t h e same t e m p e r a t u r e a t w h i c h Th a n d Pd d o p i n g i n d u c e a much l a r g e r m a g n e t i c moment ( ~ 0 . 7 ~B) o r d e r i n g i n UPt3 ( 1 5 ) a n d a t w h i c h d p / d T h a s a maximum. The s p i n a r r a n g e m e n t i s t h e same i n t h e two cases. What i s e s p e c i a l l y interesting is that t h e u n u s u a l mean f i e l d l i k e d e v e l o p m e n t o f t h e o r d e r p a r a m e t e r (M2 a TN-T ) b e l o w T N a b r u p t l y ceases

at T

c

= 0 . 5 K, c l e a r

evidence

for an

interference b e t w e e n the m a g n e t i c and s u p e r conducting order parameters (Fig. 3). In addition, the energy characterizing the magnetic correlations in this system corr e s p o n d s t o 4 kT . C

24 k

~

i

i

UPt 3

\ t"

Lo 2 3 k E 0

22k 03 o-

r"

,

21 k 0

, +3't,

0.5

1.0

1.5

T (K)

FIGURE 3 Interference between superconductivity and magnetism seen in the intensity of the ( 1 / 2 , O, 1) s c a t t e r i n g intensity i n UPt3 ( 1 4 ) .

Z. P3sk et al. /Heavy-electron uranium compounds

2.0

1731

1.0 specific heat of UBe13 - (T")

1.0

inverse spin - lattice relaxation rate of 9Be in UBe13 - (T 3)

0.8

0.5 0.3 0.6

oo ¢.-

~"

v

0.1

0.05

I-0.4

ultrasonic attenuation UBe13 - ( T 2)

0.03

magnetic field penetration depth

0.2

UBe13 - ( T z) 0.01 0

0.005 L 0.03 0.05

2

0

~ 0.1

0.3

0.5

T (K) FIGURE 4 Power l a w s i n v a r i o u s p r o p e r t i e s T (26).

of UBela b e l o w

5.

Pressure

FIGURE 5 and composition dependence

UI_×Th×Bela samples

C

U~ela UBe13

i s i n many ways a more complex s y s t e m t h a n UPt 3. The r e s i s t a n c e , s i m i l a r t o t h a t o f CeCu2Si 2, i s K o n d o - l i k e , w i t h a s h a r p p e a k n e a r 2 . 5 K. The d r o p i n r e s i s t a n c e below t h i s temperature, coupled with a sharp decrease i n t h e H a l l c o n s t a n t below 1 K i n d i c a t e t h a t T~ 1 K, v e r y c l o s e t o t h e o b s e r v e d T = 0 . 9 K. c The r e s i s t a n c e a t T i s s t i l l a p p r o x i m a t e l y I00 C

h e a t a n o m a l y a t T i s 50% c l a r g e r t h a n w e a k c o u p l i n g BCS. As T ~ 0 K, t h e t e m p e r a t u r e d e p e n d e n c e o£ t h e s p e c i f i c heat is consistent with an axial superconducting state h a v i n g n o d e s a t p o i n t s on t h e F e r m i s u r f a c e . This assignment is further supported by t e m p e r a t u r e d e p e n d e n t London p e n e t r a t i o n depth experiments which are consistent with the axial s t a t e and n o t w i t h a c o n v e n t i o n a l BCS s u p e r c o n d u c t o r (16). F i g u r e 4 shows t h e power law dependence i n v a r i o u s p r o p e r t i e s below T . C

6

o£ T

C

for

(27).

Indirect evidence for an anisotropic superconducting s t a t e c ome s f r o m t h e b i z a r r e b e h a v i o r o f T w i t h Th a d d i t i o n . Figure 5 c shows t h e v a r i a t i o n o£ T c w i t h x i n U l _ x T h x B e l 3 and with

pressure. The n e g a t i v e c u s p i n T a t c x = 1 . 7 a / o Th c o i n c i d e s w i t h t h e d e v e l o p m e n t , at larger x, of a second phase transition as indicated by the specific heat below Tcl ~ 0.6 K, a t

~D-cm. The s p e c i f i c

4

x (at %)

1.0

Tc 2 ~ 0 . 4

observed

K.

The v e r y

in ultrasonic

large

attenuation

feature at

Tc 2 ( 1 7 )

s u g g e s t e d t h a t i t was a s s o c i a t e d with an antiferromagnetic transition. Another suggestion is that it is a transition to another superconducting state. Muon e x p e r i m e n t s s u g g e s t a v e r y s m a l l moment ( ~ 0 . 0 0 1 PB/U) b e l o w Tc 2 ( 1 8 ) , b u t n e u t r o n a n d NMR ( 1 9 ) experiments have not confirmed this. We mention here that superconducting states which c a r r y a moment a r e p o s s i b l e . Current thinking is that the superconducting state is different on t h e two s i d e s o f t h e c u s p .

/Heavy-electronuranium

Z. Fisk et aL

1732

300 [

]

I

7

q

T

"~"

[-r, v 1 2 kbar 1~.~/29 kbar I[J'}(~.~. /43kbar

200 I~/ ~ , ~ , ~ , , ~

-

compounds

I

T

i

I

13 168kbar

I

I

I

I

I

UBe12.97 B 0.03

t ~ ~ 1.7 ~ L , ~ ~ ~ ,=. , 7 U983Tho,7Be13

,a ~ko,

UBe13

oJ 100

0

I I I / / q ' / - 7s kbar ~1//~] L- 97 kbar W///~_134 kbar 152 kbar

t•

(D

?:2

Uge,~ ul:~ 13

80

100

200

0

300

00

•

T (K)

• FIGURE 6 Pressure dependence of the temperature dependent electrical resistivity o f UBe13. I n s e t s h o w s d a t a f o r U . g s 3 T h . o I T B e 1 3 a t low temperature, in which T reappears.

A•~ #•

L• o•

I 0.4

0 0.2

m

I

I 0.6

I

i 0.8

h

I 1.0

T (K)

at

I t so h a p p e n s t h a t TM = 2 . 5 K c o r r e l a t e s

as x increases, through T

c

for

the resistance feature with the cusp, in that

TM d e c r e a s e s x slightly

and appears

less

than

t o go

T with pressure. So we h a v e a c o r r e l a t i o n : h i g h e r TM g o e s w i t h l o w e r T c , a n d T c i n c r e a s e s x > 1.7 a/o

Th b e c a u s e

TM i s b e l o w T c-

H o w e v e r , TM d o e s n o t a p p e a r

to be "responsible"

for

dTc2/dP < 0 (20).

Tc2.

dTM/dP > O, w h i l e

FIGURE 7 t h e l ow t e m p e r a t u r e s p e c i f i c heat that of UBe12.97B,o3 polycrystal.

the cusp

concentration. Resistance measurements under pressure show ( F i g . 6 ) t h a t T M m o v e s t o h i g h e r

for

Comparison of o f UBei3 w i t h

A b e t t e r way t o t h i n k a b o u t t h e p e a k i s , perhaps, t h a t when i t m o v e s t o l o w e r T, t h e s e other phase transitions can happen. It is interesting to note that there is a rounded maximum in C in the vicinity o£ the resistivity peak in pure UBe13. Th is the only substitution for which this curious behavior is definitely established. There is the possibility that something similar happens with B additions for Be. We can see in Fig. 7 that the specific heat anomaly at T is c very large with B doping and it is not clear that entropy can he balanced. The question arises, of course, as to why Th has this kind of effect. It does appear that n is an increasing function of Th content, at least for x at the several percent level. We note further that Cd added to Ul_xThxBe13 depresses T c at differing rates depending on whether x is > or < 1.7 a/o Th.

The effects of pressure on the normal state of UBelo is to decrease ~ much more rapidly than K, so that its point on the K-~ plot moves well below the Sommerfeld line with pressure. T drops at the same time. One c possibility is that magnetic fluctuations increase. The very high pressure resistivity actually has a shape very similar to that of UPt 3 ( F i g . 6 . ) . 6.

FINAL REMARKS The l a r g e ~ ' s p r e s e n t i n UPt3 a n d UBet3 are of clear magnetic parentage. Neutron m e a s u r e m e n t s a t l ow t e m p e r a t u r e on b o t h t h e s e materials show t h e p r e s e n c e o f a n t i f e r r o m a g netic correlations. The f a c t t h a t s u p e r c o n ductivity can occur in such systems is surprising and suggests an underlying magnetic m e c h a n i s m f o r T . The d a t a p o i n t i n g to zeros c of the superconducting g a p on t h e F e r m i s u r f a c e are suggestive of a different pairing, which is consistent with, but not required by, a nonphonon mechanism. The o c c u r r e n c e o f s u p e r c o n d u c t i v i t y in high-v materials seems to be quite rare. Large v ' s r e q u i r e s m a l l T K ' S , e i t h e r b e c a u s e TK i s naturally it there

small (21).

o r t h e RKKY i n t e r a c t i o n moves I f TK i s s m a l l , m a g n e t i c o r d e r

Z Fisk et at / Heavy-electron uranium compounds

w i l l d o m i n a t e i n most c a s e s , making s u p e r c o n ductivity less likely. The p r o b l e m p r e s e n t e d by t h e small-moment o r d e r i n g i n t h e s u p e r c o n d u c t o r s and o t h e r heavy e l e c t r o n compounds can be c l a s s e d a s c o m p l e t e l y w i t h o u t u n d e r standing. The h e a v y e l e c t r o n m a t e r i a l s remain i n t e r e s t i n g as the a r c h e t y p a l c l e a n systems where t h e r e i s an o b v i o u s c o m p e t i t i o n b e t w e e n s u p e r c o n d u c t i v i t y and magnetism f o r t h e same electrons. We a c k n o w l e d g e e x p e r i m e n t a l a s s i s t a n c e of E. F e l d e r and u s e f u l d i s c u s s i o n w i t h B. R. Coles.

(S)

(9)

(I0)

Superconductor

~(mJ/mole U-K2 )

(13) (14) To(K ) (15)

a-U U .s2Mo .Is U6Mn U6Fe U6Co U6Ni U2PtC2 URu2Si2 UPt3 UBe i3

9.6 25

75 75 450 825

2.4 2. II 2.32 3.9 2.3 .86 i. 47 1.2 .54 .9

(16)

(17)

(18) REFERENCES (1) (2)

(3)

(4)

(5)

(6)

(7)

S . D . B a d e r , N. E. P h i l l i p s , E. S. F i s h e r , Phys. Rev. B12 (1975) 4929. B . B . Goodman, J . H i l l a i r e t , J. J. V e y s s i e and L. Well, P r o c . VII I n t . Conf. Low Temp. Phys. (Univ. T o r o n t o P r e s s , 1961) 350. L . E . Delong, J . G. Huber, K. N. Yang and M. B. Maple, Phys. Rev. L e t t . 51 (1983) 312. G . P . M e i s n e r , A. L. G i o r g i , A. C. Lawson, G. R. S t e w a r t , J . O. W i l l i s , M. S. Wire and J . L. Smith, Phys. Rev. L e t t . 5__33 (1984) 1829. W. S c h l a b i t z , J . Baumann, J. D i e s i n g , W. K r a u s e , G. Neumann, C. D. B r e d l and U. R a u c h s c h w a l b e , a b s t r a c t f o r I n t . Conf. on V a l e n c e F l u c t u a t i o n s , Cologne (1984) unpublished. C. Broholm, J . Kjems, W. J . L. B u y e r s , T. T. M. P a l s t r a , A. A. Menovsky and J . A. Mydosh, Phys. Rev. L e t t . 58 (1987) 1467. J . S c h o e n e s and J . J . M. F r a n s e , Phys. Rev. B33 (1986) 5138.

G. A e p p l i , A. Goldman, G. S h i r a n e , E. Bucher and M. Ch. L u x - S t e i n e r , Phys. Rev. L e t t . 58 (1987) 808. L. T a i l l e f e r , R. Newbury, G. C. L o n z a r i c h , Z. F i s k and J . L. S m i t h , J . Magn. Magn. Mater. 63 & 64 (1987) 372. A. Sulpice, P. Gs/idit, J. C ~ u s s y , J. Flouquet, D. Jaccard, P. LeJay and J. L. Tholence, J. Low Temp. Phys. 62

(1986) 39. (11) (12)

TABLE

1733

(19)

(20)

(21) (22)

(23) (24) (25)

(26) (27)

D. J . B i s h o p , C. M. Varma, B. B a t l o g g , E. B u c h e r , Z. F i s k and J . L. S m i t h , Phys. Rev. L e t t . 5_33 (1984) 1009. B. S. S h i v a r a m , Y. H. J e o n g , T. F. Rosenbaum and D. J . K i n k s , Phys. Rev. L e t t . 56 (1986) 1078. B. B a t l o g g , i n p r e p a r a t i o n . C. A e p p l i , E. B u c h e r , C. Broholm, J . K. Kjems, J . Baumann and J . H u f n a g l , Phys. Rev. L e t t . 60 (1988) 615. A. I . Goldman, G. S h i r a n e , G. A e p p l i , B. B a t l o g g and E. Bucher, Phys. Rev. B34 (1986) 6561; P. H. F r i n g s , B. Renker and C. V e t t i e r , J . Magn. Nagn. Mater. 63 & 64 (1987) 202. D. E i n z e l , P. J . H i r s c h f e l d , F. G r o s s , B. S. C h a n d r a s e k a r , K. A n d r e s , H. R. O t t , J . B e u e r s , Z. F i s k and J . L. S m i t h , Phys. Rev. L e t t . 56 (1986) 2513. B. B a t l o g g , D. J . B i s h o p , B. C o l d i n g , C. M. Varma, Z. F i s k , J . L. S m i t h and H. R. O t t , Phys. Rev. L e t t . 55 (1985) 1319. R. H. Heffner, D. W. Cooke and D. E. MacLaughlin, Proc. 5th Int. Conf. on Valence Fluctuations (Plenum, New York, in press). D. E. MacLaughlin, C. Tien, W. G. Clark, M. D. Lan, Z. Fisk, J. L. Smith and H. R. Ott, Phys. Rev. Lett. 53 (1984) 1833. R. A. Fisher, S. E. Lacy, C. Marcenat, J. A. Olsen, N. E. Phillips, Z. Fisk and J. L. Smith, Jpn. J. Appl. Phys. 26 (1987) 1219. B. A. J o n e s and C. M. Varma, Phys. Rev. L e t t . 58 (1987) 843. S. W. T o z e r , A. W. K l e i n s a s s e r , T. Penney, D. K a i s e r and F. H o l t z b e r g , Phys. Rev. L e t t . 59 (1987) 1768. D. W. Woodward and G. D. Cordy, Phys. Rev. 136 (1964) A166. Z. F i s k and A. C. Lawson, S o l i d S t a t e Comm. 13 (1973) 277. M. B. Maple, J . W. Chen, Y. D a l i c h a o u c h , T. Kohara, C. R o s s e l , M. S. T o r i k a c h v i l i , M. W. M c E l f r e s h and J . D. Thompson, Phys. Rev. L e t t . 56 (1986) 185. Z. F i s k , H. R. O t t , T. M. R i c e and J . L. S m i t h , N a t u r e 320 (1986) 124. S. E. L a m b e r t , Y. D a l i c h a o u c h , M. B. Maple, J . L. S m i t h and Z. F i s k , Phys. Rev. L e t t . 57 (1986) 1619.