- Email: [email protected]
Specific heat of Bi2Sr2CaCu2Ox versus oxygen content (0≤B≤14T)
PHYSICA[
Physica B 194-196 (1994) 1497-1498 North-Holland
Specific h e a t o f B i 2 S r 2 C a C u 2 0 x v e r s u s o x y g e n c o n t e n t (0<_B<14T) A. Junod, K.-Q. Wang, G. Triscone and J. Muller Universit6 de Gen6ve, Section de physique, CH-1211 Gen6ve 4 (Switzerland) In order to characterize more precisely the superconducting transition of a quasi-2D superconductor, we quenched polycrystalline samples of Bi2Sr2CaCu20 x from various locations of the (T; P(O2)) equilibrium diagram. A well-defined specific heat peak at T c is observed with 0.01% resolution for the samples with the highest T c. The samples with lower Tc'S provide strong support to the normal-state background determined by an analysis of the data including phonon and fluctuation terms. We do not find any indication of a mean-field jump within experimental uncertainty, in stark contrast to YBa2Cu307. The application of a 14 Tesla field depresses the total specific heat by 0.54% only at T(peak)=92.5K, but this effect reduces to less than 0.03% already ±8K away from T c. On passing the irreversibility line, no anomaly in the specific heat is detected at the 0.01% level. 1. I N T R O D U C T I O N
General arguments and exact solutions of lattice models predict that thermal fluctuations tend to oppose the establishment of long-range order in lowdimensional systems. YBa2Cu30 7 ("YBCO") is generally considered as a 3D superconductor (at least in the vicinity of To) whereas Bi2Sr2CaCu208 CBSCCO") retains many features of a 2D system. The anisotropies of their coherence lengths differ by one order of magnitude [1]. It is therefore of interest to study and compare the nature of their superconducting transitions. 2. E X P E R I M E N T A L
Ceramics with nominal composition Bi2Sr2CaCu20 x were first sintered as described in Ref. [2]. Sample BSC-TS was then slowly cooled along the constant-T c line joining the points {846°C; 0.4 bar 02} and {468°C; 0.0005 mbar}. Sample BSC-550 was equilibrated at {500°C; lbar} and quenched. Sample BSC-400 was equilibrated at {400°C; lbar} and quenched. Their critical temperatures are Tc~92.5, 84 and 72 K, respectively. The adiabatic calorimeters are of the continuousheating type. An early design with 0.1% resolution was used in §3; an improved version with 0.01% resolution in fields B=0... 14T was used in §4. 3. E F F E C T OF O X Y G E N CONCENTRATION The absence of any sizable jump at T c in the specific heat of the BSCCO system may be due to a
vanishingly small density-of-states (DOS) at the Fermi level, to metallurgical inhomogeneities, or to the absence of long-range coherence invalidating the mean-field description. The total magnetic susceptibility in the normal state is close to zero [2], implying that the spin susceptibility is of the same order of magnitude as the core susceptibility. The DOS is therefore not particularly small in comparison to that of YBCO. The broadening due to a distribution Ax of oxygen concentrations may be largely cancelled by adjusting T c at its maximum value where 0Tc/0x vanishes. Fig. 1 shows the total specific heat for x approaching the optimum value at which Tc~95K [2]. Fig. 2 shows the "anomalous" part of the specific heat after having subtracted a common phonon baseline determined as explained in Ref [3]. The transition width remains nearly constant upon approaching the maximum T c. We conclude that the shape of the transition and its width are essentially intrinsic, and that BSCCO provides an extreme example of a non-mean-field superconductor. 4. E F F E C T OF M A G N E T I C FIELD Fig. 3 shows high resolution specific heat data for sample BSC-TS with Tc~92.5K. The applied magnetic field is 5 mT ("B=0"), 5T, 10T and 14 T. The effect of the magnetic field is exceedingly small and almost symmetrical about T c, suggesting again the absence of mean-field jump. The maximum relative difference [C(B=O,T)-C(14T,T)]/C(O,T) never exceeds 0.54%, to be compared with 2.2% in
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E1329-K
1498 0.114
o.°11 1o6
• B=0
0.113
5T
~, O.ll ~
•
~'~ 0.112
O.lO8
~/
/
10T
[
/1%
Y
~...... 0.111
0.104 ~,~ 60
80
100
120
140
90
8O
T (K)
100
110
T (K)
Fig. 1. Total specific heat of BSCCO-2212 samples.
Fig. 3. Specific heat vs B (sample BSC-TS). 0.3
468 ° O 5pb
0.2i "~
r ]
. ~
~
'~
/,:!~!"
550 ° l b
~,,~
0
400 ° l b v
o.1
, Zi
%
[~
"
-0.3
Gauss 3D
-: •
0 (..) o
~
.
.
.
60
• ....
.
80
lOO
~"-~.~
12o
crlticaE tO 1%
-0.6
40
T (K)
60
80
100 120 140 160 180 200 T (K)
Fig. 4. Residuals of various fits (sample BSC-TS). Fig. 2. Electronic specific heat at the transition (full scale z2.4% of the total specific heat). YBCO [3]. The midpoint of the anomaly is not appreciably shifted by the magnetic field, a typical 2D properly. In all cases, no sharp structure that could be attributed to the melting of the vortex lattice is observed below T c. 5. F L U C T U A T I O N S :
MODELS
Attempts to fit various models of superconducting fluctuations for B=0 were less successful than for YBCO. In the latter case, rms deviations down to 0.014% from 40 to 220K could be obtained, omitting a window Tc+IK [3]. The residuals did not show any systematic trend. In the case of BSCCO, using the same temperature interval but skipping a larger window Tc±I.5K, we obtain 0.056% with 2D Gaussian fluctuations, 0.046% with 3D Gaussian fluctuations, and 0.036% for critical fluctuations with a critical index of 0.1. The residuals near Tc+I.5K show in all cases "large" systematic
deviations, 0.7%, 0.55% and 0.32% peak-to-peak, respectively (Fig. 4). These differences represent 20 to 40 times the experimental scatter, and a substantial fraction of the electron specific heat at T c. These tests strongly suggest that the description of the thermodynamic transition of the quasi-2D superconductor BSCCO using a mean-field model corrected for fluctuations is too rough and requires additional ingredients. In such highly granular systems, finite-size corrections seem to be a promising approach [4]. REFERENCES
1. D.E. Farrell et al., Phys. Rev. Lett. 63 (1989) 782 2. G. Triscone et al., Physica C 176 (1991) 247 3. A. Junod et al., "Specific heat and magnetic susceptibility of YBa2Cu307 at the superconducting transition" and "Specific heat of single crystalline YBa2Cu307 in 20 Tesla", this conference. 4. F. Solms et al., Phys. Lett. AI70 (1992) 137
Physica B 194-196 (1994) 1497-1498 North-Holland
Specific h e a t o f B i 2 S r 2 C a C u 2 0 x v e r s u s o x y g e n c o n t e n t (0<_B<14T) A. Junod, K.-Q. Wang, G. Triscone and J. Muller Universit6 de Gen6ve, Section de physique, CH-1211 Gen6ve 4 (Switzerland) In order to characterize more precisely the superconducting transition of a quasi-2D superconductor, we quenched polycrystalline samples of Bi2Sr2CaCu20 x from various locations of the (T; P(O2)) equilibrium diagram. A well-defined specific heat peak at T c is observed with 0.01% resolution for the samples with the highest T c. The samples with lower Tc'S provide strong support to the normal-state background determined by an analysis of the data including phonon and fluctuation terms. We do not find any indication of a mean-field jump within experimental uncertainty, in stark contrast to YBa2Cu307. The application of a 14 Tesla field depresses the total specific heat by 0.54% only at T(peak)=92.5K, but this effect reduces to less than 0.03% already ±8K away from T c. On passing the irreversibility line, no anomaly in the specific heat is detected at the 0.01% level. 1. I N T R O D U C T I O N
General arguments and exact solutions of lattice models predict that thermal fluctuations tend to oppose the establishment of long-range order in lowdimensional systems. YBa2Cu30 7 ("YBCO") is generally considered as a 3D superconductor (at least in the vicinity of To) whereas Bi2Sr2CaCu208 CBSCCO") retains many features of a 2D system. The anisotropies of their coherence lengths differ by one order of magnitude [1]. It is therefore of interest to study and compare the nature of their superconducting transitions. 2. E X P E R I M E N T A L
Ceramics with nominal composition Bi2Sr2CaCu20 x were first sintered as described in Ref. [2]. Sample BSC-TS was then slowly cooled along the constant-T c line joining the points {846°C; 0.4 bar 02} and {468°C; 0.0005 mbar}. Sample BSC-550 was equilibrated at {500°C; lbar} and quenched. Sample BSC-400 was equilibrated at {400°C; lbar} and quenched. Their critical temperatures are Tc~92.5, 84 and 72 K, respectively. The adiabatic calorimeters are of the continuousheating type. An early design with 0.1% resolution was used in §3; an improved version with 0.01% resolution in fields B=0... 14T was used in §4. 3. E F F E C T OF O X Y G E N CONCENTRATION The absence of any sizable jump at T c in the specific heat of the BSCCO system may be due to a
vanishingly small density-of-states (DOS) at the Fermi level, to metallurgical inhomogeneities, or to the absence of long-range coherence invalidating the mean-field description. The total magnetic susceptibility in the normal state is close to zero [2], implying that the spin susceptibility is of the same order of magnitude as the core susceptibility. The DOS is therefore not particularly small in comparison to that of YBCO. The broadening due to a distribution Ax of oxygen concentrations may be largely cancelled by adjusting T c at its maximum value where 0Tc/0x vanishes. Fig. 1 shows the total specific heat for x approaching the optimum value at which Tc~95K [2]. Fig. 2 shows the "anomalous" part of the specific heat after having subtracted a common phonon baseline determined as explained in Ref [3]. The transition width remains nearly constant upon approaching the maximum T c. We conclude that the shape of the transition and its width are essentially intrinsic, and that BSCCO provides an extreme example of a non-mean-field superconductor. 4. E F F E C T OF M A G N E T I C FIELD Fig. 3 shows high resolution specific heat data for sample BSC-TS with Tc~92.5K. The applied magnetic field is 5 mT ("B=0"), 5T, 10T and 14 T. The effect of the magnetic field is exceedingly small and almost symmetrical about T c, suggesting again the absence of mean-field jump. The maximum relative difference [C(B=O,T)-C(14T,T)]/C(O,T) never exceeds 0.54%, to be compared with 2.2% in
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E1329-K
1498 0.114
o.°11 1o6
• B=0
0.113
5T
~, O.ll ~
•
~'~ 0.112
O.lO8
~/
/
10T
[
/1%
Y
~...... 0.111
0.104 ~,~ 60
80
100
120
140
90
8O
T (K)
100
110
T (K)
Fig. 1. Total specific heat of BSCCO-2212 samples.
Fig. 3. Specific heat vs B (sample BSC-TS). 0.3
468 ° O 5pb
0.2i "~
r ]
. ~
~
'~
/,:!~!"
550 ° l b
~,,~
0
400 ° l b v
o.1
, Zi
%
[~
"
-0.3
Gauss 3D
-: •
0 (..) o
~
.
.
.
60
• ....
.
80
lOO
~"-~.~
12o
crlticaE tO 1%
-0.6
40
T (K)
60
80
100 120 140 160 180 200 T (K)
Fig. 4. Residuals of various fits (sample BSC-TS). Fig. 2. Electronic specific heat at the transition (full scale z2.4% of the total specific heat). YBCO [3]. The midpoint of the anomaly is not appreciably shifted by the magnetic field, a typical 2D properly. In all cases, no sharp structure that could be attributed to the melting of the vortex lattice is observed below T c. 5. F L U C T U A T I O N S :
MODELS
Attempts to fit various models of superconducting fluctuations for B=0 were less successful than for YBCO. In the latter case, rms deviations down to 0.014% from 40 to 220K could be obtained, omitting a window Tc+IK [3]. The residuals did not show any systematic trend. In the case of BSCCO, using the same temperature interval but skipping a larger window Tc±I.5K, we obtain 0.056% with 2D Gaussian fluctuations, 0.046% with 3D Gaussian fluctuations, and 0.036% for critical fluctuations with a critical index of 0.1. The residuals near Tc+I.5K show in all cases "large" systematic
deviations, 0.7%, 0.55% and 0.32% peak-to-peak, respectively (Fig. 4). These differences represent 20 to 40 times the experimental scatter, and a substantial fraction of the electron specific heat at T c. These tests strongly suggest that the description of the thermodynamic transition of the quasi-2D superconductor BSCCO using a mean-field model corrected for fluctuations is too rough and requires additional ingredients. In such highly granular systems, finite-size corrections seem to be a promising approach [4]. REFERENCES
1. D.E. Farrell et al., Phys. Rev. Lett. 63 (1989) 782 2. G. Triscone et al., Physica C 176 (1991) 247 3. A. Junod et al., "Specific heat and magnetic susceptibility of YBa2Cu307 at the superconducting transition" and "Specific heat of single crystalline YBa2Cu307 in 20 Tesla", this conference. 4. F. Solms et al., Phys. Lett. AI70 (1992) 137