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Hall effect in the mixed state of Nd1.85Ce0.15CuO4−δ
PHYSICA
Physica B 194-196 (1994) 2257-2258 North-Holland
H A L L E F F E C T IN T H E M I X E D STATE OF N d L s s C e o . l s C u O 4 . 8 A. W. Smith, S. J. Hagen, M. Rajeswari, J. L. Peng, Z. Y. Li, R. L. Greene, S. N. Mat, X. X. Xi, S. Bhattacharya, Q. Li and C. J. Lobb Department of Physics, Center for Superconductivity Research, University of Maryland, College Park, MD 20742. We observe a sign reversal of the Hall resistivity in the mixed state of the n-type superconductor Ndl.s5Ceo.15CuO4. ~. Such all anomaly, which has also been observed earlier in the p-type oxide superconductors, has been widely attributed to thermoelectric effects, pinning effects, or else to complicated band structures. Recently, based on the systematics of the sign reversal in a wide class of materials, there have been attempts to explain the anomaly as an intrinsic aspect of the vortex motion. The behavior of the Hall resistivity in Ndl.ssCeo.15CuO4. 8 serves as a test for some of the models mentioned above. Particularly, a model based on thermoelectric effects which has been suggested to explain the sign reversal in the p-type superconductor YBa2Cu307. ~ does not predict the sign change in NdLssCeo.~sCuO4. ~. The observation of the Hall anomaly in this n-type system supports the idea that the sign reversal is inuinsically linked to the vortex dynamics in the flux flow state. 1. I N T R O D U C T I O N Many superconductors show a sign reversal of the Hall resistivity in the mixed state. ~ T h e ~ include most of the high-T c cuprates as well as several low temperatm'e superconductors such as Nb and V. In addition to having a wide range of critical temperatures the pinning strength of these materials also varies greatly. For ex,'unple, Nb has strong pinning effects, while TSCCO has relatively weak pinning. While most superconductors showing a Hall anomaly are p-type, NCCO is one of the few ntype materials. Adding NCCO to the list of superconductors with a Hall anomaly strengthens the view that the sign reversal is an intrinsic property of vortex dynamics rather than being due to material specific properties such as pinning or thermoelecu-ic effects. 2. E X P E R I M E N T The Hall and longitudinal resistivities of a crystal and fihns of Ndl.85Ce0A5CuO4_8 woe measured with a superconducting solenoid in fields up to 40 kG applied parallel to the c-axis. Temperature was ramped for both positive and negative field; Pxy was taken as the component of resistance odd in field to c,'mcel any lead
misalignment. Transition temperatures for the crystal and the films are 23 K and 21 K, respectively, with resistive transitions less than 1K wide. The crystal was grown from a C u t flux, see ref. 2. Films were grown by pulsed laser deposition to a thickness -_- 3000 A, see ref. 3. 3. R E S U L T S Figure 1 shows Pxx and Pxy as a function of temperature for a film. Pxy starts out negative above T c, but as 9xx decreases to about 40% of its normal state value, Pxy reverses sign, becoming positive. Finally Pxy goes to zero well below T c. Similar behavior is observed in the crystal and other films. 4. D I S C U S S I O N
A moving vortex generates an electric field given by Josephson's relation 4 E =-v L X B
(1)
where VL is the vortex velocity. The sign of the resulting Hall electric field depends upon whether the vortex moves with or against tile superfluid flow. When Pxy<0 in a p-type material, the vortex moves
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved S S D I 0921-4526(93)1761-A
& CONCLUSION
2258
0.1 0.0
-o.1
c2~ - 0 . 2
-
-
-0.5
--
200
E
15o 100
30
I
I
I
-
-
?/5
50
0 0
5
0
15
20
25
T (K)
Figure 1. Pxy& Pxx vs T lor given field in kG. upstream, against the direction of the superfluid velocity v s and cun'ent. When Pxy>0 in an n-type material, the vortex must move downstremn relative to the supercurrent, which is upsu'emn relative to v s. This suggests there is a force acting opposite to v s in both cases. Two classic theories of vortex motion are those of Bardeen-Stephen 5 (BS) ,and Nozieres-Vinen 6 (NV). Both BS and NV included a driving force balancing a dissipative drag force acting on the vortex; they both found:
F r e i m u t h et al. 8 h a v e p r o p o s e d a thermoeleca-ic model to explain the Hall anomaly in YBCO, but it does not explain the anomaly in NCCO. According to the model a thermoelectric field perpendicular to J s and opposite to the otherwise positive Hall field may dominate over some temperature range. This electric field is due to a temperature gradient set up by vortices as they carry entropy across the sample. NCCO, like YBCO, has a positive Seebeck coefficient 2 and should have the same thermoelectric field. Unlike YBCO, however, the direction of the thermoelectric field con'esponds to a negative Hall electric field resulting in no anomaly. While the sign reversal of the Hall effect below T c is still not understood, it is clear that a better understanding of vortex dynamics is necessary. For exmnple, both BS and NV assume the clean limit ( g > > ~ where e and ~ are the mean free path and coherence length, respectively) when calculating Ihe forces acting on vortices. There is, however, experimental evidence for the Hall anomaly in smnples where C - ~ . 1 The ratio e / ~ is an important parmneter in calculating scattering in a vortex core aud therefore the force acting on it. This, and the large variety of superconductors (high T c, low T o high pinning, low pinning, isotropic, anisotropic, p-type and n-type) which show a sign reversal, provide strong evidence for a vortex dynmnics picture. This work was supported in part by NSF grants 1)MR-9118826 and DMR-9115384. R
P~x = Pn B / Bc2.
E
F
E
R
E
N
C
E
S
(2)
Each theory, however, predicts a different Hall resistivity, while neither predicts it changes sign. Although NV does have a force acting opposite to the v s, it is not sufficiently large to cause a sign reversal. Recently, Ferlell 7 calculated a force acting on a vortex due to quasipm'ticle scattering. This force also acts in a direction opposite to v s, pushing vortices upstremn. While independent of the sign of the charge carrier, the force is not large enough to account for the sign reversal over the observed range of temperature and field.
1. S.J. tlagen et al. Phys. Rev. B. 47, 1064 (1993). 2. Physica C 177, 79 (1991); Phys. Rev. B 43, 13 606 (1991); ibid. 45, 7356 (1992). 3. S . N . Mad ct al., Appl Phys. Lett. 61, 2353 (1992). 4. B.D..losephson, Phys. Lett. 16, 242 (1965). 5. J. Bardeen and M. J. Stephen, Phys. Rev. 140, A1197 (1965). 6. P. Noziems ,'rod W. F. Vinen, Philos. Mag. 14, 667 (1966). 7. R. Fen'ell, Phys. Rev. Lett. 68, 2524 (1992). 8. A. Freimuth, C. Hohn, and M. Galffy, Phys. Rev. B 44, 10 396 (1991).
Physica B 194-196 (1994) 2257-2258 North-Holland
H A L L E F F E C T IN T H E M I X E D STATE OF N d L s s C e o . l s C u O 4 . 8 A. W. Smith, S. J. Hagen, M. Rajeswari, J. L. Peng, Z. Y. Li, R. L. Greene, S. N. Mat, X. X. Xi, S. Bhattacharya, Q. Li and C. J. Lobb Department of Physics, Center for Superconductivity Research, University of Maryland, College Park, MD 20742. We observe a sign reversal of the Hall resistivity in the mixed state of the n-type superconductor Ndl.s5Ceo.15CuO4. ~. Such all anomaly, which has also been observed earlier in the p-type oxide superconductors, has been widely attributed to thermoelectric effects, pinning effects, or else to complicated band structures. Recently, based on the systematics of the sign reversal in a wide class of materials, there have been attempts to explain the anomaly as an intrinsic aspect of the vortex motion. The behavior of the Hall resistivity in Ndl.ssCeo.15CuO4. 8 serves as a test for some of the models mentioned above. Particularly, a model based on thermoelectric effects which has been suggested to explain the sign reversal in the p-type superconductor YBa2Cu307. ~ does not predict the sign change in NdLssCeo.~sCuO4. ~. The observation of the Hall anomaly in this n-type system supports the idea that the sign reversal is inuinsically linked to the vortex dynamics in the flux flow state. 1. I N T R O D U C T I O N Many superconductors show a sign reversal of the Hall resistivity in the mixed state. ~ T h e ~ include most of the high-T c cuprates as well as several low temperatm'e superconductors such as Nb and V. In addition to having a wide range of critical temperatures the pinning strength of these materials also varies greatly. For ex,'unple, Nb has strong pinning effects, while TSCCO has relatively weak pinning. While most superconductors showing a Hall anomaly are p-type, NCCO is one of the few ntype materials. Adding NCCO to the list of superconductors with a Hall anomaly strengthens the view that the sign reversal is an intrinsic property of vortex dynamics rather than being due to material specific properties such as pinning or thermoelecu-ic effects. 2. E X P E R I M E N T The Hall and longitudinal resistivities of a crystal and fihns of Ndl.85Ce0A5CuO4_8 woe measured with a superconducting solenoid in fields up to 40 kG applied parallel to the c-axis. Temperature was ramped for both positive and negative field; Pxy was taken as the component of resistance odd in field to c,'mcel any lead
misalignment. Transition temperatures for the crystal and the films are 23 K and 21 K, respectively, with resistive transitions less than 1K wide. The crystal was grown from a C u t flux, see ref. 2. Films were grown by pulsed laser deposition to a thickness -_- 3000 A, see ref. 3. 3. R E S U L T S Figure 1 shows Pxx and Pxy as a function of temperature for a film. Pxy starts out negative above T c, but as 9xx decreases to about 40% of its normal state value, Pxy reverses sign, becoming positive. Finally Pxy goes to zero well below T c. Similar behavior is observed in the crystal and other films. 4. D I S C U S S I O N
A moving vortex generates an electric field given by Josephson's relation 4 E =-v L X B
(1)
where VL is the vortex velocity. The sign of the resulting Hall electric field depends upon whether the vortex moves with or against tile superfluid flow. When Pxy<0 in a p-type material, the vortex moves
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved S S D I 0921-4526(93)1761-A
& CONCLUSION
2258
0.1 0.0
-o.1
c2~ - 0 . 2
-
-
-0.5
--
200
E
15o 100
30
I
I
I
-
-
?/5
50
0 0
5
0
15
20
25
T (K)
Figure 1. Pxy& Pxx vs T lor given field in kG. upstream, against the direction of the superfluid velocity v s and cun'ent. When Pxy>0 in an n-type material, the vortex must move downstremn relative to the supercurrent, which is upsu'emn relative to v s. This suggests there is a force acting opposite to v s in both cases. Two classic theories of vortex motion are those of Bardeen-Stephen 5 (BS) ,and Nozieres-Vinen 6 (NV). Both BS and NV included a driving force balancing a dissipative drag force acting on the vortex; they both found:
F r e i m u t h et al. 8 h a v e p r o p o s e d a thermoeleca-ic model to explain the Hall anomaly in YBCO, but it does not explain the anomaly in NCCO. According to the model a thermoelectric field perpendicular to J s and opposite to the otherwise positive Hall field may dominate over some temperature range. This electric field is due to a temperature gradient set up by vortices as they carry entropy across the sample. NCCO, like YBCO, has a positive Seebeck coefficient 2 and should have the same thermoelectric field. Unlike YBCO, however, the direction of the thermoelectric field con'esponds to a negative Hall electric field resulting in no anomaly. While the sign reversal of the Hall effect below T c is still not understood, it is clear that a better understanding of vortex dynamics is necessary. For exmnple, both BS and NV assume the clean limit ( g > > ~ where e and ~ are the mean free path and coherence length, respectively) when calculating Ihe forces acting on vortices. There is, however, experimental evidence for the Hall anomaly in smnples where C - ~ . 1 The ratio e / ~ is an important parmneter in calculating scattering in a vortex core aud therefore the force acting on it. This, and the large variety of superconductors (high T c, low T o high pinning, low pinning, isotropic, anisotropic, p-type and n-type) which show a sign reversal, provide strong evidence for a vortex dynmnics picture. This work was supported in part by NSF grants 1)MR-9118826 and DMR-9115384. R
P~x = Pn B / Bc2.
E
F
E
R
E
N
C
E
S
(2)
Each theory, however, predicts a different Hall resistivity, while neither predicts it changes sign. Although NV does have a force acting opposite to the v s, it is not sufficiently large to cause a sign reversal. Recently, Ferlell 7 calculated a force acting on a vortex due to quasipm'ticle scattering. This force also acts in a direction opposite to v s, pushing vortices upstremn. While independent of the sign of the charge carrier, the force is not large enough to account for the sign reversal over the observed range of temperature and field.
1. S.J. tlagen et al. Phys. Rev. B. 47, 1064 (1993). 2. Physica C 177, 79 (1991); Phys. Rev. B 43, 13 606 (1991); ibid. 45, 7356 (1992). 3. S . N . Mad ct al., Appl Phys. Lett. 61, 2353 (1992). 4. B.D..losephson, Phys. Lett. 16, 242 (1965). 5. J. Bardeen and M. J. Stephen, Phys. Rev. 140, A1197 (1965). 6. P. Noziems ,'rod W. F. Vinen, Philos. Mag. 14, 667 (1966). 7. R. Fen'ell, Phys. Rev. Lett. 68, 2524 (1992). 8. A. Freimuth, C. Hohn, and M. Galffy, Phys. Rev. B 44, 10 396 (1991).