Magnetic susceptibility of U1-xThxAl2

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Magnetic susceptibility of U1-xThxAl2

M. Brodsky

To cite this version:

M. Brodsky. Magnetic susceptibility of U1-xThxAl2. Journal de Physique Colloques, 1979, 40 (C4),

pp.C4-147-C4-149. �10.1051/jphyscol:1979448�. �jpa-00218844�

JOURNAL DE PHYSIQUE Colloque C4, supplément au n° 4, Tome 40, avril 1979, page C4-147

Magnetic susceptibility of V

¹

_

^x

Th

^x

M

²

(*)

M . B . B r o d s k y

Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, U.S.A.

Résumé. — La susceptibilité magnétique d'alliages Ui-*ThxAl2 a été mesurée pour x « 0 , 1 0 . Tous les échantillons donnent une susceptibilité variant en T et il existe donc apparemment une contribution de liquide de Fermi.

Abstract. — Magnetic susceptibility measurements have been made on Ui-»ThxAl2 for x =£0.10. All of the samples show a low-temperature T dependence, and an apparent Fermi liquid contribution.

T h e specific h e a t s of U,_x T hx Al2 for x = 0 t o 0.10 fitted spin fluctuation t h e o r y [ 1 , 2 ] . I n r e f e r e n c e [1], t h e e x c h a n g e e n h a n c e m e n t value for UA12, S = 4, w a s a s s u m e d for all c o m p o s i t i o n s . B a r n e a [3] and M i s a w a [4] h a v e s h o w n t h a t t h e m a g n e t i c susceptibi- lity, x, of a F e r m i liquid should fit t h e e x p r e s s i o n

X=Xo-bT2ln[_(T + T)/T*] + - (1) w h e r e b is a c o n s t a n t , Ti is inversely p r o p o r t i o n a l t o t h e electronic m e a n free p a t h , a n d X* oc \/S a n d

~ Ts l, t h e spin fluctuation t e m p e r a t u r e . P r e v i o u s l y , B e a l - M o n o d et al. [5] h a d d e r i v e d

X=X0V-KS2(T/TF)2] (2) w h e r e t h e Fermi, t e m p e r a t u r e Tp = STS{. E q u a t i o n

(2) w a s d e r i v e d for s t r o n g p a r a m a g n o n effects, i . e . , spin fluctuations. K a w a b a t a [6] also d e r i v e d e q . (2) w i t h t h e coefficient K modified f r o m a v a l u e of 1.32 t o 3.17 d u e t o t h e d e p e n d e n c e of t h e chemical potential o n field.

B a r n e a s h o w e d t h a t eq. (1) is followed b y t h e e x c h a n g e - e n h a n c e d m e t a l s , P d , U2C3, Y C o2, L u C o2, a n d S c . A l t h o u g h t h e a p p r o a c h u s e d in t h e deriva- tion of e q . (2) is not self-consistent, t h e only p r o v e n spin fluctuation materials 3H e [7] a n d UA12 [1] fit e q . (2). I n this w o r k , t h e m a g n e t i c susceptibility of U ^ T h , Al2 w a s m e a s u r e d t o c o m p a r e t h e results t o e q s . (1) a n d (2).

S a m p l e s w i t h x = 0, 0.02, 0.05, a n d 0.10 w e r e p r e p a r e d b y a r c melting. X - r a y analysis verified t h a t t h e alloys w e r e cubic L a v e s p h a s e - t y p e C 1 5 . M e a s u - r e m e n t s w e r e n o t carried o u t for x > 0.10 as t h o s e samples s h o w e d a b r e a k d o w n of long-range o r d e r . It should b e n o t e d that for x = 0 . 9 5 (hexagonal-type C32) t h e r e m a y be cluster or spin-glass b e h a v i o u r [1]. M e a s u r e m e n t s w e r e carried o u t b y a F a r a d a y m e t h o d , d e s c r i b e d b e f o r e [8].

Figure 1 s h o w s x plotted versus T. T h e overall s h a p e is u n c h a n g e d for x = 0 . 0 2 a n d 0.05, b u t for U0 9T h0 jAl2 t h e plateau is not o b s e r v e d . T h e d a t a all fit a Curie-Weiss l a w a b o v e 60 K w i t h little variation in t h e p a r a m e t e r s .

E q u a t i o n (1) yields a m a x i m u m in x(T) at

T = T*/Ve.

A l t h o u g h t h e d a t a in figure 1 d o n o t s h o w a m a x i - m u m in x(T), t h e r e is a hint of s u c h a m a x i m u m from t h e p l a t e a u at ~ 50 K for UA12. T h e low-

TEMPERATURE ( K)

Fig. 1. —Molar susceptibility of U,_sTh»Al2: (•) x = 0 ; (O) x = 0.02 ; (O) x = 0.05 ; and (©) x = 0.10. The data have been offset for clarity ( — 0.4 x 10~3 emu/mole for x = 0.02 ;

- 0.8 x 10"3 emu/mole for x = 0.05 ; and + 0.3 x 10"3 emu/mole for x =0.10).

(*) Work supported by the U.S. Department of Energy.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979448

M. B. BRODSKY Table I. - Properties of Ul-, Th, Al,

xo,

emu/mole

specific heat y, mJ/(mole-K2) (" )

x

^{or,it,,, emu/mole ( b}

S (') \ ,

-

b, lop6 emu/mole

-

8 (Curie-Weiss), K

(" ) From reference [I].

( b ) From Fradin, F. Y., Brodsky, M. B., and Arko, A. J., J. Physique 32 (1971) 60.

(') Using 1

+

^A,,

+

^{A,* =} 2.24 from reference [I].

temperature data for UA1, certainly follow eq. (2), that is a T 2 dependence. The present results also fit a T 2 dependence with essentially the same slope [9], which implies a constant T,, for x = 0 to 0.10.

Regardless of the source of the low temperature

x

TZ, it is an established fact. Thus, we will combine eqs. (1) and (2) into :

where for the moment we will assume the third term on an empirical basis, and the last term is of Curie- Weiss form. The results are summarized in table I.

It shows that the calculated values for the exchange enhancements are all around S = 4, with the as- sumption of constant electron-phonon and spin- fluctuation enhancements to the specific heat (Aep and A d . Figure 2 shows the plot of

versus T for the four compositions. In each case a

TEMPERATURE ( K )

Fig. 2.

-

Fermi liquid contributions to susceptibility, AX in eq. (3). (0) x = 0, curve offset

+

0.2 x lo-' emu/mole ; (0) x = 0.2, no offset ; (9) x = 0.10, no offset ; dashed curve calculated for x = 0 from eq. (I), offset

+

^{0.2 x} lo-' emu/mole.

maximum is obtained at 43 1+ 3 K. If this maximum is due to the Fermi liquid contribution, then

T* = 71 K - 3 T,,

.

The dashed curve in figure 2 is the Fermi liquid contribution calculated for UAl,. On the low tempe- rature side of the maximum, the shapes of the experimental and calculated curves are reasonably close for T* = 71 K and b determined only from AX,,,. Use of the next order term in eq. (1) would make the fit better [3]. On the high temperature side of T,,,,, the term of Curie-Weiss form [lo] domina- tes and the fit to the Curie-Weiss term is good above 60 K where the T2 and T21n T terms have died away.

The curves are not shifted strongly due to the impurity Ti term in eq. (3). Ti only rises to a value of 6 K for Uo~,Th,~lAI, as derived from specific heat and resistivity data [l]. In the specific heat work, the impurity effects were strong because Ti modified T,, = 23 K, whereas here it modifies the much larger T*. Large variations in the Fermi liquid contribution with composition could come from changes in S ( b oc S

",

where n = 2-4) [3, 41. With the high power dependence of b on S, the small variation in b with composition is a good test of the near constancy of

S.

Thus, the Fermi liquid contribution to x ( T ) may be derived, provided that the

x

T 2 dependence is removed. In earlier work [I], it was assumed that the

x

T 2 contribution was due to spin fluctuations [S].

This was borne out by a calculated T,, = 33 K from eq. (2), which is in fair agreement with the 23 K derived from specific heat and resistivity. However, with the Kawabata correction to eq. (2), T,, = 52 K calculated from eq. (2) is not as satisfactory. If the impurity contribution to,eq. (2) also goes as ( T

+

^Ti)'

(see eq. (1) and Ref. [2]), then the slope in d X / d T 2 remains unchanged with composition (as is observed) as does the calculated T,,. Despite the uncertainty 'about the quantitative aspects of eq. (2), the

T Z

dependence of ,y at low temperatures for true paramagnon systems (3He and UAl,) cannot be ignored. Thus, the derivations of eq. (1) may fail to account properly for the spin fluctuations.

MAGNETIC SUSCEPTIBILITY OF U,-,Th,Al,

References

[I] TRAINOR, R. J . , BRODSKY, M. B . and CULBERT, H. V., Phys. [6] KAWABATA, A., J. Phys. F. Metal Phys. 4 (1974) 1477.

Rev. Lett. 34 (1975) 1019 ; and AIP Conf. Proc. 34 (1976) [7] RAMM, H., PEDRONI, P., THOMPSON, J. R. and MEYER, H., J.

224. Low Temp. Phys. 2 (1970) 539.

[2] FULDE, P. and LUTHER, A., Phys. Rev. 170 (1968) 570. [8] Ross, J. W. and LAM, D . J . , Phys. Rev. 165 (1968) 617.

[3] BARNEA, G., J. Phys. F. Metal Phys. 7 (1977) 315. [9] BRODSKY, M. B . , to be published.

[4] MISAWA, S . , J. Phys. C. Solid State Phys. 8 (1975) L 403. [lo] MURATA, K. K. and DONTACH, S . , Phys. Rev. Lett. 29 (1972) [5] BEAL-MONOD, M. T., MA, S.-K. and FREDKIN, D. R., Phys. 285.

Rev. Lett. 17 (1968) 929.