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Observation of the vortex lattice phase transition in the specific heat in La1.86Sr0.14CuO4 single crystal
Physica C 366 (2002) 129±134
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Observation of the vortex lattice phase transition in the speci®c heat in La1:86Sr0:14CuO4 single crystal H. Iwasaki a,*, T. Chigira a, T. Naito a, S. Moriyama a, Y. Iwasa a, T. Nishizaki b, N. Kobayashi b a
JAIST, School of Materials Science, Asahidai 1-1, Tatsunokuchi 923-1292, Ishikawa, Japan b Institute for Materials Research (IMR), Tohoku University, Sendai 980-8577, Japan Received 6 March 2001; received in revised form 7 May 2001; accepted 22 May 2001
Abstract Speci®c heat and magnetization have been measured on La1:86 Sr0:14 CuO4 single crystal in order to investigate the vortex lattice phase transition in the mixed state under magnetic ®eld up to 120 kOe. Clear anomaly and jump come from the phase transition of the vortex lattice were observed in the speci®c heat and the magnetization, respectively. The temperatures of the vortex lattice phase transition and the entropy change accompanied with it were consistent between both measurements. The temperature dependence of the phase transition obeys the relation of Hm Hm0 1 T =Tc 1:7 by melting of the vortex lattice in the magnetic ®eld below 50 kOe and Hd Hd0 Tc =T 1 by sublimation of the vortex lattice in the higher ®eld. The results strongly suggest a possibility of a crossover from the vortex lattice melting to the sublimation at about 50 kOe. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Vortex lattice; Phase transition; Speci®c heat; Magnetization; Crystal
In the high temperature superconductors with large anisotropy between the a (or b) axis and the c axis, the vortex system shows anomalous behaviors such as a vortex lattice melting, a dimensional crossover and an extremely large superconducting ¯uctuation etc. [1]. It is interpreted that a large thermal ¯uctuation in the oxides causes these phenomena. The phase transition of the vortex lattice has been intensively studied as a main problem. It was initially observed by the magne-
* Corresponding author. Tel.: +81-761-51-1571; fax: +81761-51-1575. E-mail address: [email protected] (H. Iwasaki).
tization measurements in the Bi±Sr±Ca±Cu±O (BSCCO) system [2] and has been discussed from the point of view of the vortex lattice melting transition. Thereafter, similar behaviors were also reported in the Y±Ba±Cu±O (YBCO) [3±9] and La±Sr±Cu±O (LSCO) [10±12] systems. In their studies the measurements have been made by the magnetization and the resistivity. It is necessary to check by the calorimetric measurement because it can provide a proof of the ®rst order by the observation of the latent heat accompanied with the phase transition. The direct con®rmation of the ®rst order transition by the calorimetric measurement has only been made in the YBCO system, [8] where the phase transition was made clear to be the ®rst order by the observation of the latent heat
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and the entropy dierence between the vortex lattice and the vortex liquid was also estimated to be approximately 0.4±0.6(kB /vortex/layer). In the other group [9] it was discussed with the order of the transition by the oxygen content of the sample which depends on the magnetic ®eld values. Though the phase transition of the vortex system in the oxides is usually interpreted to be the melting transition of the vortex lattice, the temperature dependence of the transition and the magnitude of the entropy change [2,5,6,13,14] do not always coincide with the melting theory. [15± 17] On the other hand, the insistence that the phase transition should be explained by the sublimation of the vortex lattice has been proposed [11]. In the sublimation it is physically interpreted that the vortex system loses not only a shear modulus but a tilt one and the vortex lines change to pancakevortices decoupled between the CuO2 planes. The conclusion is still open now. LSCO system is very convenient in the research of the relationship between the anisotropy and the properties of the vortex system because the anisotropy can be largely changed without any alteration of the basic structure. However, the report concerned with the vortex lattice phase transition is extremely little for LSCO system [10±12] compared with the other YBCO [3±9] and BSCCO [2,13,14] systems. This is due to a diculty of getting a clean single crystal because of the substituted system. In their studies [10±12] magnetic ®eld was limited below 50 kOe where the temperature dependence of the phase transition could be explained by the melting theory. It is expected that the correlation of the vortex between the CuO2 planes becomes negligible in higher magnetic ®eld region where the interaction between the vortices on the CuO2 plane is much dominant. So, it may be able to get an information whether the transition is due to the melting or the sublimation by the measurements in the higher magnetic ®eld region. Furthermore, the behavior of the entropy change accompanied with the phase transition in the previous studies of the LSCO system is not always consistent in both the temperature dependence and the magnitude. In the present study we carefully prepare a good quality sample and report the results related with the vortex lattice phase transition
by the speci®c heat and the magnetization measurements. Measured sample of La1:86 Sr0:14 CuO4 was synthesized by travelling solvent ¯oating zone method (TSFZ) and annealed in ¯owing oxygen at 950°C for several weeks. The growth condition by TSFZ has been described elsewhere [18]. The composition of the sample was estimated by electron probe micro analyzer (EPMA) and the Sr content x was determined to be 0.14. The sample size is 1:5 a axis 0:75 b axis 0:95 c axis mm3 . The demagnetization coecient to the c axis is small and it is expected that the magnetic induction in the sample for H kc axis is homogeneous. Tc of the sample was 34.5 K with the transition width of 0.5 K. Speci®c heat was measured by a thermal relaxation method using PPMS (Quantum Design Inc.). Magnetization was measured by SQUID magnetometer (Quantum Design Inc.) up to 70 kOe and vibrating sample magnetometer (VSM) (Oxford Instruments) up to 120 kOe, where a sweep rate of the magnetic ®eld was 0.5 kOe/min. In the SQUID RSO-option the measurements were made at a center position. The frequency is 1 Hz and the amplitude is 1 cm. In the VSM the frequency is 45 Hz and the amplitude is 3 mm. In all measurements magnetic ®eld was applied to the c axis. Fig. 1 shows the temperature dependence of Cp =T 3 just around the phase transition at H 80 kOe, where solid curve represents a back-ground heat capacity. Back-ground heat capacity is given P by ®tting by the function Cb g ai T i i 0±3 of the data except for those in the transition region. Total heat capacity Cp is given by Cp DC Cb g . Clear structure can be seen around 14±15 K. The heat capacity anomalies DC are obtained by subtracting of Cp by Cb g and are shown in Fig. 2(a)±(d). The temperatures at which the anomalies observed in the speci®c heat appear above 40 kOe coincide quite well with those at which the magnetization makes a jump described later and it is interpreted that the anomaly in the speci®c heat comes from the ®rst order vortex lattice phase transition from the liquid (or gas) phase to the solid one. Below H 30 kOe the anomaly can not be recognized as shown in Fig. 2(d). In the YBCO system [9] the trace by the transition have not also
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Fig. 1. Temperature dependence of Cp =T 3 at 80 kOe. Clear anomaly is seen accompanied with the phase transition. Solid curve indicates the back-ground heat capacity described in the text. Inset shows its temperature dependence in the wide temperature range.
been observed in the low ®elds. Because the heat capacity Cp has a large temperature dependence at high temperature which corresponds to low ®eld case in the phase transition of the LSCO system, the observation of the anomaly may be dicult in the present system. So, it is not clear whether no observation of the transition is essential or not. The entropy dierences Ds R between both phases are estimated by integral DC=T dT from the results shown in Fig. 2(a)±(c). The temperature dependence of the entropy change shows a step like behavior and the obtained values are Ds 0:23kB / vortex/layer H 40 kOe, Ds 0:20kB /vortex/ layer H 50 kOe and Ds 0:13kB /vortex/layer H 80 kOe as a average value. These values seem to be consistent with those of the other oxide system. In order to recon®rm the order of the phase transition and make a cross check of the Ds values obtained by the speci®c heat the magnetization was also measured. Fig. 3 shows the temperature dependencies of the magnetizations at H 10, 20 and 35 kOe. The magnetization has a broad maximum or a shoulder like behavior and then a
Fig. 2. Heat capacity anomaly obtained by subtraction of Cp by the back-ground heat capacity at (a) H 80 kOe, (b) H 50 kOe, (c) H 40 kOe and (d) H 30 kOe.
small jump. Similar behaviors are also observed in the magnetic ®eld dependences of the magnetization. The jumps are attributed to the ®rst order transition of the vortex lattice. Its transition width is below 0.5 K for all magnetic ®elds and is narrower than that of 1 K in the speci®c heat. The broad maximum were also observed in the previous report [10]. The irreversibility in the magnetization between increasing and decreasing ®elds appears below a temperature of the magnetization jump. The magnitude of the magnetization jump DM is estimated from the dierence between the
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Fig. 3. Temperature dependences of the magnetization around the vortex lattice phase transition at H 10, 20 and 35 kOe.
linear extrapolation lines of the magnetization above and below the jump as shown by the solid lines in Fig. 3. The entropy dierence Ds is related with DM by the modi®ed Clausius±Clapeyron equation Ds d/0 DM dBp t =dT =Bp t , where d is the inter-layer spacing of the CuO2 planes, and /0 the ¯ux quantum. The gradient dBp t =dT of the ®rst order transition curve is estimated from the magnetic phase diagram of the vortex system mentioned later. The obtained results of DM and Ds are plotted in Fig. 4 together with those of the speci®c heat. The estimated values of the entropy change coincide for both measurements well. The temperature dependence of Ds is almost constant and has a tendency of decrease at low tempera-
Fig. 4. Temperature dependences of the magnetization jump and the entropy change by the vortex lattice phase transition. Error bars in Ds by the speci®c heat measurements are given by taking account of the scattering of the speci®c data. (See Fig. 2).
tures. It is dierent from the previous study by Sasagawa et al. [12] and seems to be similar to the results by Naito et al. [10]. In the other oxides of BSCCO [2] and YBCO [8] the behavior of the decrease of Ds with an approach to the upper critical point has been also observed. The behavior of Ds in the present crystal might be due to a similar origin. In Fig. 5 the magnetization curves at 12.0 K and 25.5 K are shown, which were taken by VSM. For increasing ®eld clear magnetization jump can be seen, while it is not obvious for decreasing ®eld. Detailed magnetization behavior is dierent for both VSM and SQUID measurements, for example, how to appear the irreversibility and the absence of the magnetization maximum just below the magnetic ®eld of the jump observed in the SQUID measurements etc. This is probably due to the measurement condition because in the high Tc oxides a large magnetic relaxation is observed and the measurements by VSM have been done under
Fig. 5. Magnetic ®eld dependence of the magnetization by VSM. A large second peak is observed around 5 kOe. Upper inset indicates the magnetization in the magnetic ®eld range of the vortex lattice phase transition at 25.5 K. Lower inset at 12.0 K.
H. Iwasaki et al. / Physica C 366 (2002) 129±134 n
Fig. 6. Temperature dependence of the vortex lattice phase transition obtained by the speci®c heat and the magnetization measurements. Dotted and dashed curves correspond to the melting and the sublimation expected from the theory which is obtained by the ®tting of the data of the phase transition points, respectively.
sweeping magnetic ®elds. The estimation of Ds is not made because the irreversibility of the magnetization between increasing and decreasing ®elds is observed at the transition ®eld in VSM measurements. In Fig. 6 all phase transition points of the vortex lattice determined by the speci®c heat and the magnetization are plotted on the H ±T plane. All data are on the one universal curve and the estimated values of the entropy dierence are also similar to each other as mentioned above. So, the observed anomaly in the speci®c heat is concluded to originate from the vortex lattice phase transition. Furthermore, it should be noted that the ®rst order transition denoted by the magnetization jump was observed above 100 kOe. In the clean YBCO single crystal [19] the ®rst order transition could be observable in much high ®eld and the present sample is suggested to be quite clean crystal. Now, we discuss the temperature dependence of the vortex phase transition. Dotted and dashed curves in Fig. 6 are given by Hm T Hm0 1
133
T =Tc which means the vortex lattice melting [15± 17] and by Hd T Hd0 T =Tc 1 for the vortex lattice sublimation, [20±22] respectively. Below 50 kOe the transition points obey the former curve. (The results by SQUID magnetometer can be ®tted excellently.) In the melting theory [15±17] Hm0 is given to be /50 c4L =p4 kB2 c2 k4ab 0Tc2 , where cL is the Lindemann criterion number, kB the Boltzmann constant, c nab =nc the anisotropic parameter and kab the ab plane penetration depth. Using Hm0 177 kOe obtained by the ®tting, cL 0:12 [23] the anisotropic pa[10] and kab 0 2500 A, rameter is estimated to be c 33 and the exponent n 1:7 is consistent with the melting theory. However, the data at high ®elds deviate from the melting curve. Furthermore, it should be emphasized that it was impossible to make a ®tting by the equation based on the melting theory of all of the transition points up to 107 kOe. On the other hand, the temperature dependence becomes to ®t better by the equation based on the sublimation in the high magnetic ®eld region above 50 kOe. The sublimation scenario seems to be not valid at low ®eld because its ®tting is much worse than that by the melting transition. The temperature dependence of the phase transition of the vortex system strongly suggests that the transition changes from the melting in the low ®eld region to the sublimation in the high ®eld one. This interpretation is also supported by the following estimation. Using c 33 obtained previously, the crossover ®eld Hcr /0 =c2 d 2 from the two-dimensional to the three-dimensional vortex system [20] is estimated to be Hcr 44 kOe and the obtained Hcr value is consistent with the interpretation. Thus, we insist experimentally that a kind of the crossover from the vortex lattice melting to sublimation occurs at about 50 kOe in the present system. This interpretation can be understood if we consider that the correlation of the vortex between the CuO2 planes tends to be lost at high ®elds. In summary we observed the vortex lattice phase transition of the LSCO single crystal in both speci®c heat and magnetization. The entropy change accompanied with the transition is consistent between both measurements (Ds 1:5±2:5kB / vortex/layer). Its temperature dependence is almost constant above 19 K and shows a tendency
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of decrease in the lower temperature region. The temperature dependence of the phase transition strongly suggests a possibility of a crossover from the vortex lattice melting to sublimation occurs at about 50 kOe. The latent heat value at the crossover ®eld also supports this interpretation. In order to clarify a validity of this interpretation it is necessary to measure in samples with the other c (under doped LSCO crystals). Furthermore, whether the upper critical point con®rmed in the other oxide superconductors which segregates from the ®rst order phase transition to the second order one exists or not may be made clear in measurements at higher magnetic ®elds and it is highly desired. Acknowledgements One of the authors (Y.I.) is partly supported by the JSPS ``Future Program'', grant no. RFTF96P00104. The experiments were partly made at Institute for Materials Research, Tohoku University. References [1] G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 (1994) 1125. [2] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur, H. Shtrikman, Nature 375 (1995) 373. [3] H. Safar, P.L. Gammel, D.A. Huse, D.J. Bishop, J.P. Rice, D.M. Ginsberg, Phys. Rev. Lett. 69 (1992) 824.
[4] W.K. Kwok, S. Fleshler, U. Welp, V.M. Vinokur, J. Downey, G.W. Crabtree, Phys. Rev. Lett. 69 (1992) 3770. [5] R. Liang, D.A. Bonn, W.N. Hardy, Phys. Rev. Lett. 76 (1996) 835. [6] T. Nishizaki, Y. Onodera, N. Kobayashi, H. Asaoka, H. Takei, Phys. Rev B 53 (1996) 82. [7] K. Deligiannis, P.A.J. de Groot, S. Pinfold, R. Langan, R. Gagnon, L. Taillefer, Phys. Rev. Lett. 79 (1997) 2121. [8] A. Schilling, R.A. Fisher, N.E. Phillips, U. Welp, D. Dasgupta, W.K. Kwok, G.W. Crabtree, Nature 382 (1996) 791. [9] M. Roulin, A. Junod, A. Erb, E. Walker, Phys. Rev. Lett. 80 (1998) 1722. [10] T. Naito, T. Nishizaki, F. Matsuoka, H. Iwasaki, N. Kobayash, Czechoslovak J. Phys. 46 (1996) 1585. [11] T. Sasagawa, K. Kishio, Y. Togawa, J. Shimoyama, K. Kitazawa, Phys. Rev. Lett. 80 (1998) 4297. [12] T. Sasagawa, Y. Togawa, J. Shimoyama, A. Kapitulnik, K. Kishio, K. Kitazawa, Phys. Rev. B 61 (2000) 1610. [13] T. Hanaguri, T. Tsuboi, A. Maeda, T. Nishizzaki, N. Kobayashi, Y. Kotaka, J. Shimoyama, K. Kishio, Physica C 256 (1996) 111. [14] S. Watauchi, H. Ikuta, J. Shimoyama, K. Kishio, Physica C 259 (1996) 373. [15] A. Houghton, R.A. Pelcovits, A. Sudbù, Phys. Rev. B 40 (1989) 6763. [16] E.H. Brandt, Phys. Rev. Lett. 63 (1989) 1106. [17] G. Blatter, B.I. Ivlev, Phys. Rev. B 50 (1994) 10272. [18] H. Iwasaki, F. Matsuoka, K. Tanigawa, Phys. Rev. B 59 (1999) 14624. [19] K. Shibata, T. Nishizaki, T. Naito, N. Kobayashi, Physica C 317±318 (1999) 540. [20] L.I. Glazman, A.E. Koshelev, Phys. Rev. B 43 (1991) 2835. [21] L.L. Daemen, L.N. Bulaevskii, M.P. Maley, J.Y. Coulter, Phys. Rev. Lett. 70 (1993) 1167. [22] R. Ikeda, J. Phys. Soc. Jpn. 64 (1995) 1683. [23] Q. Li, M. Suenaga, T. Kimura, K. Kishio, Phys. Rev. B 47 (1993) 2854.
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Observation of the vortex lattice phase transition in the speci®c heat in La1:86Sr0:14CuO4 single crystal H. Iwasaki a,*, T. Chigira a, T. Naito a, S. Moriyama a, Y. Iwasa a, T. Nishizaki b, N. Kobayashi b a
JAIST, School of Materials Science, Asahidai 1-1, Tatsunokuchi 923-1292, Ishikawa, Japan b Institute for Materials Research (IMR), Tohoku University, Sendai 980-8577, Japan Received 6 March 2001; received in revised form 7 May 2001; accepted 22 May 2001
Abstract Speci®c heat and magnetization have been measured on La1:86 Sr0:14 CuO4 single crystal in order to investigate the vortex lattice phase transition in the mixed state under magnetic ®eld up to 120 kOe. Clear anomaly and jump come from the phase transition of the vortex lattice were observed in the speci®c heat and the magnetization, respectively. The temperatures of the vortex lattice phase transition and the entropy change accompanied with it were consistent between both measurements. The temperature dependence of the phase transition obeys the relation of Hm Hm0 1 T =Tc 1:7 by melting of the vortex lattice in the magnetic ®eld below 50 kOe and Hd Hd0 Tc =T 1 by sublimation of the vortex lattice in the higher ®eld. The results strongly suggest a possibility of a crossover from the vortex lattice melting to the sublimation at about 50 kOe. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Vortex lattice; Phase transition; Speci®c heat; Magnetization; Crystal
In the high temperature superconductors with large anisotropy between the a (or b) axis and the c axis, the vortex system shows anomalous behaviors such as a vortex lattice melting, a dimensional crossover and an extremely large superconducting ¯uctuation etc. [1]. It is interpreted that a large thermal ¯uctuation in the oxides causes these phenomena. The phase transition of the vortex lattice has been intensively studied as a main problem. It was initially observed by the magne-
* Corresponding author. Tel.: +81-761-51-1571; fax: +81761-51-1575. E-mail address: [email protected] (H. Iwasaki).
tization measurements in the Bi±Sr±Ca±Cu±O (BSCCO) system [2] and has been discussed from the point of view of the vortex lattice melting transition. Thereafter, similar behaviors were also reported in the Y±Ba±Cu±O (YBCO) [3±9] and La±Sr±Cu±O (LSCO) [10±12] systems. In their studies the measurements have been made by the magnetization and the resistivity. It is necessary to check by the calorimetric measurement because it can provide a proof of the ®rst order by the observation of the latent heat accompanied with the phase transition. The direct con®rmation of the ®rst order transition by the calorimetric measurement has only been made in the YBCO system, [8] where the phase transition was made clear to be the ®rst order by the observation of the latent heat
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 8 8 4 - X
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and the entropy dierence between the vortex lattice and the vortex liquid was also estimated to be approximately 0.4±0.6(kB /vortex/layer). In the other group [9] it was discussed with the order of the transition by the oxygen content of the sample which depends on the magnetic ®eld values. Though the phase transition of the vortex system in the oxides is usually interpreted to be the melting transition of the vortex lattice, the temperature dependence of the transition and the magnitude of the entropy change [2,5,6,13,14] do not always coincide with the melting theory. [15± 17] On the other hand, the insistence that the phase transition should be explained by the sublimation of the vortex lattice has been proposed [11]. In the sublimation it is physically interpreted that the vortex system loses not only a shear modulus but a tilt one and the vortex lines change to pancakevortices decoupled between the CuO2 planes. The conclusion is still open now. LSCO system is very convenient in the research of the relationship between the anisotropy and the properties of the vortex system because the anisotropy can be largely changed without any alteration of the basic structure. However, the report concerned with the vortex lattice phase transition is extremely little for LSCO system [10±12] compared with the other YBCO [3±9] and BSCCO [2,13,14] systems. This is due to a diculty of getting a clean single crystal because of the substituted system. In their studies [10±12] magnetic ®eld was limited below 50 kOe where the temperature dependence of the phase transition could be explained by the melting theory. It is expected that the correlation of the vortex between the CuO2 planes becomes negligible in higher magnetic ®eld region where the interaction between the vortices on the CuO2 plane is much dominant. So, it may be able to get an information whether the transition is due to the melting or the sublimation by the measurements in the higher magnetic ®eld region. Furthermore, the behavior of the entropy change accompanied with the phase transition in the previous studies of the LSCO system is not always consistent in both the temperature dependence and the magnitude. In the present study we carefully prepare a good quality sample and report the results related with the vortex lattice phase transition
by the speci®c heat and the magnetization measurements. Measured sample of La1:86 Sr0:14 CuO4 was synthesized by travelling solvent ¯oating zone method (TSFZ) and annealed in ¯owing oxygen at 950°C for several weeks. The growth condition by TSFZ has been described elsewhere [18]. The composition of the sample was estimated by electron probe micro analyzer (EPMA) and the Sr content x was determined to be 0.14. The sample size is 1:5 a axis 0:75 b axis 0:95 c axis mm3 . The demagnetization coecient to the c axis is small and it is expected that the magnetic induction in the sample for H kc axis is homogeneous. Tc of the sample was 34.5 K with the transition width of 0.5 K. Speci®c heat was measured by a thermal relaxation method using PPMS (Quantum Design Inc.). Magnetization was measured by SQUID magnetometer (Quantum Design Inc.) up to 70 kOe and vibrating sample magnetometer (VSM) (Oxford Instruments) up to 120 kOe, where a sweep rate of the magnetic ®eld was 0.5 kOe/min. In the SQUID RSO-option the measurements were made at a center position. The frequency is 1 Hz and the amplitude is 1 cm. In the VSM the frequency is 45 Hz and the amplitude is 3 mm. In all measurements magnetic ®eld was applied to the c axis. Fig. 1 shows the temperature dependence of Cp =T 3 just around the phase transition at H 80 kOe, where solid curve represents a back-ground heat capacity. Back-ground heat capacity is given P by ®tting by the function Cb g ai T i i 0±3 of the data except for those in the transition region. Total heat capacity Cp is given by Cp DC Cb g . Clear structure can be seen around 14±15 K. The heat capacity anomalies DC are obtained by subtracting of Cp by Cb g and are shown in Fig. 2(a)±(d). The temperatures at which the anomalies observed in the speci®c heat appear above 40 kOe coincide quite well with those at which the magnetization makes a jump described later and it is interpreted that the anomaly in the speci®c heat comes from the ®rst order vortex lattice phase transition from the liquid (or gas) phase to the solid one. Below H 30 kOe the anomaly can not be recognized as shown in Fig. 2(d). In the YBCO system [9] the trace by the transition have not also
H. Iwasaki et al. / Physica C 366 (2002) 129±134
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Fig. 1. Temperature dependence of Cp =T 3 at 80 kOe. Clear anomaly is seen accompanied with the phase transition. Solid curve indicates the back-ground heat capacity described in the text. Inset shows its temperature dependence in the wide temperature range.
been observed in the low ®elds. Because the heat capacity Cp has a large temperature dependence at high temperature which corresponds to low ®eld case in the phase transition of the LSCO system, the observation of the anomaly may be dicult in the present system. So, it is not clear whether no observation of the transition is essential or not. The entropy dierences Ds R between both phases are estimated by integral DC=T dT from the results shown in Fig. 2(a)±(c). The temperature dependence of the entropy change shows a step like behavior and the obtained values are Ds 0:23kB / vortex/layer H 40 kOe, Ds 0:20kB /vortex/ layer H 50 kOe and Ds 0:13kB /vortex/layer H 80 kOe as a average value. These values seem to be consistent with those of the other oxide system. In order to recon®rm the order of the phase transition and make a cross check of the Ds values obtained by the speci®c heat the magnetization was also measured. Fig. 3 shows the temperature dependencies of the magnetizations at H 10, 20 and 35 kOe. The magnetization has a broad maximum or a shoulder like behavior and then a
Fig. 2. Heat capacity anomaly obtained by subtraction of Cp by the back-ground heat capacity at (a) H 80 kOe, (b) H 50 kOe, (c) H 40 kOe and (d) H 30 kOe.
small jump. Similar behaviors are also observed in the magnetic ®eld dependences of the magnetization. The jumps are attributed to the ®rst order transition of the vortex lattice. Its transition width is below 0.5 K for all magnetic ®elds and is narrower than that of 1 K in the speci®c heat. The broad maximum were also observed in the previous report [10]. The irreversibility in the magnetization between increasing and decreasing ®elds appears below a temperature of the magnetization jump. The magnitude of the magnetization jump DM is estimated from the dierence between the
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Fig. 3. Temperature dependences of the magnetization around the vortex lattice phase transition at H 10, 20 and 35 kOe.
linear extrapolation lines of the magnetization above and below the jump as shown by the solid lines in Fig. 3. The entropy dierence Ds is related with DM by the modi®ed Clausius±Clapeyron equation Ds d/0 DM dBp t =dT =Bp t , where d is the inter-layer spacing of the CuO2 planes, and /0 the ¯ux quantum. The gradient dBp t =dT of the ®rst order transition curve is estimated from the magnetic phase diagram of the vortex system mentioned later. The obtained results of DM and Ds are plotted in Fig. 4 together with those of the speci®c heat. The estimated values of the entropy change coincide for both measurements well. The temperature dependence of Ds is almost constant and has a tendency of decrease at low tempera-
Fig. 4. Temperature dependences of the magnetization jump and the entropy change by the vortex lattice phase transition. Error bars in Ds by the speci®c heat measurements are given by taking account of the scattering of the speci®c data. (See Fig. 2).
tures. It is dierent from the previous study by Sasagawa et al. [12] and seems to be similar to the results by Naito et al. [10]. In the other oxides of BSCCO [2] and YBCO [8] the behavior of the decrease of Ds with an approach to the upper critical point has been also observed. The behavior of Ds in the present crystal might be due to a similar origin. In Fig. 5 the magnetization curves at 12.0 K and 25.5 K are shown, which were taken by VSM. For increasing ®eld clear magnetization jump can be seen, while it is not obvious for decreasing ®eld. Detailed magnetization behavior is dierent for both VSM and SQUID measurements, for example, how to appear the irreversibility and the absence of the magnetization maximum just below the magnetic ®eld of the jump observed in the SQUID measurements etc. This is probably due to the measurement condition because in the high Tc oxides a large magnetic relaxation is observed and the measurements by VSM have been done under
Fig. 5. Magnetic ®eld dependence of the magnetization by VSM. A large second peak is observed around 5 kOe. Upper inset indicates the magnetization in the magnetic ®eld range of the vortex lattice phase transition at 25.5 K. Lower inset at 12.0 K.
H. Iwasaki et al. / Physica C 366 (2002) 129±134 n
Fig. 6. Temperature dependence of the vortex lattice phase transition obtained by the speci®c heat and the magnetization measurements. Dotted and dashed curves correspond to the melting and the sublimation expected from the theory which is obtained by the ®tting of the data of the phase transition points, respectively.
sweeping magnetic ®elds. The estimation of Ds is not made because the irreversibility of the magnetization between increasing and decreasing ®elds is observed at the transition ®eld in VSM measurements. In Fig. 6 all phase transition points of the vortex lattice determined by the speci®c heat and the magnetization are plotted on the H ±T plane. All data are on the one universal curve and the estimated values of the entropy dierence are also similar to each other as mentioned above. So, the observed anomaly in the speci®c heat is concluded to originate from the vortex lattice phase transition. Furthermore, it should be noted that the ®rst order transition denoted by the magnetization jump was observed above 100 kOe. In the clean YBCO single crystal [19] the ®rst order transition could be observable in much high ®eld and the present sample is suggested to be quite clean crystal. Now, we discuss the temperature dependence of the vortex phase transition. Dotted and dashed curves in Fig. 6 are given by Hm T Hm0 1
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T =Tc which means the vortex lattice melting [15± 17] and by Hd T Hd0 T =Tc 1 for the vortex lattice sublimation, [20±22] respectively. Below 50 kOe the transition points obey the former curve. (The results by SQUID magnetometer can be ®tted excellently.) In the melting theory [15±17] Hm0 is given to be /50 c4L =p4 kB2 c2 k4ab 0Tc2 , where cL is the Lindemann criterion number, kB the Boltzmann constant, c nab =nc the anisotropic parameter and kab the ab plane penetration depth. Using Hm0 177 kOe obtained by the ®tting, cL 0:12 [23] the anisotropic pa[10] and kab 0 2500 A, rameter is estimated to be c 33 and the exponent n 1:7 is consistent with the melting theory. However, the data at high ®elds deviate from the melting curve. Furthermore, it should be emphasized that it was impossible to make a ®tting by the equation based on the melting theory of all of the transition points up to 107 kOe. On the other hand, the temperature dependence becomes to ®t better by the equation based on the sublimation in the high magnetic ®eld region above 50 kOe. The sublimation scenario seems to be not valid at low ®eld because its ®tting is much worse than that by the melting transition. The temperature dependence of the phase transition of the vortex system strongly suggests that the transition changes from the melting in the low ®eld region to the sublimation in the high ®eld one. This interpretation is also supported by the following estimation. Using c 33 obtained previously, the crossover ®eld Hcr /0 =c2 d 2 from the two-dimensional to the three-dimensional vortex system [20] is estimated to be Hcr 44 kOe and the obtained Hcr value is consistent with the interpretation. Thus, we insist experimentally that a kind of the crossover from the vortex lattice melting to sublimation occurs at about 50 kOe in the present system. This interpretation can be understood if we consider that the correlation of the vortex between the CuO2 planes tends to be lost at high ®elds. In summary we observed the vortex lattice phase transition of the LSCO single crystal in both speci®c heat and magnetization. The entropy change accompanied with the transition is consistent between both measurements (Ds 1:5±2:5kB / vortex/layer). Its temperature dependence is almost constant above 19 K and shows a tendency
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of decrease in the lower temperature region. The temperature dependence of the phase transition strongly suggests a possibility of a crossover from the vortex lattice melting to sublimation occurs at about 50 kOe. The latent heat value at the crossover ®eld also supports this interpretation. In order to clarify a validity of this interpretation it is necessary to measure in samples with the other c (under doped LSCO crystals). Furthermore, whether the upper critical point con®rmed in the other oxide superconductors which segregates from the ®rst order phase transition to the second order one exists or not may be made clear in measurements at higher magnetic ®elds and it is highly desired. Acknowledgements One of the authors (Y.I.) is partly supported by the JSPS ``Future Program'', grant no. RFTF96P00104. The experiments were partly made at Institute for Materials Research, Tohoku University. References [1] G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, V.M. Vinokur, Rev. Mod. Phys. 66 (1994) 1125. [2] E. Zeldov, D. Majer, M. Konczykowski, V.B. Geshkenbein, V.M. Vinokur, H. Shtrikman, Nature 375 (1995) 373. [3] H. Safar, P.L. Gammel, D.A. Huse, D.J. Bishop, J.P. Rice, D.M. Ginsberg, Phys. Rev. Lett. 69 (1992) 824.
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