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Submitted on 1 Jan 1978
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ZEEMAN CRITICAL FIELD IN
SUPERCONDUCTING SMALL PARTICLE
S. Kobayashi, K. Nomura, W. Sasaki
To cite this version:
ZEEMAN CRITICAL FIELD IN SUPERCONDUCTING SMALL PARTICLE
S.Kobayashi, K. Nomura and W. Sasaki
Department of Physios, University of Tokyo, Hongo, Tokyo, Japan
Abstract.- The superconductivity of small Al particles was destroyed by the Zeeman effect in high magnetic field. The critical field was larger than what mean field thory predicted. It is pointed out that the fluctuation of order parameter should be conside-red.
INTRODUCTION.- The magnetic field applied to a small size superconductor causes two effects which destroy the pairing of the electrons. The first one is the orbital depairing which arises from the non time reversal nature of the field. For a small spherical particle with radius R the critical field at T=0 was calculated as /l/
H°r*= 5 x X 6 1/2.H .R-3/2 (1)
c L 0 cb
where A , g H are respectively the London pene-tration depth, the coherence length and the criti-cal field for a bulk specimen. The other is the Zeeman depairing. The spins of electrons couple with the field, the up and down bands shift by u H
B and ~yRH> and roughly speaking,when 2u H exceed the
BCS energy gap the superconductivity ceases. The critical field at T=0 was calculated as /2/
Hz = 1.2 - ^ (2)
which is independent of the size. The transition in this case is of the first order. The real cri-tical field, therefore, is smaller than the smaller of these two H 's. A simple estimation for Al gives that H < H when d, the diameter of the particle
c c o
is smaller than about 130 A. The critical field H is 2.3X101* gauss which is feasible with
super-conducting magnet.
In the above discussion, the thermodyna-mical fluctuation of the order parameter is
neglec-o
ted. In a particle with d^lOOA, the fluctuation
amplitude is very large. It has been shown that the fluctuation enhances the variance of the order parameter fom the BCS values/3/. Therefore the transition with the field will be considerably smeared and higher fields will be required to sup-press completely the superconductivity.
To detect whether a particle is supercon-ducting or not, NMR is a suitable technique. The Knight shift and the spin lattice relaxation time in superconducting state differ very much from these in normal state. We have already reported the observation of the Zeeman effect in Al particles by measuring the field dependence of the relaxa-tion time in superconducting states /4/. The pur-pose of the present work is to break entirely the superconductivity of Al particles by the Zeeman effect.
EXPERIMENTS.- The NMR spin echo of Al particles was measured in the field up to 4x10^ gauss and in the temperature down to 0.5 K. The sample has a
o
mean diameter of 100 A, and the full half width of the distribution in size is about 15 % of the mean value. The samples were prepared by the gas evapo-ration method.
The spin lattice relaxation was measured as the recovery of the echo height after the complete saturation of nuclear magnetization by a long train of TT/2 pulses. The Knight shift was measured by plotting the echo height against the magnetic field.
In figure 1, the result of the spin lattice relaxation time Tj is shown. The temperature de-pendence of Tj in 8.1x10^ gauss is typical in su-perconductors, i.e., it varies as
Tx a exp — • (3)
while A is much larger than the BCS value. This result well agrees with our previous ones. When the field is increased to 3.6x10^ gauss, Tj
JOURNAL DE PHYSIQUE
Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-663
Résumé.- La supraconductivité des p a r t i c u l e s p e t i t e s d'Al a é t é d é t r u i t e par l ' e f f e t
Zeeman en fort champ magnétique. Le champ c r i t i q u e obtenu e s t plus haut que ce que l a
théorie de champ moyen p r é v o i t . I l e s t montré que l a fluctuation du paramètre d'ordre
d o i t ê t r e p r i s e en compte.
becomes c l o s e t o t h e normal v a l u e - 1
T Y ~ =
1 . 8 x T s norm although i t is s t i l l longer t h a n TI a t t h e lowest temperature.(Jb
1
)
0.5
1
.O
-1.5
2
.O
T-'( K-'
1
F i g . 1 : Spin l a t t i c e r e l a x a t i o n time i n A1 par- t i c l e s with d = 100
A.
The broken l i n e shows t h e normal value.F i g u r e 2 i s shown: t h e Knight s h i f t i n 3 . 6 ~ 1 0 ' gauss. Here t h e s h i f t a t 1.4 K i s assumed t o be equal t o t h e normal v a l u e although t h e r e i s a p o s s i b i l i t y t h a t i t i s a l r e a d y somewhat s m a l l e r than t h a t of bulk. r--I---
. /
.,:
A,'1
/' 0.5 - / / / / /BCS
/'
The s h i f t d e c r e a s e s w i t h d e c r e a s i n g T b u t t h e d e c r e a s e i s v e r y much s m a l l e r t h a n t h a t i n 8 . 1 ~ 1 0 : gauss which i s shown t o g e t h e r i n t h e f i g u r e151.
D
DISCUSSION.- For t h e p a r t i c l e s of d=100 A , t h e v a l u e of Horb i n e q u a t i o n ( 1 ) i s estimated t o b e
about 3x104 gauss and
HZ
i n e q u a t i o n (2) t o be 2 . 3 ~ 1 0 4 gauss by u s i n g known ,parameters f o r b u l k specimen. The r e s u l t s i n t h e preceding s e c t i o n shows t h a t even i n h i g h e r f i e l d of 3 . 6 ~ 1 0 4 gauss t h e r e i s a t r a c e of s u p e r c o n d u c t i v i t y though it i s weak. We a t t r i b u t e t h e o r i g i n of t h i s enhancementof
H
*
t o t h e f l u c t u a t i o n enhanced o r d e r parameter. The t h e o r y /3/ which t a k e s i n t o account t h e f l u c - t u a t i o n and both of t h e d e p a i r i n g mechanisms of t h e f i e l d , t h e Zeeman and t h e o r b i t a l d e p a i r i n g h a s s u c c e s f u l l y explained t h e temperature and f i e I d dependence of T I and t h e s h i f t i n r e l a t i v e l y lowf i e l d . I n t h e t h e o r y , i t has been shown t h a t t h e v a r i a n c e of t h e o r d e r parameter i s l a r g e l y enhanced from t h e BCS v a l u e , r e s u l t i n g t h e l o n g e r TI t h a n t h a t of BCS. Unfortunately t h i s t h e o r y i s based on some approximation which i s v a l i d o n l y i n low f i e l d , and t h e r e f o r e i t cannot be d i r e c t l y a p p l i e d t o a n a l y s e t h e p r e s e n t r e s u l t s . Reconstruction of t h e theory f o r t h e h i g h e r f i e l d s a r e being prepa- r e d .
To conclude, we measured TI and t h e s h i f t of NMR of A 1 i n p a r t i c l e s of d=100 i n which
HZ
i s expected t o be lower t h a n Horb. We found t h a t HZ i s h i g h e r t h a n t h a t c a l c u l a t e d i n mean f i e l d approximation and a t t r i b u t e d i t t o t h e e f f e c t of t h e f l u c t u a t i o n . F u r t h e r experiments w i t h t h e samples with v a r i o u s d a r e i n p r o g r e s s .References
/ I / De Gennes, P.G., and Tinkham, M., P h y s i c s
1
(1964) 107./ 2 / Sarma, G., J.Phys. Chem. S o l i d s (1963) 1029. /3/ Sone, J . , 3 . Low Temp. Phys.
2
(1976) 699. / 4 / Takahashi, T., Kobayashi, S. and Sasaki, W.,S o l i d S t a t e Commun.
2
(1975) 681./5/ Koba a s h i , S., Takahashi, T. and S a s a k i , W., 3 . P i y s . Soc. Japan
