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Submitted on 1 Jan 1978
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SURFACE RELAXATION OF CONDUCTION
ELECTRON SPINS IN SUPERCONDUCTORS
R. Meservey, F. Tedrow
To cite this version:
SURFACE RELAXATION OF CONDUCTION ELECTRON SPINS IN SUPERCONDUCTORS
R. Meservey and P.M. Tedrow
Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge,
Massachusetts 02139, U.S.A.
Abstract.- Critical magnetic field and spin-polarized tunnelling measurements of ultra-thin pure su-perconductors give values of the spin-orbit scattering time Ts o in general agreement with the Abri-kosov-Gorkov relation T / TS O = (aZ)1* when T is taken to be the surface scattering time Ts. Here
a = e2/M c and Z is the atomic number of the superconductor. Knight shift experiments on
superconduc-tors and electron spin resonance experiments in which surface scattering dominates also follow this relation.
The importance of spin-orbit scattering in high field superconductivity is well established. Originally suggested by Ferrel and Anderson to ex-plain Knight shift results, the theory of supercon-ductivity including spin-orbit scattering has been developed by Maki, Fulde, Abrikosov, Gorkov and ci-thers. Measurements of Knight shifts, critical fields and tunnelling properties of Al gave good agreement with the theory/1/. The subject has been reviewed by Fulde/2/.
However, in comparing tunnelling and criti-cal field measurements of the spin-orbit relaxation time T for various elements with theory/3/, the
so
data on elements heavier than Al did not appear to fit the theory of Abrikosov and Gorkov (AG)/4/. This theory was developed for impurity scattering and gives the relationship :
e = T/T = (aZ)1* (1) so
Here e is the probability that in a momentum scat-tering collision there will be a change in spin direction, x is the impurity scattering time,
a = e2/Kc and Z is the atomic number of the impuri-ty. For very thin pure films AG interpret x as the surface collision time x ,
ts - d/vp S (2)
where d is the film thickness and v„ is the Fermi r
velocity. In this case Z is taken to be the atomic number of the pure superconductor.
In applying equation (1) to cryogenically condensed ultra-thin films it was originally assu-med/3,5/ that the proper normalization would be
ob-tained if x was taken to be the measured transport relaxation time. However, the resulting dependence of x/x on Z was much less than Z4. Furthermore a
so
recent study of ultra-thin films of Ga/6/ has shown this normalization to be incorrect. A Ga film about
100 A thick was deposited on a substrate at 1 K and the value of x was determined by a tunnelling
so ° measurement before and after the amorphous film
was annealed at 77 K to form a crystalline film. Even though the resistivity of the film decreased by a factor of 6, the value of x did not
signi-so
ficantly change. We conclude that whatever scatte-ring was associated with the additional resistance in the amorphous state was not effective in chan-ging the spin direction and would be meaningless in equation (1).
Another method of determining the mean free path SL uses the measured perpendicular critical field H through the relation
Here 6 = h/2e and it is assumed that the coherence distance £ » i .
In the above-mentioned experiments on Ga the
o
values of 8, from equation (3) were 3 A before
an-o
nealing and 5 A after. From previous experience with polycrystalline thin films we would expect the crystallite size in the annealed film to be
o
about the film thickness, that is, 100 A. The value
o
of 5 A seems much too small for the crystallite si-ze. One explanation of the anomalously small value of i is that the film consists of grains coupled JOURNAL DE PHYSIQUE
Colloque
C6,
supplément au n°
8,
Tome
39,
août
1978,
page
C6-683
Résumé.- Les mesures de champ magnétique critique et d'effet tunnel de spins polarisés sur des su-praconducteurs purs ultra-minces donnent des valeurs pour le temps de diffusion de spin-orbite T s o
en accord avec la relation d'Abrikosov-Gorkov T / TSO = (otZ)1* si on considère T comme le temps de dif-fusion de surface Ts, a = e2/Kc et Z est le nombre atomique du supraconducteur. Les expériences de déplacement de Knight sur les supraconducteurs et les expériences de résonance de spin électronique pour lesquelles la diffusion de surface domine, suivent également cette relation.
t o g e t h e r w i t h t u n n e l b a r r i e r s . I n such a s i t u a t i o n t h e e f f e c t i v e mean f r e e p a t h Ref£ would be approxi- mately Td where d i s the c r y s t a l l i t e s i z e and T i s t h e t r a n s m i t t a n c e of t h e tunnel b a r r i e r s . For small v a l u e s of T t h i s model l e a d s t o small v a l u e s of
Ref£ and T ~ On ~ the o t h e r hand t h e a c t u a l mo- ~ . mentum s c a t t e r i n g time t o be used i n e q u a t i o n (1) would be given by e q u a t i o n ( 2 ) , t h e s u r f a c e s c a t t e - r i n g time. To t e s t t h i s simple model we p l o t t h e a v a i l a - b l e d a t a on superconductors i n f i g u r e 1 . Values of Fig. 1 : P r o b a b i l i t y E t h a t a s u r f a c e c o l l i s i o n w i l l change t h e conduction e l e c t r o n s p i n d i r e c t i o n p l o t - t e d a s a f u n c t i o n of atomic n u d e r Z . Data a r e g i - ven from c r i t i c a l f i e l d and t u n n e l l i n g measurements on superconductors ( 8 from r e f e r e n c e s 3,6 ;
r
from r e f e r e n c e 5 ) ; Knight s h i f t measurementsA
( r e f e - rence 7) ; and ESR measurements V ( r e f e r e n c e 8 ) .a r e obtained from c r i t i c a l f i e l d and tunnel- l i n g measurements/3,5,6/ and from Knight s h i f t mea- surements/7/ of superconductors. We a l s o i n c l u d e e l e c t r o n s p i n resonance (ESR) data181 f o r Na and Cu f o r which i t was shown t h a t s u r f a c e s c a t t e r i n g determined t h e l i n e widths. Actually ESR d a t a s u i - t a b l e f o r t h i s purpose can be derived only from samples i n a r a t h e r small range of s i z e s ( z lo-' t o cm). Samples must be small enough s o t h a t s u r f a c e s c a t t e r i n g dominates over impurity s c a t t e - r i n g , b u t must n o t be s o small t h a t t h e quantum s i - ze e f f e c t / 9 / on t h e energy l e v e l s becomes dominant. Figure 1 shows t h a t T ~ / v a r i e s approxima- T ~ ~ t e l y a s 2' and t h a t the a b s o l u t e value i s n o t f a r from t h e AG value of (a2)
'.
The superconducting da-t a
a r e somewhat h i g h e r than ( a ~ ) ' , b u t a d d i t i o n a l s c a t t e r i n g from vacancies and i m p u r i t i e s would tend t o decrease t h e s e v a l u e s . I t should be emphasized t h a t t h e determination of T~~ and T a r e i n mostS
i n s t a n c e s r a t h e r crude and t h e r e s u l t s of d i f f e r e n t measurements can d i f f e r by an o r d e r of magnitude.
More a c c u r a t e measurements a r e needed, b u t we can conclude t h a t t h e a v a i l a b l e d a t a support the Abri- kosov-Gorkov r e l a t i o n given by e q u a t i o n (1) using t h e s u r f a c e s c a t t e r i n g time .rs. The r e s u l t s do n o t agree with t h e c a l c u l a t i o n of L i s i n and Khabibullin / l o / on t h e r e l a x a t i o n of conduction e l e c t r o n s p i n s a t a metal s u r f a c e .
We wish t o acknowledge t h e s u p p o r t of the National Science Foundation.
References
/ I / Meservey,R., Tedrow,P.M. and Bruno,R.C., Phys. Rev. (1975) 4224
/2/ Fulde,P., Adv. Phys.
&
(1973) 667/ 3 / Meservey,R. and Tedrow,P.M., Phys. L e t t .
58A
(1976) 136/4/ Abrikosov,A.A. and Gorkov,L.P., JETP
2
(1962) 1088, Sov. Phys. JETP15
(1962) 752/5/ Crow,J.E., Strongin,M. and Bhatnagar,A.K., Phys. Rev. (1974) 135
/ 6 / Meservey,R., Tedrow,P.M. and Bruno,R.C., Phys. Rev. (1978)
/7/ Hines,W.A. and Knight,W.D., Phys. Rev.
(1971) 893 and o t h e r r e f e r e n c e s c i t e d t h e r e i n / 8 / Wang,S.K. and Schumacher,R.T., Phys. Rev.
(1973) 41 19 ; (1974) 2129 (NA) ; Schultz, S: and Latham,C., Phys. Rev. L e t t .
15
(1965)148
/9/ Kawabata,A., J. Phys. Soc. Jpn
