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Anomalous attenuation of ultrasonic waves in superconducting niobium
Volume 22, number 4
PHYSICS LETTERS
ANOMALOUS ATTENUATION OF IN SUPERCONDUCTING
1 September 1966
ULTRASONIC NIOBIUM
WAVES
N. TSUDA, S. KOIKE* and T. SUZUKI
Institute for Solid State Physics, University of Tokyo, Tokyo, Japan Received 26 July 1966
Anomalous absorption at H c l and a deviation of the temperature variation of a s / a n from the BCS relation have been found in the measurements of the ultrasonic attenuation in superconducting niobium.
In the c o u r s e of s t u d i e s of u l t r a s o n i c a t t e n u a tion of pure niobium following the p r e v i o u s work [1], an a n o m a l o u s a b s o r p t i o n h a s been found at a l i t t l e above the l o w e r c r i t i c a l f i e l d H c l , a s will d e s c r i b e d below. A s a m p l e i s about 6 m m q5 and 8 m m long c y l i n d e r , which was o u t g a s s e d at about 1700°C f o r two weak s in a v a c u u m of 3 x 10 -9 m m H g . The r e s i s t a n c e r a t i o was m e a s u r e d to be about 400 by an eddy c u r r e n t d a m p in g method. The t e m p e r a t u r e dependence of Hc2 obeys G i n z b u r g ' s f o r m u l a b a s e d on the two fluid m o d e l [2]; Hc(t) = Hc(0) (1 - t 2 ) / ( 1 +t2), w h e r e t i s the r e d u ced t e m p e r a t u r e . F o r t h i s s a m p l e , Hc2(0) = = 4228 Oe and Hc2(4.2) = 2720 Oe. K2 i s a l s o e x p r e s s e d a p p r o x i m a t e l y by the two fluid m o d e l as K(t) = 2K(0)/(1 + t2), which d o e s not d i s t i n g u i s h K1 f r o m K2 [3], h o w e v e r . K2(0) was 2.2 + 0.1, taking the a v e r a g e of the s l o p e s o f the m a g n e t i z a tion n e a r Hc2 f o r i n c r e a s i n g and d e c r e a s i n g field. U l t r a s o n i c attenuation was m e a s u r e d f o r longitudinal w a v e s of 30 and 50 M c / s e c , and so it would be taken a s ql << 1, w h e r e q i s the wave v e c t o r and l the m e a n f r e e path. Fig.1 i l l u s t r a t e s the f i e l d dependence of the r e l a t i v e attenuation a(H)/(a(H= 0)), w h e r e the m a g n e t i c f i e l d was applied p a r a l l e l to q. The r a t i o shows a f a i r l y a b r u p t d e c r e a s e j u s t above the l o w e r c r i t i c a l f i e l d then i n c r e a s e s g r a d u a l l y . The bottom of t h i s dip l o c a t e s at a f i el d w h e r e the m a g n e t i z a t i o n of the s a m p l e ch an g es m o s t s t e e p l y . When the f i e l d d e c r e a s e s f r o m above the u p p e r c r i t i c a l field, a slight h y s t e r e s i s a p p e a r s and the attenuation c o e f f i c i e n t does not i n c r e a s e s abruptly at H c l . The depth of the dip A s = a(0) - ~(H)min i s pl ott e d a g a i n s t t e m p e r a t u r e in fig. 2, w h e r e a(0) i s the attenuation c o e f f i c i e n t at z e r o field. A a / a (0) t a k e s a m a x i m u m v a lu e a l i t t l e above * On leave from Tokyo College of Science. 414
1.2 1.0 a( H) a(H=0)
0.8 0.6 0"4f 0.2 0o
011
012
0.3
014
015
0'.6 0.7 Happl./Hc~
Fig. 1. Relative attenuation coefficient ot(H)/a(0) plotted against the reduced applied field Happl/Hc2 at 4.2°K for longitudinal wave parallel to H : He2 (4.2) = 2720 Oe; o 30 Me/s; • 50 Me/s. 4.2°K. A s i t s e l f , h o w e v e r , i n c r e a s e s with r a i s ing t e m p e r a t u r e . The dip was a l s o found when the e x t e r n a l f i el d was applied in the p e r p e n d i c u l a r d i r e c t i o n to the wave v e c t o r , and A ~ / a ( 0 ) b e h a v e s s i m i l a r l y a s in the f o r e g o i n g c a s e . The dip was found even f o r t r a n s v e r s e w a v e s and Aot/or(0) i s n e a r l y equal to that f o r longitudinal wave s. As the s a m p l e b e c o m e s m o r e i m p u r e , the a n o m a l y t en d s to d i s a p p e a r . F o r i n s t a n c e , no dip was found when the s a m p l e was oxidized, of whose r e s i s t a n c e r a t i o was l o w e r e d to 200, or & ~ / ~ ( 0 ) d e c r e a s e d by 10% when it was c o l d worked by c o m p r e s s i o n of about 3%. I m p u r i t y
Volume 22, number 4
PHYSICS LETTERS
1 September 1966
1.0
I£
0.8
0.@
0.6
0.6 ~a
Qs
a( H =0)
",..~
~
0.4
0.4
0.2
02
0'.2
0.4
0.6 T/Tc
0.8
1.0
Fig.2. Relative depth of the dip Ao~/CI(H=0) plotted against the reduced temperature T/T c : A~ = ~(H)min - Ol(H= 0); 30 Me/s; Tc = 9.2°K. a t o m s such a s oxygen give m o r e d r a s t i c e f f e c t s on AOt/a (0) than d i s l o c a t i o n s . The r a t i o of the attenuation c o e f f i c i e n t s a s / a n b e h a v e s p e c u l i a r l y not only in the m a g n e t i c f i e l d a s stated above but a l s o in no m a g n e t i c field. In fig. 3, the r e l a t i v e attenuation at z e r o f i e l d i s plotted a g a i n s t the r e d u c e d t e m p e r a t u r e , w h e r e the m a g n e t o r e s i s t i v e e f f e c t in a n i s n e g l i g i b l e . The r e s u l t f o r i m p u r e n i o b i u m , whose r e s i s t a n c e r a t i o i s about 200, can be d e s c r i b e d well with the BCS t h e o r y [4], taking 2e(0) = 3.5 k T c , but the r e s u l t f o r p u r e one d e v i a t e s f r o m the t h e o r e t i c a l va l ue a s shown in fig. 3. T h i s d e v i a t i o n f r o m the BCS t h e o r y i s often o b s e r v e d in o t h e r e l e m e n t s and s o m e t i m e s it i s a t t r i b u t e d to the s m a l l ql [5-9]. But in our niobium, the d e v ia ti o n b e c o m e s l a r g e a s the s a m p l e b e c o m e s p u r e r , so t h i s can not be a t t r i b u t e d to the s m a l l ql. It should be n e c e s s a r y f o r the u n d e r s t a n d i n g of the p r e s e n t p h e n o m e n a to have m o r e p r e c i s e k n o w l e d g e s of the at t e n u a t io n of sound w a v e s in the m i x e d state a s well a s at z e r o field. The l a t t e r f a c t m a y not e x c l u d e a c o m p l e x i t y due to the p r e s e n c e of m u l t i - g a p s [10,11] or an a n i s o t r o p i c e n e r g y band in n i o b i u m [5,12]. T he p r e s e n t a u t h o r s a r e indebted to D r . Y . Wada, Tokyo U n i v e r s i t y and D r . T. Sota, Tokyo U n i v e r s i t y of E d u c a t i o n , f o r t h e i r d i s c u s s i o n and M r . M a t s u m o t o f o r h i s help throughout the p r e s e n t e x p e r i m e n t . They a r e a l s o g r a t e f u l to P r o f . Y a s u kochi and M r . O g a s a w a r a , Nihon U n i v e r s i t y , f o r
I
0.2
0.4
r/r~
0.6
0.8
1.0
Fig. 3. Relative attenuation ots/0t n plotted against the reduced temperature T/Tc: For black circles, a n is the absorption coefficient at H = 5600 Oe; for white circles, correction is made for the magneto-resistive effect. Curve 1 and curve 2 represent the BCS relation with 2E(0)=3.5 kT c and 2E(0)=4.4 kTe respectively. the m e a s u r e m e n t s of the r e s i s t a n c e r a t i o s . A f t e r the p r e s e n t w r i t t i n g , we n o t i c e d s i m i l a r r e s u l t s on the d e c r e a s e in the attenuation n e a r H c l obtained r e c e n t l y by F o r g a n and Gough [13]. T h e i r r e s u l t s s e e m to a g r e e q u a l i t a t i v e l y with ours.
References 1. A.Ikushima, M.Fujii and T.Suzuki, J. Phys. Chem, Solids 27 (1966) 327. 2. V.L.Ginzberg, Soviet Physiscs JETP 3 (1956) 621. 3. K.Maki, Physics 1 (1964) 21. 4. J.Bardeen, L.N. Cooper and J.R.Sehrieffer, Phys. Rev. 108 (1957) 1175. 5. E.R.Dobbs and J . M . P e r z , Rev. Mod. Phys. 36 (1964) 257. 6. R.Weber, Phys. Rev. 133 ~1964) A1487. 7. T.Tsuneto, Phys. Rev. 121 (1961) 402. 8. M. Levy and I.Rudnick, Phys. Rev. 132 (1963) 1073. 9. B.C.Deaton, Phys. Rev. Letters 16 (1966) 577. i0. H.Suhl, B.T.Matthiss and L.R.Walker, Phys. Rev. Letters 3 (1959) 552. 11. L. Y. L. Shen, N.M. Senozan and N. E. Phillips, Phys. Rev. Letters 14 (1965) 1025. 12. V. L. Pokrovskii, Soviet Phys. JETP 12 (1961) 628. 13. E. M. Forgan and C. E. Gough, Phys. Letters 21 (1966) 133.
415
PHYSICS LETTERS
ANOMALOUS ATTENUATION OF IN SUPERCONDUCTING
1 September 1966
ULTRASONIC NIOBIUM
WAVES
N. TSUDA, S. KOIKE* and T. SUZUKI
Institute for Solid State Physics, University of Tokyo, Tokyo, Japan Received 26 July 1966
Anomalous absorption at H c l and a deviation of the temperature variation of a s / a n from the BCS relation have been found in the measurements of the ultrasonic attenuation in superconducting niobium.
In the c o u r s e of s t u d i e s of u l t r a s o n i c a t t e n u a tion of pure niobium following the p r e v i o u s work [1], an a n o m a l o u s a b s o r p t i o n h a s been found at a l i t t l e above the l o w e r c r i t i c a l f i e l d H c l , a s will d e s c r i b e d below. A s a m p l e i s about 6 m m q5 and 8 m m long c y l i n d e r , which was o u t g a s s e d at about 1700°C f o r two weak s in a v a c u u m of 3 x 10 -9 m m H g . The r e s i s t a n c e r a t i o was m e a s u r e d to be about 400 by an eddy c u r r e n t d a m p in g method. The t e m p e r a t u r e dependence of Hc2 obeys G i n z b u r g ' s f o r m u l a b a s e d on the two fluid m o d e l [2]; Hc(t) = Hc(0) (1 - t 2 ) / ( 1 +t2), w h e r e t i s the r e d u ced t e m p e r a t u r e . F o r t h i s s a m p l e , Hc2(0) = = 4228 Oe and Hc2(4.2) = 2720 Oe. K2 i s a l s o e x p r e s s e d a p p r o x i m a t e l y by the two fluid m o d e l as K(t) = 2K(0)/(1 + t2), which d o e s not d i s t i n g u i s h K1 f r o m K2 [3], h o w e v e r . K2(0) was 2.2 + 0.1, taking the a v e r a g e of the s l o p e s o f the m a g n e t i z a tion n e a r Hc2 f o r i n c r e a s i n g and d e c r e a s i n g field. U l t r a s o n i c attenuation was m e a s u r e d f o r longitudinal w a v e s of 30 and 50 M c / s e c , and so it would be taken a s ql << 1, w h e r e q i s the wave v e c t o r and l the m e a n f r e e path. Fig.1 i l l u s t r a t e s the f i e l d dependence of the r e l a t i v e attenuation a(H)/(a(H= 0)), w h e r e the m a g n e t i c f i e l d was applied p a r a l l e l to q. The r a t i o shows a f a i r l y a b r u p t d e c r e a s e j u s t above the l o w e r c r i t i c a l f i e l d then i n c r e a s e s g r a d u a l l y . The bottom of t h i s dip l o c a t e s at a f i el d w h e r e the m a g n e t i z a t i o n of the s a m p l e ch an g es m o s t s t e e p l y . When the f i e l d d e c r e a s e s f r o m above the u p p e r c r i t i c a l field, a slight h y s t e r e s i s a p p e a r s and the attenuation c o e f f i c i e n t does not i n c r e a s e s abruptly at H c l . The depth of the dip A s = a(0) - ~(H)min i s pl ott e d a g a i n s t t e m p e r a t u r e in fig. 2, w h e r e a(0) i s the attenuation c o e f f i c i e n t at z e r o field. A a / a (0) t a k e s a m a x i m u m v a lu e a l i t t l e above * On leave from Tokyo College of Science. 414
1.2 1.0 a( H) a(H=0)
0.8 0.6 0"4f 0.2 0o
011
012
0.3
014
015
0'.6 0.7 Happl./Hc~
Fig. 1. Relative attenuation coefficient ot(H)/a(0) plotted against the reduced applied field Happl/Hc2 at 4.2°K for longitudinal wave parallel to H : He2 (4.2) = 2720 Oe; o 30 Me/s; • 50 Me/s. 4.2°K. A s i t s e l f , h o w e v e r , i n c r e a s e s with r a i s ing t e m p e r a t u r e . The dip was a l s o found when the e x t e r n a l f i el d was applied in the p e r p e n d i c u l a r d i r e c t i o n to the wave v e c t o r , and A ~ / a ( 0 ) b e h a v e s s i m i l a r l y a s in the f o r e g o i n g c a s e . The dip was found even f o r t r a n s v e r s e w a v e s and Aot/or(0) i s n e a r l y equal to that f o r longitudinal wave s. As the s a m p l e b e c o m e s m o r e i m p u r e , the a n o m a l y t en d s to d i s a p p e a r . F o r i n s t a n c e , no dip was found when the s a m p l e was oxidized, of whose r e s i s t a n c e r a t i o was l o w e r e d to 200, or & ~ / ~ ( 0 ) d e c r e a s e d by 10% when it was c o l d worked by c o m p r e s s i o n of about 3%. I m p u r i t y
Volume 22, number 4
PHYSICS LETTERS
1 September 1966
1.0
I£
0.8
0.@
0.6
0.6 ~a
Qs
a( H =0)
",..~
~
0.4
0.4
0.2
02
0'.2
0.4
0.6 T/Tc
0.8
1.0
Fig.2. Relative depth of the dip Ao~/CI(H=0) plotted against the reduced temperature T/T c : A~ = ~(H)min - Ol(H= 0); 30 Me/s; Tc = 9.2°K. a t o m s such a s oxygen give m o r e d r a s t i c e f f e c t s on AOt/a (0) than d i s l o c a t i o n s . The r a t i o of the attenuation c o e f f i c i e n t s a s / a n b e h a v e s p e c u l i a r l y not only in the m a g n e t i c f i e l d a s stated above but a l s o in no m a g n e t i c field. In fig. 3, the r e l a t i v e attenuation at z e r o f i e l d i s plotted a g a i n s t the r e d u c e d t e m p e r a t u r e , w h e r e the m a g n e t o r e s i s t i v e e f f e c t in a n i s n e g l i g i b l e . The r e s u l t f o r i m p u r e n i o b i u m , whose r e s i s t a n c e r a t i o i s about 200, can be d e s c r i b e d well with the BCS t h e o r y [4], taking 2e(0) = 3.5 k T c , but the r e s u l t f o r p u r e one d e v i a t e s f r o m the t h e o r e t i c a l va l ue a s shown in fig. 3. T h i s d e v i a t i o n f r o m the BCS t h e o r y i s often o b s e r v e d in o t h e r e l e m e n t s and s o m e t i m e s it i s a t t r i b u t e d to the s m a l l ql [5-9]. But in our niobium, the d e v ia ti o n b e c o m e s l a r g e a s the s a m p l e b e c o m e s p u r e r , so t h i s can not be a t t r i b u t e d to the s m a l l ql. It should be n e c e s s a r y f o r the u n d e r s t a n d i n g of the p r e s e n t p h e n o m e n a to have m o r e p r e c i s e k n o w l e d g e s of the at t e n u a t io n of sound w a v e s in the m i x e d state a s well a s at z e r o field. The l a t t e r f a c t m a y not e x c l u d e a c o m p l e x i t y due to the p r e s e n c e of m u l t i - g a p s [10,11] or an a n i s o t r o p i c e n e r g y band in n i o b i u m [5,12]. T he p r e s e n t a u t h o r s a r e indebted to D r . Y . Wada, Tokyo U n i v e r s i t y and D r . T. Sota, Tokyo U n i v e r s i t y of E d u c a t i o n , f o r t h e i r d i s c u s s i o n and M r . M a t s u m o t o f o r h i s help throughout the p r e s e n t e x p e r i m e n t . They a r e a l s o g r a t e f u l to P r o f . Y a s u kochi and M r . O g a s a w a r a , Nihon U n i v e r s i t y , f o r
I
0.2
0.4
r/r~
0.6
0.8
1.0
Fig. 3. Relative attenuation ots/0t n plotted against the reduced temperature T/Tc: For black circles, a n is the absorption coefficient at H = 5600 Oe; for white circles, correction is made for the magneto-resistive effect. Curve 1 and curve 2 represent the BCS relation with 2E(0)=3.5 kT c and 2E(0)=4.4 kTe respectively. the m e a s u r e m e n t s of the r e s i s t a n c e r a t i o s . A f t e r the p r e s e n t w r i t t i n g , we n o t i c e d s i m i l a r r e s u l t s on the d e c r e a s e in the attenuation n e a r H c l obtained r e c e n t l y by F o r g a n and Gough [13]. T h e i r r e s u l t s s e e m to a g r e e q u a l i t a t i v e l y with ours.
References 1. A.Ikushima, M.Fujii and T.Suzuki, J. Phys. Chem, Solids 27 (1966) 327. 2. V.L.Ginzberg, Soviet Physiscs JETP 3 (1956) 621. 3. K.Maki, Physics 1 (1964) 21. 4. J.Bardeen, L.N. Cooper and J.R.Sehrieffer, Phys. Rev. 108 (1957) 1175. 5. E.R.Dobbs and J . M . P e r z , Rev. Mod. Phys. 36 (1964) 257. 6. R.Weber, Phys. Rev. 133 ~1964) A1487. 7. T.Tsuneto, Phys. Rev. 121 (1961) 402. 8. M. Levy and I.Rudnick, Phys. Rev. 132 (1963) 1073. 9. B.C.Deaton, Phys. Rev. Letters 16 (1966) 577. i0. H.Suhl, B.T.Matthiss and L.R.Walker, Phys. Rev. Letters 3 (1959) 552. 11. L. Y. L. Shen, N.M. Senozan and N. E. Phillips, Phys. Rev. Letters 14 (1965) 1025. 12. V. L. Pokrovskii, Soviet Phys. JETP 12 (1961) 628. 13. E. M. Forgan and C. E. Gough, Phys. Letters 21 (1966) 133.
415