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Thermodynamic phase diagram of the cubic (K,Ba)BiO3 superconductor
Physica C 369 (2002) 193–195 www.elsevier.com/locate/physc
Thermodynamic phase diagram of the cubic (K,Ba)BiO3 superconductor S. Blanchard a,*, C. Marcenat b, J. Marcus a, T. Klein a, A. Sulpice c a
b
Laboratoire d’Etudes des Propri et es Electroniques des Solides, Centre National de la Recherche Scientifique, BP 166, 38042 Grenoble Cedex 9, France Commissariat a l’Energie Atomique––Grenoble, D epartement de Recherche Fondamentale sur la Mati ere Condens ee, SPSMS, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France c Centre de Recherche sur les Tr es Basses Temp eratures, Centre National de la Recherche Scientifique, BP 166, 38042 Grenoble Cedex 9, France
Abstract Specific heat, transport and reversible magnetization measurements have been performed on high quality (K,Ba)BiO3 single crystals (Tc 31 K). Calorimetric measurements up to 16 T show that the transition line between the superconducting and normal states has a strong anomalous positive curvature. The reversible magnetization deviates strongly from the standard London model above 0:8Tc emphasizing the original nature of the superconducting transition in this system. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Vortex matter; Phase diagram
1. Introduction One of the most interesting feature of the H–T phase diagram of high Tc oxides is the existence of a melting line Tm ðH Þ above which the vortex lattice melts into a liquid of entangled flux lines [1]. It is still unclear whether the classical Hc2 line still exists as a transition line or is just some smooth crossover between the vortex liquid and the normal state. Instead, the melting line would mark the first true phase transition when approaching from the normal state. In order to study this issue, we per-
formed thermodynamic (specific heat, reversible magnetization) and transport measurements on high quality (K,Ba)BiO3 single crystals. In high Tc oxides the presence of strong thermal fluctuations complicates the determination of Hc2 from these standard measurements but these fluctuations are expected to be much smaller in the cubic (K,Ba)BiO3 system for which the Ginzburg number is only of the order of 104 (typically two orders of magnitude smaller than in cuprates).
2. Calorimetric measurements * Corresponding author. Tel.: +33-476-88-74-69; fax: +33476-88-79-88. E-mail address: [email protected] (S. Blanchard).
An ac specific heat technique [2] was used to determine the thermodynamic phase transition line of new particularly homogeneous single crystals
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 1 2 4 0 - 0
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S. Blanchard et al. / Physica C 369 (2002) 193–195
Fig. 1. Normalized specific heat, transport and ac susceptibility versus temperature at H ¼ 3 T in a (K,Ba)BiO3 single crystal.
Fig. 2. Thermodynamic phase diagram deduced from specific heat measurements in three (K,Ba)BiO3 single crystals. In this figure TCp corresponds to the onset of the specific heat anomaly.
grown by electrocrystalization (DTc 0:15 K in transport measurements). Heat was supplied to the sample by a light emitting diode via an optical fiber and the induced temperature oscillations were measured by a chromel–constantan thermocouple. Fig. 1 displays typical transport, specific heat and ac susceptibility data at 3 T. In specific heat measurements, the highest field data (16 T) data have been used as a base line. Our specific heat results qualitatively agree with those previously obtained by Woodfield et al. [3] with a slightly larger value of the jump at H ¼ 0 (150 mJ mol1 K1 ). However, in our case, the specific heat anomaly remains well defined in magnetic fields (see Fig. 1) which enables us to study the magnetic field dependence of the transition in greater detail. The onset of the anomaly is close to the onset of the transport transition (R=RN 95%, where RN is the normal state value). On the other hand the onset of diamagnetism occurs at R 0, roughly corresponding to the mid-point of the specific heat anomaly. We have previously shown that the transport data close to R ¼ 0 can be well described by the so-called vortex-glass scaling formalism, suggesting the existence of a vortex liquid phase for [4].
The most striking feature is that the temperatures TCp ðH Þ corresponding to any characteristic point of the transition (e.g. the onset, mid-point or maximum of the specific heat anomaly) present a clear positive curvature. This can be seen in Fig. 2 which displays the temperatures TCp corresponding to the onset of the peak for three different samples. This is a totally unexpected feature since in conventional superconductors the location of the specific heat anomaly defines the upper critical field and is thus expected to vary linearly with T close to Tc . Indeed, none of the theoretical models which have been developed in order to explain a ‘‘possible’’ upward curvature of the upper critical field in cuprates (bipolaron scenario [5], spin– charge separation [6] or very strong coupling [7]) can be applied to the (K,Ba)BiO3 system. Moreover, the presence of inhomogeneities and/or magnetic impurities would only lead to an upward curvature at low temperature [8].
3. Reversible magnetization To complete this study of the thermodynamic properties we performed reversible magnetization
S. Blanchard et al. / Physica C 369 (2002) 193–195
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London theory are also usually observed in high Tc cuprates [10] and are commonly attributed to the presence of strong fluctuations. It is thus very surprising to observe similar deviations in the (K,Ba)BiO3 system. However, note that, in contrast to cuprates, dMrev =d lnðH Þ remains positive on the entire temperature range in (K,Ba)BiO3 .
4. Conclusions
Fig. 3. Temperature dependence of dMrev =d lnðHÞ in a (K,Ba)BiO3 single crystal. Strong deviations from the standard Werthamer–Helfang–Hohenberg dependence (dotted line) are visible close to Tc . In the inset: Semi-log plot of the magnetic field dependence of the reversible.
measurements (Mrev ) using a SQUID magnetometer. In the intermediate magnetic field range, Hc1 H Hc2 , the reversible magnetization of extreme type-II superconductors in the London model [9] 1 is expected to vary as Mrev 1=k2 lnðH =H0 Þ where k is the magnetic penetration length and H0 is proportional to Hc2 . The reversible part of the magnetization was deduced from magnetization loops writing that: Mrev ¼ 1=2ðMup þ Mdown Þ where Mup and Mdown are the ascending and descending branches of the loop, respectively. As shown in the inset of Fig. 3, Mrev varies linearly with lnðH Þ. However dMrev =d lnðH Þ clearly deviates from the standard theory for T > 0:8Tc (see Fig. 3). In clear contrast with our experimental data, the London model predicts that dMrev =d lnðH Þ 1=k2 is proportional to (1 T =Tc ) close to Tc . The dotted line in Fig. 3 corresponds to the standard Werthamer–Helfang–Hohenberg temperature dependence of 1=k2 . Strong deviations from the 1
This model has been later improved by Hao and Clem [9] taking into account the contribution of vortex core to the free energy density. Despite this non logarithmic contribution to the magnetization, it has been shown that Mrev remains approximatively linear with ln H on a large magnetic field range.
In summary, specific heat and reversible magnetization measurements demonstrate the very peculiar nature of the thermodynamic superconducting transition in cubic (K,Ba)BiO3 . The thermodynamic transition line deduced from specific heat measurements presents a clear positive curvature whose origin still has to be clarified.
References [1] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur, H. Shtrikman, Nature 375 (1995) 373. [2] P.F. Sullivan, G. Seidel, Phys. Rev. 173 (1968) 679. [3] B.F. Woodfield, D.A. Wright, R.A. Fischer, N.E. Philips, H.Y. Tang, Phys. Rev. Lett. 83 (1999) 4622. [4] T. Klein, A. Conde-Gallardo, J. Marcus, P. Szabo, P. Samuely, A.G.M. Jansen, C. Escribe-Filippini, Phys. Rev. B 58 (1998) 12411. [5] A.S. Alexandrov, Phys. Rev. B 48 (1993) 10571. [6] R.G. Dias, J.M. Wheatley, Phys. Rev. B 50 (1994) R13887. [7] F. Marsiglio, J.P. Carbotte, Phys. Rev. B 36 (1987) 3633. [8] Y.N. Ovchinnikov, V.Z. Kresin, Phys. Rev. B 54 (1996) 1251. [9] P. De Gennes, Superconductivity of Metals and Alloys, Addison-Wesley, New York, 1989; M. Tinkham, Introduction to Superconductivity, McGraw-Hill, New York, 1996; A.A. Abrikosov, Fundamentals of the Theory of Metals, North-Holland, New York, 1988; Z. Hao, J.R. Clem, Phys. Rev. Lett. 67 (1991) 2371. [10] D.R. Nelson, H.S. Seung, Phys. Rev. B. 39 (1989) 9153; L.N. Bulaevskii et al., Phys. Rev. Lett. 68 (1992) 3773.
Thermodynamic phase diagram of the cubic (K,Ba)BiO3 superconductor S. Blanchard a,*, C. Marcenat b, J. Marcus a, T. Klein a, A. Sulpice c a
b
Laboratoire d’Etudes des Propri et es Electroniques des Solides, Centre National de la Recherche Scientifique, BP 166, 38042 Grenoble Cedex 9, France Commissariat a l’Energie Atomique––Grenoble, D epartement de Recherche Fondamentale sur la Mati ere Condens ee, SPSMS, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France c Centre de Recherche sur les Tr es Basses Temp eratures, Centre National de la Recherche Scientifique, BP 166, 38042 Grenoble Cedex 9, France
Abstract Specific heat, transport and reversible magnetization measurements have been performed on high quality (K,Ba)BiO3 single crystals (Tc 31 K). Calorimetric measurements up to 16 T show that the transition line between the superconducting and normal states has a strong anomalous positive curvature. The reversible magnetization deviates strongly from the standard London model above 0:8Tc emphasizing the original nature of the superconducting transition in this system. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Vortex matter; Phase diagram
1. Introduction One of the most interesting feature of the H–T phase diagram of high Tc oxides is the existence of a melting line Tm ðH Þ above which the vortex lattice melts into a liquid of entangled flux lines [1]. It is still unclear whether the classical Hc2 line still exists as a transition line or is just some smooth crossover between the vortex liquid and the normal state. Instead, the melting line would mark the first true phase transition when approaching from the normal state. In order to study this issue, we per-
formed thermodynamic (specific heat, reversible magnetization) and transport measurements on high quality (K,Ba)BiO3 single crystals. In high Tc oxides the presence of strong thermal fluctuations complicates the determination of Hc2 from these standard measurements but these fluctuations are expected to be much smaller in the cubic (K,Ba)BiO3 system for which the Ginzburg number is only of the order of 104 (typically two orders of magnitude smaller than in cuprates).
2. Calorimetric measurements * Corresponding author. Tel.: +33-476-88-74-69; fax: +33476-88-79-88. E-mail address: [email protected] (S. Blanchard).
An ac specific heat technique [2] was used to determine the thermodynamic phase transition line of new particularly homogeneous single crystals
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 1 2 4 0 - 0
194
S. Blanchard et al. / Physica C 369 (2002) 193–195
Fig. 1. Normalized specific heat, transport and ac susceptibility versus temperature at H ¼ 3 T in a (K,Ba)BiO3 single crystal.
Fig. 2. Thermodynamic phase diagram deduced from specific heat measurements in three (K,Ba)BiO3 single crystals. In this figure TCp corresponds to the onset of the specific heat anomaly.
grown by electrocrystalization (DTc 0:15 K in transport measurements). Heat was supplied to the sample by a light emitting diode via an optical fiber and the induced temperature oscillations were measured by a chromel–constantan thermocouple. Fig. 1 displays typical transport, specific heat and ac susceptibility data at 3 T. In specific heat measurements, the highest field data (16 T) data have been used as a base line. Our specific heat results qualitatively agree with those previously obtained by Woodfield et al. [3] with a slightly larger value of the jump at H ¼ 0 (150 mJ mol1 K1 ). However, in our case, the specific heat anomaly remains well defined in magnetic fields (see Fig. 1) which enables us to study the magnetic field dependence of the transition in greater detail. The onset of the anomaly is close to the onset of the transport transition (R=RN 95%, where RN is the normal state value). On the other hand the onset of diamagnetism occurs at R 0, roughly corresponding to the mid-point of the specific heat anomaly. We have previously shown that the transport data close to R ¼ 0 can be well described by the so-called vortex-glass scaling formalism, suggesting the existence of a vortex liquid phase for [4].
The most striking feature is that the temperatures TCp ðH Þ corresponding to any characteristic point of the transition (e.g. the onset, mid-point or maximum of the specific heat anomaly) present a clear positive curvature. This can be seen in Fig. 2 which displays the temperatures TCp corresponding to the onset of the peak for three different samples. This is a totally unexpected feature since in conventional superconductors the location of the specific heat anomaly defines the upper critical field and is thus expected to vary linearly with T close to Tc . Indeed, none of the theoretical models which have been developed in order to explain a ‘‘possible’’ upward curvature of the upper critical field in cuprates (bipolaron scenario [5], spin– charge separation [6] or very strong coupling [7]) can be applied to the (K,Ba)BiO3 system. Moreover, the presence of inhomogeneities and/or magnetic impurities would only lead to an upward curvature at low temperature [8].
3. Reversible magnetization To complete this study of the thermodynamic properties we performed reversible magnetization
S. Blanchard et al. / Physica C 369 (2002) 193–195
195
London theory are also usually observed in high Tc cuprates [10] and are commonly attributed to the presence of strong fluctuations. It is thus very surprising to observe similar deviations in the (K,Ba)BiO3 system. However, note that, in contrast to cuprates, dMrev =d lnðH Þ remains positive on the entire temperature range in (K,Ba)BiO3 .
4. Conclusions
Fig. 3. Temperature dependence of dMrev =d lnðHÞ in a (K,Ba)BiO3 single crystal. Strong deviations from the standard Werthamer–Helfang–Hohenberg dependence (dotted line) are visible close to Tc . In the inset: Semi-log plot of the magnetic field dependence of the reversible.
measurements (Mrev ) using a SQUID magnetometer. In the intermediate magnetic field range, Hc1 H Hc2 , the reversible magnetization of extreme type-II superconductors in the London model [9] 1 is expected to vary as Mrev 1=k2 lnðH =H0 Þ where k is the magnetic penetration length and H0 is proportional to Hc2 . The reversible part of the magnetization was deduced from magnetization loops writing that: Mrev ¼ 1=2ðMup þ Mdown Þ where Mup and Mdown are the ascending and descending branches of the loop, respectively. As shown in the inset of Fig. 3, Mrev varies linearly with lnðH Þ. However dMrev =d lnðH Þ clearly deviates from the standard theory for T > 0:8Tc (see Fig. 3). In clear contrast with our experimental data, the London model predicts that dMrev =d lnðH Þ 1=k2 is proportional to (1 T =Tc ) close to Tc . The dotted line in Fig. 3 corresponds to the standard Werthamer–Helfang–Hohenberg temperature dependence of 1=k2 . Strong deviations from the 1
This model has been later improved by Hao and Clem [9] taking into account the contribution of vortex core to the free energy density. Despite this non logarithmic contribution to the magnetization, it has been shown that Mrev remains approximatively linear with ln H on a large magnetic field range.
In summary, specific heat and reversible magnetization measurements demonstrate the very peculiar nature of the thermodynamic superconducting transition in cubic (K,Ba)BiO3 . The thermodynamic transition line deduced from specific heat measurements presents a clear positive curvature whose origin still has to be clarified.
References [1] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur, H. Shtrikman, Nature 375 (1995) 373. [2] P.F. Sullivan, G. Seidel, Phys. Rev. 173 (1968) 679. [3] B.F. Woodfield, D.A. Wright, R.A. Fischer, N.E. Philips, H.Y. Tang, Phys. Rev. Lett. 83 (1999) 4622. [4] T. Klein, A. Conde-Gallardo, J. Marcus, P. Szabo, P. Samuely, A.G.M. Jansen, C. Escribe-Filippini, Phys. Rev. B 58 (1998) 12411. [5] A.S. Alexandrov, Phys. Rev. B 48 (1993) 10571. [6] R.G. Dias, J.M. Wheatley, Phys. Rev. B 50 (1994) R13887. [7] F. Marsiglio, J.P. Carbotte, Phys. Rev. B 36 (1987) 3633. [8] Y.N. Ovchinnikov, V.Z. Kresin, Phys. Rev. B 54 (1996) 1251. [9] P. De Gennes, Superconductivity of Metals and Alloys, Addison-Wesley, New York, 1989; M. Tinkham, Introduction to Superconductivity, McGraw-Hill, New York, 1996; A.A. Abrikosov, Fundamentals of the Theory of Metals, North-Holland, New York, 1988; Z. Hao, J.R. Clem, Phys. Rev. Lett. 67 (1991) 2371. [10] D.R. Nelson, H.S. Seung, Phys. Rev. B. 39 (1989) 9153; L.N. Bulaevskii et al., Phys. Rev. Lett. 68 (1992) 3773.