ULTRASONIC ATTENUATION IN MIXED STATE OF NIOBIUM

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ULTRASONIC ATTENUATION IN MIXED STATE OF NIOBIUM

J. Dominec, K. Míšek

To cite this version:

J. Dominec, K. Míšek. ULTRASONIC ATTENUATION IN MIXED STATE OF NIOBIUM. Journal

de Physique Colloques, 1987, 48 (C8), pp.C8-489-C8-494. �10.1051/jphyscol:1987876�. �jpa-00227180�

ULTRASONIC ATTENUATION I N MIXED STATE OF NIOBIUM

J. DOMINEC and K.

~f

^{~ E K}

Institute of Physics of the Czechoslovak Academy of Sciences.

Na Slovance 2 , 180 40 Praha 8, Czechoslovakia

We have i n v e s t i g a t e d t h e a t t e n u a t i o n of u l t r a s o n i c waves i n t h e mixed s t a t e of niobium, where a remarkable d i p a p p e a r s n e a r t h e lower c r i t i c a l f i e l d . The measurement h a s been performed on one sample f o r v a r i o u s o r i e n t a t i o n s of t h e wave v e c t o r and of t h e p r i n c i p a l c r y s t a l l o g r a p h i c a x e s of t h e sample w i t h r e s p e c t t o ex- t e r n a l magnetic f i e l d .

I. I n t r o d u c t i o n

The d i a m a g n e t i c s t a t e p e r s i s t s i n t y p e I1 s u p e r c o n d u c t o r s u p t o t h e f i e l d Hcl ( l - D ) , where H c l i s t h e lower c r i t i c a l f i e l d and D s t a n d s f o r t h e demagnetizing f a c t o r . Then magnetic f l u x pen- e t r a t e s i n t o t h e sample and t h e mixed s t a t e a p p e a r s . Flux l i n e s e n t e r m a t e r i a l i n bundles of c o n s t a n t l i n e s p a c i n g

/I/.

There e x i s t domains i n t h e Meissner s t a t e and domains i n t h e v o r t e x s t a t e . The volume of t h e l a t t e r i n c r e a s e s l i n e a r l y w i t h i n c r e a s - i n g f i e l d , t i l l f i e l d Hcl,(l-D)

+

D . B i s reaohed, where Bo i s

0

t h e f l u x d e n s i t y i n t h e v o r t e x s t a t e . When t h e f i e l d r i s e s f u r - t h e r , t h e f l u x d e n s i t y i n c r e a s e s and e v e n t u a l l y t h e m a t e r i a l goes o v e r i n t o t h e normal s t a t e .

This change m a n i f e s t s i t s e l f i n a t t e n u a t i o n of sound waves.

The a t t e n u a t i o n i n t h e Meissner s t a t e i s c o n s t a n t . The a t t e n u - a t i o n i n t h e mixed s t a t e ( w i t h t h e e x c e p t i o n of a d i p n e a r Hcl) i n c r e a s e s a t f i r s t s l o w l y , t h e n more and more r a p i d l y up t o t h e upper c r i t i c a l f i e l d . T h i s dependence i s w e l l e s t a b l i s h e d , but due t o complex i n t e r a c t i o n s (unbound e l e c t r o n s , f l u x l i n e s , phonons, i m p u r i t i e s ) , t h e r e i s no t h e o r y , t h a t would account f o r t h e e n t i r e mixed s t a t e .

The aim of o u r work was t o i n v e s t i g a t e t h e mixed s t a t e n e a r Hcl, where a d i p i n t h e a t t e n u a t i o n a p p e a r s i n samples of h i g h e r

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987876

JOURNAL DE PHYSIQUE

p u r i t y / 2 - 5 / . The n a t u r e of t h e d i p and t h e behaviour of t h e a t - t e n u a t i o n i n t h e v i c i n i t y of H i s n o t y e t f u l l y u n d e r s t o o d . We

c 1

have i n t e n d e d t o s e p a r a t e i n f l u e n c e s of i m p u r i t i e s , o t h e r c r y s t a l i m p e r f e c t i o n s and of t h e a n i s o t r o p y ( ~ s u p e r c o n d u c t i v e n q u a n t i t i e s a r e a p p a r e n t l y a n i s o t r o p i c / 6 / ) . We have t h e r e f o r e p r e p a r e d a sample t h a t allowed t h e e x c i t a t i o n of sound waves a l o n g t h r e e p r i n c i p a l c r y s t a l l o g r a p h i c d i r e c t i o n s and we have measured t h e a t t e n u a t i o n i n v a r i o u s o r i e n t a t i o n s of magnetic f i e l d w i t h r e - s p e c t t o t h e sample.

11. Sample and e x p e r i m e n t a l procedure

The sample (denoted a s A-I-R) was s p a r k - c u t from a s i n g l e c r y s t a l of a h i g h p u r i t y i n t h a t way, t h a t i t s f a c e s were p e r - p e n d i c u l a r t o t h e c r y s t a l l o g r a p h i c d i r e c t i o n s (1 0 0 )

,

( 1 1 0 ) and ( 1 1 1 )

,

( s e e F i g . 1 . ) .

F i g . 1 . O r i e n t a t i o n and dimensions of t h e sample.

1 ) The s i n g l e c r y s t a l was prepared i n t h e I n s t i t u t e of Metal P h y s i c s of t h e Ukrainian Academy of S c i e n c e s by t h e e l e c t r o n zone m e l t i n g method.

.2 dB/cm

100 0_ 100

^„H ^m

ftHDnTJ

F i g . 2 . - The (*= CX (H) d e p e n d e n c e f o r H JJ < 1 1 2 > , q || <^111> , s a m p l e p o s i t i o n C I . The q u a n t i t i e s involved i n T a b l e 1 a r e a l s o d r a w n .

H 0 0 1 O O l 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 2 1 1 2

q 0 0 1 1 1 0 0 0 1 0 0 1 1 1 O 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1

K Al A2 B l CI B2 C2 B l A2 Al C2 CI

(W.

0

H* [mf]

87 9 0 1 0 6 1 0 1 1 0 4 1 0 3 1 0 4 86 88 1 0 5

98

<U,H

m

[«T3

1 1 0 1 3 2 136 136 1 2 0 1 3 4 138 119 1 1 2 135 1 3 0

ACjjdB/cnf]

0 . 2 0 0 . 2 3 0.23 0 . 3 3 0 . 3 2 0 . 4 0 0 . 3 9 0 . 2 8 0.43 0 . 4 0 Table 1. The results of measurements.

There, in the Table 1, column denoted H (resp.q) involves the direction of magnetic field (resp. of the wave vector), K is the position of the sample (these are drawn in Appendix); values

(W

0

H =(W

0

H

cl

.(l-D), (*„ H

n

tad At* are explained in Fig. 2.

Frequency of longitudinal sound waves was 81 MHz. The accuracy

of determination of Q*

0

H was - 3mT, the one of M

0

H was - '

m

*

Normalized attenuation <\$/0fy, is not used as the attenuation in

the normal state was too high for measurement.

JOURNAL DE PHYSIQUE

The sample h a s been annealed i n s low p r e s s u r e ( 1.10-~ ~ o r r ) oxygen atmosphere a t 2 1 0 0 ~ ~ and then i n high vacuum ( 1.10-lo T o r r ) a t 2 3 0 0 ~ ~ . The r e s i d u a l r e s i s t i v i t y of t h e sample has not been measured, but from comparison with p r o p e r t i e s of o t h e r samples we expect, t h a t RRR

>

1500. 1 )

The measurement was performed by t h e pulse-echo method with t h e h e l p of t h e device Mate0

6600

u s i n g p i e z o e l e c t r i c transducers LINb03. Temperature w a s

4.2 K

and t h e frequency of u l t r a s o n i c waves ranged from 81 MHz t o 200 MHz.

When we t a k e i n t o accougt t h e approximate r e l a t i o n

1 =

R R R . S . ~ O - ~ I E /7/ and t h e v e l o c i t i e s of sound i n niobium, we g e t

q.az

^{1 f o r}

frequency f

=

81

MHa.

Magnetic f i e l d was provided by a superconducting solenoid and monitored by a H a l l probe.

111. R e s u l t s

We have measured t h e dependence O(

=

0( ( H ) f o r v a r i o u s orien- t a t i o n s of t h e sample and of wave v e c t o r t o t h e magnetic f i e l d . The t y p i o a l curve t o g e t h e r with t h e used symbols i s depicted i n Fig.2, t h e r e s u l t s a r e l i s t e d i n Table 1.

IV.

Discussion

The shape of our sample does not allow t o d i a c u s s our r e s u l t s d i r e c t l y i n terms of

Hal

due t o unknown and possibly position-de- pendent demagnetizing f a c t o r D. A s t o t h e measured value8 of &,H,

*

they f a l l d i s t i n c t l y i n t o two groups : (103

2

3)mT f o r d i r e c t i o n s

1 ) E.g. t h e a t t e n u a t i o n i n t h e normal s t a t e a t low temperatures -which i s p r o p o r t i o n a l t o t h e mean f r e e path of e l e c t r o n s

-

has been so high, t h a t echoes have vanished completely.

o n 1 1 1 1 1 1 (and p o s i t i o n A ) . T h i s d i f f e r e n c e may be e x p l a i n e d by a d i f f e r e n t demagnetizing f a c t o r (even i f common s e n s e seems t o i n d i c a t e l a r g e r s i m i l a r i t y between A and C p o s i t i o n s t h a n t h a t between B and c ) . The a n i s o t r o p y of Hcl i t s e l f can a l s o be excluded, s i n c e i t should n o t exceed

5%

i n Nb /6,8/.

The v a l u e s of &Hm a r e approximately 30 mT h i g h e r t h a n &H*.

The d e p t h of t h e d i p A ~ ( ( i n s p i t e of some d i s p e r s i o n of v a l u e s ) seems t o depend on t h e d i r e c t i o n of magnetic f i e l d . It h a s i n

-

c r e a s e d more than l i n e a r l y , but l e s s t h e n q u a d r a t i c a l l y w i t h f r e - quency. We have observed no h y s t e r e s i s above Hm i n c o n t r a s t t o works of Tsuda e t a1./4/ and G o t t l i e b a t e1./3/. T h i s may be due t o a h i g h e r p u r i t y of our sample.

There a r e a s f a r a s we know t h r e e t h e o r i e s , t h a t could e x p l a i n t h e d e c r e a s e of t h e a t t e n u a t i o n above Hcl:

Forgan and Gough /2/ supposed o r i g i n a l l y , t h a t when v o r t i c e s e n t e r t h e sample a t Hcl.(l-D), they s c a t t e r e l e c t r o n s and t h i s way s h o r t e n t h e i r mean f r e e p a t h . A l i n e a r d e c r e a s e of t h e a t t e n u - a t i o n f o l l o w s . But t h i s p r o c e s s and t h e d e c r e a s e must c o n t i n u e t i l l t h e c o n d i t i o n s change

-

i . e . a t l e a s t t i l l t h e f i e l d H c l . ( l - ~ ) + ~ . B o i s reached. T h i s i s n o t t h e c a s e : if we t a k e B = 85 mT /6/ and we s e e , t h a t t h e l i n e a r p a r t of t h e c u r v e

0

O((H) i s s e v e r a l mT wide,. we g e t unreasonably s m a l l D .

Cooper e t a l . /9/ proposed, t h a t f o r a c e r t a i n s t r e n g t h of t h e f i e l d and c e r t a i n o r i e n t a t i o n of t h e wave v e c t o r t o t h e f i e l d t h e r e a p p e a r s a l o g a r i t h m i c s i n g u l a r i t y i n t h e a t t e n u a t i o n . T h i s dependence on o r i e n t a t i o n h a s n o t been observed.

Andreev's s c a t t e r i n g / l O / , f u r t h e r developed by Forgan /11/, supposes a d d i t i o n a l s c a t t e r i n g of q u a s i p a r t i c l e s from e l e c t r o n - l i - ke s t a t e s t o h o l e - l i k e s t a t e s and v i c e v e r s a , by a s p a t i a l l y v a r y i n g o r d e r parameter. T h i s i d e a i s a l s o supported i n a paper of Vinen a t a1./12/, where i t i s observed, b e s i d e s t h e u l t r a s o n i c a t t e n u a t i o n , s i m i l a r dependence of The e l e c t r o n i c p a r t of thermal c o n d u c t i v i t y . We have n o t u n f o r t u n a t e l y g o t d a t a enough t o d i s c u s s i t .

References

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Essmann U . : Physica 55 (1971), 83

C8-494 JOURNAL DE PHYSIQUE

Forgan E.M. ,Gough C .E. :Phys .Letters 21 (1966), 133

Gottlieb M. ,Garbuny M., Jones C

.K. :Phys

.Letters 28A (1968), 148 Tsuda N.,Koike S.,Suzuki T.: Phys.Letters 22 (1966),414

MiSek K.: acta phys.slov.33 (1983),321

Ohta N., Ohtsuka T.

:

J.Phys.Soc.J n. 45 (1978), 59 Forgan E.M . , ^{Gough C} . ^E.

^:

^{J. Phy s} . F 371973), 1596

Kiessig H. ,Essmann U. ,Wieshaupt W.

:

Phys .Letters 71~(1979) ,467 Cooper N., Houghton A. ,Lee H. J.

:

Phys.Rev. 148 (1966), 198 Andrev A.F.: Sov.Phys. - JETP19 (1964), 1228

Forgan E.M.: J.Phys. F 3 (1973), 1429 9 4 Vinen W. F. , Forgan E.M . , ^Gough

^C

. ^{E. ,Hood M. J.}

^:

Physica 55 (1971),

Appendix

Positions of the sample with regard to magnetic field and to the

wave vector.