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Scaling of the longitudinal and Hall resistivities in superconducting L2−xCexCuO4 (L Nd, Sm) single crystals
PHYSIGA® ELSEVIER
Physica C 248 (1995) 155-161
Scaling of the longitudinal and Hall resistivities in superconducting L2_xCexCuO4 (L = Nd, Sm) single crystals M. Cagigal b, j. Fontcuberta a,*, M.A. Crusellas a, J.L. Vicent b, S. Pifiol a a Institut de Ci~ncia de Materials, Consell Superior de lnvestigacions Cientifiques, Campus UniversitatAut6noma de Barcelona, 08193 Bellaterra, Spain b Departamento de Fisica de Materiales, Universidad Complutense, 28040 Madrid, Spain Received 28 February 1995; revised manuscript received 13 April 1995
Abstract
We report measurements of the longitudinal (Pxx) and transverse (p~y) resistivities in the mixed state of superconducting Lz_xCexCuO4 (L =Sm and Nd) single crystals. We show that the Hall resistivity displays a pronounced anomaly when cooling the crystals through the transition temperature To(H). Just below Tc the anomalous Hall signal pxy(H) has the same sign as in the normal state whereas at lower temperatures the sign is reversed. Analysis of the resistivity data has revealed a scaling behavior pxy(H) = A Px~(H) with /3 = 0.8 (+ 0.2) for all crystals. Significantly the scaling behavior holds for both the positive and negative regions of pxy(T, H). The significance of these results is discussed in connection with the current models for vortex motion.
1. Introduction
The Hall effect in the mixed state of type-II superconductors is one of the most striking features of the vortex dynamics. Experimental measurements of the Hall resistivity in the mixed state of different hole-doped high-temperature superconducting cuprates (HTSC's) [1-3] show a sign change, with respect to the normal state, when cooling the sample below the transition temperature. More detailed analysis of Pxy(T, H) has revealed a richer structure: in TI2Ba2CaCu208 [4,5] and Bi2Sr2CaCu208 oxides [6,7], the Hall resistivity Pxy displays a double change of sign from positive to negative and back to positive when cooling. At even lower temperature the vor-
* Corresponding author.
tices become immobile and both the Hall and the longitudinal resistivities ( Pxy, Pxx) decrease rapidly. The occurrence and amplitude of the resulting negative minima in pxy(T) depend on the applied field and it becomes progressively reduced when increasing the field. Different models have been proposed to understand the sign reversal of the Hall effect, but the origin of this phenomenon is still an open question. Although it was early suggested that the reverse sign of the Hall resistivity could be related to backflow currents due to flux pinning [8], recent experimental data [9,10] seem to question such a model. Another approach suggests that the sign reversal is an intrinsic property of the vortex motion [4]. In this framework, Dorsey [11] and Kopnin et al. [12] have proposed that the Hall conductivity can be written as the sum of the Hall conductivities of quasiparticles (O'x~)
0921-4534/95//$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD! 0 9 2 1 - 4 5 3 4 ( 9 5 ) 0 0 2 2 0 - 0
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M. Cagigalet al. /Physica C 248 (1995) 155-161
and hydrodynamics of vortices (trxfy): trxr = (trx%) + (trfy). The large quasiparticle term dominates the vortex term at high fields, whereas the reverse is true at low fields. There is some experimental evidence for such a decomposition. Samoilov et al. [5] found that in TI oxides O'xy = C - B / H whereas in YBa2Cu30 7 Harris et al. [13] found that Orgy= CH - B / H (C, B > 0). The field dependence of tr,fy = 1 / H is in agreement with theoretical predictions [11,12]. A second feature of the Hall effect is the scaling behavior of p , y ( T ) = A ( T , H)Pxx(T) ~ which has been observed in YBazCu3OT, Bi2Sr2CaCu208 and T1EBa2CaCu208 with /3 = 1.4-2 [10,14-17]. There is experimental evidence that the scaling behavior of Pxy (Pxx) is an independent property of the existence of the Hall anomaly [9] and it has been observed in both the region of positive and negative Hall resistivities [15,16]. Vinokur et al. [18] have argued that this scaling is a general feature of any vortex state with disorder-dominated vortex dynamics and they have
predicted that P x y_- A p x 2x , i.e. f l = 2. It has been suggested that discrepancies of /3 ( = 2) could be due to a non-negligible temperature dependence of A(T, H ) [18]. From a completely different approach, Dorsey and Fisher [19] early suggested that such a scaling could be expected as a result of the glassy scaling near the vortex-glass transition. Observation of scaling of the transverse and longitudinal resistivities in Bi2Sr2CaCu20 8 well above the glass temperature [10] appears to favor the Vinokur view. It is thus clear that the Hall resistivity can provide important information regarding the nature of flux dynamics in the vortex state. A sign reversal of the Hall conductivity in L2_ xCexCuO 4 electron-doped superconducting cuprates has also been reported [20-22]. More interesting, Cagigal et al. [23] noticed that in the mixed state Pxy can be positive or negative depending on the temperature and field range. In this work we examine the detailed behavior of the longitudinal and Hall resistivities in the mixed state of two electron-doped
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H(T) Fig. 1, Magnetic-fielddependenceof the Hall resistivity(opensymbols)and the longitudinalresistivity(solid symbols)of a Sm2-xCe,CuO4 single crystalmeasuredat differenttemperatures(T = 1.5 K, 5.08 K, 6.89 K and 12 K).
M. Cagigal et al. / Physica C 248 (1995) 155-161
157
L2_xCexCuO4 (L = Sm, Nd) single crystals. We will show that in close similarity with the hole-type HTS the electron-doped superconductors also display a scaling behavior of the form Pxy(T, H)=A(T, H)px~(T, H) ~ for both the positive and negative regions o f Pxy(T). However, the observed exponent /3 results in a value much smaller than the one predicted by the available theory (/3 = 2) [18]. We discuss the origin of this difference and analyze the methodology of data analysis. We will conclude that scaling of pxr(H) versus pxx(H) in these materials is hidden by the strong field dependence of the A(T, H) term which reflects the weaker broadening of the p~x(H) curves in these lower-Tc superconducting oxides.
0.09 mm 3 in size, respectively. The critical temperatures and transition widths (between 10%-90%) are 13.5 K and 0.5 K for the Sm crystal and 15.9 K and 0.5 K for the Nd one. Four Au contacts were painted on the corners of the samples. After annealing at 400°C, Pt wires were attached by using Ag paint yielding low-resistance contacts. DC currents of 2-7 mA were used to measure the dependence with magnetic field and temperature of the Hall and longitudinal resistivities. The magnetic field was perpendicular to the ab plane and the field was slowly swept (5-20 X 10 - 4 T / / s ) u p to ± 5 T with a temperature stability better than 10 mK. The Hall signal was obtained from the antisymmetric part of the transverse voltage under field reversal.
2. Experimental
3. Results and discussion
We report data obtained from two superconducting single crystals: Sm2_xCexCuO4 and NdE_~Ce xCuO4 of 1.2X0.7×0.025 mm 3 and 1 . 3 x 1 . 3 x
The field dependence of the Hall and longitudinal resistivities at several temperatures (T = 1.5 K, 5.08 K, 6.89 K and 12 K) of a Sm2_xCexCuO4 single
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Fig. 2. Log-log plot of pxv(H) vs. px~(H) obtained for three different temperatures. The solid lines represent a fit to the scaling law Pxr ~-"Pffx with fl = 0.8 5: 0.2.
M. Cagigalet al./ Physica C 248 (1995) 155-161
158
crystal in the mixed state are shown in Fig. 1. The observed onset of px~(H) occurs at the same magnetic field (within the experimental resolution) as the field at which the Hall resistivity Pxy(H) b e c o m e s different from zero. It is clear from the data of Fig. 1 that O~r(H) displays a peak which is similar to those previously observed in other hole-type and electrondoped superconducting cuprates. At high field, in the normal s t a t e , Pxy(H) is positive and linear with H [23,24]. When reducing the field I pxy(H) l experiences a pronounced enhancement before vanishing at the irreversibility line. However, the amplitude and the sign of pxy(H) changes with temperature. The most noticeable variation is the change of polarity of Pxy(H): whereas at a high temperature (6.89 K and 12 K) the Hall resistivity has the same polarity as in the normal state (positive) it becomes negative at lower temperatures (5 K and 1.5 K). According to Vinokur et al. [18], the dependence of pxy(H) with the longitudinal resistivity pxx(H) should display a scaling behavior independently on
6.0
the sign of the Hall conductivity. In Fig. 2 we explore that prediction by plotting log Pxy(H) v e r s u s log pxx(H) at several temperatures (6.89 K, 5.08 K and 1.5 K). Irrespectively of the sign of the Hall peak all data display a common behavior in the log-log plot reflecting a power-law relationship in the low-resistivity region of the curves. The scaling can be written a s Pxy(T, H) =A(T, H)pxx(T, H) ~, /3 being 0.8 + 0.2. Inspection of the data of Fig. 2 reveals that A(T, H) is temperature dependent and the sign of Pxy is included in this parameter which changes its sign between 5 and 7 K. The observation of the pxy(H) versus px~(H) scaling independently of the sign of the Hall effect, is one of the central findings in this paper and provides evidence of the decoupling of both effects. The field dependence of pxr(H) of the Nd2_xCexCuO 4 single crystal at several temperatures close to Tc is shown in Fig. 3. Similarly to what has been observed for the Sm2_~CexCuO 4 crystal, pxr(H) displays a pronounced positive peak,
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H(T) Fig. 3. Magnetic-field dependence of the Hall resistivity of a Nd 2_ xCexCuO4 single crystal measured at different temperatures. The inset shows the L o g - L o g plot of pxy(H) and pxx(H) for the Nd2_xCexCuO 4 single crystal at T = 15.18 K, 13.92 K and 12.95 K; The solid line through the data has slope /3 = 0.8 ± 0.3,
M. Cagigalet al. /Physica C 248 (1995)155-161
above, for the Sm2_xCexCu04 crystal, A(T, H ) increases with temperature. Notice that due to the sharpness of the resistive transition at high temperature (see Figs. 1 and 3), the positive Hall peaks are
i.e. of the same polarity as the Hall resistivity in the normal state. The log-log plot of pxy(H) versus pxx(H) (inset Fig. 3) allows one to observe the same power law with /3 = 0.8 ( + 0.3). As it was found
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160
M. Cagigal et al. / Physica C 248 (1995) 155-161
very narrow and thus scaling can only be observed in narrow field regions; consequently the error in the coefficient is higher than in the low-temperature measurements, where the px~(H) and Pxy(n) curves broadens. Sharp pxy(H) peaks are a consequence of the parallel shift without significant broadening of the resistance versus temperature under field curves that these low-Tc cuprates display [24]. This behavior simply reflects the narrow reversible region above the irreversibility line [25]. In summary, for two different crystals and from the field dependence of p~y and Pxx at several temperatures, we have obtained a scaling behavior pxr(H) = A(T, H)Oxx(H) t3 which is independent of the sign of the Hall conductivity, and a unique value for the coefficient /3 = 0.8 (+0.2). Notice that our observation of /3 = 0.8 in isothermal experiments is important because it excludes the temperature dependence of A(T, H) as a possible cause for the discrepancy with respect to the predicted value. It could be argued that /3--0.8 results from a field dependence of A(T, H) that remains indistinguishable in the pxy(H) versus px~(H) plots of Figs. 2 and 3. With respect to the possible dependence of A with magnetic field, it is worth to recall that in other hole-type HTS is a scaling behavior with /3 = 2 (+0.2) and a field-independent A(T) factor has been reported [10,17]. According to Vinokur et al. [18], 13---2 and the prefactor A(T, H) contains the Hall drag coefficient t~: A(T, H ) = a/~oH. In terms of the simplest Bardeen-Stephen model, the Hall effect is due to the normal carriers within the vortex cores and should increase with field; therefore a -- H. Within this approach A(T, H) is predicted to be field independent in agreement with the data reported for Bi2Sr2CaCu208 [17]. We explore now the field dependence of A(H) from our data. First, we note that the Hall conductivity can be written as O'~y= p~y/( p 2 + p2y) = Pxy/p2x . This expression is equivalent to that proposed by Vinokur et al if we identify o-xr = A. In Fig. 4 we present the Hall conductivity measured experimentally; a strong field dependence is revealed with a divergence at the onset of the non-dissipative state. A similar behavior for ~xy has been recently reported for Y B a 2 C u 3 0 7 [26]. The sharp variation of o-~y with field is the result of the narrow magnetoresistive transitions typical of these low-To materials
[24]. In view of these results it is clear that in the log-log plot of Fig. 2 the exponent /3 = 0.8 contains contributions of both the trxy(H) and pxx(H) terms. In other words, due to the strong field dependence of the Hall conductivity, the observed scaling of Fig. 2 does not fit the predictions of the Vinokur model. Notice, however, that it does not mean that the Vinokur scaling Pxy "~ p2x does not hold but only indicates that in the present materials it cannot be tested because it is masked by the important field dependence of the Hall conductivity. This situation is in contrast to what is found in other hole-type materials, particularly Bi2Sr2CaCu2Os, where the extreme broadening of the resistivity curves under a field reduces the field dependence of O'xy(H) ~ A(H) and the p~y -- p 2 scaling becomes apparent. Having established that a unique power-law Pxy = A P~x holds irrespectively of the sign of the Hall effect, we will focus now our attention to this point. As mentioned above the overall Hall conductivity should contain two terms. One is arising from the quasiparticles within the vortex cores and should be proportional to the normal state O-x~ and the other reflecting the hydrodynamics of the vortices trxfy which is proportional to the imaginary part of the damping (Y2). Y2 is known to depend on the details of the band structure, particularly of the derivative of the density of states at the Fermi level. According to Dorsey et al. [18].
O'x, = C - B ( y 2 ) / H , where B(y 2) is positive. In order to explore to what extent such a decomposition of tr~y is appropriate for the present case we have plotted in Figs. 4, exy(H, T) evaluated from the data of Figs. 1 and 3 for the Smz_xCexCuO 4 and Ndz_xeexCuO 4 single crystals, respectively. Unlike the non-monotonical behavior of Pxy(n) with the peak anomaly, Orxy(H) is monotonical in H at any temperature. The data of Fig. 4 reveal that O'xy(H , T ) approaches the form trxy (H) ~ C - B/H (B can be positive or negative depending on the electronic band structure of the sample) at fields well above the onset of dissipation. The functional form of trxy(H) is closely related to that proposed by Dorsey et al. Similar to what has been found in YBa2Cu30 7 [26,13], it seems that at low temperature a n d / o r low field the vortex term (~ ")/2) dominates and thus p~y can be negative or
M. Cagigal et al. / Physica C 248 (1995) 155-161
positive whereas at higher temperature the normal component (positive) [24] becomes relatively more important.
4. Conclusions We have measured the temperature and magnetic-field dependences of the longitudinal and the Hall resistivities of two L2_xCexCuO4 single crystals (L = Sm and Nd). The Hall effect pxy(H, T) displays a reversed sign with respect to the normal state at low temperatures. However, positive peaks of the same polarity as in the normal state have been observed at higher temperatures. We have found in both crystals a unique power-law relationship Pxy=A(T, H)p~x with f l = 0 . 8 + 0 . 2 , irrespectively of the sign of the Hall effect, and we have provided conclusive evidence that both effects are not coupled. The deviation of the exponent fl from the theoretical predictions cannot be attributed to the dependence of A(T, H) on temperature. We have shown that the measured exponent contains important contributions from the field dependence of the Hall conductivity which masks the pxy (p~x(H)) relationship. As a consequence testing of the current ideas about P x y ( H ) -~ p~(H) scalings in these materials remains challenging.
Acknowledgements This work was supported by the CICYT-MIDAS (Spain) projects MAT92-388 and (MAT94-1024) and the CEE-SCIENCE project SCI-0389 M(A).
References [1] M. Galffy and E. Zirgiebl, Solid State Commun. 68 (1988) 929. [2] S.J. Hagen, C.J. Lobb, R.L. Greene, M.G. Forrester and J.H. Kang, Phys. Rev. B 41 (1990) 11630.
161
[3] T.R. Chien, T.W. Jing, N.P. Ong and Z.Z. Wang, Phys. Rev. Lett. 66 (1991) 3075; M.A. Gonz~ilez, P. Prieto, D. Oyola and J.L. Vicent, Physica C 180 (1991) 220. [4] S.J. Hagen, C.J. Lobb, R.L. Greene and M. Eddy, Phys. Rev. B 43 (1991) 6246 [5] A.V. Samoilov, Z.G. Ivanov and L.G. Johansson, Phys. Rev. B 49 (1994) 3667. [6] Y. lye, S. Nakamura and T. Tamegai, Physica C 159 (1989) 616. [7] N.V. Zavaritsky, A.V. Samoilov and A.A. Yurgens, Physica C 180 (1991) 417. [8] Z.D. Wang and C.S. Ting, Phys. Rev. B 46 (1992) 284. [9] R.C. Budhani, S.H. Liou and Z.X. Cai, Phys. Rev. Lett. 71 (1993) 621. [10] H.C. Ri, R. Gross, F. Gollnik, A. Beck, R.P. Huebner, P. Wagner and H. Adrian, Phys. Rev. B 50 (1994) 3312; idem, Phys. Rev. Lett. 72 (1994) 2259. [11] A.T. Dorsey, Phys. Rev. B 46 (1992) 8376. [12] N.B. Kopnin, B.I. lvlev and V.A. Kalatsky, J. Low Temp. Phys. 90 (1993) 1 [13] J.M. Harris, Y.F. Yan, O.K.C. Tsui, Y. Matsuda and N.P. Ong, Phys. Rev. Lett. 73 (1994) 1711. [14] J.L. Martin, M. V61ez, J. Colino, P. Prieto and J.L. Vicent, Solid State Commun., to be published. [15] J. Luo, T.P. Orlando, J.M. Graybeal, X.D. Wu and R. Muenchausen, Phys. Rev. Lett. 68 (1992) 690. [16] A.V. Samoilov, Phys. Rev Lett. 71 (1993) 617. [17] P.J.M. W61tgens, C Dekker and H.W. de Wijn, Phys. Rev. Lett 27 (1993) 3858. [18] V.M. Vinokur, V.B. Geshkenbein, M.V. Feigel'man and G. Blatter, Phys. Rev. Lett. 71 (1993) 1242. [19] A.T. Dorsey and M.P.A. Fisher, Phys. Rev. Lett. 68 (1992) 694. [20] S.J. Hagen, A.W. Smith, M. Rajeswari, J.L. Peng, Z,Y. Li, R.L. Greene, S.N. Mao, X.X. Xi, S. Bhattacharya, Q. Li and C.J. Lobb, Phys. Rev. B 47 (1993) 1064. [21] M. Cagigal, A. Seffar, J. Fontcuberta, M.A. Crusellas, J.L. Vicent and S. Pifiol, Physica C 235-240 (1994) 3177. [22] W. Jiang, S.N. Mao, X.X. Xi, X. Jiang, J.L. Peng, T. Venkatesan, C.J. Lobb and R.L. Greene, Phys. Rev. Lett 73 (1994) 1291. [23] M. Cagigal, J. Fontcuberta, M.A. Crusellas, J.L. Vicent and S. Pifiol, Phys. Rev. B 50 (1994) 15993. [24] M.A. Crusellas, J. Fontcuberta, S. Pifiol, M. Cagigal and J.L. Vicent, Physica C 210 (1993) 221; M.A. Crusellas, J. Fontcuberta and S. Pifiol, Phys. Rev. B 48 (1993) 4223. [25] L. F:~brega, J. Fontcuberta, X. Obradors, S. Pifiol, U. Welp and G.W. Crabtree, Europhels. Lett. 24 (1993) 595. [26] J.M. Harris, N.P. Ong and Y.F. Yah, Phys. Rev. Lett. 73 (1994) 610.
Physica C 248 (1995) 155-161
Scaling of the longitudinal and Hall resistivities in superconducting L2_xCexCuO4 (L = Nd, Sm) single crystals M. Cagigal b, j. Fontcuberta a,*, M.A. Crusellas a, J.L. Vicent b, S. Pifiol a a Institut de Ci~ncia de Materials, Consell Superior de lnvestigacions Cientifiques, Campus UniversitatAut6noma de Barcelona, 08193 Bellaterra, Spain b Departamento de Fisica de Materiales, Universidad Complutense, 28040 Madrid, Spain Received 28 February 1995; revised manuscript received 13 April 1995
Abstract
We report measurements of the longitudinal (Pxx) and transverse (p~y) resistivities in the mixed state of superconducting Lz_xCexCuO4 (L =Sm and Nd) single crystals. We show that the Hall resistivity displays a pronounced anomaly when cooling the crystals through the transition temperature To(H). Just below Tc the anomalous Hall signal pxy(H) has the same sign as in the normal state whereas at lower temperatures the sign is reversed. Analysis of the resistivity data has revealed a scaling behavior pxy(H) = A Px~(H) with /3 = 0.8 (+ 0.2) for all crystals. Significantly the scaling behavior holds for both the positive and negative regions of pxy(T, H). The significance of these results is discussed in connection with the current models for vortex motion.
1. Introduction
The Hall effect in the mixed state of type-II superconductors is one of the most striking features of the vortex dynamics. Experimental measurements of the Hall resistivity in the mixed state of different hole-doped high-temperature superconducting cuprates (HTSC's) [1-3] show a sign change, with respect to the normal state, when cooling the sample below the transition temperature. More detailed analysis of Pxy(T, H) has revealed a richer structure: in TI2Ba2CaCu208 [4,5] and Bi2Sr2CaCu208 oxides [6,7], the Hall resistivity Pxy displays a double change of sign from positive to negative and back to positive when cooling. At even lower temperature the vor-
* Corresponding author.
tices become immobile and both the Hall and the longitudinal resistivities ( Pxy, Pxx) decrease rapidly. The occurrence and amplitude of the resulting negative minima in pxy(T) depend on the applied field and it becomes progressively reduced when increasing the field. Different models have been proposed to understand the sign reversal of the Hall effect, but the origin of this phenomenon is still an open question. Although it was early suggested that the reverse sign of the Hall resistivity could be related to backflow currents due to flux pinning [8], recent experimental data [9,10] seem to question such a model. Another approach suggests that the sign reversal is an intrinsic property of the vortex motion [4]. In this framework, Dorsey [11] and Kopnin et al. [12] have proposed that the Hall conductivity can be written as the sum of the Hall conductivities of quasiparticles (O'x~)
0921-4534/95//$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD! 0 9 2 1 - 4 5 3 4 ( 9 5 ) 0 0 2 2 0 - 0
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M. Cagigalet al. /Physica C 248 (1995) 155-161
and hydrodynamics of vortices (trxfy): trxr = (trx%) + (trfy). The large quasiparticle term dominates the vortex term at high fields, whereas the reverse is true at low fields. There is some experimental evidence for such a decomposition. Samoilov et al. [5] found that in TI oxides O'xy = C - B / H whereas in YBa2Cu30 7 Harris et al. [13] found that Orgy= CH - B / H (C, B > 0). The field dependence of tr,fy = 1 / H is in agreement with theoretical predictions [11,12]. A second feature of the Hall effect is the scaling behavior of p , y ( T ) = A ( T , H)Pxx(T) ~ which has been observed in YBazCu3OT, Bi2Sr2CaCu208 and T1EBa2CaCu208 with /3 = 1.4-2 [10,14-17]. There is experimental evidence that the scaling behavior of Pxy (Pxx) is an independent property of the existence of the Hall anomaly [9] and it has been observed in both the region of positive and negative Hall resistivities [15,16]. Vinokur et al. [18] have argued that this scaling is a general feature of any vortex state with disorder-dominated vortex dynamics and they have
predicted that P x y_- A p x 2x , i.e. f l = 2. It has been suggested that discrepancies of /3 ( = 2) could be due to a non-negligible temperature dependence of A(T, H ) [18]. From a completely different approach, Dorsey and Fisher [19] early suggested that such a scaling could be expected as a result of the glassy scaling near the vortex-glass transition. Observation of scaling of the transverse and longitudinal resistivities in Bi2Sr2CaCu20 8 well above the glass temperature [10] appears to favor the Vinokur view. It is thus clear that the Hall resistivity can provide important information regarding the nature of flux dynamics in the vortex state. A sign reversal of the Hall conductivity in L2_ xCexCuO 4 electron-doped superconducting cuprates has also been reported [20-22]. More interesting, Cagigal et al. [23] noticed that in the mixed state Pxy can be positive or negative depending on the temperature and field range. In this work we examine the detailed behavior of the longitudinal and Hall resistivities in the mixed state of two electron-doped
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H(T) Fig. 1, Magnetic-fielddependenceof the Hall resistivity(opensymbols)and the longitudinalresistivity(solid symbols)of a Sm2-xCe,CuO4 single crystalmeasuredat differenttemperatures(T = 1.5 K, 5.08 K, 6.89 K and 12 K).
M. Cagigal et al. / Physica C 248 (1995) 155-161
157
L2_xCexCuO4 (L = Sm, Nd) single crystals. We will show that in close similarity with the hole-type HTS the electron-doped superconductors also display a scaling behavior of the form Pxy(T, H)=A(T, H)px~(T, H) ~ for both the positive and negative regions o f Pxy(T). However, the observed exponent /3 results in a value much smaller than the one predicted by the available theory (/3 = 2) [18]. We discuss the origin of this difference and analyze the methodology of data analysis. We will conclude that scaling of pxr(H) versus pxx(H) in these materials is hidden by the strong field dependence of the A(T, H) term which reflects the weaker broadening of the p~x(H) curves in these lower-Tc superconducting oxides.
0.09 mm 3 in size, respectively. The critical temperatures and transition widths (between 10%-90%) are 13.5 K and 0.5 K for the Sm crystal and 15.9 K and 0.5 K for the Nd one. Four Au contacts were painted on the corners of the samples. After annealing at 400°C, Pt wires were attached by using Ag paint yielding low-resistance contacts. DC currents of 2-7 mA were used to measure the dependence with magnetic field and temperature of the Hall and longitudinal resistivities. The magnetic field was perpendicular to the ab plane and the field was slowly swept (5-20 X 10 - 4 T / / s ) u p to ± 5 T with a temperature stability better than 10 mK. The Hall signal was obtained from the antisymmetric part of the transverse voltage under field reversal.
2. Experimental
3. Results and discussion
We report data obtained from two superconducting single crystals: Sm2_xCexCuO4 and NdE_~Ce xCuO4 of 1.2X0.7×0.025 mm 3 and 1 . 3 x 1 . 3 x
The field dependence of the Hall and longitudinal resistivities at several temperatures (T = 1.5 K, 5.08 K, 6.89 K and 12 K) of a Sm2_xCexCuO4 single
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M. Cagigalet al./ Physica C 248 (1995) 155-161
158
crystal in the mixed state are shown in Fig. 1. The observed onset of px~(H) occurs at the same magnetic field (within the experimental resolution) as the field at which the Hall resistivity Pxy(H) b e c o m e s different from zero. It is clear from the data of Fig. 1 that O~r(H) displays a peak which is similar to those previously observed in other hole-type and electrondoped superconducting cuprates. At high field, in the normal s t a t e , Pxy(H) is positive and linear with H [23,24]. When reducing the field I pxy(H) l experiences a pronounced enhancement before vanishing at the irreversibility line. However, the amplitude and the sign of pxy(H) changes with temperature. The most noticeable variation is the change of polarity of Pxy(H): whereas at a high temperature (6.89 K and 12 K) the Hall resistivity has the same polarity as in the normal state (positive) it becomes negative at lower temperatures (5 K and 1.5 K). According to Vinokur et al. [18], the dependence of pxy(H) with the longitudinal resistivity pxx(H) should display a scaling behavior independently on
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the sign of the Hall conductivity. In Fig. 2 we explore that prediction by plotting log Pxy(H) v e r s u s log pxx(H) at several temperatures (6.89 K, 5.08 K and 1.5 K). Irrespectively of the sign of the Hall peak all data display a common behavior in the log-log plot reflecting a power-law relationship in the low-resistivity region of the curves. The scaling can be written a s Pxy(T, H) =A(T, H)pxx(T, H) ~, /3 being 0.8 + 0.2. Inspection of the data of Fig. 2 reveals that A(T, H) is temperature dependent and the sign of Pxy is included in this parameter which changes its sign between 5 and 7 K. The observation of the pxy(H) versus px~(H) scaling independently of the sign of the Hall effect, is one of the central findings in this paper and provides evidence of the decoupling of both effects. The field dependence of pxr(H) of the Nd2_xCexCuO 4 single crystal at several temperatures close to Tc is shown in Fig. 3. Similarly to what has been observed for the Sm2_~CexCuO 4 crystal, pxr(H) displays a pronounced positive peak,
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H(T) Fig. 3. Magnetic-field dependence of the Hall resistivity of a Nd 2_ xCexCuO4 single crystal measured at different temperatures. The inset shows the L o g - L o g plot of pxy(H) and pxx(H) for the Nd2_xCexCuO 4 single crystal at T = 15.18 K, 13.92 K and 12.95 K; The solid line through the data has slope /3 = 0.8 ± 0.3,
M. Cagigalet al. /Physica C 248 (1995)155-161
above, for the Sm2_xCexCu04 crystal, A(T, H ) increases with temperature. Notice that due to the sharpness of the resistive transition at high temperature (see Figs. 1 and 3), the positive Hall peaks are
i.e. of the same polarity as the Hall resistivity in the normal state. The log-log plot of pxy(H) versus pxx(H) (inset Fig. 3) allows one to observe the same power law with /3 = 0.8 ( + 0.3). As it was found
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H(T) Fig. 4. Hallconductivityo-xyvs. magneticfieldof (a) the Sm2_xCexCuO4and (b) Nd2_xCexCuO4singlecrystal.
160
M. Cagigal et al. / Physica C 248 (1995) 155-161
very narrow and thus scaling can only be observed in narrow field regions; consequently the error in the coefficient is higher than in the low-temperature measurements, where the px~(H) and Pxy(n) curves broadens. Sharp pxy(H) peaks are a consequence of the parallel shift without significant broadening of the resistance versus temperature under field curves that these low-Tc cuprates display [24]. This behavior simply reflects the narrow reversible region above the irreversibility line [25]. In summary, for two different crystals and from the field dependence of p~y and Pxx at several temperatures, we have obtained a scaling behavior pxr(H) = A(T, H)Oxx(H) t3 which is independent of the sign of the Hall conductivity, and a unique value for the coefficient /3 = 0.8 (+0.2). Notice that our observation of /3 = 0.8 in isothermal experiments is important because it excludes the temperature dependence of A(T, H) as a possible cause for the discrepancy with respect to the predicted value. It could be argued that /3--0.8 results from a field dependence of A(T, H) that remains indistinguishable in the pxy(H) versus px~(H) plots of Figs. 2 and 3. With respect to the possible dependence of A with magnetic field, it is worth to recall that in other hole-type HTS is a scaling behavior with /3 = 2 (+0.2) and a field-independent A(T) factor has been reported [10,17]. According to Vinokur et al. [18], 13---2 and the prefactor A(T, H) contains the Hall drag coefficient t~: A(T, H ) = a/~oH. In terms of the simplest Bardeen-Stephen model, the Hall effect is due to the normal carriers within the vortex cores and should increase with field; therefore a -- H. Within this approach A(T, H) is predicted to be field independent in agreement with the data reported for Bi2Sr2CaCu208 [17]. We explore now the field dependence of A(H) from our data. First, we note that the Hall conductivity can be written as O'~y= p~y/( p 2 + p2y) = Pxy/p2x . This expression is equivalent to that proposed by Vinokur et al if we identify o-xr = A. In Fig. 4 we present the Hall conductivity measured experimentally; a strong field dependence is revealed with a divergence at the onset of the non-dissipative state. A similar behavior for ~xy has been recently reported for Y B a 2 C u 3 0 7 [26]. The sharp variation of o-~y with field is the result of the narrow magnetoresistive transitions typical of these low-To materials
[24]. In view of these results it is clear that in the log-log plot of Fig. 2 the exponent /3 = 0.8 contains contributions of both the trxy(H) and pxx(H) terms. In other words, due to the strong field dependence of the Hall conductivity, the observed scaling of Fig. 2 does not fit the predictions of the Vinokur model. Notice, however, that it does not mean that the Vinokur scaling Pxy "~ p2x does not hold but only indicates that in the present materials it cannot be tested because it is masked by the important field dependence of the Hall conductivity. This situation is in contrast to what is found in other hole-type materials, particularly Bi2Sr2CaCu2Os, where the extreme broadening of the resistivity curves under a field reduces the field dependence of O'xy(H) ~ A(H) and the p~y -- p 2 scaling becomes apparent. Having established that a unique power-law Pxy = A P~x holds irrespectively of the sign of the Hall effect, we will focus now our attention to this point. As mentioned above the overall Hall conductivity should contain two terms. One is arising from the quasiparticles within the vortex cores and should be proportional to the normal state O-x~ and the other reflecting the hydrodynamics of the vortices trxfy which is proportional to the imaginary part of the damping (Y2). Y2 is known to depend on the details of the band structure, particularly of the derivative of the density of states at the Fermi level. According to Dorsey et al. [18].
O'x, = C - B ( y 2 ) / H , where B(y 2) is positive. In order to explore to what extent such a decomposition of tr~y is appropriate for the present case we have plotted in Figs. 4, exy(H, T) evaluated from the data of Figs. 1 and 3 for the Smz_xCexCuO 4 and Ndz_xeexCuO 4 single crystals, respectively. Unlike the non-monotonical behavior of Pxy(n) with the peak anomaly, Orxy(H) is monotonical in H at any temperature. The data of Fig. 4 reveal that O'xy(H , T ) approaches the form trxy (H) ~ C - B/H (B can be positive or negative depending on the electronic band structure of the sample) at fields well above the onset of dissipation. The functional form of trxy(H) is closely related to that proposed by Dorsey et al. Similar to what has been found in YBa2Cu30 7 [26,13], it seems that at low temperature a n d / o r low field the vortex term (~ ")/2) dominates and thus p~y can be negative or
M. Cagigal et al. / Physica C 248 (1995) 155-161
positive whereas at higher temperature the normal component (positive) [24] becomes relatively more important.
4. Conclusions We have measured the temperature and magnetic-field dependences of the longitudinal and the Hall resistivities of two L2_xCexCuO4 single crystals (L = Sm and Nd). The Hall effect pxy(H, T) displays a reversed sign with respect to the normal state at low temperatures. However, positive peaks of the same polarity as in the normal state have been observed at higher temperatures. We have found in both crystals a unique power-law relationship Pxy=A(T, H)p~x with f l = 0 . 8 + 0 . 2 , irrespectively of the sign of the Hall effect, and we have provided conclusive evidence that both effects are not coupled. The deviation of the exponent fl from the theoretical predictions cannot be attributed to the dependence of A(T, H) on temperature. We have shown that the measured exponent contains important contributions from the field dependence of the Hall conductivity which masks the pxy (p~x(H)) relationship. As a consequence testing of the current ideas about P x y ( H ) -~ p~(H) scalings in these materials remains challenging.
Acknowledgements This work was supported by the CICYT-MIDAS (Spain) projects MAT92-388 and (MAT94-1024) and the CEE-SCIENCE project SCI-0389 M(A).
References [1] M. Galffy and E. Zirgiebl, Solid State Commun. 68 (1988) 929. [2] S.J. Hagen, C.J. Lobb, R.L. Greene, M.G. Forrester and J.H. Kang, Phys. Rev. B 41 (1990) 11630.
161
[3] T.R. Chien, T.W. Jing, N.P. Ong and Z.Z. Wang, Phys. Rev. Lett. 66 (1991) 3075; M.A. Gonz~ilez, P. Prieto, D. Oyola and J.L. Vicent, Physica C 180 (1991) 220. [4] S.J. Hagen, C.J. Lobb, R.L. Greene and M. Eddy, Phys. Rev. B 43 (1991) 6246 [5] A.V. Samoilov, Z.G. Ivanov and L.G. Johansson, Phys. Rev. B 49 (1994) 3667. [6] Y. lye, S. Nakamura and T. Tamegai, Physica C 159 (1989) 616. [7] N.V. Zavaritsky, A.V. Samoilov and A.A. Yurgens, Physica C 180 (1991) 417. [8] Z.D. Wang and C.S. Ting, Phys. Rev. B 46 (1992) 284. [9] R.C. Budhani, S.H. Liou and Z.X. Cai, Phys. Rev. Lett. 71 (1993) 621. [10] H.C. Ri, R. Gross, F. Gollnik, A. Beck, R.P. Huebner, P. Wagner and H. Adrian, Phys. Rev. B 50 (1994) 3312; idem, Phys. Rev. Lett. 72 (1994) 2259. [11] A.T. Dorsey, Phys. Rev. B 46 (1992) 8376. [12] N.B. Kopnin, B.I. lvlev and V.A. Kalatsky, J. Low Temp. Phys. 90 (1993) 1 [13] J.M. Harris, Y.F. Yan, O.K.C. Tsui, Y. Matsuda and N.P. Ong, Phys. Rev. Lett. 73 (1994) 1711. [14] J.L. Martin, M. V61ez, J. Colino, P. Prieto and J.L. Vicent, Solid State Commun., to be published. [15] J. Luo, T.P. Orlando, J.M. Graybeal, X.D. Wu and R. Muenchausen, Phys. Rev. Lett. 68 (1992) 690. [16] A.V. Samoilov, Phys. Rev Lett. 71 (1993) 617. [17] P.J.M. W61tgens, C Dekker and H.W. de Wijn, Phys. Rev. Lett 27 (1993) 3858. [18] V.M. Vinokur, V.B. Geshkenbein, M.V. Feigel'man and G. Blatter, Phys. Rev. Lett. 71 (1993) 1242. [19] A.T. Dorsey and M.P.A. Fisher, Phys. Rev. Lett. 68 (1992) 694. [20] S.J. Hagen, A.W. Smith, M. Rajeswari, J.L. Peng, Z,Y. Li, R.L. Greene, S.N. Mao, X.X. Xi, S. Bhattacharya, Q. Li and C.J. Lobb, Phys. Rev. B 47 (1993) 1064. [21] M. Cagigal, A. Seffar, J. Fontcuberta, M.A. Crusellas, J.L. Vicent and S. Pifiol, Physica C 235-240 (1994) 3177. [22] W. Jiang, S.N. Mao, X.X. Xi, X. Jiang, J.L. Peng, T. Venkatesan, C.J. Lobb and R.L. Greene, Phys. Rev. Lett 73 (1994) 1291. [23] M. Cagigal, J. Fontcuberta, M.A. Crusellas, J.L. Vicent and S. Pifiol, Phys. Rev. B 50 (1994) 15993. [24] M.A. Crusellas, J. Fontcuberta, S. Pifiol, M. Cagigal and J.L. Vicent, Physica C 210 (1993) 221; M.A. Crusellas, J. Fontcuberta and S. Pifiol, Phys. Rev. B 48 (1993) 4223. [25] L. F:~brega, J. Fontcuberta, X. Obradors, S. Pifiol, U. Welp and G.W. Crabtree, Europhels. Lett. 24 (1993) 595. [26] J.M. Harris, N.P. Ong and Y.F. Yah, Phys. Rev. Lett. 73 (1994) 610.