Doping level dependence of magnetization anomalies and heat capacity of Bi2Sr2CaCu2O8 + δ in the mixed state

PHYSICA® ELSEVIER

Physica C 263 (1996) 434-437

Doping level dependence of magnetization anomalies and heat capacity of Bi2Sr2CaCu2Os+ in the mixed state Tetsuo Hanaguri a, *, Takashi Tsuboi a, Atsutaka Maeda a, Terukazu Nishizaki h, Norio Kobayashi b, Yasutoshi Kotaka c Jun-ichi Shimoyama c, Kohji Kishio c a Department of Pure and Applied Sciences, The University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153, Japan b Institute for Materials Research, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-77, Japan c Department of Applied Chemistry, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113, Japan

Abstract Magnetization M and heat capacity C were measured around the first order vortex phase transition lines of two Bi2Sr2CaCu2Os+ ~ single crystals having different oxygen contents. The entropy jump per vortex per layer, As, at the transition was estimated from the step in M. The oxygen-content dependence of A s was contradictory to the simple vortex lattice melting theory based on the Lindemann criterion. In both crystals, no anomalies in C were observed at the transition owing to both the small A s and the broadening of the transition.

Because of the high superconducting transition temperature, T~, and large Ginzburg-Landau parameter, K, of high-TC cuprate superconductors, the vortex lattice (VL) in high-T~ superconductors fluctuates thermally and is predicted to melt at a field much lower than the mean-field upper critical field [1]. Although the concept of the VL melting transition is clear, it is difficult to establish this transition experimentally, because the transport measurements which are commonly used to investigate the vortex dynamics cannot distinguish the phase transition from simple depinning [2]. It is necessary to examine the thermodynamical quantities such as the magnetization M and heat capacity C to establish the existence of the phase

* Corresponding author. Fax: +81 3 3467 8945; e-mail: [email protected] tokyo.ac.jp.

transition. According to recent M measurements on Bi2Sr2CaCu2Os+ 8 single crystals in the mixed state, the temperature (T) and the magnetic-field ( H ) dependence of M show a distinct step which manifests the first-order phase transition [3-5]. This step is widely considered as evidence of the VL melting transition. However, the relationship between the step in M and the VL melting transition is not fully established since there remain some unsolved problems. For example, the temperature dependence of the entropy jump, which can be calculated from the height of the step in M, is inconsistent with the theory [4]. Therefore, experiments from a different point of view are needed. Since the physical properties of Bi2SrzCaCu208 + are known to depend strongly on the oxygen content [6,7], it is important to investigate the oxygen-content dependence of the above-mentioned first-order phase transition line. In addition, heat capacity mea-

0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 0 8 8 - 3

T. Hanaguri et a l . / Physica C 263 (1996) 434-437

surements will bring us information on the transition which is complementary to that from M. In this article, we report on the results of the magnetization and heat capacity measurements performed on an over-doped (OVD) and an optimally doped (OPD) Bi2Sr2CaCu2Os+a single crystal. Single crystals of Bi2Sr2CaCu208 + a were grown by the FZ method and they were annealed under various oxygen partial pressures in the sealed quartz tube to obtain OVD and OPD Bi2Sr2CaCu2Os+ ~ [6]. From the DC magnetization measurements, T~'s of these two samples were determined to be 77 K (for OVD) and 86 K (for OPD). The magnetic field dependence of the magnetization was measured at selected temperatures using a SQUID magnetometer. All the data were taken after zero-field cooling. Temperature dependence of the heat capacity was also measured on the same samples used for the magnetization measurements, using a laboratory made AC calorimeter. The measuring frequency and the amplitude of the AC temperature modulation were 9.27 Hz and TPc p = 10 mK, respectively. The data were taken in the warming process after field cooling. In both measurements, the magnetic field was applied along the c-axis. Fig. 1 shows the part of the magnetic hysteresis curves of the OVD Bi 2Sr2CaCu 208 + a single crystal at several temperatures. Above 50 K, a clear step in M is observed at a certain magnetic field H~ in the -5

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Temperature (K) Fig. 2. Magnetic phase diagrams of the OVD and the OPD Bi2Sr2CaCu2Os+ a single crystals. Open circles and closed circles indicate the fields where the step and the kink in M are observed, respectively. Open diamonds indicate the position of the second peak. The lines are guides to the eye. Inset: temperature dependence of A M.

almost reversible region. This step is considered to manifest the first-order phase transition, since A M m ( H s ÷ ) - M(Hs_) is positive in sign, as is expected from the Clausius-Clapeyron relation AS = - A M ( d H s / d T ) > O . Here, H~+ (Hs_) is the field just above (below) H s and AS is the entropy jump at the transition. Below 50 K, the step in M changes to the kink. At the same time, the diamagnetic moment just below H s is enhanced and an apparent "negative step" is formed. It seems that the "negative step" is not related to the phase transition since AM < 0 conflicts with the Clausius-Clapeyron relation. In addition, the position of the "negative step" and the position of the positive step at high temperatures do not meet together. Although the origin of the enhancement of the diamagnetic moment is unclear, thermodynamical arguments show that the origin of the kink is the first-order phase transition with very small AM less than the detection limit [8]. Below 40 K, the so-called second peak [6,9] dominates the M - H curve and the anomalies at H s vanish. All of these characteristics of the magnetization curves can also be observed in the OPD sample. In Fig. 2, the above-mentioned characteristic fields of both samples are plotted on the H - T plane. In both samples, the relationship between these characteristic fields is qualitatively the same. The slope of

436

T. Hanaguri et aL / Physica C 263 (1996) 434-437 I

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the first-order phase transition line of the OVD sample is steeper than that of the OPD sample, similar to the behavior of the irreversibility line [6]. The temperature dependence of A M is plotted in the inset of Fig. 2. In the OVD sample, A M is almost constant at high temperatures, while that of the OPD sample linearly increases with increasing temperature. To examine the relationship between the step in M and the VL melting, we estimate the entropy jump at the transition and discuss its oxygen-content dependence. The entropy jump per vortex per layer, As, is given by As = - d ~ b o A S / H s , where d is the distance between the adjacent CuO2 planes and 4)0 is the flux quantum. The magnetic field and the temperature dependence of A s of the OVD and OPD samples are shown in Fig. 3. In the whole magnetic field and temperature range studied, A s of the OVD sample is larger than that of the OPD sample. From the theoretical point o f view, As can be derived from the following factors, namely, the difference in the internal energy between the VL and the vortex liquid and the transition temperature, which is estimated from the Lindemann criterion, as [1,4]

with increasing oxygen content [7], A s should decrease with increasing oxygen content at a given H s. On the other hand, our result shown in Fig. 3 is contrary to the prediction of Eq. (1). As has already been posited [4], the temperature and the magnetic field dependences of As are also inconsistent with Eq. (1). Therefore, further studies are still needed to clarify the relation between the magnetization step and the VL melting. Finally, we show the results of the heat capacity measurements in the vicinity of the transition. As shown in Fig. 4, no obvious anomalies in C / T were observed in both samples within the resolution of 0.1%. In both samples, the latent heat calculated from AM is expected to bring the effective change in C of 0.2-0.3%, provided the transition width is smaller than TAC. This value is very small and is close to our detection limit. In addition, the distribution of the transition temperature owing to the non-

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T. Hanaguri et al./ Physica C 263 (1996) 434-437

uniform field distribution inside the sample is likely to smear the anomaly. An effort to improve the resolution is now in progress. In summary, we investigated the first-order vortex phase transition in an O V D and an O P D Bi2Sr2CaCu208+ ~ single crystal by magnetization and heat capacity measurements. It is found that the doping-level dependence of the entropy jump at the transition cannot be explained by the simple VL melting picture. No anomalies in C were detected around the transition, which is probably because of both the small latent heat and the distribution of the transition temperature.

437

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