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Temperature dependence of the lower critical field under the effect of surface barriers in Bi2Sr2CaCu2O8 crystal
Ill
Physica C 199 (1992) 32-36 North-Holland
Temperature dependence of the lower critical field under the effect of surface barriers in Bi2Sr2CaCu208 crystal N. C h i k u m o t o 1 a n d M. K o n c z y k o w s k i Laboratoire des Solides Irradi~s, Ecole Polytechnique, 91128 Palaiseau, France N. M o t o h i r a a n d K. K i s h i o Department of Industrial Chemistry, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan Received 12 June 1992
The magnetization properties of Bi-2212 single crystals were measured by local Hall probe magnetometry (LHPM). Features characteristic of the Bean-Livingston surface barrier were observed. The lower critical field Hc~ was determined by considering the effect of the surface barrier on the magnetization. The temperature variation of Hemshows saturation at low temperature which is consistent with the prediction based on the BCS theory.
1. Introduction The determination o f the lower critical field Hc~ has been a challenging and controversial problem from the early stage o f high-temperature superconductivity ( H T S C ) research. Reported values of H~ are extremely scattered over a wide range but the most striking feature is the anomalous temperature dependence o f H¢~. In m a n y cases, a well pronounced up-turn in the T versus H¢~ curve was observed at low temperature [ 1-6 ] in contrast to the predictions from the BCS theory. Even more complicated features such as a down-turn close to Tc have been reported [ 6 - 8 ] . Several methods have been proposed to extract the value of H cl from magnetization curves [ 9-11 ]. Most o f them are based on the detection of the first deviation from an ideal Meissner state within the framework o f Bean's critical state model [ 12 ]. It is well known that there is a surface barrier [ 13,14 ] impeding the vortex penetration and this effect is expected to become pronounced in the case o f high-x superconductors. McElfresh et al. [4 ] and
On leave from University of Tokyo.
Kopylov et al. [ 5 ] suggested that the low-temperature up-turn o f He1 in HTSC was due to the temperature dependence of the surface barrier. Recently it was clearly demonstrated in untwinned YBaECU307 single crystals, that the first magnetic penetration was limited by the Bean-Livingston (BL) surface barrier and it caused the down-turn in the T versus H~I curves near T~ as well [ 7,8,15,16 ]. They also showed that the low temperature up-turn in He1 was due to the use of an inappropriate model in determining Hcl and proposed a new model [ 17 ] which accounts for the efficiency o f the surface barrier. In this paper we present precise magnetic measurements of BiESrECaCu208single crystals for a field parallel to the crystal c-axis. We demonstrate evidence of the significant role of the surface barrier in the present system and derived the value of H¢I considering its effect.
2. Experimental Single crystals o f Bi2Sr2CaCu2Os o f Tc ~ 87 K were grown by the floating zone method from a sintered feed rod prepared from high purity starting oxides and carbonates with a nominal composition of
0921-4534/92/$05.00 © 1992 Elsevier Science Publishers B.V. All fights reserved.
N. Chikumoto et al. / Temperature dependence of lower critical field
Bi2 zSrLsCaCu208. Details of crystal growth and its characterization are described in ref. [ 18 ]. The crystals are rectangular platelets parallel to the a, b-plane, while the c-axis was along the thin direction. In this experiment we used a crystal with dimension of 1.0× 1.0×0.093 m m 3, which was carefully cleaved and cut from a large boule. Magnetic measurements were performed by a noncommercial local Hall probe magnetometer (LHPM) with a typical active area of 8 0 × 100 ~tm2 [19]. LHPM provides a temperature independent sensitivity below 120 K, with a value of about 50 m f U Oe. The probe was placed directly on the sample surface and measured the local field. We define the difference between measured field and applied field as the surface stray field H~, which is proportional to the surface persistent current. As we have two pairs of contacts of the Hall sensor, we could detect the field distribution on the sample surface. All of the magnetization curves presented here were recorded by the sensor placed at the center of the sample surface. The external magnetic field Ha was applied parallel to the c-axis. The demagnetization factor D for the sample with this configuration was calculated to be D ~ 0.87 using an ellipsoidal approximation [20 ], which was consistent with the value derived from zero-field-cooled magnetization data measured with a SQUID magnetometer.
3. Results and discussion
3.1. The evidence of the surface barrier An example of a zero-field-cooled (ZFC) magnetization curve measured at T = 70 K is shown in fig. l with open circles. The sharp kink at Ha ~, 9 0 e in the field increasing branch shows the first flux penetration field Hp and its sharpness indicates the weak contribution of bulk pinning and the good quality of the crystal. On the high field portion of the descending branch, quite a distinct Ha-Hs dependence was observed. Namely, this region shows a flat variation with Hs ~ 0. This is the characteristic feature of the Bean-Livingston surface barrier [ 21 ]. It is known that the BL surface barrier to the vortex motion, which causes the retardation of the flux
33
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_o
a
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°°oo o °
oaa o o a ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° o
0
N -4 T=70 K H//c
-6
a
0
5
10
15 20 H a (Oe)
25
30
Fig. 1. Magnetization curves measured at T = 70 K, ( O ) zerofield-cooled magnetization curve, ( O ) isothermal remanent magnetization (REM); solid line : a fit with the equation Hs = ( H 2 - H p 2) 1/2 - H .
entry below Hp( > Hc~ ), arises from the competition between Lorentz force from the Meissner surface current and the image force. At Hp vortex starts to penetrate the sample. Clem [ 22 ] calculated the magnetization M above Hp to be M = ( H 2 - H 2) '/2-H. From this formula, we can expect a very sharp kink at Hp. The solid line in fig. 1 shows the fitting curve using this formula, and it seems to fit the observed curve reasonably well. On decreasing the field, there is always an effective barrier preventing the vortex to exit the superconductor, until M reaches a positive value [ 21 ]. We also measured the isothermal remanent magnetization (REM) as a function of Ha. REM was obtained by turning off the applied field. The result is shown in fig. 1 with solid circles. It is found that there is almost no flux entry until Ha reaches Hp. Above Hp, REM immediately saturates to a maximum value in contrast to the gradual saturation expected under the conventional Bean's critical state model. Instead, the present feature is in accord with the surface barrier mechanism with negligible bulk pinning. Kishio et al. [23 ] reported that there is no sample size dependence of the hysteresis at temperatures above 30 K, indicating the irreversible magnetization was possibly caused by the surface barrier in the absence of bulk pinning. When the temperature was lowered, the hysteresis loop became more like the Bean model behaviour with broadened kinks, as shown in fig. 2. Here we
34
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(b) also observed a rapid rise of the field gradient, which was deduced by means of two Hall sensors, and this indicates the increase of bulk pinning.
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3.2. The temperature variation of Hal In order to determine the first penetration field Hp from the magnetization curve, we need to find the point where the deviation from perfect diamagnetism starts. At high temperatures above 40 K, where the bulk pinning is negligible, Hp was determined mainly from the position of the kink in the zero-field-cooled magnetization curve. At the same time we measured REM and made a cross-check for the value from the onset of REM. As shown in fig. 1, the position of the kink in the ZFC magnetization curve coincided with the onset of REM. It should be mentioned that the position of the kink was independent of the Hall probe position. When the temperature was lowered to below 40 K, it became ~luite difficult to identify Hp, since the kink was smeared by the effect of strong bulk pinning (fig. 3 (a)). According to the conventional Bean's critical state model, the amount of the deviation from perfect diamagnetism, AH~, is expected to be proportional to (Ha-H~I)2 [ 10,11 ]. Thus it is used to determine H~ by extrapolating the linear part of AH~/2 to zero as a function of applied field Ha. But as mentioned in section 3. l., the Bean-Livingston barrier is observed to be effective in this system. We assume that the vortices penetrate from a few points
00
•
~100
200
300
Ha(Oe) Fig. 3. (a) The magnetization curve recorded at T=20 K (0) and the deviation fromperfect diamagnetismAH, ( • ). (b) The field dependenceof/2kH~/2 ( O ) and AH~/3 ( • ). like surface irregularities, where the effect of the surface barrier is weakened, and penetrated vortices spread into the sample from this point under the effect of a pinning force. In such a case, Burlachkov et al. [ 17] have recently shown that 8H~ grows as (Ha-Hc~)3 instead of (Ha-Hd)2. Thus by extrapolating (AH~)~/3 to zero we can get the value of Hc~. In fig. 3(b) we show the field dependence of (AHs) 1/2 and (AHs) 1/3. We can see that the (AH~) 1/3 versus Ha plot agrees with a linear fir over a wider range of Ha. This implies the determination of H¢~ by extrapolating (AH,) t/3 to zero is more suitable in this case. The temperature variation of H~t obtained in this study is shown in fig. 4. At temperatures above 40 K, the value was determined from the kink (open circles). It is important to mention that the value de-
N. Chikumoto et al. I Temperature dependence of lower critical field 60
. , . , . , . , . , , , . ~ . , .
50 two-fluid model
40
30 ~
35
Acknowledgements
We w o u l d like to t h a n k K. K i t a z a w a , Y. Y e s h u r u n and A.P. M a l o z e m o f f for v e r y useful discussions. N C w o u l d like to a p p r e c i a t e the h o s p i t a l i t y o f colleagues in the Ecole P o l y t e c h n i q u e .
20 10 0
References
H//c ,
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I
,
I
20
,
I
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40 T (K)
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Fig. 4. The temperature variation of Her; The demagnetization factor for the sample is D=0.87. (O) The value derived from the position of the kink, ( 0 ) the value derived from a (AHs) '/3 -,0 extrapolation. The solid line is the fit to the BCS clean limit, while the dashed line is the fit to the two-fluid model. t e r m i n e d by this p r o c e d u r e is a c t u a l l y Hp. But we c o n s i d e r h e r e t h e d i f f e r e n c e b e t w e e n Hp a n d He, is small b e c a u s e o f t h e i m p e r f e c t i o n o f t h e s a m p l e surface a n d p l o t t e d the v a l u e o f l i p as H~1. At low t e m p e r a t u r e s b e l o w 40 K, w h e r e the effect o f the b u l k p i n n i n g b e c o m e s significant, t h e v a l u e was determ i n e d by a (AHs)1/3--*0 e x t r a p o l a t i o n ( s o l i d circles). A c c o r d i n g to the G i n z b u r g - L a n d a u theory, H ~ is r e l a t e d to the p e n e t r a t i o n depth ;t as H~l ~ ~ o ( 4 n 2 2 ) - q n x. T h o u g h t h e r e are o n l y few reliable i n v e s t i g a t i o n s o f t h e t e m p e r a t u r e d e p e n d e n c e o f ; t in this system, the d a t a o b t a i n e d f r o m IxSR m e a surement [24] showed the BCS-form with the weak c o u p l i n g l i m i t r a t h e r t h a n the t w o - f l u i d f o r m ( 2 - 2 o z l - t 4 ) . T h i s result is in a c c o r d a n c e w i t h o u r result. T h e d e d u c e d v a l u e o f H ~ ( T = 0 ) was a b o u t 340 O e by t a k i n g the d e m a g n e t i z a t i o n f a c t o r as D=0.87.
4. C o n c l u s i o n T h e e v i d e n c e for B e a n - L i v i n g s t o n surface b a r r i e r s in the high quality Bi2Sr2CaCu208 single crystals were p r e s e n t e d . T h e l o w e r critical field Hc~ was determ i n e d a c c o u n t i n g for the effect o f t h e surface b a r r i e r and bulk pinning. The obtained temperature variat i o n o f H¢~ s h o w e d t h e B C S - l i k e low t e m p e r a t u r e saturation.
[ 1 ] B. Batlogg, T.T.M. Palstra, L.F. Schneemeyer, R.B. van Dover and R.J. Cava, Physica C 153-155 (1988) 1062. [2] A.A. Zhukov, V.V. Moshalkov, A.A. Bush, I.V. Gladyshev, S.N. Gordeyev, S.E. Mrost, A.S. Sigov and Yu.V. Titov, Physica C 162-164 (1989) 1631. [3 ] A. Umezawa, G.W. Crabtree, K.G. Vandervoort, U. Welp, W.K. Kwok and J.Z. Liu, Physica C 162-164 ( 1989 ) 733. [4] M.W. McElfresh, Y. Yeshurun, A.P. Malozemoff and F. Holzberg, Physica A 168 (1990) 308. [5]V.N. Kopylov, A.E. Koshelev, I.F. Schegolev and T.G. Togonidze, Physica C 170 (1990) 291. [6] N. Chikumoto, M. Konczykowski, N. Motohira, K. Kishio and K. Kitazawa, Physica C 185-189 ( 1991 ) 1835. [7] M. Konczykowski, L.I. Burlachkov, Y. Yeshurun and F. Holzberg, Phys. Rev. B 43 ( 1991 ) 13707. [8] L. Burlachkov, M. Konczykowski, Y. Yeshurun and F. Holtzberg, J. Appl. Phys. 70 ( 1991 ) 5759. [9]L. Krusin-Elbaum, A.P. Malozemoff and G.V. Chandrasekhar, Physica C 162-164 ( 1989 ) 1553. [ 10 ] M. Naito, A. Matsuda and K. Kitazawa, Phys. Rev. B 41 (1990) 4823. [ 11 ] V.V. Moshchalkov, J.Y. Henry, C. Martin, J. Rossat-Mignod and J.F. Jacquot, Physica C 175 ( 1991 ) 407. [ 12] C.P. Bean, Rev. Mod. Phys. 36 (1964) 31. [ 13 ] C.P. Bean and J.D. Livingston, Phys. Rev. Lett. 12 (1964) 14. [ 14] P.G. de Gennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966) p. 76. [15]M. Konczykowski, L.I. Burlachkov, Y. Yeshurun and F. Holzberg, Physica C 194 ( 1991 ) 155. [ 16 ] M. Konczykowski, in: Critical Current Limitation in High Temperature Superconductors (World Scientific, Singapore, 1992) p. 152. [ 17] L. Burlachkov, Y. Yeshurun, M. Konczykowski nd F. Holtzberg, Phys. Rev. B 45 (1992) 8193. [ 18 ] N. Motohira, K. Kuwahara, T. Hasegawa, K. Kishio and K. Kitazawa, J. Ceram. Soc. Jpn. Int. Ed. 97 (1989) 994. [ 19] M. Konczykowski, F. Holtzberg and P. Lejay, Supercond. Sci. Technol. 4 (1991) $331. [20] J.A. Osborn, Phys. Rev. 67 (1945) 351. [21]A.M. Campbell and J.E. Evetts, Critical Currents in Superconductors (Taylor and Francis, London, 1972). [ 22 ] J.R. Clem, in: Low Temperature Physics-LT 13, vol. 3, eds. K.D. Timmerhaus, W.J. O'Sullivan and E.F. Hammel (Plenum, New York, 1974)p. 102.
36
N. Chikumoto et al. / Temperature dependence of lower criticalfield
[23] K. Kishio, S. Komiya, N. Motohira, K. Kitazawa and K. Yamafuji, Physica C 185-189 ( 1991 ) 2383. [24]M. Weber, A. Amato, P. Birrer, V.N. Duginov, V.G. Grebinnik, F.N. Gygax, S. Kapusta, B.F. Kirillov, E. Lippelt,
H. Maletta, V.G. Olshevsky, A.V. Pirogov, V.Yu. Pomjakushin, A.N. Ponomarev, A. Schenck, V.G. Storchak and V.A. Zhukov, Supercond. Sci. Technol. 4 ( 1991 ) $403.
Physica C 199 (1992) 32-36 North-Holland
Temperature dependence of the lower critical field under the effect of surface barriers in Bi2Sr2CaCu208 crystal N. C h i k u m o t o 1 a n d M. K o n c z y k o w s k i Laboratoire des Solides Irradi~s, Ecole Polytechnique, 91128 Palaiseau, France N. M o t o h i r a a n d K. K i s h i o Department of Industrial Chemistry, University of Tokyo, Bunkyo-ku, Tokyo 113, Japan Received 12 June 1992
The magnetization properties of Bi-2212 single crystals were measured by local Hall probe magnetometry (LHPM). Features characteristic of the Bean-Livingston surface barrier were observed. The lower critical field Hc~ was determined by considering the effect of the surface barrier on the magnetization. The temperature variation of Hemshows saturation at low temperature which is consistent with the prediction based on the BCS theory.
1. Introduction The determination o f the lower critical field Hc~ has been a challenging and controversial problem from the early stage o f high-temperature superconductivity ( H T S C ) research. Reported values of H~ are extremely scattered over a wide range but the most striking feature is the anomalous temperature dependence o f H¢~. In m a n y cases, a well pronounced up-turn in the T versus H¢~ curve was observed at low temperature [ 1-6 ] in contrast to the predictions from the BCS theory. Even more complicated features such as a down-turn close to Tc have been reported [ 6 - 8 ] . Several methods have been proposed to extract the value of H cl from magnetization curves [ 9-11 ]. Most o f them are based on the detection of the first deviation from an ideal Meissner state within the framework o f Bean's critical state model [ 12 ]. It is well known that there is a surface barrier [ 13,14 ] impeding the vortex penetration and this effect is expected to become pronounced in the case o f high-x superconductors. McElfresh et al. [4 ] and
On leave from University of Tokyo.
Kopylov et al. [ 5 ] suggested that the low-temperature up-turn o f He1 in HTSC was due to the temperature dependence of the surface barrier. Recently it was clearly demonstrated in untwinned YBaECU307 single crystals, that the first magnetic penetration was limited by the Bean-Livingston (BL) surface barrier and it caused the down-turn in the T versus H~I curves near T~ as well [ 7,8,15,16 ]. They also showed that the low temperature up-turn in He1 was due to the use of an inappropriate model in determining Hcl and proposed a new model [ 17 ] which accounts for the efficiency o f the surface barrier. In this paper we present precise magnetic measurements of BiESrECaCu208single crystals for a field parallel to the crystal c-axis. We demonstrate evidence of the significant role of the surface barrier in the present system and derived the value of H¢I considering its effect.
2. Experimental Single crystals o f Bi2Sr2CaCu2Os o f Tc ~ 87 K were grown by the floating zone method from a sintered feed rod prepared from high purity starting oxides and carbonates with a nominal composition of
0921-4534/92/$05.00 © 1992 Elsevier Science Publishers B.V. All fights reserved.
N. Chikumoto et al. / Temperature dependence of lower critical field
Bi2 zSrLsCaCu208. Details of crystal growth and its characterization are described in ref. [ 18 ]. The crystals are rectangular platelets parallel to the a, b-plane, while the c-axis was along the thin direction. In this experiment we used a crystal with dimension of 1.0× 1.0×0.093 m m 3, which was carefully cleaved and cut from a large boule. Magnetic measurements were performed by a noncommercial local Hall probe magnetometer (LHPM) with a typical active area of 8 0 × 100 ~tm2 [19]. LHPM provides a temperature independent sensitivity below 120 K, with a value of about 50 m f U Oe. The probe was placed directly on the sample surface and measured the local field. We define the difference between measured field and applied field as the surface stray field H~, which is proportional to the surface persistent current. As we have two pairs of contacts of the Hall sensor, we could detect the field distribution on the sample surface. All of the magnetization curves presented here were recorded by the sensor placed at the center of the sample surface. The external magnetic field Ha was applied parallel to the c-axis. The demagnetization factor D for the sample with this configuration was calculated to be D ~ 0.87 using an ellipsoidal approximation [20 ], which was consistent with the value derived from zero-field-cooled magnetization data measured with a SQUID magnetometer.
3. Results and discussion
3.1. The evidence of the surface barrier An example of a zero-field-cooled (ZFC) magnetization curve measured at T = 70 K is shown in fig. l with open circles. The sharp kink at Ha ~, 9 0 e in the field increasing branch shows the first flux penetration field Hp and its sharpness indicates the weak contribution of bulk pinning and the good quality of the crystal. On the high field portion of the descending branch, quite a distinct Ha-Hs dependence was observed. Namely, this region shows a flat variation with Hs ~ 0. This is the characteristic feature of the Bean-Livingston surface barrier [ 21 ]. It is known that the BL surface barrier to the vortex motion, which causes the retardation of the flux
33
eoaaaooaoooDooooooao 2
_o
a
REM
°°oo o °
oaa o o a ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° ° o
0
N -4 T=70 K H//c
-6
a
0
5
10
15 20 H a (Oe)
25
30
Fig. 1. Magnetization curves measured at T = 70 K, ( O ) zerofield-cooled magnetization curve, ( O ) isothermal remanent magnetization (REM); solid line : a fit with the equation Hs = ( H 2 - H p 2) 1/2 - H .
entry below Hp( > Hc~ ), arises from the competition between Lorentz force from the Meissner surface current and the image force. At Hp vortex starts to penetrate the sample. Clem [ 22 ] calculated the magnetization M above Hp to be M = ( H 2 - H 2) '/2-H. From this formula, we can expect a very sharp kink at Hp. The solid line in fig. 1 shows the fitting curve using this formula, and it seems to fit the observed curve reasonably well. On decreasing the field, there is always an effective barrier preventing the vortex to exit the superconductor, until M reaches a positive value [ 21 ]. We also measured the isothermal remanent magnetization (REM) as a function of Ha. REM was obtained by turning off the applied field. The result is shown in fig. 1 with solid circles. It is found that there is almost no flux entry until Ha reaches Hp. Above Hp, REM immediately saturates to a maximum value in contrast to the gradual saturation expected under the conventional Bean's critical state model. Instead, the present feature is in accord with the surface barrier mechanism with negligible bulk pinning. Kishio et al. [23 ] reported that there is no sample size dependence of the hysteresis at temperatures above 30 K, indicating the irreversible magnetization was possibly caused by the surface barrier in the absence of bulk pinning. When the temperature was lowered, the hysteresis loop became more like the Bean model behaviour with broadened kinks, as shown in fig. 2. Here we
34
N. Chikumoto et al. / Temperature dependence of lower critical fieM
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(b) also observed a rapid rise of the field gradient, which was deduced by means of two Hall sensors, and this indicates the increase of bulk pinning.
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3.2. The temperature variation of Hal In order to determine the first penetration field Hp from the magnetization curve, we need to find the point where the deviation from perfect diamagnetism starts. At high temperatures above 40 K, where the bulk pinning is negligible, Hp was determined mainly from the position of the kink in the zero-field-cooled magnetization curve. At the same time we measured REM and made a cross-check for the value from the onset of REM. As shown in fig. 1, the position of the kink in the ZFC magnetization curve coincided with the onset of REM. It should be mentioned that the position of the kink was independent of the Hall probe position. When the temperature was lowered to below 40 K, it became ~luite difficult to identify Hp, since the kink was smeared by the effect of strong bulk pinning (fig. 3 (a)). According to the conventional Bean's critical state model, the amount of the deviation from perfect diamagnetism, AH~, is expected to be proportional to (Ha-H~I)2 [ 10,11 ]. Thus it is used to determine H~ by extrapolating the linear part of AH~/2 to zero as a function of applied field Ha. But as mentioned in section 3. l., the Bean-Livingston barrier is observed to be effective in this system. We assume that the vortices penetrate from a few points
00
•
~100
200
300
Ha(Oe) Fig. 3. (a) The magnetization curve recorded at T=20 K (0) and the deviation fromperfect diamagnetismAH, ( • ). (b) The field dependenceof/2kH~/2 ( O ) and AH~/3 ( • ). like surface irregularities, where the effect of the surface barrier is weakened, and penetrated vortices spread into the sample from this point under the effect of a pinning force. In such a case, Burlachkov et al. [ 17] have recently shown that 8H~ grows as (Ha-Hc~)3 instead of (Ha-Hd)2. Thus by extrapolating (AH~)~/3 to zero we can get the value of Hc~. In fig. 3(b) we show the field dependence of (AHs) 1/2 and (AHs) 1/3. We can see that the (AH~) 1/3 versus Ha plot agrees with a linear fir over a wider range of Ha. This implies the determination of H¢~ by extrapolating (AH,) t/3 to zero is more suitable in this case. The temperature variation of H~t obtained in this study is shown in fig. 4. At temperatures above 40 K, the value was determined from the kink (open circles). It is important to mention that the value de-
N. Chikumoto et al. I Temperature dependence of lower critical field 60
. , . , . , . , . , , , . ~ . , .
50 two-fluid model
40
30 ~
35
Acknowledgements
We w o u l d like to t h a n k K. K i t a z a w a , Y. Y e s h u r u n and A.P. M a l o z e m o f f for v e r y useful discussions. N C w o u l d like to a p p r e c i a t e the h o s p i t a l i t y o f colleagues in the Ecole P o l y t e c h n i q u e .
20 10 0
References
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~
80
Fig. 4. The temperature variation of Her; The demagnetization factor for the sample is D=0.87. (O) The value derived from the position of the kink, ( 0 ) the value derived from a (AHs) '/3 -,0 extrapolation. The solid line is the fit to the BCS clean limit, while the dashed line is the fit to the two-fluid model. t e r m i n e d by this p r o c e d u r e is a c t u a l l y Hp. But we c o n s i d e r h e r e t h e d i f f e r e n c e b e t w e e n Hp a n d He, is small b e c a u s e o f t h e i m p e r f e c t i o n o f t h e s a m p l e surface a n d p l o t t e d the v a l u e o f l i p as H~1. At low t e m p e r a t u r e s b e l o w 40 K, w h e r e the effect o f the b u l k p i n n i n g b e c o m e s significant, t h e v a l u e was determ i n e d by a (AHs)1/3--*0 e x t r a p o l a t i o n ( s o l i d circles). A c c o r d i n g to the G i n z b u r g - L a n d a u theory, H ~ is r e l a t e d to the p e n e t r a t i o n depth ;t as H~l ~ ~ o ( 4 n 2 2 ) - q n x. T h o u g h t h e r e are o n l y few reliable i n v e s t i g a t i o n s o f t h e t e m p e r a t u r e d e p e n d e n c e o f ; t in this system, the d a t a o b t a i n e d f r o m IxSR m e a surement [24] showed the BCS-form with the weak c o u p l i n g l i m i t r a t h e r t h a n the t w o - f l u i d f o r m ( 2 - 2 o z l - t 4 ) . T h i s result is in a c c o r d a n c e w i t h o u r result. T h e d e d u c e d v a l u e o f H ~ ( T = 0 ) was a b o u t 340 O e by t a k i n g the d e m a g n e t i z a t i o n f a c t o r as D=0.87.
4. C o n c l u s i o n T h e e v i d e n c e for B e a n - L i v i n g s t o n surface b a r r i e r s in the high quality Bi2Sr2CaCu208 single crystals were p r e s e n t e d . T h e l o w e r critical field Hc~ was determ i n e d a c c o u n t i n g for the effect o f t h e surface b a r r i e r and bulk pinning. The obtained temperature variat i o n o f H¢~ s h o w e d t h e B C S - l i k e low t e m p e r a t u r e saturation.
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