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Double sign reversal of the Hall effect in the mixed state of L2−xCexCuO4 crystals
Physica C 235-240 (1994)3177-3178 North-Holland
PHYSIgA
Double sign reversal of the Hall effect in the mixed state of L2_xCexCuO4 crystals. M. Cagigal a, A. Seffarb, J. Fontcuberta b, M. A. Crusellas b J. L. Vicent ~ and S. Pifiolb. aDepartamento de Fisiea de Materiales, Universidad Complutense, 28040 Madrid. Spain. bInstitut de Cifncia dels Materials, Consell Superior de Investigacions Cientifiques, Campus Universitat Autbnoma de Barcelona, 08193 Bellaterra, Spain. One of the most intringuing observations in type II superconductors is the anomalous behavior of the Hall effect To some extent the vortex dynamics is controlled by the ratio between the coherence length ({) and the mean free path (1) of the charge carries, so that, a change of one of these parameters may alter the dynamic. Most of the flux dynamics studies, particularly the Hall effect in the mixed state, in the HTSC superconducting cuprates have been performed on hole-type materials as YBaCuO and BiSCCO where { is rather short (typically {<= 10A). It is then interesting to explore the motion of vortex lines in the ease of higher { and {/1 ratios. The electron superconductors of the L2.xCexCuO 4 family are specially suited for this purpose because of its longer (about one order of magnitude) coherence length ~ and very short 1 values. In this work we present the field dependence of the Hall resistivity (Pxy) of LvxCexCuO4 single crystals. We have found that, the polarity of the Hall anomaly can have either the same sign or opposite to the Hall effect in the normal state. However, the crystals with higher resistivities do not show the anomalous pxy(H) peak. 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 (p~y) in the mixed state of different hole-doped HTSC cuprates show a sign change, with respect to the normal state, of the Hall voltage just below the transition temperature. This anomaly has also been observed in electron-doped HTSC cuprates [1.]. This observed behavior of the Hall effect leads to question the theory of vortex motion as well as the nature of the vortex state. Different models have been proposed to explain the sign change of Pxy(H). Among them Dorsey [2] proposed an intermediate model between the hydrodynamic description of Bardeen and Stephen, and Nozifres and Vinen, and the microscopic calculations of the Hall effect based on the Bogoliubov-de Gennes equations for a moving vortex. There have been suggestions of the importance of the values of the mean free path related to the coherence length, 1/~, in the vortex dynamics [1,3], but the origin of the Hall anomaly remains still unclear. In this paper we examine the behavior of the Hall resistivity in the mixed state of electrondoped L2_xCexCuO4 single crystals. Thus we have 0921-4534194/$07.00 © 1994 SS! ~I 0921-4534(94)02154-6
investigated thoroughly the influence of the mean free path and the coherence length on the vortex dynamics of these compounds. We measure the inplane Hall resistivity versus magnetic field at fixed temperatures in the mixed state with the magnetic field perpendicular to the ab-plane of the crystals. The Hall component was calculated by the four sweep method (H+,J+). The dependence of the Hall resistivity Pxy(H) with applied magnetic field at constant temperatures of a Sm2.xCexCuO 4 single crystal in the mixed state is shown in Fig.1. The most remarkable feature in the figure is that the Hall peak is positive or negative depending on the temperature range. It is worth to mentioning that the normal-state Hall coefficient RH(T) measured in these compounds is negative at high temperatures (T>80K), but at lower temperatures it becomes positive [4]. Thus, the Hall voltages measured in Sm single crystal have the same polarity than the normal state at temperatures close to T c, and a reverse polarity at lower temperatures. The presence of both positive and negative peaks in 9xy(H) cannot be explained on basis of the proposed theories. With the alternative explanation developed by A.T. Dorsey [2] both negative and positive behaviors in the mixed state of
ElsevierScience B.V. All rights reserved.
3178
M. Cagigal et al./Physica C 235-240 (1994) 3177 3178
35
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Fig.1 Hall resistivity vs magnetic field in a Sm z. xCexCuO4 crystal (Tc=13.5) measured at different temperatures. Pxy(H) can be reproduced, the sign change depends of a parameter (x related with the detailed electronic structure of the material. A phenomenological description based on disorder-dominated dynamics is proposed by Vinokur et al. [5], where they predict that the Hall voltage also depends on the same ct mentioned before in the Dorsey calculations. The scaling law PxyO~p,=p is independent on disorder and predicts an exponent 13=2. In our experimental data in Fig.2 it is found the same power-law but the exponent in these electron-doped compounds, 13=0.8:k-0.1, differs from the predicted value. A connection between the sign reversal ofthe Hall effect and the ratio between the coherence length ({) and the mean free path (1) of the charge carriers has been empirically observed in thin films of the 123 cuprates family [3]. The motion of vortex lines can be afected by higher values of { as it is the case (~ ~70~) in electron like cuprates. However, the calculation of the mean free path is not straitghtforward in these compounds with two type of charge carriers [4]. We have found a correlation between the resistivity above T c and the possible existence of the anomaly in the Hall resistivity. Several results from different L2.xCexCuO4 single crystals present the Hall anomaly with an amplitude of about 0 . 2 g ~ n [1], 3~f2cm and 20pf2cm (Fig. l), which correspond to values of the p,= just above T c of about 80pD.em, 590g~zrn and 580pD.m respectivelly. Measurements on a Ndl.ssCe0.15CuO4 crystal which presents higher p,=, 730p~-n, do not
100
1000
P~
Fig.2 Log-Log plot of I Pxy(H) I vs pxx(H). A scaling law PxyC~p~x~ has been observed with 13=0.8+0.1. show such peaks. The amplitude of the Hall anomaly presents a maximum at intermediate values of the resistivity and disapears on increasing it. In summary, the Hall anomaly in the present case of electron-doped HTSC is doubly manifestated with positive peaks of the same sign as in the normal state at high temperatures below T~ and negative peaks at low temperatures. The mean free path toghether with the coherence length are important parameters that affect to the vortexdynamics and so to the appearance of the Hall anomaly. The observed scaling law is universal and independent on the sign of the Hall anomaly. However the origin of the sign change remains still unclear and cannot be explained on the basis of the different theories developed at the moment. A CKNOWLEDGEMENTS. This work was supported by the CICYTMIDAS (Spain) projects MAT91-0742, MAT92-0388 and the CEE-SCIENCE project SCI-0389. REFERENCES. [1] S. J. Hagen et al. Phys. Rev. B 47, 1064 (1993). [2] A. Dorsey Phys. Rev. B 46, 8376 (1992). [3] J. Colino et al. Phys. Rev. B 49, 3496 (1994). [4] M. A Crusellas et al. Phys. C 210, 221 (1993). [5] V. M. Vinokur et al. Phys. Rev. Lett 71, 1242 (1993).
PHYSIgA
Double sign reversal of the Hall effect in the mixed state of L2_xCexCuO4 crystals. M. Cagigal a, A. Seffarb, J. Fontcuberta b, M. A. Crusellas b J. L. Vicent ~ and S. Pifiolb. aDepartamento de Fisiea de Materiales, Universidad Complutense, 28040 Madrid. Spain. bInstitut de Cifncia dels Materials, Consell Superior de Investigacions Cientifiques, Campus Universitat Autbnoma de Barcelona, 08193 Bellaterra, Spain. One of the most intringuing observations in type II superconductors is the anomalous behavior of the Hall effect To some extent the vortex dynamics is controlled by the ratio between the coherence length ({) and the mean free path (1) of the charge carries, so that, a change of one of these parameters may alter the dynamic. Most of the flux dynamics studies, particularly the Hall effect in the mixed state, in the HTSC superconducting cuprates have been performed on hole-type materials as YBaCuO and BiSCCO where { is rather short (typically {<= 10A). It is then interesting to explore the motion of vortex lines in the ease of higher { and {/1 ratios. The electron superconductors of the L2.xCexCuO 4 family are specially suited for this purpose because of its longer (about one order of magnitude) coherence length ~ and very short 1 values. In this work we present the field dependence of the Hall resistivity (Pxy) of LvxCexCuO4 single crystals. We have found that, the polarity of the Hall anomaly can have either the same sign or opposite to the Hall effect in the normal state. However, the crystals with higher resistivities do not show the anomalous pxy(H) peak. 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 (p~y) in the mixed state of different hole-doped HTSC cuprates show a sign change, with respect to the normal state, of the Hall voltage just below the transition temperature. This anomaly has also been observed in electron-doped HTSC cuprates [1.]. This observed behavior of the Hall effect leads to question the theory of vortex motion as well as the nature of the vortex state. Different models have been proposed to explain the sign change of Pxy(H). Among them Dorsey [2] proposed an intermediate model between the hydrodynamic description of Bardeen and Stephen, and Nozifres and Vinen, and the microscopic calculations of the Hall effect based on the Bogoliubov-de Gennes equations for a moving vortex. There have been suggestions of the importance of the values of the mean free path related to the coherence length, 1/~, in the vortex dynamics [1,3], but the origin of the Hall anomaly remains still unclear. In this paper we examine the behavior of the Hall resistivity in the mixed state of electrondoped L2_xCexCuO4 single crystals. Thus we have 0921-4534194/$07.00 © 1994 SS! ~I 0921-4534(94)02154-6
investigated thoroughly the influence of the mean free path and the coherence length on the vortex dynamics of these compounds. We measure the inplane Hall resistivity versus magnetic field at fixed temperatures in the mixed state with the magnetic field perpendicular to the ab-plane of the crystals. The Hall component was calculated by the four sweep method (H+,J+). The dependence of the Hall resistivity Pxy(H) with applied magnetic field at constant temperatures of a Sm2.xCexCuO 4 single crystal in the mixed state is shown in Fig.1. The most remarkable feature in the figure is that the Hall peak is positive or negative depending on the temperature range. It is worth to mentioning that the normal-state Hall coefficient RH(T) measured in these compounds is negative at high temperatures (T>80K), but at lower temperatures it becomes positive [4]. Thus, the Hall voltages measured in Sm single crystal have the same polarity than the normal state at temperatures close to T c, and a reverse polarity at lower temperatures. The presence of both positive and negative peaks in 9xy(H) cannot be explained on basis of the proposed theories. With the alternative explanation developed by A.T. Dorsey [2] both negative and positive behaviors in the mixed state of
ElsevierScience B.V. All rights reserved.
3178
M. Cagigal et al./Physica C 235-240 (1994) 3177 3178
35
n
a
i
3O
i
n
8m
1 O0
. . . . . . . .
i
. . . . . . . .
[
. . . . .
l'Ot~
25 I 2o
o v
1.BO fLON
•
a.158
10
1
10 5 0.1
0 --5
0.01
--10 --15 --20
I
i
I
i
I
1
2
3
4
5
0.001 10
H(T)
Fig.1 Hall resistivity vs magnetic field in a Sm z. xCexCuO4 crystal (Tc=13.5) measured at different temperatures. Pxy(H) can be reproduced, the sign change depends of a parameter (x related with the detailed electronic structure of the material. A phenomenological description based on disorder-dominated dynamics is proposed by Vinokur et al. [5], where they predict that the Hall voltage also depends on the same ct mentioned before in the Dorsey calculations. The scaling law PxyO~p,=p is independent on disorder and predicts an exponent 13=2. In our experimental data in Fig.2 it is found the same power-law but the exponent in these electron-doped compounds, 13=0.8:k-0.1, differs from the predicted value. A connection between the sign reversal ofthe Hall effect and the ratio between the coherence length ({) and the mean free path (1) of the charge carriers has been empirically observed in thin films of the 123 cuprates family [3]. The motion of vortex lines can be afected by higher values of { as it is the case (~ ~70~) in electron like cuprates. However, the calculation of the mean free path is not straitghtforward in these compounds with two type of charge carriers [4]. We have found a correlation between the resistivity above T c and the possible existence of the anomaly in the Hall resistivity. Several results from different L2.xCexCuO4 single crystals present the Hall anomaly with an amplitude of about 0 . 2 g ~ n [1], 3~f2cm and 20pf2cm (Fig. l), which correspond to values of the p,= just above T c of about 80pD.em, 590g~zrn and 580pD.m respectivelly. Measurements on a Ndl.ssCe0.15CuO4 crystal which presents higher p,=, 730p~-n, do not
100
1000
P~
Fig.2 Log-Log plot of I Pxy(H) I vs pxx(H). A scaling law PxyC~p~x~ has been observed with 13=0.8+0.1. show such peaks. The amplitude of the Hall anomaly presents a maximum at intermediate values of the resistivity and disapears on increasing it. In summary, the Hall anomaly in the present case of electron-doped HTSC is doubly manifestated with positive peaks of the same sign as in the normal state at high temperatures below T~ and negative peaks at low temperatures. The mean free path toghether with the coherence length are important parameters that affect to the vortexdynamics and so to the appearance of the Hall anomaly. The observed scaling law is universal and independent on the sign of the Hall anomaly. However the origin of the sign change remains still unclear and cannot be explained on the basis of the different theories developed at the moment. A CKNOWLEDGEMENTS. This work was supported by the CICYTMIDAS (Spain) projects MAT91-0742, MAT92-0388 and the CEE-SCIENCE project SCI-0389. REFERENCES. [1] S. J. Hagen et al. Phys. Rev. B 47, 1064 (1993). [2] A. Dorsey Phys. Rev. B 46, 8376 (1992). [3] J. Colino et al. Phys. Rev. B 49, 3496 (1994). [4] M. A Crusellas et al. Phys. C 210, 221 (1993). [5] V. M. Vinokur et al. Phys. Rev. Lett 71, 1242 (1993).