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Low temperature relaxation in YBaCuO
Physiea
C
185-189
(1991)
1807-1808
North-Holland
LOW TEMPERATURE RELAXATION IN YBaCuO P.A. GODELAIN (+), C. HANNAY(+), R. CLOOTS(*), and M. AUSLOOS(§) S.U.P.R.A.S.,(+) Institut d'Electrieit~ Montefiore B28,(*)lnstitut de Chimie, B6, (§) Institut de Physique, B5 Universit~ de Liege, B.4000 LIEGE Belg,um
Magnetic relaxation measurements and electrical resistance measurements (in presence of a magnetic field) have been made below the critical temperature and at low temperature respectively in order to observe the behavior of trapped flux on both sides of the so called irreversibility line. The relaxation is logarithmic and the resistance shows a decreasing exponential behavior. Both obser,-ations c.~,'a~ interpreted fol!ovfng the flux creep model. The activation er,ergy values found in the flux creep model depend on the type of measurements.
Miiller et al. 1 have shown that field cooled (FC) and zero field cooled (ZFC) magnetization of high temperature superconductors (HTS) have to be distinguished below some temperature T*. Above the latter value the materials have reversible magnetization. This defines a field dependent "irreversibility line" T* (H)- Tc - T*(H) ~ H zt3 reminiscent of the behavior of spin glasses. The theoretical basis stands from Ebner and Stroud work 2 on the behavior of coupled Josephson junction networks. In HTS ceramics, it seems natural to identify such Josephson junctions with weak links at inter~rrain boundaries or even with intrinsic or extrinsic defects, like twins in grains. However in single crystals or in other "good quality samples" such an identification is less obvious, eventhough the "irreversibility line" is still present. This led to another interpretation of the line in terms of a "giant flux creep" model 3. A detailed analysis has corroborated the same 2/3 exponent. An extension of the theory by Tinkham 4 for the resistivity has given some understanding into the nature of the broadening of the resistivity transition near the critical temperature Tc in presence of a DC field. An other extremely important prediction for the flux creep phenomenon is the exponential decrease of the resistance R with temperature much below Tc 5 . . . . . t . ~ . mvcsagate -,~. "-~"~"~ b , ~ l o , , , It. ~-~tt~ u^~c - iiltClW~ttV. cltttut~,l "~"~ Tc. Here we study relaxation effects of the magnetization in polycristalline YBaCuO following an AC technique which we have already used near Tc in other HTS 6,7, as well as the resistance behavior below Tc. I 't.~
it ~ 1 i~l,.,
kz
rv
YBazCu307 ceramics were prepared using a classical solid state reaction method from an initial mixture of stoichiometric quantities of BaCO3, CuCO3.Cu(OH)2 and Y203 high purity powders. The mixture was heated to 925°C in an alumina crucible. This temperature was maintained for two days with two intermediary grindings:
The annealing in oxygen atmosphere was realised at ~ C in order to obtain a strongly heterogeneous sample. lodometric titration analysis gives 6.8 for the average of the entire oxygen concentration in the bulk, as confirmed by X Ray microprobe observation. Analysis with SEM has shown a large porosity and _mains which can have a linear dimension of the order of 10 Wn A secondary, phase BaCuO3 is sometimes present at grain boundaries. In absence of magnetic field, the resistance transition occurs above 90 K, but the curve already presents a foot structure. Above Tc the curve shows a slight semiconducfing behavior which confirms the presence of YBa2Cu~O,,., with O
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All fights reserved.
P.A. Goddaine et at / Low temperature relaxation in YBaCuO
1808
Jci -
.~6309 Hz 237 Hz
(1)
where fs = (1 - p*/R) 2 in which p* is obtained from the intercept of the straight line fit to the data with the h^c= 0 axis. For such a field no frequency dependence is seen for Jcj. However for larger fields (110 and 185 G) the frequency effect is well marked 9. This hints toward a frequency de?endence of the irreversibility line. "12:e variation of the intergranular critical current with frequency is quasi logarithmic Jcj = a In f + b
4 v
"
1
(2)
0 0.0
with for the 110 G case a = 2.0 + 0.2, b = 9.9 + 1.3 as determined by a least square fit. Eq. (2) reproduces flux creep theory results which predicts
k.r
,n
]
3
0.1 0.2 0.3 0.4 0.5
p/R Fig.1. Flux profile showing frequency independence below a small H field.
where Jco is the critical current in absence of thermal activation, U(T,H) is the activation energy and fo is a characteristic frequency8.
REFERENCES
From a physical point of view, it is understandable that thermal activation displaces the vortex center and homogenizes the vortex concentration over the sample, thereby reducing the critical current. Also the least is the exciting frequency the greatest is the relaxation. Consequently the penetration depth decreases and the critical current increases with frequency. For fo between 109 Hz and 1012 Hz we have U (T = 26.5 K, H = 110G~ 61 +14 meV
1. K.A. MOLLER, M. TAKASHIGE and J.G. BEDNORZ, Phys. Rev. Lett. 58, (1987) 1143.
This value is in agreement with other results 10. They found U = 60 meV. It is also similar to values obtained by Yeshurun et al.11 from direct magnetization measurements 03, = 20 meV and U£ = 50 meV, for H / / o r _Lto the c axis).
5. Ch. LAURENT, M. LAGUESSE, S.K. PATAPIS, H.W. VANDERSCHUEREN, G.V. LECOMTE, A. RULMONT, P. TARTE and M. AUSLOOS, Z. Phys. B69,(1988) 435.
2. C. EBNER and D. STROUD, Phys. Rev. B31, (1985) 165. 3. Y. YESHURUN and A.P. MALOZEMOFF, Phys. Rev. Lett 60 ,(1988) 2202. 4. M. TINKHAM, Phys. Rev. Lett. 61,(1988) 1658.
6. P.A. GODELAINE and M. AUSLOOS, Solid State Comm. 73 ,(1990) 759. On the other hand, flux creep theory predicts that R(T,H) = Ro(H) exp (-U(T,H)fF)
(4)
7. P.A. GODELAINE and M. AUSLOOS, Solid State Comm. 76 ,(1990) 785. 8. A.M. CAMPBELL and J.E. EVETTS, Adv. Phys. 2.__!.!, (1972) 199.
If U (T,H) is considered a quasi constant as a function of temperature, it can be easily obtained from a serrfi-log plot. Activation energy values are in the range 100-750 meV for B between 0-400 G and T between 60-80 K. U(T,H) decreases with the field. Such (resistive) values are always larger than those determined from magnetization data.
9. P.A. GODELAINE, unpublished results.
In conclusion, we have shown that flux creep theory can be reproduced by magnetization and resistive data in strongly heterogeneous HTS, for not too low H fields. Also the thermal activation energy has to receive further attention.
l l. Y. YESHURUN, A.P. MALOZEMOFF, F. HOLTZBERG and T.R. DINGER, Phys. Rev. B 3 8 , (1988) 1 ! 828 .
10. M. TUOMINEN, A.M. GOLDMAN and M.L. McCARTNEY, Phys. Rev. B37, (1988) 548.
C
185-189
(1991)
1807-1808
North-Holland
LOW TEMPERATURE RELAXATION IN YBaCuO P.A. GODELAIN (+), C. HANNAY(+), R. CLOOTS(*), and M. AUSLOOS(§) S.U.P.R.A.S.,(+) Institut d'Electrieit~ Montefiore B28,(*)lnstitut de Chimie, B6, (§) Institut de Physique, B5 Universit~ de Liege, B.4000 LIEGE Belg,um
Magnetic relaxation measurements and electrical resistance measurements (in presence of a magnetic field) have been made below the critical temperature and at low temperature respectively in order to observe the behavior of trapped flux on both sides of the so called irreversibility line. The relaxation is logarithmic and the resistance shows a decreasing exponential behavior. Both obser,-ations c.~,'a~ interpreted fol!ovfng the flux creep model. The activation er,ergy values found in the flux creep model depend on the type of measurements.
Miiller et al. 1 have shown that field cooled (FC) and zero field cooled (ZFC) magnetization of high temperature superconductors (HTS) have to be distinguished below some temperature T*. Above the latter value the materials have reversible magnetization. This defines a field dependent "irreversibility line" T* (H)- Tc - T*(H) ~ H zt3 reminiscent of the behavior of spin glasses. The theoretical basis stands from Ebner and Stroud work 2 on the behavior of coupled Josephson junction networks. In HTS ceramics, it seems natural to identify such Josephson junctions with weak links at inter~rrain boundaries or even with intrinsic or extrinsic defects, like twins in grains. However in single crystals or in other "good quality samples" such an identification is less obvious, eventhough the "irreversibility line" is still present. This led to another interpretation of the line in terms of a "giant flux creep" model 3. A detailed analysis has corroborated the same 2/3 exponent. An extension of the theory by Tinkham 4 for the resistivity has given some understanding into the nature of the broadening of the resistivity transition near the critical temperature Tc in presence of a DC field. An other extremely important prediction for the flux creep phenomenon is the exponential decrease of the resistance R with temperature much below Tc 5 . . . . . t . ~ . mvcsagate -,~. "-~"~"~ b , ~ l o , , , It. ~-~tt~ u^~c - iiltClW~ttV. cltttut~,l "~"~ Tc. Here we study relaxation effects of the magnetization in polycristalline YBaCuO following an AC technique which we have already used near Tc in other HTS 6,7, as well as the resistance behavior below Tc. I 't.~
it ~ 1 i~l,.,
kz
rv
YBazCu307 ceramics were prepared using a classical solid state reaction method from an initial mixture of stoichiometric quantities of BaCO3, CuCO3.Cu(OH)2 and Y203 high purity powders. The mixture was heated to 925°C in an alumina crucible. This temperature was maintained for two days with two intermediary grindings:
The annealing in oxygen atmosphere was realised at ~ C in order to obtain a strongly heterogeneous sample. lodometric titration analysis gives 6.8 for the average of the entire oxygen concentration in the bulk, as confirmed by X Ray microprobe observation. Analysis with SEM has shown a large porosity and _mains which can have a linear dimension of the order of 10 Wn A secondary, phase BaCuO3 is sometimes present at grain boundaries. In absence of magnetic field, the resistance transition occurs above 90 K, but the curve already presents a foot structure. Above Tc the curve shows a slight semiconducfing behavior which confirms the presence of YBa2Cu~O,,., with O
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All fights reserved.
P.A. Goddaine et at / Low temperature relaxation in YBaCuO
1808
Jci -
.~6309 Hz 237 Hz
(1)
where fs = (1 - p*/R) 2 in which p* is obtained from the intercept of the straight line fit to the data with the h^c= 0 axis. For such a field no frequency dependence is seen for Jcj. However for larger fields (110 and 185 G) the frequency effect is well marked 9. This hints toward a frequency de?endence of the irreversibility line. "12:e variation of the intergranular critical current with frequency is quasi logarithmic Jcj = a In f + b
4 v
"
1
(2)
0 0.0
with for the 110 G case a = 2.0 + 0.2, b = 9.9 + 1.3 as determined by a least square fit. Eq. (2) reproduces flux creep theory results which predicts
k.r
,n
]
3
0.1 0.2 0.3 0.4 0.5
p/R Fig.1. Flux profile showing frequency independence below a small H field.
where Jco is the critical current in absence of thermal activation, U(T,H) is the activation energy and fo is a characteristic frequency8.
REFERENCES
From a physical point of view, it is understandable that thermal activation displaces the vortex center and homogenizes the vortex concentration over the sample, thereby reducing the critical current. Also the least is the exciting frequency the greatest is the relaxation. Consequently the penetration depth decreases and the critical current increases with frequency. For fo between 109 Hz and 1012 Hz we have U (T = 26.5 K, H = 110G~ 61 +14 meV
1. K.A. MOLLER, M. TAKASHIGE and J.G. BEDNORZ, Phys. Rev. Lett. 58, (1987) 1143.
This value is in agreement with other results 10. They found U = 60 meV. It is also similar to values obtained by Yeshurun et al.11 from direct magnetization measurements 03, = 20 meV and U£ = 50 meV, for H / / o r _Lto the c axis).
5. Ch. LAURENT, M. LAGUESSE, S.K. PATAPIS, H.W. VANDERSCHUEREN, G.V. LECOMTE, A. RULMONT, P. TARTE and M. AUSLOOS, Z. Phys. B69,(1988) 435.
2. C. EBNER and D. STROUD, Phys. Rev. B31, (1985) 165. 3. Y. YESHURUN and A.P. MALOZEMOFF, Phys. Rev. Lett 60 ,(1988) 2202. 4. M. TINKHAM, Phys. Rev. Lett. 61,(1988) 1658.
6. P.A. GODELAINE and M. AUSLOOS, Solid State Comm. 73 ,(1990) 759. On the other hand, flux creep theory predicts that R(T,H) = Ro(H) exp (-U(T,H)fF)
(4)
7. P.A. GODELAINE and M. AUSLOOS, Solid State Comm. 76 ,(1990) 785. 8. A.M. CAMPBELL and J.E. EVETTS, Adv. Phys. 2.__!.!, (1972) 199.
If U (T,H) is considered a quasi constant as a function of temperature, it can be easily obtained from a serrfi-log plot. Activation energy values are in the range 100-750 meV for B between 0-400 G and T between 60-80 K. U(T,H) decreases with the field. Such (resistive) values are always larger than those determined from magnetization data.
9. P.A. GODELAINE, unpublished results.
In conclusion, we have shown that flux creep theory can be reproduced by magnetization and resistive data in strongly heterogeneous HTS, for not too low H fields. Also the thermal activation energy has to receive further attention.
l l. Y. YESHURUN, A.P. MALOZEMOFF, F. HOLTZBERG and T.R. DINGER, Phys. Rev. B 3 8 , (1988) 1 ! 828 .
10. M. TUOMINEN, A.M. GOLDMAN and M.L. McCARTNEY, Phys. Rev. B37, (1988) 548.