Hysteresis loop, irreversibility line and flux creep studies in TlBa2Ca3Cu4O11−δ single crystals

Hysteresis loop, irreversibility line and flux creep studies in TlBa2Ca3Cu4O11−δ single crystals

PHYSICA ELSEVIER Physica C 268 (1996) 287-294 Hysteresis loop, irreversibility line and flux creep studies in T1Ba2Ca3CU4Oll_ 8 single crystals Lu Z...

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PHYSICA ELSEVIER

Physica C 268 (1996) 287-294

Hysteresis loop, irreversibility line and flux creep studies in T1Ba2Ca3CU4Oll_ 8 single crystals Lu Zhang a, , J.Z. Liu b, C. Hoellwarth b, S.H. Irons b, R.N. Shelton b, M.D. Lan c *

a Department of Physics, California State University, Stanislaus, Turlock, CA 95382, USA b Department of Physics, University of California, Davis, CA 95616, USA c Department of Physics, National Chung Hsing University, Taiwan Received 14 May 1996; revised manuscript received 31 May 1996

Abstract

Achievement of high critical current density is a challenge for the application of high temperature superconductors. The critical current density is strongly correlated to the underlying material properties of high temperature superconductors, such as layering and anisotropy. The T1Ba2Ca3Cu40 H_ ~ compound is a four-CuO2-1ayersuperconductor with a superconducting transition temperature of 128 K. We have performed magnetic experiments on single crystals of TlBa2Ca3Cu4Oll_ ~, which include hysteresis loop, irreversibility line and time relaxation measurements. From these measurements, we have determined the critical current density and thermally activated energy barrier. The results were compared with the double-layer superconductors, YBa2Cu307_ ~ and Bi2SrECaCu20 s.

I. Introduction

Recently, substantial progress has been reported for high temperature superconducting (HTS) materials in thin film technology, superconducting wires for magnets, and fast-switch and narrow-band detector [1,2]. These applications will lead to major changes in communication, computer technology and medical diagnosis technology. However, the new industrial applications of superconducting technology are often limited by the suppression of superconductivity by large currents or large magnetic fields. A key requirement for technological application is to have materials with high critical current density ( > 105 A / c m 2) at practical operating temperatures

* Corresponding author. Fax: + 1 209 667 3099; e-mail: [email protected] toto.csustan.edu.

and magnetic fields [3,4]. Obtaining a useful, high critical current density requires the materials to have strong flux pinning centers. One major problem in HTS materials is that flux pinning is not always effective. In contrast to conventional low temperature superconducting (LTS) materials, there is a large area above the so called irreversibility line where HTS materials do not pin flux and the critical current density vanishes [5]. Even below the irreversibility line, strong flux creep is observed due to the ease of thermal activation of the vortices out of their pinning wells [6,7]. At much lower temperatures, small but non-negligible flux creep due to quantum tunneling of vortices through pinning wells is observable [8,9]. These mechanisms of flux motion lead to dissipation and a strong reduction of the critical current density. In LTS materials, macroscopic defects such as crystal grain boundaries, twin planes, dislocations,

0921-4534/96/$15.00 Copyright © 1996. Published by Elsevier Science B.V. All fights reserved PH S092 1 - 4 5 3 4 ( 9 6 ) 0 0 3 8 7 - 5

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intergrowth of second phases will work as strong pinning centers. However, they do not serve as effective pinning in HTS materials [10,11]. The reason is that HTS materials are among those materials with a very short coherence length in the range of 0.3-5 nm. The vortex core size is extremely small. The most effective size range of defects is the one compatible with the coherence length. Therefore, the critical current density, flux pinning and other superconducting properties are strongly related to the underlying intrinsic crystal structure of HTS materials, such as vertical distance between CuO 2 multilayers (interlayer spacing) and the thickness of the CuO 2 layers (related to the number of CuO 2 layers in a unit cell). One significant observation is that superconducting transition temperature (Tc) increases with increasing number of CuO 2 layers (up to three layers). Single layer 2-1-4 compounds have T~ above 20 K, the double-layer YBa2Cu307_ ~ (YBCO) and Bi2Sr2CaCu208 (BSCCO) have Tc in the order of 90 K, and triple- or four- layer compounds have T~ exceeding 100 K. The thallium-based superconductors attracted attention at an early stage, mainly due to their high Tc. Discovered in early 1988 [12], the thallium-based superconductors encompass the broad homologous series, T1Ba2Can_lCunOan+3+~ (n = 1-5), T12Ba2Ca n_ iCuO2~+4+~ (n = 1-4), (TI,Pb)Sr2Ca n_ iCunO2~+3+8 (n = 1-3) and various substituted phases [13]. In the application arena, the low resistivity values observed in TI2Ba2CaCu2Oj0+~ films are particularly encouraging and augur well for use in high-frequency devices. In addition, faster processes at high temperatures and the higher T~ (up to 128 K) make them more promising candidates for fabrication of high-speed, thin-film radiation detectors. In addition to the high Tc, the one-thallium-layer superconductors, T1Ba2Ca ._ iCu,O2,+3+~ (n = 1-5), are interesting because of relatively small interlayer spacing and relatively large thickness of CuO 2 layers compared with the YBCO and BSCCO compounds. On the other hand, the thallium-based superconductors have extremely large anisotropic mass ratio of 105 [14]. The relatively strong inter~ layer coupling between superconducting layers and the extremely large anisotropy in thallium-based superconductors are intrinsic properties of the material

and affect the way the magnetic flux vortices are pined. Therefore, the thallium-based superconductors appear to be a much better bet for achieving higher critical current density and stronger flux pinning. However, few attempts have been made to study the superconducting properties in the thallium-based superconducting crystals (except T1Ba2CaCuzOT+ ~, T o = 9 0 K and T12Ba2CaCu2Oi0+8, T c = l l 0 K) because of the complex crystal structures, toxic and volatile material, and the difficulty in obtaining good quality single crystals. We have successfully grown T1Ba2Ca3CUaOll_ 8 crystals with Tc of 128 K. The X-ray analysis confirmed that the crystals contained four CuO 2 layers in a unit cell and had a structure of T1Ba2Ca3Cu 4O1~_~. In the present study, we report magnetic properties of T1Ba2Ca3Cu40~_ ~ crystals including hysteresis measurement, irreversibility line, critical current density and flux creep. We compared the results with two well-studied systems, double-layer YBCO and BSCCO.

2. Experimental methods and results TlBa2Ca3CU4Oll_ ~ single crystals were grown using a self-flux growth method [15]. The crystal structure was characterized using X-ray diffraction and the superconducting transition. The X-ray analysis showed that the crystals had a tetragonal structure with space group of P 4 / m m m and lattice parameters of a = b = 0.384 nm and c = 1.873 nm. This confirmed that the crystals contained one net layer of thallium oxide, two barium oxide layers, and four CuO 2 layers with calcium spacers between each of the CuO 2 layers [13]. X-ray diffraction showed a = b and so there was no twinning within the crystal. The superconducting transition temperature of 128 K with a 10-90% transition width of 8 K was measured by dc susceptibility (Fig. 1). Three crystals were carefully glued next to each other in a sample capsule with GE-7031 Varnish in order to obtain a large signal/noise ratio. This also insured that the crystals did not move and that the magnetic field was applied along the c-axis during the measurement. The total mass of the crystals was about 0.1 mg. X-ray and SEM analysis indicated that these crystals

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had similar microstructures [16]. T~ and hysteresis loop measurements also confirmed that these crystals had similar superconducting properties. The magnetic properties of the sample were measured using a superconducting quantum interference device (SQUID) magnetometer. Before the start of each experiment, the sample was first warmed to 150 K well above T~. The superconducting magnet was reset such that the remnant field was less than 1 0 e . Once the field was quenched, the sample was zerofield-cooled to a desired temperature. Brief M versus H measurement was made at H < Hc~ to insure that the magnetic field was applied parallel to the c-axis of the crystal. Then the magnetic field was applied using the SQUID no overshoot mode. The scan length, the distance at which a specimen travels through a set of detection coils, was set at 3.0 cm to minimize the variation in the magnetic field through which the specimen travels. An iterative regression mode was used to calculate the magnetization of the sample.

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From magnetic hysteresis measurement at 5 K (Fig. 2a), the diamagnetism first increased linearly with the applied field. The initial slope M ( H ) ( H < Hc~) corresponded to almost 100% shielding and the demagnetization factor was about 0.8 with 5% variation for all the measurements with the magnetic field applied to the c-axis of T1Ba2Ca3Cu40~I :-~ crystals. At a field of 1 kOe, corresponding to the lower critical field Hc~ (at 5 K), the magnetization began to deviate away from linearity and the field started to penetrate into the sample. After H > Hc~, the magnitude of the magnetization was still increasing, and reached a maximum value at H * (full penetration field). Then the diamagnetism was observed to decrease gradually and was expected to approach to zero at the upper critical field Hc2. Unfortunately, the applied field in our experiments could only reach a maximum value of 5.5 T, which was much smaller than the expected value of upper critical field (on the order of 100 T). When the field was decreased from

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2.1. Magnetic hysteresis experiments Magnetic hysteresis experiments are the measurements of the magnetization versus field at a fixed temperature. Fig. 2 shows measured hysteresis loops of TlBaECa3Cu4Oil_~ crystals at 5 K and 50 K with the field increasing from zero to a maximum value of 5.5 T, then decreasing, reversing in sign to a maximum negative value of - 5 . 5 T, and finally :ncreasing back to 5.5 T.

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5.5 T, the magnetization changed sign, increased gradually, and reached a maximum at zero field (maximum remnant magnetization).

2.2. Irreversibility line experiments The irreversibility line experiment was performed by cooling the sample to 5 K, well below Ti~, in zero field, applying a magnetic field, and measuring magnetization at different temperatures by warming up the sample to 150 K (ZFC), and then cooling to 5 K with the same field (FC). Thus, Tirr is the point, in M versus T measurement, at which AM(T) between ZFC and FC curves becomes less than the standard deviation [17] (inset of Fig. 3). The irreversibility field is plotted in Fig. 3 as a function Of temperature. The irreversibility line can also be determined from the hysteresis loop measurement. It is the point at which the M versus H curve is no longer double valued at a given temperature (Fig. 2b). After reaching the maximum field (5.5 T) at a given temperature, when field is reduced, flux lines are free to move, so the trajectory of magnetization retraces it path. The superconductor is " s o f t " . It reflects an equilibrium state and very week or no flux pinning. There comes a point when flux pinning becomes stronger, the magnetization deviates from the increasing field curve. The superconductor becomes " h a r d " , and irreversibility appears. In our experiments, the irreversibility line determined from the hysteresis loop is about the same as the results obtained from M versus T curve.

2.3. Flux creep experiments The magnetic relaxation experiments were carried out at temperatures above 2K and in external magnetic fields up to 5 T. The magnetization at fixed temperatures and fields was measured as a function of time, M(t) [18-20]. The initial time for the first measurement was about 20 seconds. The relaxation of the magnetization was taken over a time period of 3,000 seconds. In all the relaxation measurements, the field applied was chosen to be greater than the penetration field ( H > H *) to assure a well-defined fully penetrated state for a field parallel to the c-axis of the crystal. Fig. 4 shows the M versus t curves for H = 1 T and H > H * using log-log scale. The slopes of each 0.12

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L. Zhang et al./ Physica C 268 (1996) 287-294

curve gave the relaxation rates which correspond to each point in Fig. 5. The relaxation rates increase linearly with increasing temperature and change significantly from 0.007 at 2 K to 0.1 at 30 K for H=lT.

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In superconductors, hysteresis arises from flux pinning. When there is no pinning, the magnetic behavior of the superconductor is perfectly reversible. Structural imperfection or chemical impurities serve as pinning centers and prevent flux lines from moving freely through the crystal. By the 1960s, the niobium compounds were well known to pin flux lines at sites of crystal imperfections, and the practical goal of material engineers has been to introduce as many pinning sites as possible in order to permit high currents to flow under high magnetic fields. TlBa2Ca3CU4Oll- 8 crystals have a complicated magnetic history, similar to other HTS materials [5]. There is no sudden change in magnetization as field passes through He1 - only a deviation from linearity of M versus H curve. The deviation tells that the dimagnetism is no longer perfect and that some amount of flux is penetrating the material. When the field rises, the magnetic flux continues to penetrate into the sample from the edge and then collapse at the center to form the full penetration state at H *. The decline in H * with increasing temperature (Fig. 6) suggests that the flux easily penetrated into sample with the help of thermally activated flux motion. The size of the hysteresis loop was reduced more than 90% from 5 K to 30 K. At high temperatures above 30 K, the hysteresis was observed to disappears at higher fields, (e.g. 5.5 T at 30 K), leaving an equilibrium diamagnetism which is the reversible magnetization. The critical current density can be estimated by analysis of magnetic hysteresis measurements [5]. In the extended 2-dimensional Bean model [22] the critical current densities were field-independent which led to an evaluation of the critical current density through the magnetic hysteresis loops, Ic = 3 0 ( A M ) / a ,

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where a is the dimension of in the ab plane for a square shape single crystal and A M the width of the hysteresis loop and roughly equal to twice of the maximum remnant magnetization at zero field. The critical current density is estimated to be 2.5 × 10 6 A / c m 2 at 5K, which is higher than the results obtained in detwinned YBa2Cu307_ 8 (1.4× 106 A / c m 2) and Bil.TPb0.3Sr2CaCu20 8 (1 × 105 A / c m 2) single crystals at the same temperature [18,19]. Furthermore, the critical current density measured in TIBa2Ca3Cu4Oll_ 8 crystals has a strong temperature dependence (40% drop every 5 K) between 5 and 30 K (see Fig. 7) and reaches a plateau on the order of 105 A / c m 2 up to 50 K. The strong temperature dependence of the critical current density below 30 K may be caused by the large thermally activated flux motion in TIBa2Ca3Cu 4Olt_ , system.

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3.2. lrreversibility line experiments The irreversibility line delineates the superconducting region in the H - T plane in which Jc 4:0 and the magnetization M(H, T) exhibits irreversible behavior below the irreversibility line. The reversible magnetization region above the irreversibility line reflects an equilibrium state and no flux pinning. Therefore, this irreversibility line contains information about the phases and dynamics of the vortices in the mixed state between lower critical field Hc~(T) and upper critical field Hc2(T). The irreversibility field measured in T1Ba2Ca 3Cu4OII_ ~ crystals is replotted in Fig. 8 using H versus 1 - Tirr/Tc. The data follow a power dependence H ~ (1 - T i r J T c ) m (see solid line in Fig. 8) with m = 5. This power law dependence was also observed in other HTS materials where m was varied from 4 / 3 to 2 [5]. Some single crystal studies on YBa2Cu307_8 found an irreversibility line with power law dependence of m = 3 / 2 . [6,20]. The large value for m found in the present studies implies that the irreversibility line has a strong temperature dependence in T1Ba2Ca3Cu4Oil_ ~ system. This may lead to large flux creep due to thermal activation. Some previous experiments [3] showed that the Tir r is 20--30 K higher for YBa2Cu3OT_ ~ than for Bi2Sr2CaCu208 for H II c. Our data in T1BazCa 3 Cu4011 _ ~ crystals indicate the irreversibility line in is 35-40 K higher than our previous measurements on Bil.TPb0.3SrzCaCu208 crystals [21]. The high irreversibility line shows that flux pinning may be

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more effective in a large range of temperature and field for ZlBa2Ca3Cu4Oil_,~ system than other HTS materials. This holds promise for high field applications.

3.3. Flux creep experiments Since the discovery of the large magnetic relaxation in high temperature superconductors [23], a great amount of research on flux creep has been conducted based on thermally assisted hopping of the flux lines [5,6,20]. The early experiments demonstrated a logarithmic time dependence of the magnetization in a time period of l03 seconds, i.e. M ~ In t, where M is the magnetization at time t. The experimental results could be well described using classical phenomenological theories, which were developed in the 1960's for interpreting the relaxation behavior in conventional superconductors. In the theory [24-26], the application of a magnetic field to a superconductor in a mixed state led to a critical state where J ~ arc and the energy barrier was obtained to be linear dependent on the critical current density, U ( J ) = U0 (1 - J/Jc). However, the rate of flux creep in HTS materials is observed to be large and have a strong temperature dependence. This behavior affects the current density at finite temperature significantly. Therefore, both the magnetic and transport experiments in HTS materials are performed well below the critical state, J << Jc. The dependence of the activation barrier U on the current J was found to be logarithmic experimentally [27,28]. Vinokur et al. [29] proposed a collective pinning model on the assumption of a logarithmic current dependence for U(J). They developed a power-law behavior for the magnetization as a function of time in HTS materials: I d In M / d In t l = kaT/U. The theoretic prediction was confirmed with the experimental observations in a long time period (up to 10 6 S) [19,30,31]. At zero temperature, the collective pinning model for thermally activated flux motion also predicts zero relaxation rate. A power-law decay of the magnetization is also observed in TlBa2Ca3Cu4Oil_ ~ crystals. This observation is consistent with the prediction of Vinokur, Feigel'man and Geshkenbein taking into consideration the logarithmic current dependent activation energy for fully penetrated samples. The ex-

L. Zhang et al. / Physica C 268 (1996) 287-294

perimental results also showed that the relaxation rate is linearly temperature dependent between 2 and 30 K (Fig. 5), which results in a temperature independent activation energy of 0.024 eV compared with 0.01 eV observed in BSCCO crystals [18]. All the previous relaxation experiments yielded a finite intercept of the flux-creep rate by extrapolating linearly to zero temperature [30-36]. This indicates that the relaxation rate does not vanish when T ~ 0, which corresponds to a quantum creep of vortices. The zero temperature quantum creep rates were estimated to be 0.01 in YBa2Cu307_ ~ [37] and 0.02 in Bi2Sr2CaCu208 [38], which were comparable with the flux creep rate due to thermal activation at 5 K. Some recent experimental studies indicated the quantum creep to be dissipative in single crystals of double-layer YBa2Cu307_ ~ [39] and single-layer La2CuO4+ 8 [40]However, the relaxation rate is shown to vanish when the temperature extrapolates linearly to zero in TIBa2Ca3Cu4Oll_ ~ crystals (Fig. 5), which indicates the flux creep is only thermally assisted. The unobservable flux creep rate in TIBa2Ca3Cu40 ll_~ crystals at low temperatures (quantum creep) may be related to the observed high irreversibility line and large critical current density in this system.

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with 0.01 in Bil.7Pbo.3Sr2CaCu208 crystals. The relaxation rate was also shown to vanish when the temperature approaches zero, which reflects quantum creep is unmeasurable above 2 K in T1Ba2Ca 3Cu4Oll_ 8 crystals in contrast to non-negligible quantum creep rates observed in YBa2Cu307_ 8 and Bi2Sr2CaCu208. The large critical current density and high irreversibility line exhibit that the flux pinning is relatively effective over a large range of temperatures in the TIBaECa3Cu4Oll_ ~ compound. The strong temperature dependence of the critical current density and flux creep rate is due to the ease of thermal activation of the vortices out of the pinning wells.

Acknowledgments This work is supported by the National Science Foundation under grant numbers DMR-95-32-085 and DMR-94-03895, and by the U.S. Air Force Office of Scientific Research under grant number AFOSR-F49620-92-J-0514.

References 4. Conclusion The four-CuO2-1ayer T1Ba2CaaCu4Oll_8 compound has a higher transition temperature, stronger interlayer coupling and a much larger anisotropic mass ratio than the double-layer YBaECU307_ ~ and Bi2Sr2CaCu208 compounds. Large hysteresis was observed in TlBa2Ca3Cu40~l_ 8 crystals and the critical current density was estimated to be 2.5 × 106 A / c m 2 at 5 K compared with 1.4 × 10 6 A / c m 2 in detwinned YBa2Cu3OT_ ~ crystals and 1 × 105 A / c m 2 in Bil.7Pbo,3Sr2CaCu208 crystals at the same temperature. The irreversibility line experiments show that the irreversible temperature was 35-40 K higher for T1Ba2Ca3CU4Oll_ 8 than for BiL7Pbo.3Sr2CaCu20 s. The time-dependent magnetic relaxation experiments indicate that the relaxation rate increased linearly with increasing temperature below 30 K, which leads to a temperature independent intrinsic activation energy of 0.024 eV compared

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