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Spin diffusion coefficient of normal liquid 3He in infinite and bounded geometries under pressure
QE 5
Physica 108B (1981/1059-1060 North-Holland Publishing Company
SPIN D I F F U S I O N C O E F F I C I E N T O F N O R M A L L I Q U I D 3HE IN INFINITE A N D B O U N D E D G E O M E T R I E S UNDER PRESSURE D.F. Brewer %, D.S. Betts, A. S a c h r a j d a and W.S. T r u s c o t t P h y s i c s Laboratory, U n i v e r s i t y of Sussex, Brighton, Sussex, England.
We report m e a s u r e m e n t s of the spin diffusion coefficients of normal liquid 3He in bulk, and in 5~m d i a m e t e r glass capillary tub~s, as a function of p r e s s u r e (O-30 bar) and t e m p e r a t u r e (3mK-15mK). The bulk e x p e r i m e n t s are well into the l i m i t i n g low temperature Fermi fluid regime, and p r o v i d e the first reliable m e a s u r e m e n t s of the p r e s s u r e variation of A = DT 2. In the 5~m capillaries, d e v i a t i o n s from this relation are found as the q u a s i p a r t i c l e m e a n free p a t h become comparable w i t h the diameter. The results indicate that the spin m o m e n t u m a c c o m m o d a t i o n c o e f f i c i e n t at this surface is less than unity. 1
INTRODUCTION
The i n t e r a c t i o n b e t w e e n liquid 3He q u a s i p a r t i c l e s and surfaces is of interest for a n u m b e r o f reasons, for example in the theory of t r a n s p o r t of liquid 3He in the c o l l i s i o n l e s s regime (i) or in the surface e n h a n c e m e n t of the nuclear m a g n e t i c s u s c e p t i b i l i t y (2). We have m e a s u r e d the spin d i f f u s i o n c o e f f i c i e n t D of 3He as a function of pressure in the array of glass capillaries, each of d i a m e t e r 5~m, w h i c h we also used to investigate the e n h a n c e d s u s c e p t i b i l i t y (2). The temperature range was 15 to 3 mK, at the lower end of w h i c h the q u a s i p a r t i c l e mean free path is about h a l f the individual tube d i a m e t e r and the results d e p e n d on the specular r e f l e c t i o n coefficient. The spin d i f f u s i o n c o e f f i c i e n t well into the c o l l i s i o n l e s s regime has b e e n m e a s u r e d before, in V y c o r porous glass (3). The p r e s e n t geometry is a simpler one a l l o w i n g the nature of the interactions w i t h the wall to be observed, a l t h o u g h we still know n o t h i n g d i r e c t l y of the state of the glass surface. A n o t h e r sample of the glass itself is known to be m a g n e t i c (2,4). We have also m e a s u r e d D for bulk liquid 3He in the same range of temperature and p r e s s u r e (O30 bar); the l i m i t i n g low t e m p e r a t u r e v a r i a t i o n of D w i t h p r e s s u r e was not p r e v i o u s l y well determined. 2.
long T2 and T 1 b e l i e v e d to originate from the bulk liquid outside the glass array. The long TI, T 2 component was also found to be in a lower R.F. field consistent w i t h its o r i g i n a t i n g from the bulk liquid which was further from the centre of the R.F. coil. In the pore m e a s u r e m e n t s the g r a d i e n t was d i r e c t e d along the axis of the capillaries. The T 2 contribution to the decay of the echo was m e a s u r e d in a separate experiment w i t h no g r a d i e n t p r e s e n t and was found to vary linearly from 18 msec to 7 msec b e t w e e n 15mK and 3mK. T e m p e r a t u r e s were m e a s u r e d by a CW p l a t i n u m NMR t h e r m o m e t e r w h i c h was c a l i b r a t e d against the T 1 of platinum. The K o r r i n g a relationship was found to be temperature independent with a K o r r i g a constant of 27.76 m s K at the frequency used.
I0-7 crn2 K 2 l~eG-1
I
,5 !
I0
--
O
O
APPARATUS
The apparatus was exactly the same as that used for the e n h a n c e d s u s c e p t i b i l i t y m e a s u r e m e n t s (2). Measurements were made u s i n g a s t a n d a r d two echo C a r t - P u r c e l l sequence in a field of 218 gauss. For the bulk liquid m e a s u r e m e n t s the value of the field g r a d i e n t was chosen to make the T 2 c o n t r i b u t i o n to the decay of the echo negligible, and was t y p i c a l l y 1.9 gauss/cm. The w i d t h o f the bulk liquid NMR lines w i t h no g r a d i e n t present was of the order of a few cycles. The signal o r i g i n a t i n g from the pores was found to consist of two separate contributions. A c o m p o n e n t w i t h s h o r t T 2 and T , b e l i e v e d to I originate from the liquid in the pores, was shifted by about 1.5KHz from a component w i t h
0378-4363/81/0000-0000/$02.50
I
© North-HollandPublishingCompany
5
•
O
o
0 I~
I I0
I 20 P bors
0
dl
I 30
Figure i. The limiting low t e m p e r a t u r e q u a n t i t y A = DT 2 as a function of p r e s s u r e in normal bulk liquid 3He. e, ref. (5); O, ref. (6), D , ref. (7) m , p r e s e n t work.
1059
1060
3.
RESULTS A N D D I S C U S S I O N
This work was s u p p o r t e d by the Science R e s e a r c h Council under Grant No. GR/A/7526.2.
The limiting low-temperature variation of the diffusion coefficient of a Fermi liquid is D = A T -2 In all cases our bulk m e a s u r e m e n t s were well into this regime. They give results for A shown in Figure 1 as a function of p r e s s u r e and compared with other values. The only previous results comparable in extent with o u r s are those of Abel et al (5), w h i c h except for the zero p r e s s u r e result e x t e n d e d only down to 25mK and may not have been in the low-temperature regime. These are the first such reliable results to be obtained, and they show some difference in the p r e s s u r e dependence. Figure 2 shows the measurements at zero pressure for the 5Hm capillary array, p l o t t e d as Dversus T -l. The h i g h temperature results again follow the DT 2 = constant variation (with the constant equal within 5% to the values shown in Figure i) but clear deviations are seen at lower temperatures as the mean free path b e c o m e s comparable with the tube diameter. At the lowest temperature (% 3mK) the mean free path is about one h a l f of the tube diameter. The b r o k e n line in the Figure is the result of a theoretical c a l c u l a t i o n with a specular reflection coefficient taken as zero while the straight line corresponds to ~ = i. The results fall between the two, s u g g e s t i n g that the q u a s i p a r t i c l e s have approximately equal p r o b a b i l i t y of diffuse and specular reflection. It might be e x p e c t e d that this number was very dependent on the m i c r o s c o p i c geometry of the surface; we do not believe this to be the case because the m i n i m u m size of a thermal q u a s i p a r t i c l e wave packet, g i v e n by Ak -I = hVF/kT, is of the order of iOOO A in these experiments. On the other h a n d the spin m o m e n t u m a c c o m m o d a t i o n c o e f f i c i e n t which we have m e a s u r e d could be s i g n i f i c a n t l y larger than the m o m e n t u m a c c o m m o d a t i o n coefficient m e a s u r e d by, for example, flow, b e c a u s e of spin exchange p r o c e s s e s with an immobile layer at the surface.
1~/2orbitrory units _
.i
T.I mk:12
.3
Figure 2. D ½ in arbitrary units against T -I for the 5pm d i a m e t e r capillaries at zero pressure. Also shown are theoretical curves for s p e c u l a r reflection coefficients one ( ~ ) and zero (---).
% Science R e s e a r c h Council Senior Fellow. REFERENCES 10 H.H. Jansen, H. Smith, P. wolfle, K. Nagai and T.M. Bigaard, J. Low Temp. Phys. 41 (1980) 473. E2_-I See, for example, A. Sachrajda, D.S. Betts, D.F. B r e w e r and W.S. Truscott, this Conference. E3-1 D.F. Brewer and J.S. Rolt, Physics Letters 48A (1974) 141. E4-1 J. Saunders, D.S. Betts, D.F. Brewer, S.T. Swithenby and W.S. Truscott, Phys. Rev. Letters 40 (1978) 1278. F5-1 W.R. Abel, A.C. Anderson, W.C. Black and J.C. Wheatley, Phys. Rev. Letters 7 (1961) 337. E6_-I A.C. Anderson, W. Reese, R.J. Sarwinski and J.C. Wheatley, Phys. Ray. Letters 7 (1961) 220. [7- I L.R. Corrucini, D.D. Osheroff, D.M. Lee and R.C. Richardson, J. Low Temp. Phys. 8 (1972) 229.
Physica 108B (1981/1059-1060 North-Holland Publishing Company
SPIN D I F F U S I O N C O E F F I C I E N T O F N O R M A L L I Q U I D 3HE IN INFINITE A N D B O U N D E D G E O M E T R I E S UNDER PRESSURE D.F. Brewer %, D.S. Betts, A. S a c h r a j d a and W.S. T r u s c o t t P h y s i c s Laboratory, U n i v e r s i t y of Sussex, Brighton, Sussex, England.
We report m e a s u r e m e n t s of the spin diffusion coefficients of normal liquid 3He in bulk, and in 5~m d i a m e t e r glass capillary tub~s, as a function of p r e s s u r e (O-30 bar) and t e m p e r a t u r e (3mK-15mK). The bulk e x p e r i m e n t s are well into the l i m i t i n g low temperature Fermi fluid regime, and p r o v i d e the first reliable m e a s u r e m e n t s of the p r e s s u r e variation of A = DT 2. In the 5~m capillaries, d e v i a t i o n s from this relation are found as the q u a s i p a r t i c l e m e a n free p a t h become comparable w i t h the diameter. The results indicate that the spin m o m e n t u m a c c o m m o d a t i o n c o e f f i c i e n t at this surface is less than unity. 1
INTRODUCTION
The i n t e r a c t i o n b e t w e e n liquid 3He q u a s i p a r t i c l e s and surfaces is of interest for a n u m b e r o f reasons, for example in the theory of t r a n s p o r t of liquid 3He in the c o l l i s i o n l e s s regime (i) or in the surface e n h a n c e m e n t of the nuclear m a g n e t i c s u s c e p t i b i l i t y (2). We have m e a s u r e d the spin d i f f u s i o n c o e f f i c i e n t D of 3He as a function of pressure in the array of glass capillaries, each of d i a m e t e r 5~m, w h i c h we also used to investigate the e n h a n c e d s u s c e p t i b i l i t y (2). The temperature range was 15 to 3 mK, at the lower end of w h i c h the q u a s i p a r t i c l e mean free path is about h a l f the individual tube d i a m e t e r and the results d e p e n d on the specular r e f l e c t i o n coefficient. The spin d i f f u s i o n c o e f f i c i e n t well into the c o l l i s i o n l e s s regime has b e e n m e a s u r e d before, in V y c o r porous glass (3). The p r e s e n t geometry is a simpler one a l l o w i n g the nature of the interactions w i t h the wall to be observed, a l t h o u g h we still know n o t h i n g d i r e c t l y of the state of the glass surface. A n o t h e r sample of the glass itself is known to be m a g n e t i c (2,4). We have also m e a s u r e d D for bulk liquid 3He in the same range of temperature and p r e s s u r e (O30 bar); the l i m i t i n g low t e m p e r a t u r e v a r i a t i o n of D w i t h p r e s s u r e was not p r e v i o u s l y well determined. 2.
long T2 and T 1 b e l i e v e d to originate from the bulk liquid outside the glass array. The long TI, T 2 component was also found to be in a lower R.F. field consistent w i t h its o r i g i n a t i n g from the bulk liquid which was further from the centre of the R.F. coil. In the pore m e a s u r e m e n t s the g r a d i e n t was d i r e c t e d along the axis of the capillaries. The T 2 contribution to the decay of the echo was m e a s u r e d in a separate experiment w i t h no g r a d i e n t p r e s e n t and was found to vary linearly from 18 msec to 7 msec b e t w e e n 15mK and 3mK. T e m p e r a t u r e s were m e a s u r e d by a CW p l a t i n u m NMR t h e r m o m e t e r w h i c h was c a l i b r a t e d against the T 1 of platinum. The K o r r i n g a relationship was found to be temperature independent with a K o r r i g a constant of 27.76 m s K at the frequency used.
I0-7 crn2 K 2 l~eG-1
I
,5 !
I0
--
O
O
APPARATUS
The apparatus was exactly the same as that used for the e n h a n c e d s u s c e p t i b i l i t y m e a s u r e m e n t s (2). Measurements were made u s i n g a s t a n d a r d two echo C a r t - P u r c e l l sequence in a field of 218 gauss. For the bulk liquid m e a s u r e m e n t s the value of the field g r a d i e n t was chosen to make the T 2 c o n t r i b u t i o n to the decay of the echo negligible, and was t y p i c a l l y 1.9 gauss/cm. The w i d t h o f the bulk liquid NMR lines w i t h no g r a d i e n t present was of the order of a few cycles. The signal o r i g i n a t i n g from the pores was found to consist of two separate contributions. A c o m p o n e n t w i t h s h o r t T 2 and T , b e l i e v e d to I originate from the liquid in the pores, was shifted by about 1.5KHz from a component w i t h
0378-4363/81/0000-0000/$02.50
I
© North-HollandPublishingCompany
5
•
O
o
0 I~
I I0
I 20 P bors
0
dl
I 30
Figure i. The limiting low t e m p e r a t u r e q u a n t i t y A = DT 2 as a function of p r e s s u r e in normal bulk liquid 3He. e, ref. (5); O, ref. (6), D , ref. (7) m , p r e s e n t work.
1059
1060
3.
RESULTS A N D D I S C U S S I O N
This work was s u p p o r t e d by the Science R e s e a r c h Council under Grant No. GR/A/7526.2.
The limiting low-temperature variation of the diffusion coefficient of a Fermi liquid is D = A T -2 In all cases our bulk m e a s u r e m e n t s were well into this regime. They give results for A shown in Figure 1 as a function of p r e s s u r e and compared with other values. The only previous results comparable in extent with o u r s are those of Abel et al (5), w h i c h except for the zero p r e s s u r e result e x t e n d e d only down to 25mK and may not have been in the low-temperature regime. These are the first such reliable results to be obtained, and they show some difference in the p r e s s u r e dependence. Figure 2 shows the measurements at zero pressure for the 5Hm capillary array, p l o t t e d as Dversus T -l. The h i g h temperature results again follow the DT 2 = constant variation (with the constant equal within 5% to the values shown in Figure i) but clear deviations are seen at lower temperatures as the mean free path b e c o m e s comparable with the tube diameter. At the lowest temperature (% 3mK) the mean free path is about one h a l f of the tube diameter. The b r o k e n line in the Figure is the result of a theoretical c a l c u l a t i o n with a specular reflection coefficient taken as zero while the straight line corresponds to ~ = i. The results fall between the two, s u g g e s t i n g that the q u a s i p a r t i c l e s have approximately equal p r o b a b i l i t y of diffuse and specular reflection. It might be e x p e c t e d that this number was very dependent on the m i c r o s c o p i c geometry of the surface; we do not believe this to be the case because the m i n i m u m size of a thermal q u a s i p a r t i c l e wave packet, g i v e n by Ak -I = hVF/kT, is of the order of iOOO A in these experiments. On the other h a n d the spin m o m e n t u m a c c o m m o d a t i o n c o e f f i c i e n t which we have m e a s u r e d could be s i g n i f i c a n t l y larger than the m o m e n t u m a c c o m m o d a t i o n coefficient m e a s u r e d by, for example, flow, b e c a u s e of spin exchange p r o c e s s e s with an immobile layer at the surface.
1~/2orbitrory units _
.i
T.I mk:12
.3
Figure 2. D ½ in arbitrary units against T -I for the 5pm d i a m e t e r capillaries at zero pressure. Also shown are theoretical curves for s p e c u l a r reflection coefficients one ( ~ ) and zero (---).
% Science R e s e a r c h Council Senior Fellow. REFERENCES 10 H.H. Jansen, H. Smith, P. wolfle, K. Nagai and T.M. Bigaard, J. Low Temp. Phys. 41 (1980) 473. E2_-I See, for example, A. Sachrajda, D.S. Betts, D.F. B r e w e r and W.S. Truscott, this Conference. E3-1 D.F. Brewer and J.S. Rolt, Physics Letters 48A (1974) 141. E4-1 J. Saunders, D.S. Betts, D.F. Brewer, S.T. Swithenby and W.S. Truscott, Phys. Rev. Letters 40 (1978) 1278. F5-1 W.R. Abel, A.C. Anderson, W.C. Black and J.C. Wheatley, Phys. Rev. Letters 7 (1961) 337. E6_-I A.C. Anderson, W. Reese, R.J. Sarwinski and J.C. Wheatley, Phys. Ray. Letters 7 (1961) 220. [7- I L.R. Corrucini, D.D. Osheroff, D.M. Lee and R.C. Richardson, J. Low Temp. Phys. 8 (1972) 229.