THE rf RESISTIVITY OF A PERFORATED SUPERCONDUCTING FILM IN A MAGNETIC FIELD

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THE rf RESISTIVITY OF A PERFORATED

SUPERCONDUCTING FILM IN A MAGNETIC

FIELD

A. Fiory, A. Hebard, R. Minnich

To cite this version:

JOURNAL DE PHYSIQUE

Colloque

C6, suppliment au no 8, Tome 39, aofit 1978, page C6-633

THE

r f

RESISTIVITY

OF A PERFORATED

SUPERCONDUCTING FILM

I N

A

MAGNETIC FIELD

A.T. F j o r y , A.F. Hebard and R.P. Minnich

BeZZ Laboratories,

Murray

HiZZ,

NJ

07974, USA

Rlsum6.- Des mesures d e r l s i s t i v i t l r f complexe 5 75 MHz o n t S t 6 e f f e c t u L e s en f o n c t i o n d e l a temperature e t du champ magnltique s u r une couche d'aluminium dople S l1oxygSne e t p e r f o r l e s u i v a n t un r l s e a u t r i a n g u l a i r e d e t r o u s . La r6ponse r f pour d e s champs magnLti- ques commensurables e s t i n t e r p r l t l e c o m e r l s u l t a n t d e l a s u p e r p o s i t i o n cohgrente du mouvement d e s v o r t e x dans un p o t e n t i e l parabolique

.

Une d i s s i p a t i o n anormalement f a i b l e

a B t L t r o w l e pour l e s quanta p i d g s s , e n r a i s o n de l ' a b s e n c e d ' e x c i t a t i o n s dans l e coeur. La c o n s t a n t e d e r a p p e l du p o t e n t i e l d e piBgeage a l t l d l d u i t e e t exprimle e n f o n c t i o n d e l a templrature.

A b s t r a c t . - We r e p o r t measurements of t h e complex r f r e s i s t i v i t y a t 75 MHz a s a f u n c t i o n of temperature and magnetic fie1.d on an oxygen-doped aluminum f i l m , p e r f o r a t e d w i t h a t r i a n g u l a r l a t t i c e of h o l e s . The r f response a t commensurate magnetic f i e l d s i s modeled i n terms of coherent superimposition of v o r t e x motion i n a p a r a b o l i c p o t e n t i a l . Anomalously small d i s s i p a t i o n i s found f o r trapped quanta, owing t o t h e absence of core e x c i t a t i o n s . The f o r c e c o n s t a n t of t h e pinning p o t e n t i a l i s found a s a f u n c t i o n of temperature.

We have measured t h e r f response a t 75 MHz of a Type I1 aluminum f i l m , p e r f o r a t e d with a t r i a n g u l a r l a t t i c e of l u m h o l e s spaced 3 pm a p a r t , / 1 , 2 / i n o r d e r t o o b t a i n a c h a r a c t e r i z a t i o n of t h e s u b c r i t i c a l vortex-hole coupling f o r c e s . Our r e - s u l t s can be used t o measure t h e " s p r i n g constant" of t h e pinning f o r c e and s e r v e a s a d i a g n o s t i c f o r d e t e c t i n g t h e presence of comparatively weakly bound v o r t i c e s l o c a t e d i n t e r s t i t i a l l y between t h e h o l e s . S i n c e t h e trapped v o r t i c e s do n o t have t h e u s u a l normal-like c o r e , we expect on t h e b a s i s of t h e theory of v o r t e x motion /3/ t h a t t h e i r c o n t r i - b u t i o n t o t h e power d i s s i p a t i o n would be s m a l l e r .

The phenomenological e q u a t i o n o f motion used h e r e h a s been t e s t e d i n p r e v i o u s a p p l i c a t i o n s / 4 , 5 / and i s s i m i l a r t o t h a t used by Rosenblum and Gittleman i n bulk superconductor measurements / 6 , 7 / . I n t h e p r e s e n t work t h e coherent a c t i o n of t h e pinning p o t e n t i a l p e r m i t s a r e a l i s t i c i n t e r - p r e t a t i o n of t h e average pinning f o r c e c o n s t a n t k.

The model e q u a t i o n i s w r i t t e n i n terms of a unique v o r t e x displacement x about t h e q u i e s c e n t p o s i t i o n ll ir

+

kx

-

J$o/c, ( 1 ) where q is t h e v i s c o s i t y c o e f f i c i e n t and J an a p p l i e d c u r r e n t d e n s i t y . Using t h e r e l a t i o n E = f B / c f o r t h e e l e c t r i c f i e l d , i t f o l l o w s t h a t t h e s o l u t i o n f o r t h e complex r e s i s t i v i t y p(w) = E(w)/

J(w) a t frequency wcan be expressed i n terms of

i t s r e a l and imaginary p a r t s .

~ e b= lpf cos2+ (2)

1 m E = B+ow s i n 2 + / k c 2 . (3) Where pf = B + ~ / ~ C ~ i s t h e f lux-flow r e s i s t i v i t y ,

T = n/k i s t h e r e l a x a t i o n time, and t h e phase angle

+

= cot-l ( w ~ ) .

F i g u r e 1 i s a p l o t showing t h e two compo- n e n t s of t h e complex r f r e s i s t i v i t y a s a f u n c t i o n of t h e magnetic f i e l d B normalized t o t h e matching f i e l d B where t h e f l u x d e n s i t y i s equal t o t h e M h o l e d e n s i t y . A t T = 1.845 K t h e r e i s pronounced s t r u c t u r e a t B = B and a t B = 2BM. A t T = 1.7 K

M

t h e r f r e s i s t i v i t y i n c r e a s e s d r a m a t i c a l l y a t a t h r e s h o l d f i e l d Bth = 3BM. The t h r e s h o l d f i e l d Bth i n c r e a s e s monotonically w i t h d e c r e a s i n g tem- p e r a t u r e . Wefind t h a t w~ Q 1 over t h e f i e l d r e g i o n s t u d i e d a t 1 . 7 K . However,

~mb]

tends t o be l a r g e r than ~ e]for h B <

nth.

The f lux-f low r e - s i s t i v i t y p f deduced from a f i t t o Equation (2) i n c r e a s e s by an o r d e r of magrlitude a s t h e f i e l d i s swept through

nth.

A s i m i l a r r e s u l t i s found a t lower temperatures. The r e s u l t s f o r B c Bth can be understood i n terms of t h e complete t r a p p i n g of a l l of t h e f l u x i n t h e h o l e s a s quanta without c o r e s .

Both rl and k a r e markedly s m a l l e r f o r

B > Bth, which we assume i s because the r f response

i s dominated by more weakly bound v o r t i c e s h a v i n g Only d a t a f o r which B < Bth were used. There i s o r d i n a r y c o r e s . a n a b r u p t change i n s l o p e a t T % 1.8 K , a t which

t e m p e r a t u r e

5

= 0.13um. W e b e l i e v e t h a t t h e edge d e f i n i t i o n of t h e h o l e s i n t h e h o l e s i n t h e f i l m

i s about t h e same l e n g t h . The v a l u e k

2

8 0 dyn/cm2 a t T = 1.7 K g i v e s a v o r t e x d i s p l a c e m e n t of about 40 induced by t h e r f e x c i t a t i o n .

We a l s o a p p l i e d a d c c u r r e n t t o t h e sample i n o r d e r t o d i s p l a c e t h e q u i e s c e n t p o s i t i o n s of t h e v o r t i c e s w i t h r e s p e c t t o t h e h o l e s . R e l a t i v e l y minor changes i n t h e r f r e s i s t i v i t y were found f o r b i a s e s up t o t h e d c c r i t i c a l c u r r e n t . The d c c r i t i c a l c u r r e n t s a r e a b o u t 50 % of t h e magnitudes found u s i n g p u l s e d c u r r e n t s , r e s u l t s r e p o r t e d F i g . 1 : The r e a l and imaginary components o f t h e

rf resistivity measured a t 75 MHz as a function of p r e v i o u s l y

111.

The s p r i n g c o n s t a n t c a n t h e r e f o r e reduced magnetic f i e l d . T = 1.875 K , BM = 2.76 Oe b e used t o f i n d t h e v o r t e x d i s p l a c e m e n t s c o r r e s - and t h e Ginzburg-Landau p&ameter i s K = 1 1 . _{ponding t o b i a s e s n e a r t h e c r i t i c a l c u r r e n t . Remar-}

At f i e l d s B > Bth t h e added f l u x c r e a t e s i n t e r s t i t i a l v o r t i c e s which a r e l o c a t e d between t h e h o l e s and a r e i n d i r e c t l y coupled t o t h e p i n n i n g c e n t e r s by t h e e l a s t i c i n t e r a c t i o n s i n t h e v o r t e x s a t t i l e . We o b t a i n t h e s p r i n g c o n s t a n t o f t h e t r a p - p i n g p o t e n t i a l from d a t a t a k e n w i t h BIB e q u a l t o M

a n i n t e g e r , and make u s e o f E q u a t i o n ( 3 ) . The r e - s u l t s a r e p l o t t e d i n F i g u r e 2 a s a f u n c t i o n of tem- p e r a t u r e . k a b l y , these d i s p l a c e m e n t s t u r n o u t t o b e much s m a l l e r t h a n t h e h o l e r a d i u s . A t T

a

1.7 K t h i s d i s p l a c e m e n t i s 700 a t t h i s t e m p e r a t u r e . Appa- r e n t l y , t h e c r i t i c a l c u r r e n t i s n o t a s s o c i a t e d w i t h a l a r g e d i s p l a c e m e n t of t h e c u r r e n t d i s t r i b u - t i o n s a b o u t t h e h o l e s 181, which would r e s u l t i n a c r i t i c a l c u r r e n t a p p r o x i m a t e l y a f a c t o r of s i x h i g h e r t h a n a c t u a l l y o b s e r v e d . T h i s c o n f i r m s our e a r l i e r p i c t u r e t h a t t h e o n s e t of v o r t e x motion c o r r e s p o n d s t o c o r e n u c l e a t i o n a t ' t h e e d g e s of t h e h o l e s / I / . R e f e r e n c e s

/.I/ Hebard, A.F., F i o r y , A.T., and Somekh, S., IEEE T r a n s . Magn. MAG-13 (1977) 589. 121 F i o r y , A.T., Hebard, A.F., and Somekh, S . ,

Appl. Phys. L e t t e r s

2

(1978) 73.

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/ 4 / Ekin, J . W . , _{and Clem, J . R . , Phys. Rev. B}

₁₂

(1975) 1753.

151

F i o r y , A.T., IEEE Trans. Magn. MAG-13 (1977) 385.

/ 6 / G i t t l e m a n , J . I . , and Rosenblum, B., Phys. Rev. L e t t e r s

3

(1966) 734.

/ 7 / G i t t l e m a n , J . E . , and Rosenblum, S . , J. Appl. Phys.

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(1968) 2617.

/8/ Mkrtchyan, C.S., and Schmidt, V . V . , Zh. Eksp Teor. F i z . 61 (1971) 367 ( S o v i e t Phys. JETP 34 (1972)

195

) .

-