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Anisotropic specific heat of a Bi2Sr2CaCu2O8 single crystal in magnetic fields up to 14 T
Physiea C 235-240 (1994) 1761-1762 North-Holland
PHYSICA
Anisotropic Specific Heat ofa Bi2Sr2CaCu200 Single Crystal in Magnetic Fields up to 14 T A. Juned, K.-Q. Wang, T. Tsukamoto, B. Revaz, G. Triscone, E. Walker and J. Muller Universit+ de Gen+ve,D+partement de Physique de la Mati+re Condens~e, 24 quai Ernest-Ansermet, CH-1211 Gen+ve 4, Switzerland A 0.25 g single crystal ofBi2Sr2CaCu20s with a sharp superconducting transition at 85 K was characterized by AC susceptibility, X-ray diffraction, Meissner effect, normal-state susceptibility, magnetization in the nuxed state, and specific heat from I to 300K. Many unconventional features are found in the specific heat which may be intrinsic features of a 2D superconductor, e.g. a field-independent linear term y*T at low T, the absence of a specific heat jump at T c, a symmetrical logarithmic anomaly at T~, an almost field-independent transition temperature which coincides with the crossing point of the magnetization, a new crossing point of the specific heat, etc. The accurate data near T¢ (<0.02%) allow an expression of 0(C/T)/c3I-I by an empirical formula that describes the variation of the specific heat and magnetization over a wide temperature and field range about Tc 1. INTRODUCTION Preliminary investigations have shown that the magnetic and thermal properties of quasi-2D high temperature superconductors based e.g. on Bi differ markedly from those of the more 3D Y-123. We document this point by presenting high resolution adiabatic specific heat data near T c m high magvetic fields (_IT
term is y*=2.1mJ/K=mole. The latter value is comparable per Cu atom to that of high quality Y123. Unexpectedly, 3'* does not increase with field. The specific heat near T c is shown in Fig. 2 for fields 0<__B//c<14"[ B/c=14T has less effect than B/lc=O.25T, i e the anisotropy of the upper critical field is larger than 50, and posstbly mfimte if we allow for a 1° alignment error The cnucal temperature m zero field, gwen by the maxamum of C/T, is 85 I_+0 1K. This definmon of T almost coincides with the crossing point T* of the magnettzaUon Extenswe tests [1] show that by using any reasonable phonon spectrum (i.e positive and normalised to 3N modes/gat) for the lattice specific heat, the remaining electromc part is charactenzed by a vanishingly small mean-field jump, =20 tames smaller than for Y-123, practically zero within error limits. The goodness-of-fit criterion %~-is more than 6 t~mes bette: if thermal fluctuations are taken as
B=BT PL=PT ,
2 t~ t3~
°'°'~
~c
• Boo-
~IS
.-.-S
~
B/lab
+
05
3. SPECIFIC HEAT
0
,
0
The low T specific heat is shown m Fig. 1 for B=0 and B=8T, B/c. The imtial Debye temperature is 283K and the coefficient of the residual hnear
oof
fit
,
'
'
I
5
'
I
I
I
I
l
10
l
'
I
:
.
.
.
.
15
[K~] Fig. 1 Low temperature specific heat CF[" vs T 2
0921-4534/94/$07 00 © 1994 - l-lsevser Soence B V LH rights reserved SSDI 0921-4534(94)01447-7
20
1762
A Junod et al./Physzca C 235-240 (1994) 1761-1762
0 0005
0 113 B=0
01125
0
0112 I~" -0 0005
.~. 0 1115
o.
0 111 O
..........--b-P/;--~ V~~
....
I~" -0 001
g
01105
B=0 S.l-2-4-B-14T, BI/c
~
"
B=14T
-0.0015
0 11
60
65
01095
70
75
80
85
90
95
100
T [K] 80
75
85
90
95
100
Temperature [K]
Fig. 3 Variation of C/T with the field (B//c). Fig. 2 Specific heat C/T near T c, B=0 to 14T (Bile) crttical rather than 2D or 3D Gaussian. Gaussian
models are acceptable only _3.5K away from T¢. The variation of the specific heat as a function of the field (Fig. 3) is almost symmetrical, in contrast to Y-123 [2], providing again evidence for the absence of a jump at To. It discloses a new crossing point C0-I, T~)=C ~ where T×=75K. Scaling models [31 [41 are found to be unsuitable for various mathematical or experimental reasons [1]. The high resolution of the present experiment rather allows us to measure a(C/T)/OH and to define an empirical analytic function that gives a quantitative description of both the specific heat and reversible magnetization" 0(C ,T) 0-----if-- -
Lo(B ,Tesla) -2,3 D(B) T (~_aretgx)
X= A(T-Tc) ~ '
l+x:
+
~. +Bext ?-:5B=B~2nt
q ~, 2
)
(1)
where Tc=85K. The parameters Lo=25x10 -4 J/(K2Tgat), A=4 (T/K) 1~2and Bmt~0.05 T are easily determined from the data [1]. D(B) is determined by the entropy balance with the result D(B) [J/(K:Tgat)]~-12.85× 10-6-2.2x 10-61n(B/Tesla) The variable x is essentially 2D in nature. The first term represents the Lorentzian variation of the fluctuation specific heat with field, and the second term is related to the mixed state London specific heat and the penetration depth. By lntegrat=o'~ and careful apphcation of the tlurd principle and Maxwell relation ~SI~H=0M/EIf. the sp~,lfic heat and reversible magnetization curves can be reconstructed with quantitative accuracy, including the crossing points T* and T × [1]
The maximum of la(C/T)/0HI is a natural definition of To(H); we find that it increases initially with field up to 85.8_+0.3K in 1.5T, and then decreases to 83.2_+0.7K in lIT. The error of our temperature scale is <50mK for B_<14T. Eq. (1) gives an excellent fit of all data without having to make a distinction between l~gh feld scaling, low field scaling, Gaussian or critical regimes. The zero-field anomaly appears as a sum of elementary Lorentzian peaks of la(C/T)/~HI that can be integrated from the normal state in very high fields to the superconducting state in B=0 or rather B'mr Analytically, we obtain then the formula Cs-C . =-Aln[I+A:(T-Tc)V03'mtT)] for the full anomaly in zero external field. Tills formula fits the zero-field data within 0.016% rms, 75-100K, without excluding a single point at Tc CONCLUSION The absence of specific heat jump makes the analysis of fluctuations in the 2D superconductor simpler than for the more 3D-like Y-123. It is found that the variation of the specific heat with the field obeys a simple experimental law It is hoped that this observation will promote further theoreUcal investigatmns on the nature of the transition of 2D superconductors, which apparently is of order >2 REFERENCES i
A June,d, K -Q Wang, T. Tsttkamoto, B Revaz, G Tnscone, E Walker and J Muller, submitted to Phvslca C (1994) 2 A Junod et al, Phys~ca C211 (1993) 304 3 L N Bulaevskil et al, Phys Rev Lett. 68 (1992) 3773 4 Z Tesanowc et al. Phys Rev. Lett. 24 (1992) 3563
PHYSICA
Anisotropic Specific Heat ofa Bi2Sr2CaCu200 Single Crystal in Magnetic Fields up to 14 T A. Juned, K.-Q. Wang, T. Tsukamoto, B. Revaz, G. Triscone, E. Walker and J. Muller Universit+ de Gen+ve,D+partement de Physique de la Mati+re Condens~e, 24 quai Ernest-Ansermet, CH-1211 Gen+ve 4, Switzerland A 0.25 g single crystal ofBi2Sr2CaCu20s with a sharp superconducting transition at 85 K was characterized by AC susceptibility, X-ray diffraction, Meissner effect, normal-state susceptibility, magnetization in the nuxed state, and specific heat from I to 300K. Many unconventional features are found in the specific heat which may be intrinsic features of a 2D superconductor, e.g. a field-independent linear term y*T at low T, the absence of a specific heat jump at T c, a symmetrical logarithmic anomaly at T~, an almost field-independent transition temperature which coincides with the crossing point of the magnetization, a new crossing point of the specific heat, etc. The accurate data near T¢ (<0.02%) allow an expression of 0(C/T)/c3I-I by an empirical formula that describes the variation of the specific heat and magnetization over a wide temperature and field range about Tc 1. INTRODUCTION Preliminary investigations have shown that the magnetic and thermal properties of quasi-2D high temperature superconductors based e.g. on Bi differ markedly from those of the more 3D Y-123. We document this point by presenting high resolution adiabatic specific heat data near T c m high magvetic fields (
term is y*=2.1mJ/K=mole. The latter value is comparable per Cu atom to that of high quality Y123. Unexpectedly, 3'* does not increase with field. The specific heat near T c is shown in Fig. 2 for fields 0<__B//c<14"[ B/c=14T has less effect than B/lc=O.25T, i e the anisotropy of the upper critical field is larger than 50, and posstbly mfimte if we allow for a 1° alignment error The cnucal temperature m zero field, gwen by the maxamum of C/T, is 85 I_+0 1K. This definmon of T almost coincides with the crossing point T* of the magnettzaUon Extenswe tests [1] show that by using any reasonable phonon spectrum (i.e positive and normalised to 3N modes/gat) for the lattice specific heat, the remaining electromc part is charactenzed by a vanishingly small mean-field jump, =20 tames smaller than for Y-123, practically zero within error limits. The goodness-of-fit criterion %~-is more than 6 t~mes bette: if thermal fluctuations are taken as
B=BT PL=PT ,
2 t~ t3~
°'°'~
~c
• Boo-
~IS
.-.-S
~
B/lab
+
05
3. SPECIFIC HEAT
0
,
0
The low T specific heat is shown m Fig. 1 for B=0 and B=8T, B/c. The imtial Debye temperature is 283K and the coefficient of the residual hnear
oof
fit
,
'
'
I
5
'
I
I
I
I
l
10
l
'
I
:
.
.
.
.
15
[K~] Fig. 1 Low temperature specific heat CF[" vs T 2
0921-4534/94/$07 00 © 1994 - l-lsevser Soence B V LH rights reserved SSDI 0921-4534(94)01447-7
20
1762
A Junod et al./Physzca C 235-240 (1994) 1761-1762
0 0005
0 113 B=0
01125
0
0112 I~" -0 0005
.~. 0 1115
o.
0 111 O
..........--b-P/;--~ V~~
....
I~" -0 001
g
01105
B=0 S.l-2-4-B-14T, BI/c
~
"
B=14T
-0.0015
0 11
60
65
01095
70
75
80
85
90
95
100
T [K] 80
75
85
90
95
100
Temperature [K]
Fig. 3 Variation of C/T with the field (B//c). Fig. 2 Specific heat C/T near T c, B=0 to 14T (Bile) crttical rather than 2D or 3D Gaussian. Gaussian
models are acceptable only _3.5K away from T¢. The variation of the specific heat as a function of the field (Fig. 3) is almost symmetrical, in contrast to Y-123 [2], providing again evidence for the absence of a jump at To. It discloses a new crossing point C0-I, T~)=C ~ where T×=75K. Scaling models [31 [41 are found to be unsuitable for various mathematical or experimental reasons [1]. The high resolution of the present experiment rather allows us to measure a(C/T)/OH and to define an empirical analytic function that gives a quantitative description of both the specific heat and reversible magnetization" 0(C ,T) 0-----if-- -
Lo(B ,Tesla) -2,3 D(B) T (~_aretgx)
X= A(T-Tc) ~ '
l+x:
+
~. +Bext ?-:5B=B~2nt
q ~, 2
)
(1)
where Tc=85K. The parameters Lo=25x10 -4 J/(K2Tgat), A=4 (T/K) 1~2and Bmt~0.05 T are easily determined from the data [1]. D(B) is determined by the entropy balance with the result D(B) [J/(K:Tgat)]~-12.85× 10-6-2.2x 10-61n(B/Tesla) The variable x is essentially 2D in nature. The first term represents the Lorentzian variation of the fluctuation specific heat with field, and the second term is related to the mixed state London specific heat and the penetration depth. By lntegrat=o'~ and careful apphcation of the tlurd principle and Maxwell relation ~SI~H=0M/EIf. the sp~,lfic heat and reversible magnetization curves can be reconstructed with quantitative accuracy, including the crossing points T* and T × [1]
The maximum of la(C/T)/0HI is a natural definition of To(H); we find that it increases initially with field up to 85.8_+0.3K in 1.5T, and then decreases to 83.2_+0.7K in lIT. The error of our temperature scale is <50mK for B_<14T. Eq. (1) gives an excellent fit of all data without having to make a distinction between l~gh feld scaling, low field scaling, Gaussian or critical regimes. The zero-field anomaly appears as a sum of elementary Lorentzian peaks of la(C/T)/~HI that can be integrated from the normal state in very high fields to the superconducting state in B=0 or rather B'mr Analytically, we obtain then the formula Cs-C . =-Aln[I+A:(T-Tc)V03'mtT)] for the full anomaly in zero external field. Tills formula fits the zero-field data within 0.016% rms, 75-100K, without excluding a single point at Tc CONCLUSION The absence of specific heat jump makes the analysis of fluctuations in the 2D superconductor simpler than for the more 3D-like Y-123. It is found that the variation of the specific heat with the field obeys a simple experimental law It is hoped that this observation will promote further theoreUcal investigatmns on the nature of the transition of 2D superconductors, which apparently is of order >2 REFERENCES i
A June,d, K -Q Wang, T. Tsttkamoto, B Revaz, G Tnscone, E Walker and J Muller, submitted to Phvslca C (1994) 2 A Junod et al, Phys~ca C211 (1993) 304 3 L N Bulaevskil et al, Phys Rev Lett. 68 (1992) 3773 4 Z Tesanowc et al. Phys Rev. Lett. 24 (1992) 3563