MAGNETIC bcc 3He : A CALL FOR MORE ACCURATE MEASUREMENTS OF SPECIFIC HEAT AND SUSCEPTIBILITY IN SOLID 3He

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MAGNETIC bcc 3He : A CALL FOR MORE

ACCURATE MEASUREMENTS OF SPECIFIC HEAT AND SUSCEPTIBILITY IN SOLID 3He

J. Hetherington

To cite this version:

J. Hetherington. MAGNETIC bcc 3He : A CALL FOR MORE ACCURATE MEASUREMENTS OF

SPECIFIC HEAT AND SUSCEPTIBILITY IN SOLID 3He. Journal de Physique Colloques, 1978,

39 (C6), pp.C6-126-C6-127. �10.1051/jphyscol:1978657�. �jpa-00218060�

JOURNAL DE PHYSIQUE

Colloque C6, supplkment au no 8, Tome 39, aolit 1978, page C6-126

MAGNETIC bcc 3 ~ e : A CALL FOR MORE ACCURATE MEASUREMENTS OF SPECIFIC HEAT AND SUSCEPTIBILITY IN SOLID ^{3 ~ e}

J.H. Hetherington

Physics Department, Michigan S t a t e U n i v e r s i t y , East Lansing, Michigan 48824, U. S. A.

RSsum6.- On suggere que les mesures disponibles concernant les coefficients e3 et B n'ont pas suffi- sament de pr6cision pour qu'on puisse Otre certain de leurs signes. On suggsre un ddveloppement thdorique possible oii ces quantitds diffgreraieit des valeurs prdsentement acceptses mais sans in- troduire un desaccord avec les mesures actuelles de la susceptibilitd et de la chaleur specifique.

Abstract.- It is suggested that the quantities e3and B which have been given approximate values based on experiment, may not be known even to within the correct sign. A possible line of theoreti- cal development is outlined which makes this possibility more plausible.

Recent experiments

/1-51

have determined how than specific heat measurements and they measure the specific heat and susceptibility behave as the only the derivative de /dv so that they cannot be temperature of bcc 3 ~ e is lowered toward the magne- used to settle this quistion.

tic ordering temperature of 1

mK.

These trends have

been analyzed in terms of the "model independent"

5 ? g ? l

coefficients of the logarithm of the partition

function

-3 ^\

,

+%,

\ F%$

1 1 1

1nZ

=

In2 + g e 82 + - e 8 3

+...

- e:

^-4

"">

48

3

(1)

.

^%\

1 1 2

- ''

^\

+

(W~H)' I [ + L a ²

¹

8 + - a ⁸

²

8

+

...- ¹

^+...

:

^C\\

^++\

In particular, earlier measurements /6-13/ have gi- 4:1,

^{, , ,}

^,

^{, qA%%\ ,}

,I

ven moderate agreement with each other and have es-

-8

tablished values for e and a . Lower temperature \\

measurements give values for e and a (related to

‘9 o I 2 3 4

Rn T B by a,

=

2a: - 8B) when it is assumed that the

terms explicit in eq.

(1)

adequately represent 1nZ

_{- -}

only a few

mk

above the transition temperature. Fig.

1 :

Logarithm of the spin specific heat plotted -against log T. The data of Greywall and of Halperin However, the "correct" way to make these measure- are shown. Should there be a rising curve which con- ments would be to measure the high

temperature re-

nects the data of Greywall with that of Halperin

?

gion more accurately and extend the measurements to

Greywall's measurement of e as far as quoted errors

slightly lower temperature so as to be sure that

²

goes is by far the most accurate value so far de- only the next term of the expansion is being mea-

termined. Furthermore, it is in substantial agree- sured.

ment with the values given by all previous workers Partly for reasons of expediancy and partly

(except Dondon and Goodkind who were at a low tem- because of the unavailability of accurate data the

niceties of this "correct" procedure have generally been ignored.

Consider the problem of the specific heat measurements. It should be mentioned that the pres- sure measurements of Panczyk and Adams cover the temperature region from about 14

mK

to about

50 mK

where specific heat experimental information is not available. However, they are less sensitive to e

perature earlier). Halperin's (and Dondon and Good- kind's) measurements give e larger, than when mea- sured at higher temperatures by other workers. Their error bars are larger, however, and we might simply let the problem of the value of e rest as a simple statistical problem. But it is not to be

!

Halperin States that his error in e is correlated with his error in e .

~alperin's figure 35, reproduced somewhat sche-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978657

m a t i c a l l y h e r e a s f i g u r e 2 s h e d s some l i g h t on t h e problem. T h i s p l o t shows

a s a f u n c t i o n o f B,The e r r o r b a r s i n f a c t a r e n o t un- c o r r e l a t e d b u t i n d i c a t e c o r r e l a t e d e r r o r s which

" d i s p l a c e a l l o f t h e d a t a t o g e t h e r

...

( i n p r o p o r t i o n t o t h e ) magnitudes of t h e s e b a r s " 121.

F i g . 2 : Showing a c u r v e drawn o n t o H a l p e r i n ' s f i - g u r e 35 which f i t s a l l t h e e n t r o p y and s p e c i f i c h e a t a t a l l t e m p e r a t u r e s . The p o s i t i v e s l o p e n e a r

B

= 0 i m p l i e s t h a t e > 0.

A s t r i c t a d h e r a n c e t o a l l e x p e r i m e n t s t h e n l e a d s t o t h e c o n c l u s i o n t h a t t h e s p e c i f i c h e a t f i r s t r i s e s above t h e e x t r a p o l a t e d h i g h t e m p e r a t u r e b e h a v i o r , t h e n f a l l s below i t a t lower t e m p e r a t u r e . It s h o u l d be s a i d t h a t H a l p e r i n n o t e s t h i s p o s s i b i l i t y a l o n g w i t h o t h e r s on p. 116 of h i s t h e s i s . I f t h i s h o l d s t r u e e i s p o s i t i v e i n c o n t r a d i c t i o n t o v a l u e s quo- t e d by H a l ~ e r i n and by Dondon and Goodkind.

T h e r e f o r e , I hope t h a t some good and c a r e f u l e x p e r i m e n t e r s w i l l t a k e i t upon t h e m s e l v e s t o d e t a i l t h e h i g h t t e m p e r a t u r e s p i n s i t u a t i o n i n s o l i d 3 ~ e .

One r e a s o n f o r c a l l i n g a t t e n t i o n t o t h e above s i t u a t i o n i s a p o s s i b l e f u t u r e l i n e of theo- r e t i c a l development which c a n n o t now b e e l i m i n a t e d . A s o l u t i o n may e x i s t which on f u r t h e r i n v e s t i g a t i o n may f i t t h e d a t a a s w e l l a s t h e W i l l a r d 114, 151 s o l u t i o n . T h i s i s t h e r e g i o n of SCAF

I I

magnetism f i r s t mentioned by "RDL" w h e r e i n K >> KF and n e a r

P

and p r o b a b l y r e l a t e d t o t h e s i m i l a r s i t u a t i o n d i s - c u s s e d by Okada and I s h i k a w a 1161. U n f o r t u n a t e l y Okada and Ishikawa have n o t i n c l u d e d J i n t h e i r H a m i l t o n i a n . The t r e n d s i n s p e c i f i c h e a t and suscep- t i b i l i t y i u s t above 1 mK which a r e r e s p o n s i b l e f o r t h e p r e s e n t e s t i m a t e s of e and B may s t i l l b e pre- s e r v e d , however.

T h e r e f o r e , t h e t h e o r e t i c a l p i c t u r e ( i n t h e f r a - mework o f exchange models) h a s two l i k e l y a l t e r n a - t i v e l i n e s of development : a ) t h e W i l l a r d (KF>>Kp) s o l u t i o n s u r v i v e s . T h i s w i l l r e q u i r e a major change i n t h e m i c r o s c o p i c p i c t u r e of exchange, b) o r a s s u g g e s t e d h e r e , t h e

$

>> I$ s o l u t i o n c o u l d become t h e p r e f e r r e d phenomenology i n which c a s e a r e v i s i o n ( a l b e i t l a r g e ) m i c r o s c o p i c t h e o r y might b e s u f f i c i e n t t o e x p l a i n t h e exchange i n s o l i d 3 ~ e .

It may n o t be s o s i m p l e ! Other c o m p l e t e l y d i f f e r e n t t h e o r e t i c a l i d e a s have been proposed and on- l y c a r e f u l e x p e r i m e n t s can r e d u c e t h e a l t e r n a t i v e s .

R e f e r e n c e s

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-

/ 2 / H a l p e r i n , W.P., T h e s i s , C o r n e l l U n i v e r s i t y . 1 3 1 Berni'er, M. and D e l r i e u , J . M . , Phys. L e t t . %A

(1977) 156.

/ 4 / B a h a l y e r , D.M., B r i t t o n , C.V., Adams, E.D., and Hwang, Y.C., Phys. L e t t . E A (1977) 208.

/ 5 1 P r e w i t t , T.C. and Goodkind, J.M., Phys. Rev.

L e t t .

2

(1977) 1283.

1 6 1 Greywall, D.S., Phys. Rev.

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(1977) 2604.

171 C a s t l e s , S.H. and Adams, E.D., Phys. Rev. L e t t . 30 (1973) 1125.

-

I 8 1 K i r k , W.P. and Adams, E . D . , Phys. Rev. L e t t .

11

(1971) 392.

/ 9 / Panczyk, M.F. and Adams, E.D., Phys. Rev.

g

(1970) 1356.

/ l o / K i r k , W.P., Osgood, E.B. and G a r b e r , Phys. Rev.

L e t t .

3

(1969) 833.

/ I l l S i t e s , J . R . < O s h e r o f f , D . D . , R i c h a r d s o n , R.C.

and Lee, D.M., Phys. Rev. L e t t .

3

(1969) 836.

1121 P i p e s , P.B. and F a i b a n k , W.M., Phys. Rev. L e t t . 23 (1969) 520.

-

1131 B e r n a t , T.P. and Cohen, H.Db., Phys. Rev.

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