Thermodynamic fluctuation in doped BiSrCaCuO superconductors with 110K phase
2
Physica B 194-196 (1994) 1513-1514 North-Holland PHYSICA+ THERMODYNAMIC FLUCTUATION IN DOPED Bi-Sr-Ca-Cu-O SUPER- CONDUCTORS WITH ll0K PHASE S.H. Han and M.Andersson Department of Solid State Physics, The Royal Institute of Technology, S-100 44 Stockholm The resistivity has been carefully measured for four sintered samples of Pb and Pb/Sb doped Bi-Sr-Ca-Cu-O superconductors with the 110 K phase from zero resistance temperature up to 300 K. The thermodynamical fluctuation have been fitted on the form A~ x (e=(T-Tc)/Tc) in the regions -4 < In e < -2. By choosing T¢ in different ways, it is shown that consistent results only could be obtained when T~ is defined according to the Lawrence -Doniach theory. 1. INTRODUC~ON Recently the thermodynamic fluctuations of the superconducting order parameter have attracted much interest. The significant rounding of the resistance vs temperature, R(T), curve above the critical temperature, To, in high temperature superconductors, can be explained by thermodynamic fluctuations of the superconducting order parameter. In order to understand how the thermodynamic fluctuations are affected by secondary phases and impurities , four different ceramic Bi-based samples with impurity phases were studied. To clarify how the choice of Tc (the mean field critical temperature) affects the exponent in the fitting equation, Tc was defined in three different ways. It was found that in the temperature range considered the results are not much affected by the presence of the secondary phase, but the definition of T¢ is im pot tan t. 2. EXPERIMENTAL DETAILS Four Bi-Sr-Ca-Cu-O samples with 110 K phase were prepared by a standard solid state reaction. These samples are designated A, B, C and D. Sample characterization suggested D to be the best sample (almost single 2223 phase) and A to be the most impure one ( with 2223 and 1112 phase ). The experimental details were described in a previous paper (1). Electrical resistivity was measured with a standard four-probe method using low current densities (< 0.2 A/ cm 2 ). The measurements were performed in a flowing gas cryostat and the temperature was controlled to better than several mK. 3. RESULTS AND DISCUSSION Fig.1 shows the temperature dependence of the reduced electrical resistance for our four samples. The samples B, C and D 1.0 o, o ~ - I I I I I o J°e°QO 0.8 oooO • g O o ° o o° ~ 0~.,. +7 0.6 ** o4 y: / ~ • sample C 0.2 J ~ , sample D 0.0 / , _~ , , , 50 100 150 200 250 300 T(K) Fig.1 Normalized electrical resistance of samples A, B, C, D. The straight line is a guide for the eye, illustrating a straight fine extrapolation of normal state resistance through the origin. 0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E1337-L
Transcript of Thermodynamic fluctuation in doped BiSrCaCuO superconductors with 110K phase
Physica B 194-196 (1994) 1513-1514 North-Holland PHYSICA+
T H E R M O D Y N A M I C F L U C T U A T I O N I N D O P E D B i - S r - C a - C u - O S U P E R -
C O N D U C T O R S W I T H l l 0 K P H A S E
S.H. Han and M.Andersson
Department of Solid State Physics, The Royal Inst i tute of Technology, S-100 44 Stockholm
The resistivity has been carefully measured for four sintered samples of Pb and Pb/Sb doped Bi-Sr-Ca-Cu-O superconductors with the 110 K phase from zero resistance temperature up to 300 K. The thermodynamical fluctuation have been fitted on the form A ~ x (e=(T-Tc) /Tc) in the regions -4 < In e < -2. By choosing T¢ in different ways, it is shown that consistent results only could be obtained when T~ is defined according to the Lawrence -Doniach theory.
1. I N T R O D U C ~ O N
Recently the thermodynamic fluctuations of the superconducting order parameter have attracted much interest. The significant rounding of the resistance vs temperature, R(T), curve above the critical temperature, To, in high temperature superconductors, can be explained by thermodynamic fluctuations of the superconducting order parameter.
In order to understand how the thermodynamic fluctuations are affected by secondary phases and impurities , four different ceramic Bi-based samples with impurity phases were studied. To clarify how the choice of Tc (the mean field critical temperature) affects the exponent in the fitting equation, Tc was defined in three different ways. It was found that in the temperature range considered the results are not much affected by the presence of the secondary phase, but the definition of T¢ is im pot tan t.
2. E X P E R I M E N T A L DETAILS
Four Bi-Sr-Ca-Cu-O samples with 110 K phase were prepared by a standard solid state reaction. These samples are designated A, B, C and D. Sample characterization suggested D to be the best sample (almost single 2223 phase) and A to be the most impure one ( with 2223 and 1112 phase ).
The experimental details were described in a previous paper (1).
Electrical resistivity was measured with a standard four-probe method using low current densities (< 0.2 A/ cm 2 ). The measurements were performed in a flowing gas cryostat and the temperature was controlled to better than several mK.
3. RESULTS AND DISCUSSION
Fig.1 shows the temperature dependence of the reduced electrical resistance for our four samples. The samples B, C and D
1.0 o, o ~ - I I I I I o
J ° e ° Q O 0.8 oooO • g
O o °
o o ° ~ 0~.,. + 7
0.6 **
o4 y : / ~ • sample C
0.2 J ~ , sample D
0.0 / , _~ , , ,
50 100 150 200 250 300
T(K)
Fig.1 Normalized electrical resistance of samples A, B, C, D. The straight line is a guide for the eye, illustrating a straight fine extrapolation of normal state resistance through the origin.
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E1337-L
1 5 1 4
Table 1: The exponen t x as obtained from different definitions of Tc:
x A B C D
T ~ 107.0 107.0 107.0 109.6
Tg 108.4 107.4 107.3 108.4
Te mf 106.3 108.4 107.0 109.4
x (T m) -0.81 -1.38 -1.05 -0.96
x(Tc p) -0.65 - 1.27 - 1.03 - 1.13
x(T mr) -0.93 - 1.06 -1.05 -0.99
show a nearly linear tempera ture dependence between 160 K and 300 K with a linear extrapolat ion roughly to the origin. Sample A shows a nearly linear t empera tu re dependence be tween 200 K and 300 K.
The data have been fitted on the form A(ro~e x to compare with different samples and theoretical models . A linear extraplat ion has been chosen to est imate the normal state resistivity Pn , assuming
2 , ~ ~ i i
"6 -2
- 4
- 6 2
8o [
'4:1 -, ~,..,° 0 0
102 106 110 T(K}
I I I I I
I I I I I
0 x ~ . D
C ¢,1
-4 0" ' " " " x 106 109 112
TIK) - 6 1 T i f i
-6 -5 -4 -3 -2 -1 0
In(T-Te)/T e Fig.2 Fluctuat ion conductivi ty above
Te mf for samples A and D. The inset shows A~ -z vs T to d e t e r m i n e T g f.
9n = A + BT. To was defined in three different ways: i)
T m - where R is half of the normal state value; ii) Tg - where d R / d T has a cusp peak and iii) T mf according to Lawrence- Doniach (LD) theory (2).
Data were analyzed in the regions -4< In < - 2 , where the effect of the rmodynamic fluctuations is impor tan t and the fluctuations can be assumed to be 2 - dimensional, due to the large anisotropy in BSCCO.
Table 1 shows the results of using different To. It is obvious, that consistent results among the four samples only are obtained when To is defined as in the LD model. In this case an exponent of x : - 1 is obtained as expected from 2D fluctuation theory ( the details of crossover from 2D-3D will be described elsewhere) . Examples of the fits are shown in Fig.2.
A CKN OWL ED G E M EN TS
We would like to thank Dr. O. Rapp for st imulating discussions. This work has been supported by the Swidish National Science Research Council and by the Chinese Natural Science Foundat ion .
R E F E R E N CES
1. Hart, S. H., Hegedus , Z., Andersson, M., Nygren, M., Rapp, (3., Yan, Y.F., Chen, Q., Wei, Y. N. and He, Y. S., Physica C169, 250 (1990). 2. Lawrence W. E. and Doniach S. in Proc. 12th Int. Conf. Low Tempera tu re Physics, Kyoto 1970, edited by E. Kanda (Academic, Kyoto, 1971), p. 361.
