Influence of overdoping on fishtail magnetization in single-crystal Tl2Ba2CuO6+δ

PHYSICA ELSEVIER

Physica C 261(1996)289-294

Influence of overdoping on fishtail magnetization in single-crystal T12Ba2CuO6 + F. Zuo ~'*, V.N. Kopylov b a Physics Department, University of Miami, Coral Gables, FL 33124, USA b Institute of Solid State Physics, 142432 Chernogolovka, Russian Federation Received 18 July 1995; revised manuscript received 19 January 1996

Abstract

Anomalous fishtail magnetization is studied on two single crystals of T12Ba2CuO6+ a with Tc = 92 K and 34 K. Fishtail magnetization is observed for both samples at low temperatures. For the high-Tc sample, the fishtail magnetization disappears above a characteristic temperature of 60 K. For the low-To sample, the fishtail magnetization remains near T~. The results are inconsistent with the oxygen-deficiency model. On the other hand, it agrees qualitatively with the dimensional-crossover model for the anomalous fishtail magnetization.

Fishtail magnetization where the magnetization increases anomalously with increasing field in the mixed state, in a field parallel to the c-axis direction, has been first reported in ceramic and single crystals of YBa2Cu307_ x [1-3] and Bi2Sr2CaCu208+y [4-6]. Similar features have been observed in many other systems such as La2_xSrxCuO4_y [7], Ndl.85Ce0.15CuOa_y [8], YBa2Cu408 [9] and G e / P b superlattices [10]. The enhancement of the critical current was initially explained in terms of increased pinning at the oxygen-deficient sites in field. Other models based on collective pinning [11], effects of surface barriers [4,12], lattice matching between vortex and defect structures [5], and dimensional crossover have been proposed [6]. Although the mechanism giving rise to the anomalous effect re-

* Corresponding author. Fax: + 1 305 284 4222.

mains controversial [13,15,16], a recent study on a high-Tc TI2Ba2CuO 6 single crystal provides strong evidence of dimensional crossover for the fishtail magnetization [17]. To test this model, we have performed comparative studies on two single crystals of T12Ba2CuO6+ a with Tc = 92 K and 34 K. Fishtail magnetization is observed for both systems. However, the anomalous magnetization is found to disappear above some characteristic temperature for the high-T~ system while it remains near Tc in the low-Tc system. The larger secondary peak field for the low-Tc sample, combined with the absence of the anomalous magnetization in the H I[ ab-plane direction, contradict the oxygen-deficient phase model. Instead, the results are consistent with the dimensional-crossover model. Single crystals of Ti2Ba2CuO6+ a were grown using a solid-state self-flux method [4]. Several crystals were used in the measurements with average

0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved PII S0921 - 4 5 3 4 ( 9 6 ) 0 0 1 80-3

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F. Zuo, V.N. Kopylov / Physica C 261 (1996)289-294

reduced to zero. At T = 48 K, the magnetization data is rather similar to that at 30 K, except for the fact that the second peak is now smaller in magnitude than the magnetization at the first penetration field. A further increase in temperature leads to a gradual decrease of the secondary peak. The anomalous peak disappears at about 60 K. At T > 60 K, the magnetization decreases monotonically with field after the penetration field, as shown at T = 75 K. On the descending branch, M increases with decreasing H. Fig. 3 plots the magnetization hysteresis loops at T = 28 K, 15 K, and 5 K for sample B. At a low temperature, T = 5 K, M decreases in magnitude for

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dimensions of 1 x 0.5 x 0.1 mm. Extensive measurements were made on two crystals A and B with Tc = 92 K and 34 K, respectively. Measurements were performed using a Quantum Design magnetometer with low field options. A typical hysteresis loop was measured after the sample was zero-field cooled (ZFC) to a set temperature and the magnetization was measured with the superconducting magnet in the persistent mode. The typical remanent field was less than 20 mG. Samples were placed with the field parallel to the c-axis. Shown in Fig. 1 is an overlay of the normalized magnetization M/Mo(T= 5K) versus temperature T for both sample A and B, with Tc = 92 K and 34 K, respectively. The magnetization is measured in a field of 1 G (ZFC). Both samples show relatively sharp transitions, as shown. Plotted in Fig. 2 are magnetizations measured at three different temperatures, T = 75 K, 48 K, and 30 K for sample A. At T = 30 K, a typical fishtail magnetization is observed. M increases in magnitude with H initially, followed by a dip after the first penetration field H o. M reaches a local minimum at Hmi. and increases again to a second peak at Hmax, followed by a monotonic decrease in M with increasing field. On the descending branch of the hysteresis loop, an almost mirror image of the second peak is observed. M increases as the field is

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F. Zuo, V.N. Kopylov / Physica C 261 (1996)289-294 10

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the fishtail magnetization is clearly present at temperatures very close to T~ in sample B, it disappears when T/T~ > 0.6 for sample A. Shown in Fig. 5 is an overlay of Hmin for both samples. Hmi, is defined as the field at which M reaches a local minimum, as illustrated in Figs. 2 and 3. For sample A, Hmin is almost constant, ~ 450 G, at low temperatures. Hmi. increases slightly with increasing T toward the crossover temperature ( ~ 60

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H > Hp. M reaches a broad peak at Hm,x = 5 kG. At a higher temperature T = 15 K, the secondary peak is relatively sharp with Hma, = 2.5 kG. At a temperature close to Tc, T = 28 K, a much narrower second peak is observed with Hm,x = 250 G. In all three cases, the secondary peaks are larger in magnitude than the first peak at the penetration field. Shown in Fig. 4 is an overlay of the secondary peak field Hma, versus reduced temperature T / T c for both samples in semi-log scale. The open circles are for the lower-T~ sample (B), and the open triangles are for the high-T~ sample (A). Clearly, Hmax is much larger in sample B than in sample A when compared in the reduced temperature scale. While

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F. Zuo, V.N. Kopylov / Physica C 261 (1996) 289-294

K). For sample B, Hmi. increases rapidly with decreasing T, reaching ~ 1 kG at T = 5 K. The dashed line is a fit to Hmi,(T)= H0/(1 + aT"), with n = 2.3, H ~ = 1250 G, and a = 6.8 × 10 - 3 . A fit of similar quality can also be obtained with an exponential temperature dependence, Hmi n = H c exp( - T/To). The anomalous fishtail magnetization has been initially explained in terms of oxygen-deficient phases for the YBCO material [1,2]. In this model, the superconducting order parameter at the oxygendeficient sites, which have a lower Tc than the bulk, is strongly suppressed in the field. A peak in the pinning strength is expected when the applied field is of the order of Hc2(T) of the secondary phase. However, recent studies on high-quality single crystals of YBCO indicate that the anomalous magnetization is not likely due to this inhomogeneity. These include the work on: (1) high-quality YBa2Cu30 7 [11]; (2) oxygen-insensitive YBa2Cu408 [9]; (3) low-T~ (58 K) TmBa2Cu306.45 [16]. In the case of TI 2Ba2CuO 6 + 8, Tc depends strongly on the oxygen content 6. Unlike YBCO, Tc decreases with increasing 6. Some inhomogeneities in the oxygen content are inevitable. However, the effects of inhomogeneity on the fishtail magnetization are not important for three reasons. First, the observation of gma x of a few kG at low temperatures (for example, HmaX= 2 kG at T = 20 K for sample A) and its temperature dependence Hmax(T) is uncharacteristic of Hc2(T). Second, if the oxygen-deficiency model were correct, sample B would have a lower-Tc phase than sample A. The secondary phase in sample B would likely have a lower T~ than that of the sample A, implying a lower peak field (assuming Hc2 scales with To). Although we cannot rule out other possibilities, the experimental observation of higher Hmax in sample B than in sample A when compared in the reduced temperature scale seems to contradict the oxygen-deficiency model. On the other hand, the larger peak field Hmax suggests that it is related closely with the anisotropy of the system. Third, the simple secondary phase model would expect a similar fishtail effect in all directions. However, magnetic measurements performed in the H 11ab-plane geometry have not shown any secondary peak in the M(H) dependence [14]. The

absence of the anomalous effect in this direction rules against the secondary-phase model. We noted some similar results such as the pronounced peak effect reported for the overdoped BISCO samples [15], although the authors there attributed the effect mostly to the relaxation of the induced electric field in the sample. Another model for the fishtail magnetization is the possibility of lattice matching between the vortex and the impurity structures. In the case here, the overdoped sample B (6 -- 0.06) has an average spacing of ( l / v ~ ) a 0 = 4oa0 between the excess oxygen sites, with a 0 - 3 . 8 A being the lattice constant in the ab-plane. The characteristic field for this spacing is of the order of 100 T. Moreover, the model predicts the peak field Hmax tO be temperature independent. Although it is possible that structural modulation may give rise to a much larger effective spacing between the pinning sites [5], the extremely small peak field observed and its temperature dependence rule against the lattice-matching model. The disappearance of the fishtail magnetization at a crossover temperature (T0r = 60 K) in sample A has been associated with a crossover in the temperature dependence of the irreversibility line Hrev(T) [17]. For temperature greater than Tcr, the irreversible field has a power-law dependence on temperature with Hrev(T) o t ( 1 - T / T c ) " with n = 3 [18]; for a temperature less than Tcr, Hrev(T) increases with 1/T exponentially. The exponential 1/T dependence is expected for the melting line of 2D vortices in Josephson coupled layered superconductors. The melting line has been obtained [19] and is given by

Bm-~ (Ys)

exp

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where ~b0 is the flux quantum, y = Ac/Aab is the anisotropy constant, s is the separation between the superconducting layers, c L is the Lindemann number, and h~o is the penetration depth in the layer. The temperature dependence of Hrc~(T) at low T suggests strongly that vortices are in 2D form at the secondary peak. Since the vortex will always be in 3D form when H is small (when in-plane interaction can be neglected compared to the Josephson coupling), the fishtail magnetization may result from

F. Zuo, V.N. Kopylov / Physica C 261 (1996) 289-294

dimensional crossover from a 3D to a 2D vortex structure. Evidence for dimensional crossover has indeed been confirmed by neutron diffraction and ix-spin relaxation measurements [20,21]. The disappearance of the anomalous magnetization at a temperature above T~r in sample A is thus due to the fact that vortices cross the boundary of the vortex-lineliquid melting first [17,22]. The critical field for dimensional crossover is derived and given by [23] H e - ~b0/Aj2, where Aj = Ts. A large anisotropy corresponds to a smaller critical field. Experimentally, the critical field is identified by a crossover in the magnetization at Hm~n. For sample A, nmi n is almost a constant ~ 450 G at low temperatures. Using s = 12 A, y ~ - 1 9 0 is obtained, consistent with the large anisotropy of this material. Unlike the high-T~ counterpart, the fishtail magnetization in the low-Tc crystal remains at a temperature very close to its T~. nmi n increases rapidly with decreasing temperature, changing from a few G at temperature near Tc to 1 kG at 5 K. To understand the difference observed among the two samples, it is necessary to study the effects of overdoping in the TIzBa2CuO6+ 8 system. It is known that Tc decreases monotonically from about 90 K to 0 K with a corresponding change in 6 from ~ 0 to ~ 0.1 [24,25]. For the two samples studied here, T~ = 92 K and 34 K correspond to having 6 ~ 0 and ~ 0.06 for sample A and B, respectively. Transport measurements in the normal state in the TI2Ba2CuO6÷ 8 system show that the in-plane resistivity can be fit with Pab = 190+AT" [24]. ct increases from 1 to about 2 with increasing 6 from 0 to 0.1. The c-axis resistivity Pc is metallic in nature for all 6, with pc(T) decreasing monotonically with T. Measurement of resistivity anisotropy Pc/P,b shows that pc//Pab increases strongly with decreasing temperature in the high-T~ samples [24]. The strong temperature dependence of Pc/Pab demonstrates that Pc depends weakly on T in the high-Tc sample. If pc = pc0(1 +aT"), the results indicate that n changes from << 1 in the high-Tc sample to about 2 in the non-superconducting sample. In another words, the temperature dependence of Pc(T) increases strongly with decreasing T~. In the model of superconducting layers coupled with Josephson interaction J, a strong temperatureo

293

dependent J for the low-Tc sample may thus be expected. Qualitatively, J can be related with the resistivity in the c-axis direction by using the Ambegaoka-Baratoff result [26] J = [TrA(T)/ 2eR n] tanh[A(T)/2kBT], where A(T) is the energy gap and R n is the tunneling resistance between the layers. Since R n a Pc, a rapid increase in J(T) with decreasing T is expected. Since HminOt 1 / y 2 o t J , and pc(T) = pc0(1 + aT"), one can write Hmin(T) = H0/(1 + aT"), with H 0, a and n as fitting parameters. For sample A, the almost constant H ~ , indicates a constant J at low temperatures. The dashed line in Fig. 5 with n = 2.3, H 0 = 1250 G, and a = 6.8 × 10 - 3 for sample B shows a reasonable fit to the experimental results. However, it is noted that a and n obtained from the fit are somewhat larger than the values estimated from pc(T) [24]. The discrepancy may be due to the temperature-dependent gap function A(T). The temperature dependence of the crossover field can also arise from a recent theoretical model [27], in which the anisotropy constant depends strongly on temperature and field Tot 1 / J ~ . The critical current Jc decreases with field and temperature, because the thermal fluctuation of vortices induces phase differences cross the layers. For moderate anisotropy ¢,b/s << To << Aab/S and neglecting pinning effects, the decoupling field has been derived

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A~Js, the decoupling

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In both cases, the crossover field decreases sharply with increasing T, qualitatively consistent with the data for sample B, as shown in Fig. 5. However, the almost c o n s t a n t Hmin(T) at low temperature for sample A contradicts the fluctuation model. Although pinning effects have to be considered in this model, since the crossover field in both cases is below the irreversibility line. It is unlikely that the thermal fluctuation plays drastically different roles among the two samples.

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F. Zuo, V.N. Kopylov / Physica C 261 (1996)289-294

In summary, we have reported magnetic measurements on two single crystals of T12Ba2CuO6+ ~ with T¢ = 92 K and 34 K. The anomalous fishtail magnetization disappears above a characteristic temperature of 60 K in the high-T~ sample, while it remains near T~ in the low-T~ sample. The larger secondary peak field n m a x in the low-T~ sample and the absence of anomalous magnetization in the H II ab-plane direction rule against the oxygen-deficiency model. Unlike the high-Tc sample, Hmi°(T) increases rapidly with decreasing temperature for the low-T~ sample. The different temperature dependence of n m i n ( T ) observed may be attributed to different coupling strength and its temperature dependence due to the effects of overdoping in this compound.

Acknowledgements We acknowledge many useful discussions with Stewart Barnes and George Alexandrakis. This work is supported in part by a general research grant from the University of Miami.

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