STUDIES OF RAPID MELTING AND FREEZING OF 3He IN HIGH MAGNETIC FIELDS

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STUDIES OF RAPID MELTING AND FREEZING OF 3He IN HIGH MAGNETIC FIELDS

B. Yurke, E. Polturak, D. Sagan, D. Lee

To cite this version:

B. Yurke, E. Polturak, D. Sagan, D. Lee. STUDIES OF RAPID MELTING AND FREEZING OF 3He IN HIGH MAGNETIC FIELDS. Journal de Physique Colloques, 1980, 41 (C7), pp.C7-129-C7-132.

�10.1051/jphyscol:1980720�. �jpa-00220157�

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JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n o 7 , Tome 41, juiZZet 2980, page C 7 - 1 2 9

STUDIES OF RAPID MELTING A N D FREEZING O F

3 ~ e

IN HIGH MAGNETIC FIELDS*

B. Yurke, E. P o l t u r a k , 0. Sagan and D.M. Lee

Laboratory of Atomic and Solid State Physics and MateriaZs Science Center, CorneZZ University, Ithaca, New York 14853, USA.

Resume.- Nous avons e n r e g i s t r e des courbes de p r e s s i o n de f u s i o n en f o n c t i o n du temps dans une c e l - l u l e de Pomeranchuk avec des champs magnetiques a l l a n t de 2,O

a

2,5 T e t pour des t a u x de compres- s i o n v a r i a b l e s . Nous avons u t i l i s e des mesures de l t a t t @ n u a t i o n de son z&ro, e f f e c t u e e s dans l a c e l l u l e simultanement, pour d 6 t e c t e r l e s t r a n s i t i o n s Al e t A2 dans 3He s u p e r f l u i d e . Nous avons @ t u - d i e l e s anomalies de l a courbe de f u s i o n antgrieurement observ&es p a r Shuberth, Bakalyar e t Adams /3/. Nos r e s u l t a t s vont dans l e sens de 1 'i n t e r p r e t a t i o n de Yu e t Anderson /6/, q u i r e l i e n t ces anomalies aux p r o p r i 6 t g s de t r a n s p o r t du s p i n dans 3He l i q u i d e .

A b s t r a c t . - M e l t i n g pressure vs. t i m e t r a c e s have been obtained i n a Pomeranchuk c e l l i n magnetic f i e l d s o f 2.0 and 2.5 T a t v a r y i n g compression r a t e s . Zero sound a t t e n u a t i o n measurements, which have been condu t e d i n t h e c e l l simultaneously, were used t o d e t e c t t h e A1 and A2 t r a n s i t i o n s of

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t h e s u p e r f l u i d He. The m e l t i n g curve anomalies p r e v i o u s l y observed by Shuberth, Bakalyar and Adams /3/, have been studied. Our r e s u l t s support t h e i n t e r p r e t a t i o n o f Yu and Anderson /6/, i n which these anomalies a r e r e l a t e d t o t h e s p i n t r a n s p o r t p r o p e r t i e s o f t h e l i q u i d 3He.

Studies o f t h e m e l t i n g curve o f 3 ~ e i n a mag- peated t h e SBA experiment over a wide range of com- n e t i c f i e l d a r e o f i n t e r e s t w i t h r e s p e c t t o t h e p r e s s i o n r a t e s , and our observations f u r t h e r sup- phase diagram o f b o t h s u p e r f l u i d He /1/ ( t h e A1 3 p o r t t h e Yu-Anderson p i c t u r e .

and A2 t r a n s i t i o n s ) and t h e n u c l e a r s p i n o r d e r i n g The experiment was performed i n a Poaeranchuk o f s o l i d He /2/. 3 Recently Shuberth e t a l . /3/ c e l l a t magnetic f i e l d s o f 2.0 and 2.5 T. Over t h e (SBA) discovered a "barkstep" on t h e pressure vs. wide range o f compression r a t e s used, t h e A1 and t i m e t r a c e d u r i n g f a s t compressional c o o l i n g i n a A2 t r a n s i t i o n s were n o t always v i s i b l e on t h e pres- Pomeranchuk c e l l a t 2.0 T and 2.8 T magnetic f i e l d s . sure vs. t i m e t r a c e s . We t h e r e f o r e used t h e a t t e n - They i n t e r p r e t e d t h e backstep as a p o s s i b l e i n d i - u a t i o n peaks o f u l t r a s o u n d i n t h e l i q u i d as a mark- c a t i o n o f a f i r s t o r d e r t r a n s i t i o n i n t h e s o l i d He 3 e r o f these two t r a n s i t i o n s /7/. The s o n i c c e l l i n t o a new phase. Also, t h e pressure d i f f e r e n c e contained a p a i r o f 10 MHz X c u t q u a r t z transducers.

between t h e A, and A2 t r a n s i t i o n s on t h e m e l t i n g The t r a n s m i t t i n g c r y s t a l was pulsed a t r a t e s be- curve, PAT-PA2, obtained by SBA, imp1 i e d a temper- tween 10 and 100 Hz t o ensure a s u f f i c i e n t l y f a s t a t u r e d i f f e r e n c e , TA1-TA2, l a r g e r than t h a t expected response even a t t h e h i g h e s t compression rates.

on the basis o f t h e l i n e a r temperature s p l i t t i n g - The sonic c e l l was l o c a t e d near t h e s t r a i n gauge i n magnetic f i e l d r e l a t i o n of 64 uK/T measured by t h e Pomeranchuk c e l l . The thermal l a g between t h e

G u l l y e t a l . /I/. sound c e l l and t h e s t r a i n gauge was estimated by

A number o f authors /4//5//6/ suggested t h a t comparing t h e l o c a t i o n i n time o f t h e sound a t t e n - t h e observed backstep might be associated w i t h t h e u a t i o n and pressure f e a t u r e s associated w i t h t h e A1 1 iq u i d r a t h e r than t h e s o l i d . I n p a r t i c u l a r , Yu and and A2 t r a n s i t i o n s . Using 64 uK/T t o c o n v e r t PA1- Anderson /6/ suggested t h a t t h e f e a t u r e s observed by PA2 i n t o TA1-TA2, we found a l a g o f 3 pK t o 15 vK, SBA c o u l d be explained i n terms o f s p i n t r a n s p o r t depending onthe compression r a t e . This i s much p r o p e r t i e s o f l i q u i d He.

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We have e s s e n t i a l l y r e - s m a l l e r than t h e e f f e c t s discussed here and we d i d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980720

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C 7 - 1 3 0 JOURNAL DE PHYSIQUE

n o t c o r r e c t t h e data f o r i t .

To determine t h e e f f e c t o f compression r a t e on t h e shape o f t h e m e l t i n g curve, one would l i k e t o p l o t pressure vs. temperature, f o r v a r y i n g compres- s i o n r a t e s . T h i s i s n o t p o s s i b l e , s i n c e t h e r e i s p r e s e n t l y no thermometer having a s u f f i c i e n t l y f a s t response. A l t e r n a t i v e l y , we used one o f t h e A t r a n s i t i o n s i n t h e l i q u i d as a f i x e d p o i n t , and t h e slope dP/dt a t some pressure, Po, as a measure o f t h e c o o l i n g r a t e through t h e r e l a t i o n (dP/dt) =

Po ( d P / d ~ ) ~ , ( d T / d t ) ~ ~ . We then normalized t h e t i m e scales f o r a l l t h e t r a c e s t o have t h e same (dP/dt')po, where t ' i s t h e normalized time, i . e . t h e t i m e scaled by a constant f a c t o r , d i f f e r e n t f o r each compression r a t e . The ( a r b i t r a r y ) o r i g i n o f t h e t ' scale was s e t a t t h e f i x e d temperature p o i n t . The h o r i z o n t a l a x i s o f t h e P vs. t ' p l o t i s then a monotonic f u n c t i o n o f temperature which should be r o u g h l y t h e same f o r a l l t h e t r a c e s . We found t h i s procedure t o be q u a l i t a t i v e l y independent o f t h e choice o f Po, provided t h a t Po was chosen i n r e g i o n where t h e pressure t r a c e was l i n e a r i n t i m e f o r a l l t h e data obtained w i t h v a r i o u s compression r a t e s .

F i g u r e 1 shows a s e t o f P vs. t ' t r a c e s ob- t a i n e d a t 2.5 T. Here t h e A2 t r a n s i t i o n was taken as t h e f i x e d p o i n t and t h e t -+ t ' n o r m a l i z a t i o n was done t o g e t t h e same dP/dtl a t some pressure a f t e r t h e backstep occurred. Note t h a t t h i s procedure does n o t r e q u i r e the t r a c e s t o overlap, y e t a l l t h e t r a c e s c o l l a p s e onto a s i n g l e curve f o l l o w i n g t h e backstep. The lowest l y i n g curve i n F i g u r e 1 was obtained d u r i n g a very slow compression and does n o t show any backstep. By suddenly i n c r e a s i n g t h e compression r a t e a f t e r t h e backstep occurred, we were a b l e t o b r i n g t h e pressure up again, and t o observe another backstep when t h e compression r a t e was again decreased sometime l a t e r .

These observations can be q u a l i t a t i v e l y ex- p l a i n e d u s i n g t h e magnetization d e f i c i t model of Yu and Anderson /6/. I n t h i s model, t h e lowest l y i n g curve i n F i g u r e 1 i s i d e n t i f i e d as a m e l t i n g curve along which t h e s o l i d i s formed w i t h t h e e q u i l i b r i u m magnetization a p p r o p r i a t e t o t h e magnetic f i e l d and temperature. During t h e f a s t compression, s p i n t r a n s p o r t i n t h e normal l i q u i d cannot supply t h e necessary amount o f s p i n s f o r t h e s o l i d t o form w i t h an e q u i l i b r i u m magnetization. A lower magnetization r e s u l t s i n a lower e f f e c t i v e f i e l d on t h e s o l i d surface and thus a h i g h e r m e l t i n g pressure ( t h e m e l t i n g curve i s depressed by magnetic f i e l d s /1//2/). Ac- c o r d i n g t o t h e model, below t h e s u p e r f l u i d t r a n s i - t i o n , s p i n t r a n s p o r t becomes much f a s t e r , presumably due t o onset o f supercurrents /6/. Once t h e r a t e o f s p i n t r a n s p o r t becomes s u f f i c i e n t l y f a s t f o r t h e so-

l i d t o form w i t h the e q u i l i b r i u m magnetization, t h e - 3 - 2 -1 0 1 2 3 4

Rescaled Time m e l t i n g curve should r e t u r n t o i t s e q u i l i b r i u m value. We suggest t h a t t h e pressure backstep i t s e l f F i g . 1 : Pressure ( r e l a t i v e to PA2) vs. normalized may be viewed i n t h i s model as t h e magnetic analog t i m e t r a c e s f o r v a r i o u s compression r a t e s a t 2.5 T.

~h~ horizontal axis is proportional to temperature of t h e t r a n s i t i o n t h a t occurs i n a c u r r e n t c a r r y i n g ( d e t a i l s o f the normal i z a t i o n procedure a r e g i v e n i n

t h e t e x t ) . The arrows show t h e p o s i t i o n of t h e ~ u ~ e r c o n d u c t o r once t h e temperature drops enough f o r and A2 t r a n s i t i o n s f o r each t r a c e . The compression

r a t e s used ( t o p t o bottom) were 5.89,5.78,3.16,2.41,

'

^{' 9} ^{where Ic}^and^I^{are the} ^{and ac-}

1.49,1.00, and 0.44 m b a r b i n , r e s p e c t i v e l y , a t

pressures f o l l o w i n g t h e backstep. t u a l c u r r e n t s /8/. Here, t h e s p i n c u r r e n t i s analo-

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gous t o I , whereas magnetization d e f i c i t ( o r equi- v a l e n t l y , t h e pressure d i f f e r e n c e between the measured and e q u i l i b r i u m me1 t i n g curves) i s analogous t o t h e v o l t a g e d i f f e r e n c e , which vanishes f o r Ic >

I. The f a c t t h a t t h e backstep i s observed o n l y i n t h e presence o f a s u p e r f l u i d i s a l s o supported by t h e r e c e n t measurements i n Grenoble, i n which no backstep was observed f o r f i e l d s above 5 T, where t h e lowest temperature a t t a i n e d by Pomeranchuk c o o l i n g (determined by t h e o r d e r i n g o f t h e sol i d ) was h i g h e r than t h e Tc o f t h e l i q u i d /9/.

0.3 1 .O 3.0 10 3 0

Compression

Rate (

mbar/ min)

Fig. 2: PA and PA2 a t 2.5 T as a f u n c t i o n o f com- p r e s s i o n

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and decompression (a) r a t e . S o l i d l i n e s a r e a guide t o t h e eye.

I n F i g u r e 2, we show t h e pressures a t which t h e A1 and A2 t r a n s i t i o n s occur i n t h e l i q u i d (as d e t e r - mined by t h e sound a t t e n u a t i o n ) as a f u n c t i o n o f compression (and decompress i o n ) r a t e s . Note t h a t PAl s h i f t s even a t v e r y low compression r a t e s i n c o n t r a s t t o PA2, which remains c o n s t a n t over a much wider range

/lo/.

T h i s i n d i c a t e s , w i t h i n t h e Yu- Anderson p i c t u r e , t h a t t h e c r i t i c a l v e l o c i t y f o r s p i n supercurrents, vc, i s s i g n i f i c a n t l y h i g h e r i n t h e A2 phase. It i s i m p o r t a n t t o mention, i n t h a t respect, t h a t we c o u l d n o t observe any backstep between t h e A1 and A t r a n s i t i o n s no m a t t e r how slow

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t h e compression was. The backstep, when observed, always occurred e i t h e r a t A2 o r a t a temperature below it. The f a c t t h a t t h e p o s i t i o n o f t h e backstep f a l l s very near t h e A2 t r a n s i t i o n over a range o f compression r a t e s ( F i g u r e 1 ) i m p l i e s a r a p i d i n - crease i n vc below t h e A2 t r a n s i t i o n . T h i s i s i n q u a l i t a t i v e agreement w i t h t h e dramatic increase of t h e s p i n r e l a x a t i o n r a t e below A2 observed by Cor- r u c c i n i and Osheroff /11/. Assuming t h a t t h e spins a r e t r a n s p o r t e d uniformly from t h e b u l k l i q u i d t o t h e c e l l w a l l s , where the s o l i d nucleates, we ob- t a i n an approximate expression f o r vc by equating t h e r a t e o f l i q u i d t o s o l i d conversion ( c o o l i n g r a t e ) t o t h e s u p e r f l u i d mass t r a n s p o r t r a t e w i t h v e l o c i t y vc:

here, C i s t h e s p e c i f i c heat o f t h e l i q u i d , AS i s t h e entropy d i f f e r e n c e between l i q u i d and s o l i d /9/, V and A a r e t h e volume and surface area o f t h e c e l l , r e s p e c t i v e l y , and O ~ / O S t h e s u p e r f l u i d den- s i t y f r a c t i o n /12/. I n a d d i t i o n , we took T ( ~ P / ~ T )

= AQ/AV from t h e SBA paper / 3 / . Near t h e A2 t r a n - s i t i o n , we o b t a i n v % 0.1 mmlsec, which i s n o t un-

C

reasonable when compared w i t h measurements done i n r e s t r i c t e d geometries / 1 3 / .

F i n a l l y , t h e pressure s p l i t t i n g , PA1 -PA2, i n Fig'ure 2 c l e a r l y depends on t h e compression ( o r decompression) r a t e . By e x t r a p o l a t i n g t o zero com- p r e s s i o n r a t e r a t e , we f i n d (PA1-PA2)/H = 0.018 mbar/T both a t 2.0 and 2.5 T, which agrees w e l l w i t h 0.02 mbar/T measured by G u l l y e t a l . /I/.

I n conclusion, our work supports t h e i n t e r p r e - t a t i o n o f t h e SBA observations i n terms o f l i q u i d r e l a t e d e f f e c t s . We a r e indebted t o L. Friedman f o r h e l p w i t h t h e experiment, and R.C. Richardson and D.D. Osheroff f o r u s e f u l discussions.

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JOURNAL D E PHYSIQUE

REFERENCES

*The work described h e r e i n was supported by t h e N a t i o n a l Science Foundation by Grant #DMR-78-10901 and through t h e C o r n e l l M a t e r i a l s Science Center under Grant #DMR-76-81083A02. MSC Report #4242.

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/TO/ A t 2.5 T, t h e c r i t i c a l compression r a t e above which PA2 s t a r t e d t o s h i f t , was lower by a fac- t o r o f 2 from t h e r a t e measured a t 2.0 T. T h i s may be r e l a t e d t o t h e f i e l d dependence o f t h e c r i t i c a l v e l o c i t y and t h e TI r e l a x a t i o n time.

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