- Email: [email protected]
Observation of asymmetric transverse voltage in granular high-Tc superconductors
Physica C 419 (2005) 71–78 www.elsevier.com/locate/physc
Observation of asymmetric transverse voltage in granular high-Tc superconductors M.S. da Luz a, F.J.H. de Carvalho Jr. a, C.A.M. dos Santos A.J.S. Machado a, R. Ricardo da Silva b a
a,*
, C.Y. Shigue a,
Grupo de Supercondutividade, Departamento de Engenharia de Materiais, FAENQUIL, Polo Urbo Industrial Gleba AI-6, 12.600-970 Lorena-SP, Brazil b Instituto de Fı´sica ‘‘Gleb Wataghin’’, Unicamp, 13083-970, Campinas-SP, Brazil Received 28 October 2004; received in revised form 15 December 2004; accepted 16 December 2004 Available online 25 January 2005
Abstract This work reports the influence of the granularity on the transverse voltage as a function of the temperature, VXY(T), in polycrystalline samples of Bi2Sr2Ca0.8Pr0.2Cu2O8+d composition. It is observed nonzero transverse voltage at zero external magnetic field in the vicinity of the superconducting transition while far away from it, both above and below, no such voltage was detected. Measurements of VXY(T) in both directions of magnetic field allowed to calculate the symmetric and asymmetric transverse voltages in the full range of the applied magnetic field studied (zero up to 9 T). The symmetric transverse voltage as a function of the temperature presents sign reversal of the Hall resistance and positive Hall voltage at normal state such as expected for hole-doped high critical temperature superconductors. On the other hand, the asymmetric component of VXY(T) shows a peak near the superconducting transition which has been recently reported in literature. VXY(T) curves measured in a sample with double superconducting transition, which was confirmed by ac-susceptibility measurements and hysteresis loops of the magneto-resistance, present two peaks in the asymmetric component. These peaks are related to the intergranular and intragranular transitions and can be explained within the framework of Josephson and Abrikosov vortices and anti-vortices motion. By comparing the temperature dependence of the asymmetric transverse voltage and the derivative of longitudinal voltage is possible to observe a specific relation between both transport properties, which is noted to be valid not only at zero applied magnetic field but also under applied field. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Fy; 74.50.+r; 74.72.h Keywords: Double superconducting transition; Granularity; Hall effect
*
Corresponding author. Tel.: +55 12 3159 9911; fax: +55 12 553 3006. E-mail address: [email protected] (C.A.M. dos Santos).
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.12.005
72
M.S. da Luz et al. / Physica C 419 (2005) 71–78
1. Introduction High temperature superconductors (HTS) have been greatly studied by resistivity and Hall effect measurements. There are several aspects both experimental and theoretical which have been considered to explain the behavior of these transport properties. In the normal state Hall resistance of HTS presents an anomaly which is related to the formation of carriers in this class of superconductors [1,2]. Close to the superconducting transition there is an appearance of the sign reversal of the Hall resistance [3–5]. There are several models trying to explain this effect but agreement has not been achieved up to now [6–9]. Several authors have also observed a second sign reversal of the Hall resistance [8,10–14]. These sign reversals in the transverse component have been considered to be related to the quasiparticle or vortex–core contributions which are associated with the normal state excitations, superconducting dissipation resulting from vortex hydrodynamics and superconducting fluctuations [13]. Additionally, another important feature of the Hall resistance in the superconducting state is the scaling of the transverse and longitudinal resistivity, qXY (qXX)b, which has been observed to occur with b 1.7 [13,15]. An universal scaling law was derived near vortex–glass transition with the specific prediction of b = 2 [13,16]. More recently great attention has been given to the appearing of a transverse voltage at zero external magnetic field in HTS near superconducting transition [17–23]. Francavilla and co-workers [17,18] observed peaks in the transverse voltage at zero applied magnetic field near Tc both in low and high critical temperature superconductors. They attributed this effect to the GlazmanÕs model prediction in which a transverse voltage should be observed at zero external magnetic field [19]. This model proposed that magnetic field produced by the current can penetrate in form of vortices and anti-vortices at the sample edges. As the current increases, the Lorentz force acting on the vortices also increases and when pinning force is overcame, vortices and anti-vortices start to move to the center of the sample in opposite direction. If their attractive interaction overcomes the Lorentz
force vortices and anti-vortices motion will be distorted and transverse voltage will appear according to the JosephsonÕs equation E ¼ nv U0 ;
ð1Þ
where E is the electric field induced by motion of vortices, n is the superficial density of vortices, U0 = U0B/B with U0 = h/2e, v is the velocity of the vortex motion and B is the magnetic field. For high enough current the trajectories of the vortices and anti-vortices are not influenced by their interaction resulting in a decreasing of the transverse voltage. Vasˇek et al. [20–23] have also observed transverse voltage at zero applied magnetic field in superconducting samples. During the last years VasˇekÕs group introduced the idea of guiding force to explain their results. It considers the influence of the guide force on the moving of the vortex and anti-vortex. Vasˇek et al. supposed that an intrinsic pinning force related to linear channels inside the sample can induce vortex and anti-vortex motion in an specific direction giving a nonzero macroscopic transverse voltage [20,22]. On the other hand, several groups have noted that weak coupling effects between grains or superconducting clusters have great influence on the transport properties in HTS [24–27]. The main effect is generally observed in measurements of electrical resistance as a function of the temperature in which the broadening of the superconducting transition is current dependent and exhibits double transition. At the onset of the superconducting transition (T ci ) the reduction of the electrical resistance is related to the formation of isolated superconducting clusters and at a temperature labeled T cj the connection of these superconducting clusters, which is mediated by Josephson effect, reaches zero resistance superconducting state at low temperatures [24–27]. In this work is shown results concerning the influence of the granularity on the transverse voltage at zero and under applied magnetic field. 2. Experimental procedure Polycrystalline samples of Bi2Sr2Ca1xPrxCu2O8+d compositions were prepared by solid state
M.S. da Luz et al. / Physica C 419 (2005) 71–78
reaction technique using high purity Bi2O3, SrCO3, CaCO3, Pr6O11 and CuO powders. The measurements presented in this work were performed in two single phase polycrystalline samples of Bi2Sr2Ca0.8Pr0.2Cu2O8+d composition heat treated at 820 °C for 48 (sample B) and 96 h (sample A). X-ray powder diffractometry show that the samples are single phase. Scanning electron microscopy (SEM) performed in both samples present microstructure with lamellar grains of approximately 10 lm in length and 1 lm in thickness similar to other Bi2Sr2CaCu2O8 (Bi2212) samples. However, different degree of densification were observed for both samples. Samples A and B present density of 3.27 and 2.19 g/cm3, respectively. More details about samples preparation and characterization can be observed in previous papers [28,29]. Magneto-transport properties were carried out in a Maglab Oxford system of 9 T by means of the van der Pauw technique using two square samples of x = 0.2 composition with contacts made at the corners of the samples as shown schematically in the inset of the Fig. 1. The electrical terminals were prepared by using low resistance sputtered Au contacts (0.1 X). The voltage signals were measured using a nanovoltmeter Keithley model 181. In order to obtain longitudinal (VXX) and transverse voltage (VXY) eight voltage signals were
0.015
A
B
VXX (V)
0.010
D
B( T) zero 0.1 0.3 1.0 3.0 5.0 9.0
C
0.005
I= 30 mA
0.000 0
20
40
60
80
100
120
Temperature (K)
Fig. 1. Longitudinal voltage as a function of the temperature measured in the sample A at different applied magnetic fields. In the inset is shown an schematic view of the electrical contacts in the samples.
73
measured. The results for the VXX and VXY components are given by the following equations: þ V XX ¼ 1=4f½V þ AB V AB þ ½V BC V BC g
ð2Þ
and þ V XY ¼ 1=4f½V þ AC V AC ½V BD V BD g;
ð3Þ
where the voltage between ij was measured when applied current was passed through lm contacts. The alternating of the applied current allowed to eliminate thermopower effects produced in the voltage contacts. Other disturbing voltage signals (107 V) of the circuit were evaluated by switching off the applied current and subtracted of the VXY(T) curves. Ac-susceptibility measurements of the samples were performed in a PPMS of 9 T (Quantum Design). 3. Results and discussion In Figs. 1 and 2 are shown results of the longitudinal and transverse voltage as a function of the temperature measured at different applied magnetic field from zero up to 9 T for the sample A. In the longitudinal component one can see the broadening of the transition increasing applied magnetic field. On the other hand, in the transverse component is possible to observe several important features in the curves. There is nonzero transverse voltage at zero applied magnetic field which is similar to the results reported by Francavilla et al. [17,18] and Vasˇek et al. [20–23]. This transverse voltage asymmetry presents a peak in the vicinity of the superconducting transition and far away from T ci , both above and below, no such voltage was observed in superconducting and normal state such as expected [21,23]. With increasing magnetic field to 0.1 or 0.3 T we can see that the asymmetry in the transverse voltage has been kept. By comparing the magnitude of the VXY(T) curves for B = 0 and 0.1 T it is possible to conclude that the asymmetry originated in the transverse voltage is independent of the magnetic field direction. Further increasing of the magnetic field makes VXY start to recuperate its symmetry. For instance, VXY(T) measured at B = 9 T has essentially the same behavior for VXY(T) obtained at B = 9 T.
74
M.S. da Luz et al. / Physica C 419 (2005) 71–78 1.0x10
-6
zero 0.0 1.0x10
-6
0.1T
0.0 1.0x10
-6
0.3T
0.0
VXY (V)
1.0x10
-6
1.0T
0.0
1.0x10
-6
3.0T
0.0
1.0x10
5.0T
-6
0.0 -1.0x10 2.0x10
-6
-6
9.0T
0.0 -2.0x10
-6
40
60
80
100
Temperature(K) Fig. 2. Transverse voltage as a function of the temperature measured in the sample A at different applied magnetic fields using I = 30 mA. Open and full symbols are related to the measurements performed with applied magnetic field in positive and negative directions, respectively.
In these figures, we can also see the existence of the sign reversal in the vicinity of the superconducting transition and the positive Hall voltage at normal state such as expected by previous results for hole-doped HTS [3–9]. By using VXY measurements performed in both direction of the magnetic field we can calculate the asymmetric transverse voltage ðV A XY Þ through the þ equation V A ¼ 1=2½V þ V , where Vþ XY XY XY XY and V XY were measured under magnetic field applied in positive and negative directions, respectively.
To obtain the symmetric transverse voltage ðV SXY Þ, which is due to the applied magnetic field, we must calculate V SXY ¼ 1=2½V þ XY V XY . In Fig. 3 are presented the results for V A XY ðT Þ and V SXY ðT Þ obtained from Fig. 2. One can see in the V SXY component the sign reversal of the Hall resistance such as pointed by several authors [3–9]. In the normal state the transverse voltage is positive and increases linearly with increasing applied magnetic field at T > Tc (VXY is proportional to B) as expected for hole-doped HTS [1,2]. Therefore, in
S
VXY (V)
M.S. da Luz et al. / Physica C 419 (2005) 71–78 2.0x10
-6
1.0x10
-6
(a)
75
B( T) 0.1 0.3 1.0 3.0 5.0 9.0
0.0
40 1.0x10
60
80
100
-6
B( T) zero 0.1 0.3 1.0 3.0 5.0 9.0
A
VXY (V)
(b)
5.0x10
-7
0.0 70
75
80
85
90
Temperature (K) Fig. 3. (a) Symmetric and (b) asymmetric voltage calculated from results of the Fig. 2.
the V A XY we can observe the existence of such nonzero transverse voltage at all applied magnetic field. At low magnetic field the asymmetry in the VXY component is evident and can be related to the behavior pointed out by Francavilla et al. [17,18] and Vasˇek et al. [20–23]. The symmetry in the transverse voltage tends to be recovered at high magnetic field because symmetric contribution becomes higher than the asymmetric contribution at zero applied magnetic field. In order to obtain information concerning about the influence of the granularity on the transverse voltage in the vicinity of the superconducting transition we have measured another sample (sample B) which presents double transition. Fig. 4 presents some results of the longitudinal and transverse voltage as a function of the temperature measured at low magnetic field in which dissipation is mainly dominated by weak coupling effects. Looking at RXX(T) curves for different applied magnetic field we can see branching points at T cj which are clearly current dependent for T < T cj indicating the granular behavior of this sample as pointed out by other works [24–27]. Results of clockwise hysteresis loop of the magneto-resistance, RXX(H), [27,30,31] and double transition
in ac-susceptibility, vac(T), [32] shown in Fig. 5, unambiguously demonstrate the granular character of the sample B. In VXY(T) curves for the sample B we can observe the existence of two behaviors which can be related to the intragranular and intergranular transitions (see arrows indicating T ci and T cj ). The peak near T ci is similar to that one observed in the sample A whose origin is related to the description of the intragranular vortices and anti-vortices motion given by previous papers [17–23]. However, the VXY(T) broadening in the vicinity of T cj is clearly related to the intergranular transition meaning that the mechanism which describes nonzero transverse voltage at zero applied magnetic field must take into account not only intragranular mechanisms due to Abrikosov motion but also intergranular or weak coupling effects related to the Josephson vortices. Finally, we have analyzed our experimental results in order to evaluate if there is the specific relation between transverse voltage and derivative of longitudinal voltage such as pointed out recently by Vasˇek et al. [23]. Fig. 6 presents curves of dRXX(T)/dT and RA XY ðT Þ for some results of the both samples. One can see that there is a clear
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M.S. da Luz et al. / Physica C 419 (2005) 71–78
(a) B=zero
TCi
TCj
1E-4
0.000006
0.000003
VXY (V)
RXX (Ω )
0.01
1E-6 0.000000
(b) B=0.2T
TCi
TCj
1E-4
0.000004
0.000002
VXY (V)
RXX (Ω )
0.01
1E-6 0.000000
40
60
80
100
Temperature (K) Fig. 4. Longitudinal resistance (upper curves) and transverse voltage (lower curves) as a function of the temperature measured in the sample B at: (a) B = zero and (b) B = 0.2 T. The following applied currents were used in the measurements: I = 30 mA (j), I = 50 mA (), and I = 70 mA (m).
χ '' (emu/Oe.g)
0.0003
χ ''
0.0002
0.0001
0.0000 60
70
80
0.00
Resistance (Ω )
ac susceptibility (emu/Oe.g)
0.01
-0.01
χ'
0.015
0.010
0.005
0.000 0
5000
10000
Applied magnetic field (Oe)
-0.02 0
20
40
60
80
100
Temperature ( K) Fig. 5. Real (v 0 ) and imaginary (v00 ) ac-susceptibility components as a function of the temperature measured in the sample B at frequency = 10 Hz, applied magnetic field = 100 Oe, and field amplitude = 2.5 Oe. Upper inset shows the intragranular peak in the v00 component close to the onset of the superconducting transition. In lower inset is presented the clockwise hysteresis loop of the magneto-resistance measured at 20.6 K with I = 50 mA by using the conventional four probe technique.
interplay between dRXX(T)/dT and RA XY ðT Þ curves for both samples at zero and nonzero applied magnetic field. Peaks, broadening, and offset and onset temperatures are essentially in same place in both
longitudinal and transverse components. Both intragranular and intergranular peaks suggest a good agreement with the following form RA XY ðT Þ dRXX ðT Þ=dT . Other results for both sam-
M.S. da Luz et al. / Physica C 419 (2005) 71–78
77 0.0015
(a)
A
B = zero I = 30 mA
A
0.00002
RXY (Ω )
dRXX/dT (Ω /K) RXY (Ω )
Sample A
0.0010
0.00001
0.0005
0.00000
0.0000
0.00006
(b)
0.00004
B = 0.2 T I = 30 mA
0.001
0.00002
0.000
0.00000 0.00006 0.00004
0.002
Sample B
dRXX/dT (Ω /K)
0.00003
(c)
B = 3.0 T I = 70 mA
Sample B
0.0010 0.0005
0.00002
0.0000
0.00000 20
40
60
80
100
Temperature ( K)
Fig. 6. Comparison between
RA XY ðT Þ
and dRXX/dT(T) for sample A at B = zero (a) and sample B at B = 0.2 T (b), and B = 3.0 T (c).
ples present essentially the same picture. It is important to stress that our experimental observations include a new aspect not considered by Vasˇek et al. [23]. The RA XY ðT Þ curves, which were calculated by subtracting the transverse voltage produced by the applied magnetic field, indicate that the scaling form published before [23] has validity not only at zero applied magnetic field but also under applied field. The origin of this effect needs theoretical clarifications.
relation reported recently by Vasˇek et al. [23]. We have observed that this relation has validity not only at zero applied magnetic field but also under applied field.
4. Conclusion
References
This work presents results concerning the influence of granularity on the asymmetry of the Hall voltage. Results at zero applied magnetic field seem similar to those recently reported by Francavilla et al. [17,18] and Vasˇek et al. [20–23]. By using VXY(T) curves measured in both directions of the applied magnetic field was possible to calculate the symmetric and asymmetric transverse voltage in the full range of applied magnetic field studied. Transverse voltage measurements of the sample with double superconducting transition showed double peaks which can be related to the intragranular and intergranular effects. By comparing transverse voltage and derivative of longitudinal voltage was possible to obtain a similar scaling
Acknowledgement This work has been supported by the FAPESP (97/11113-6, 00/03610-4) and CNPq.
[1] T.R. Chien, T.W. Jing, N.P. Ong, Z.Z. Wang, Phys. Rev. Lett. 66 (1991) 3075. [2] A. Malinowski, M.Z. Cieplak, S. Guha, Q. Wu, B. Kim, A. Krickser, A. Perali, K. Karpinska, M. Berkowski, C.H. Shang, P. Lindenfeld, Phys. Rev. B 66 (2002) 104512, and references therein. [3] J.M. Harris, N.P. Ong, Y.F. Yan, Phys. Rev. Lett. 71 (1993) 1455. [4] W. Lang, G. Heine, P. Schwab, X.Z. Wang, D. Ba¨uerle, Phys. Rev. B 49 (1994) 4209. [5] A.W. Smith, T.W. Clinton, Wu Liu, C.C. Tsuei, A. Pique, Qi Li, C.J. Lobb, Phys. Rev. B 56 (1997) R2944. [6] A. Freimuth, C. Hohn, M. Galffy, Phys. Rev. B 44 (1991) 10396. [7] R.A. Ferrel, Phys. Rev. Lett. 68 (1992) 2524. [8] W. Lang, W. Go¨b, J.D. Pedarnig, R. Ro¨ssler, D. Ba¨uerle, Phys. C 364–365 (2001) 518. [9] Y. Yamamoto, K. Ogawa, Phys. C 371 (2002) 209.
78
M.S. da Luz et al. / Physica C 419 (2005) 71–78
[10] S.J. Hagen, C.J. Lobb, R.L. Greene, M. Eddy, Phys. Rev. B 43 (1991) 6246. [11] A.V. Samoilov, A. Legris, F. Rullier-Albenque, P. Lejay, S. Bouffard, Z.G. Ivanov, L.-G. Johansson, Phys. Rev. Lett. 74 (1995) 2351. [12] J.M. Graybeal, J. Luo, W.R. White, Phys. Rev. B 49 (1994) 12923. [13] W. Go¨b, W. Liebich, W. Lang, I. Puica, R. Sobolewski, R. Ro¨ssler, J.D. Pedarnig, D. Ba¨uerle, Phys. Rev. B 62 (2000) 9780. [14] H. Khosroabadi, V. Daadmehr, M. Akhavan, Phys. C 384 (2003) 169. [15] J. Luo, T.P. Orlando, J.M. Graybeal, X.D. Wu, R. Muenchausen, Phys. Rev. Lett. 68 (1992) 690. [16] V.M. Vinokur, V.B. Geshkenbein, M.V. FeigelÔman, G. Blatter, Phys. Rev. Lett. 71 (1993) 1242. [17] T.L. Francavilla, R.A. Hein, IEEE Trans. Mag. 27 (1991) 1039. [18] T.L. Francavilla, E.J. Cukauskas, L.H. Allen, P.R. Broussard, IEEE Appl. Suppl. 5 (1995) 1717. [19] L.I. Glazman, Sov. Low. Temp. Phys. 12 (1986) 389.
[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
P. Vasˇek, I. Janecˇek, V. Plecha´cˇek, Phys. C 247 (1995) 381. P. Vasˇek, Phys. C 364–365 (2001) 194. I. Janecˇek, P. Vasˇek, Phys. C 390 (2003) 330. P. Vasˇek, H. Shimakage, Z. Wang, Phys. C 411 (2004) 164. A. Gerber, T. Grenet, M. Cyrot, J. Beille, Phys. Rev. Lett. 65 (1990) 3201. A. Gerber, T. Grenet, M. Cyrot, J. Beille, Phys. Rev. B 43 (1991) 12935. M.J.R. Sandim, R.F. Jardim, Phys. C 328 (1999) 246. C.A.M. dos Santos, M.S. da Luz, B. Ferreira, A.J.S. Machado, Phys. C 391 (2003) 345. C.A.M. dos Santos, G.S. Pinto, B. Ferreira, A.J.S. Machado, Phys. C 354 (2001) 388. C.A.M. dos Santos, S. Moehlecke, Y. Kopelevich, A.J.S. Machado, Phys. C 390 (2003) 21. Y. Kopelevich, V.V. Lemanov, V.V. Makarov, Sov. Phys. Solid State 32 (1990) 2095. L. Ji, M.S. Rzchowski, N. Anand, M. Tinkham, Phys. Rev. B 47 (1993) 470. R.B. Goldfarb, A.F. Clark, A.I. Braginski, A.J. Panson, Cryogenics 27 (1987) 475.
Observation of asymmetric transverse voltage in granular high-Tc superconductors M.S. da Luz a, F.J.H. de Carvalho Jr. a, C.A.M. dos Santos A.J.S. Machado a, R. Ricardo da Silva b a
a,*
, C.Y. Shigue a,
Grupo de Supercondutividade, Departamento de Engenharia de Materiais, FAENQUIL, Polo Urbo Industrial Gleba AI-6, 12.600-970 Lorena-SP, Brazil b Instituto de Fı´sica ‘‘Gleb Wataghin’’, Unicamp, 13083-970, Campinas-SP, Brazil Received 28 October 2004; received in revised form 15 December 2004; accepted 16 December 2004 Available online 25 January 2005
Abstract This work reports the influence of the granularity on the transverse voltage as a function of the temperature, VXY(T), in polycrystalline samples of Bi2Sr2Ca0.8Pr0.2Cu2O8+d composition. It is observed nonzero transverse voltage at zero external magnetic field in the vicinity of the superconducting transition while far away from it, both above and below, no such voltage was detected. Measurements of VXY(T) in both directions of magnetic field allowed to calculate the symmetric and asymmetric transverse voltages in the full range of the applied magnetic field studied (zero up to 9 T). The symmetric transverse voltage as a function of the temperature presents sign reversal of the Hall resistance and positive Hall voltage at normal state such as expected for hole-doped high critical temperature superconductors. On the other hand, the asymmetric component of VXY(T) shows a peak near the superconducting transition which has been recently reported in literature. VXY(T) curves measured in a sample with double superconducting transition, which was confirmed by ac-susceptibility measurements and hysteresis loops of the magneto-resistance, present two peaks in the asymmetric component. These peaks are related to the intergranular and intragranular transitions and can be explained within the framework of Josephson and Abrikosov vortices and anti-vortices motion. By comparing the temperature dependence of the asymmetric transverse voltage and the derivative of longitudinal voltage is possible to observe a specific relation between both transport properties, which is noted to be valid not only at zero applied magnetic field but also under applied field. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Fy; 74.50.+r; 74.72.h Keywords: Double superconducting transition; Granularity; Hall effect
*
Corresponding author. Tel.: +55 12 3159 9911; fax: +55 12 553 3006. E-mail address: [email protected] (C.A.M. dos Santos).
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.12.005
72
M.S. da Luz et al. / Physica C 419 (2005) 71–78
1. Introduction High temperature superconductors (HTS) have been greatly studied by resistivity and Hall effect measurements. There are several aspects both experimental and theoretical which have been considered to explain the behavior of these transport properties. In the normal state Hall resistance of HTS presents an anomaly which is related to the formation of carriers in this class of superconductors [1,2]. Close to the superconducting transition there is an appearance of the sign reversal of the Hall resistance [3–5]. There are several models trying to explain this effect but agreement has not been achieved up to now [6–9]. Several authors have also observed a second sign reversal of the Hall resistance [8,10–14]. These sign reversals in the transverse component have been considered to be related to the quasiparticle or vortex–core contributions which are associated with the normal state excitations, superconducting dissipation resulting from vortex hydrodynamics and superconducting fluctuations [13]. Additionally, another important feature of the Hall resistance in the superconducting state is the scaling of the transverse and longitudinal resistivity, qXY (qXX)b, which has been observed to occur with b 1.7 [13,15]. An universal scaling law was derived near vortex–glass transition with the specific prediction of b = 2 [13,16]. More recently great attention has been given to the appearing of a transverse voltage at zero external magnetic field in HTS near superconducting transition [17–23]. Francavilla and co-workers [17,18] observed peaks in the transverse voltage at zero applied magnetic field near Tc both in low and high critical temperature superconductors. They attributed this effect to the GlazmanÕs model prediction in which a transverse voltage should be observed at zero external magnetic field [19]. This model proposed that magnetic field produced by the current can penetrate in form of vortices and anti-vortices at the sample edges. As the current increases, the Lorentz force acting on the vortices also increases and when pinning force is overcame, vortices and anti-vortices start to move to the center of the sample in opposite direction. If their attractive interaction overcomes the Lorentz
force vortices and anti-vortices motion will be distorted and transverse voltage will appear according to the JosephsonÕs equation E ¼ nv U0 ;
ð1Þ
where E is the electric field induced by motion of vortices, n is the superficial density of vortices, U0 = U0B/B with U0 = h/2e, v is the velocity of the vortex motion and B is the magnetic field. For high enough current the trajectories of the vortices and anti-vortices are not influenced by their interaction resulting in a decreasing of the transverse voltage. Vasˇek et al. [20–23] have also observed transverse voltage at zero applied magnetic field in superconducting samples. During the last years VasˇekÕs group introduced the idea of guiding force to explain their results. It considers the influence of the guide force on the moving of the vortex and anti-vortex. Vasˇek et al. supposed that an intrinsic pinning force related to linear channels inside the sample can induce vortex and anti-vortex motion in an specific direction giving a nonzero macroscopic transverse voltage [20,22]. On the other hand, several groups have noted that weak coupling effects between grains or superconducting clusters have great influence on the transport properties in HTS [24–27]. The main effect is generally observed in measurements of electrical resistance as a function of the temperature in which the broadening of the superconducting transition is current dependent and exhibits double transition. At the onset of the superconducting transition (T ci ) the reduction of the electrical resistance is related to the formation of isolated superconducting clusters and at a temperature labeled T cj the connection of these superconducting clusters, which is mediated by Josephson effect, reaches zero resistance superconducting state at low temperatures [24–27]. In this work is shown results concerning the influence of the granularity on the transverse voltage at zero and under applied magnetic field. 2. Experimental procedure Polycrystalline samples of Bi2Sr2Ca1xPrxCu2O8+d compositions were prepared by solid state
M.S. da Luz et al. / Physica C 419 (2005) 71–78
reaction technique using high purity Bi2O3, SrCO3, CaCO3, Pr6O11 and CuO powders. The measurements presented in this work were performed in two single phase polycrystalline samples of Bi2Sr2Ca0.8Pr0.2Cu2O8+d composition heat treated at 820 °C for 48 (sample B) and 96 h (sample A). X-ray powder diffractometry show that the samples are single phase. Scanning electron microscopy (SEM) performed in both samples present microstructure with lamellar grains of approximately 10 lm in length and 1 lm in thickness similar to other Bi2Sr2CaCu2O8 (Bi2212) samples. However, different degree of densification were observed for both samples. Samples A and B present density of 3.27 and 2.19 g/cm3, respectively. More details about samples preparation and characterization can be observed in previous papers [28,29]. Magneto-transport properties were carried out in a Maglab Oxford system of 9 T by means of the van der Pauw technique using two square samples of x = 0.2 composition with contacts made at the corners of the samples as shown schematically in the inset of the Fig. 1. The electrical terminals were prepared by using low resistance sputtered Au contacts (0.1 X). The voltage signals were measured using a nanovoltmeter Keithley model 181. In order to obtain longitudinal (VXX) and transverse voltage (VXY) eight voltage signals were
0.015
A
B
VXX (V)
0.010
D
B( T) zero 0.1 0.3 1.0 3.0 5.0 9.0
C
0.005
I= 30 mA
0.000 0
20
40
60
80
100
120
Temperature (K)
Fig. 1. Longitudinal voltage as a function of the temperature measured in the sample A at different applied magnetic fields. In the inset is shown an schematic view of the electrical contacts in the samples.
73
measured. The results for the VXX and VXY components are given by the following equations: þ V XX ¼ 1=4f½V þ AB V AB þ ½V BC V BC g
ð2Þ
and þ V XY ¼ 1=4f½V þ AC V AC ½V BD V BD g;
ð3Þ
where the voltage between ij was measured when applied current was passed through lm contacts. The alternating of the applied current allowed to eliminate thermopower effects produced in the voltage contacts. Other disturbing voltage signals (107 V) of the circuit were evaluated by switching off the applied current and subtracted of the VXY(T) curves. Ac-susceptibility measurements of the samples were performed in a PPMS of 9 T (Quantum Design). 3. Results and discussion In Figs. 1 and 2 are shown results of the longitudinal and transverse voltage as a function of the temperature measured at different applied magnetic field from zero up to 9 T for the sample A. In the longitudinal component one can see the broadening of the transition increasing applied magnetic field. On the other hand, in the transverse component is possible to observe several important features in the curves. There is nonzero transverse voltage at zero applied magnetic field which is similar to the results reported by Francavilla et al. [17,18] and Vasˇek et al. [20–23]. This transverse voltage asymmetry presents a peak in the vicinity of the superconducting transition and far away from T ci , both above and below, no such voltage was observed in superconducting and normal state such as expected [21,23]. With increasing magnetic field to 0.1 or 0.3 T we can see that the asymmetry in the transverse voltage has been kept. By comparing the magnitude of the VXY(T) curves for B = 0 and 0.1 T it is possible to conclude that the asymmetry originated in the transverse voltage is independent of the magnetic field direction. Further increasing of the magnetic field makes VXY start to recuperate its symmetry. For instance, VXY(T) measured at B = 9 T has essentially the same behavior for VXY(T) obtained at B = 9 T.
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M.S. da Luz et al. / Physica C 419 (2005) 71–78 1.0x10
-6
zero 0.0 1.0x10
-6
0.1T
0.0 1.0x10
-6
0.3T
0.0
VXY (V)
1.0x10
-6
1.0T
0.0
1.0x10
-6
3.0T
0.0
1.0x10
5.0T
-6
0.0 -1.0x10 2.0x10
-6
-6
9.0T
0.0 -2.0x10
-6
40
60
80
100
Temperature(K) Fig. 2. Transverse voltage as a function of the temperature measured in the sample A at different applied magnetic fields using I = 30 mA. Open and full symbols are related to the measurements performed with applied magnetic field in positive and negative directions, respectively.
In these figures, we can also see the existence of the sign reversal in the vicinity of the superconducting transition and the positive Hall voltage at normal state such as expected by previous results for hole-doped HTS [3–9]. By using VXY measurements performed in both direction of the magnetic field we can calculate the asymmetric transverse voltage ðV A XY Þ through the þ equation V A ¼ 1=2½V þ V , where Vþ XY XY XY XY and V XY were measured under magnetic field applied in positive and negative directions, respectively.
To obtain the symmetric transverse voltage ðV SXY Þ, which is due to the applied magnetic field, we must calculate V SXY ¼ 1=2½V þ XY V XY . In Fig. 3 are presented the results for V A XY ðT Þ and V SXY ðT Þ obtained from Fig. 2. One can see in the V SXY component the sign reversal of the Hall resistance such as pointed by several authors [3–9]. In the normal state the transverse voltage is positive and increases linearly with increasing applied magnetic field at T > Tc (VXY is proportional to B) as expected for hole-doped HTS [1,2]. Therefore, in
S
VXY (V)
M.S. da Luz et al. / Physica C 419 (2005) 71–78 2.0x10
-6
1.0x10
-6
(a)
75
B( T) 0.1 0.3 1.0 3.0 5.0 9.0
0.0
40 1.0x10
60
80
100
-6
B( T) zero 0.1 0.3 1.0 3.0 5.0 9.0
A
VXY (V)
(b)
5.0x10
-7
0.0 70
75
80
85
90
Temperature (K) Fig. 3. (a) Symmetric and (b) asymmetric voltage calculated from results of the Fig. 2.
the V A XY we can observe the existence of such nonzero transverse voltage at all applied magnetic field. At low magnetic field the asymmetry in the VXY component is evident and can be related to the behavior pointed out by Francavilla et al. [17,18] and Vasˇek et al. [20–23]. The symmetry in the transverse voltage tends to be recovered at high magnetic field because symmetric contribution becomes higher than the asymmetric contribution at zero applied magnetic field. In order to obtain information concerning about the influence of the granularity on the transverse voltage in the vicinity of the superconducting transition we have measured another sample (sample B) which presents double transition. Fig. 4 presents some results of the longitudinal and transverse voltage as a function of the temperature measured at low magnetic field in which dissipation is mainly dominated by weak coupling effects. Looking at RXX(T) curves for different applied magnetic field we can see branching points at T cj which are clearly current dependent for T < T cj indicating the granular behavior of this sample as pointed out by other works [24–27]. Results of clockwise hysteresis loop of the magneto-resistance, RXX(H), [27,30,31] and double transition
in ac-susceptibility, vac(T), [32] shown in Fig. 5, unambiguously demonstrate the granular character of the sample B. In VXY(T) curves for the sample B we can observe the existence of two behaviors which can be related to the intragranular and intergranular transitions (see arrows indicating T ci and T cj ). The peak near T ci is similar to that one observed in the sample A whose origin is related to the description of the intragranular vortices and anti-vortices motion given by previous papers [17–23]. However, the VXY(T) broadening in the vicinity of T cj is clearly related to the intergranular transition meaning that the mechanism which describes nonzero transverse voltage at zero applied magnetic field must take into account not only intragranular mechanisms due to Abrikosov motion but also intergranular or weak coupling effects related to the Josephson vortices. Finally, we have analyzed our experimental results in order to evaluate if there is the specific relation between transverse voltage and derivative of longitudinal voltage such as pointed out recently by Vasˇek et al. [23]. Fig. 6 presents curves of dRXX(T)/dT and RA XY ðT Þ for some results of the both samples. One can see that there is a clear
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M.S. da Luz et al. / Physica C 419 (2005) 71–78
(a) B=zero
TCi
TCj
1E-4
0.000006
0.000003
VXY (V)
RXX (Ω )
0.01
1E-6 0.000000
(b) B=0.2T
TCi
TCj
1E-4
0.000004
0.000002
VXY (V)
RXX (Ω )
0.01
1E-6 0.000000
40
60
80
100
Temperature (K) Fig. 4. Longitudinal resistance (upper curves) and transverse voltage (lower curves) as a function of the temperature measured in the sample B at: (a) B = zero and (b) B = 0.2 T. The following applied currents were used in the measurements: I = 30 mA (j), I = 50 mA (), and I = 70 mA (m).
χ '' (emu/Oe.g)
0.0003
χ ''
0.0002
0.0001
0.0000 60
70
80
0.00
Resistance (Ω )
ac susceptibility (emu/Oe.g)
0.01
-0.01
χ'
0.015
0.010
0.005
0.000 0
5000
10000
Applied magnetic field (Oe)
-0.02 0
20
40
60
80
100
Temperature ( K) Fig. 5. Real (v 0 ) and imaginary (v00 ) ac-susceptibility components as a function of the temperature measured in the sample B at frequency = 10 Hz, applied magnetic field = 100 Oe, and field amplitude = 2.5 Oe. Upper inset shows the intragranular peak in the v00 component close to the onset of the superconducting transition. In lower inset is presented the clockwise hysteresis loop of the magneto-resistance measured at 20.6 K with I = 50 mA by using the conventional four probe technique.
interplay between dRXX(T)/dT and RA XY ðT Þ curves for both samples at zero and nonzero applied magnetic field. Peaks, broadening, and offset and onset temperatures are essentially in same place in both
longitudinal and transverse components. Both intragranular and intergranular peaks suggest a good agreement with the following form RA XY ðT Þ dRXX ðT Þ=dT . Other results for both sam-
M.S. da Luz et al. / Physica C 419 (2005) 71–78
77 0.0015
(a)
A
B = zero I = 30 mA
A
0.00002
RXY (Ω )
dRXX/dT (Ω /K) RXY (Ω )
Sample A
0.0010
0.00001
0.0005
0.00000
0.0000
0.00006
(b)
0.00004
B = 0.2 T I = 30 mA
0.001
0.00002
0.000
0.00000 0.00006 0.00004
0.002
Sample B
dRXX/dT (Ω /K)
0.00003
(c)
B = 3.0 T I = 70 mA
Sample B
0.0010 0.0005
0.00002
0.0000
0.00000 20
40
60
80
100
Temperature ( K)
Fig. 6. Comparison between
RA XY ðT Þ
and dRXX/dT(T) for sample A at B = zero (a) and sample B at B = 0.2 T (b), and B = 3.0 T (c).
ples present essentially the same picture. It is important to stress that our experimental observations include a new aspect not considered by Vasˇek et al. [23]. The RA XY ðT Þ curves, which were calculated by subtracting the transverse voltage produced by the applied magnetic field, indicate that the scaling form published before [23] has validity not only at zero applied magnetic field but also under applied field. The origin of this effect needs theoretical clarifications.
relation reported recently by Vasˇek et al. [23]. We have observed that this relation has validity not only at zero applied magnetic field but also under applied field.
4. Conclusion
References
This work presents results concerning the influence of granularity on the asymmetry of the Hall voltage. Results at zero applied magnetic field seem similar to those recently reported by Francavilla et al. [17,18] and Vasˇek et al. [20–23]. By using VXY(T) curves measured in both directions of the applied magnetic field was possible to calculate the symmetric and asymmetric transverse voltage in the full range of applied magnetic field studied. Transverse voltage measurements of the sample with double superconducting transition showed double peaks which can be related to the intragranular and intergranular effects. By comparing transverse voltage and derivative of longitudinal voltage was possible to obtain a similar scaling
Acknowledgement This work has been supported by the FAPESP (97/11113-6, 00/03610-4) and CNPq.
[1] T.R. Chien, T.W. Jing, N.P. Ong, Z.Z. Wang, Phys. Rev. Lett. 66 (1991) 3075. [2] A. Malinowski, M.Z. Cieplak, S. Guha, Q. Wu, B. Kim, A. Krickser, A. Perali, K. Karpinska, M. Berkowski, C.H. Shang, P. Lindenfeld, Phys. Rev. B 66 (2002) 104512, and references therein. [3] J.M. Harris, N.P. Ong, Y.F. Yan, Phys. Rev. Lett. 71 (1993) 1455. [4] W. Lang, G. Heine, P. Schwab, X.Z. Wang, D. Ba¨uerle, Phys. Rev. B 49 (1994) 4209. [5] A.W. Smith, T.W. Clinton, Wu Liu, C.C. Tsuei, A. Pique, Qi Li, C.J. Lobb, Phys. Rev. B 56 (1997) R2944. [6] A. Freimuth, C. Hohn, M. Galffy, Phys. Rev. B 44 (1991) 10396. [7] R.A. Ferrel, Phys. Rev. Lett. 68 (1992) 2524. [8] W. Lang, W. Go¨b, J.D. Pedarnig, R. Ro¨ssler, D. Ba¨uerle, Phys. C 364–365 (2001) 518. [9] Y. Yamamoto, K. Ogawa, Phys. C 371 (2002) 209.
78
M.S. da Luz et al. / Physica C 419 (2005) 71–78
[10] S.J. Hagen, C.J. Lobb, R.L. Greene, M. Eddy, Phys. Rev. B 43 (1991) 6246. [11] A.V. Samoilov, A. Legris, F. Rullier-Albenque, P. Lejay, S. Bouffard, Z.G. Ivanov, L.-G. Johansson, Phys. Rev. Lett. 74 (1995) 2351. [12] J.M. Graybeal, J. Luo, W.R. White, Phys. Rev. B 49 (1994) 12923. [13] W. Go¨b, W. Liebich, W. Lang, I. Puica, R. Sobolewski, R. Ro¨ssler, J.D. Pedarnig, D. Ba¨uerle, Phys. Rev. B 62 (2000) 9780. [14] H. Khosroabadi, V. Daadmehr, M. Akhavan, Phys. C 384 (2003) 169. [15] J. Luo, T.P. Orlando, J.M. Graybeal, X.D. Wu, R. Muenchausen, Phys. Rev. Lett. 68 (1992) 690. [16] V.M. Vinokur, V.B. Geshkenbein, M.V. FeigelÔman, G. Blatter, Phys. Rev. Lett. 71 (1993) 1242. [17] T.L. Francavilla, R.A. Hein, IEEE Trans. Mag. 27 (1991) 1039. [18] T.L. Francavilla, E.J. Cukauskas, L.H. Allen, P.R. Broussard, IEEE Appl. Suppl. 5 (1995) 1717. [19] L.I. Glazman, Sov. Low. Temp. Phys. 12 (1986) 389.
[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
P. Vasˇek, I. Janecˇek, V. Plecha´cˇek, Phys. C 247 (1995) 381. P. Vasˇek, Phys. C 364–365 (2001) 194. I. Janecˇek, P. Vasˇek, Phys. C 390 (2003) 330. P. Vasˇek, H. Shimakage, Z. Wang, Phys. C 411 (2004) 164. A. Gerber, T. Grenet, M. Cyrot, J. Beille, Phys. Rev. Lett. 65 (1990) 3201. A. Gerber, T. Grenet, M. Cyrot, J. Beille, Phys. Rev. B 43 (1991) 12935. M.J.R. Sandim, R.F. Jardim, Phys. C 328 (1999) 246. C.A.M. dos Santos, M.S. da Luz, B. Ferreira, A.J.S. Machado, Phys. C 391 (2003) 345. C.A.M. dos Santos, G.S. Pinto, B. Ferreira, A.J.S. Machado, Phys. C 354 (2001) 388. C.A.M. dos Santos, S. Moehlecke, Y. Kopelevich, A.J.S. Machado, Phys. C 390 (2003) 21. Y. Kopelevich, V.V. Lemanov, V.V. Makarov, Sov. Phys. Solid State 32 (1990) 2095. L. Ji, M.S. Rzchowski, N. Anand, M. Tinkham, Phys. Rev. B 47 (1993) 470. R.B. Goldfarb, A.F. Clark, A.I. Braginski, A.J. Panson, Cryogenics 27 (1987) 475.