Physica C 422 (2005) 41–45

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Hall anomaly in the mixed state of overdopedY1�xCaxBa2Cu3O7�d thin film

Z. Wang, Y.Z. Zhang, X.F. Lu, H. Gao, L. Shan, H.H. Wen *

National Laboratory for superconductivity, Beijing National Laboratory for Condensed Matter Physics,

Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China

Received 10 September 2004

Available online 13 April 2005

Abstract

The longitudinal qxx and Hall resistivity qxy of Y0.8Ca0.2Ba2Cu3O7�d thin film were measured in different magnetic

fields up to 10.0 T. The anomalous sign reversal and a second sign reversal were observed in the overdoped sample. A

scaling law, qxy / qbxx with b = 1.7 ± 0.1, was determined for the field above 1 T. The experimental results indicate that

the first sign reversal and the scaling law may have no close connection with each other.

� 2005 Elsevier B.V. All rights reserved.

PACS: 74.25.Fy; 74.25.Ha; 74.25.Op

Keywords: Y1�xCaxBa2Cu3O7�d; Hall anomaly; Sign reversal; Scaling law

1. Introduction

Since the discovery of high-Tc superconductors

(HTSCs), Hall effect in the mixed state has at-

tracted considerable interest. There are two inter-

esting features in the Hall effect of HTSCs. One

is the sign reversal of Hall coefficient RH in mag-

netic fields at the temperature just below the super-

conducting transition temperature. This feature isobserved in many HTSCs [1–3] and some conven-

0921-4534/$ - see front matter � 2005 Elsevier B.V. All rights reserv

doi:10.1016/j.physc.2005.03.003

* Corresponding author.

E-mail address: hhwen@aphy.iphy.ac.cn (H.H. Wen).

tional superconductors [4]. Some materials exhibiteven double sign reversals in mixed states [1,5–7].

The sign reversal is not predicted by the classical

theories [8,9] in which the sign of RH should be

the same in both the superconducting and the nor-

mal states. A variety of theories were proposed to

explain the sign reversal, such as models of two

band [10], pinning induced backflow [11], and

superconducting fluctuation [12,13]. The otherinteresting feature is the striking scaling law

qxy / qbxx in the low longitudinal resistivity regime,

where b � 1.7 � 2 for different HTSCs systems

[14–17]. This power relation is explained in several

ed.

42 Z. Wang et al. / Physica C 422 (2005) 41–45

theories. Vinokur et al. [18], Samoilov [15] and

Budhani et al. [16] asserted that the sign reversal

and the scaling law had no close connection with

each other.

Most of the experiments about the Hall anom-aly were carried out on the optimal-doped sam-

ples. Nagaoka et al. [19] suggested that sign

reversals occur only in the range from underdoped

to slightly overdoped level. In the paper, we mea-

sured the Hall resistance with a Ca-doped Y-123

thin film to study the Hall anomaly in the overd-

oped region. We found that both the sign reversal

(including a second sign change) and the scalinglaw appear in this superconductor.

Fig. 1. Top: the mixed state resistivity of the Y0.8Ca0.2Ba2-

Cu3O7�d thin film in different magnetic fields; the inset shows

the case of zero field from superconducting state to room

temperature. Bottom: the mixed state Hall coefficient of the

Y0.8Ca0.2Ba2Cu3O7�d thin film in different magnetic fields; the

inset shows the case for B = 10 T from superconducting state to

room temperature.

2. Experimental techniques

Y0.8Ca0.2Ba2Cu3O7�d thin films were made by

DC magnetron sputtering from a stoichiometric

target onto substrates of (100) SrTiO3. The pro-cess of preparing the thin films was described in

detail elsewhere [20]. The thickness of the film is

2000 ± 100 A. A Hall bridge was lithographically

patterned with the length of 8 mm and the width

of 1 mm. Hall electrical leads are patterned around

the center of the bridge, while the resistance leads

are symmetrically patterned around the Hall leads

with the distance of 4 mm from one lead to theother. The connection between the bridge and each

lead is patterned with a micro-bridge in the size of

200 lm · 100 lm (length · width). A thin layer of

Au was sputtered onto these leads and the couple

leads of current (separated by the Hall bridge) for

reducing the contact resistance.

Hall resistivity qxy(T,B) and longitudinal resis-

tivity qxx(T,B) of an epitaxial c-axis orientedY0.8Ca0.2Ba2Cu3O7�d thin film were studied in sev-

eral fixed magnetic fields from 0.25 T to 10 T. In

the measurements, the fields were applied perpen-

dicular to the thin film and a bipolar DC current

of 5 mA (a current density of �2.5 kA/cm2) was

used. Generally, temperature was scanned over

the mixed state. In particular, qxy and qxx were

tested from zero resistance temperature to roomtemperature in magnetic fields of 10.0 T and 0 T

respectively for comparison. The longitudinal

resistivity was obtained by averaging the positive

and the negative current longitudinal resistivity

data and the Hall resistivity by subtracting the po-

sitive and the negative magnetic-field transverse

resistivity data, which are expressed as following:

qxx ¼ ½qxxðIÞ þ qxxð�IÞ�=2qxy ¼ ½qxyðI ;BÞ þ qxyð�I ;BÞ � qxyðI ;�BÞ

� qxyð�I ;�BÞ�=4

3. Result and discussion

The top panel of Fig. 1 shows qxx(T,B) data of

the film in the mixed state with the inset presenting

qxx(T,B = 0) from superconducting state to room

temperature. The bottom panel of Fig. 1 shows

the Hall coefficient RH = qxy/B of the film for the

field from 0.25 T to 10.0 T and the inset showsthe RH for B = 10.0 T from low temperature to

Z. Wang et al. / Physica C 422 (2005) 41–45 43

room temperature. In Fig. 1, all the RH curves in

the normal state merge together, which indicates

that in the normal state, Hall coefficient RH is

nearly independent of the magnetic field; besides,

it is strongly magnetic field dependent in the mixedstate. The sign reversal of RH(T,B) can be found

for 0 < B 6 7.0 T, but can not be found for

B = 10.0 T in Fig. 1. Comparing the upper and

the lower panel of Fig. 1, one will find that for

most fixed magnetic fields, sign reversals happen

above the middle point temperature of the super-

conducting transition, indicating that the reversals

are the behaviors in the flux flow region, and maynot be the behaviors in the thermally assisted flux

flow region.

Considering that rxy ¼ qxy=ðq2xy þ q2

xxÞ � qxy=q2xx

and qxy = RHB, we have rxy=B � RH=q2xx being

approximately independent of B in the normal

state. Fig. 2 shows rxy(T,B)/B in different mag-

netic fields. We can see from Fig. 2 that each

rxy(T,B)/B shows a sign reversal in low tempera-ture for 0 < B 6 7.0 T, while rxy(T,B)/B increases

with decreasing temperature and no reversal trend

appears in low temperature for the case of

B = 10.0 T. This implies that the sign reversal is

strongly dependent on the magnitude of the ap-

plied magnetic field.

On the basis of an analogy to the case of the

vortex motion in superfluid 4He, Hagen [21] attrib-uted the sign reversal of Hall resistivity to a com-

ponent of flux flow velocity opposite to the

direction of the superfluid transport current. Chen

Fig. 2. The rxy(T,B)/B curves of the Y1�xCaxBa2Cu3O7�d thin

film for different magnetic fields.

et al. [22] thought vortex charge could make an

additional contribution to the sign reversal of the

Hall conductivity. Based on the time dependent

Ginsburg–Landau (TDGL) equation, Dorsey [23]

and Koppin, Ivlev and Kalataky [24] proposedthat sign reversal could arise if quasiparticle Hall

current and vortex Hall current have opposite

signs. Many authors [2,3,25,26] explained their

experimental results by Dorsey and Koppin�s the-ory and showed that the sign reversal is a result

of the sum of a positive term varying with H and

a negative term varying with �1/H.

According to TDGL, Hall conductivity in thevortex state can be expressed as the sum of two

contributions rxy ¼ rnxy þ rf

xy , where rnxy arises from

the motion of the quasiparticles in the vortex core

and rfxy is the contribution of the vortex flow. rn

xy

has the same sign as the normal state effect and

is proportional to H, while rfxy has the sign oppo-

site to the normal state effect and is proportional

to �1/H. In low field, the absolute value of rfxy ex-

ceeds that of rnxy , leading to a consequence of sign

reversal. Hence, the distribution of rxy/B in Fig. 2

can be explained by the competition of the two

terms for different fields.

One can see in the bottom panel of Fig. 1 that a

second sign reversal appears in the RH for

B = 0.25 T. As can also be seen in the Hall conduc-

tivity presented in Fig. 2, with decreasing temper-ature, the mixed state Hall conductivity for the

field of 0.25 T first decreases, changes its sign from

positive to negative, arrives at its minimum, and

then increases rapidly, changing its sign again,

which clearly indicates the double sign reversals.

The second sign reversal was early observed in

highly anisotropic material BSCCO [15], TBCCO

[16] and HBCCO [6]. Nakao et al. [27] first ob-served the second sign reversal in Y-123 thin film

using high density pulse current. Lang [7,28]

et al. observed the double sign reversals in Y-123

thin film by conventional method in very low

magnetic fields. Our observation of the overdoped

Y-123 thin film agrees with those of all the samples

mentioned above.

Kopnin and Vinokur [29] attributed the secondsign reversal to the contribution of strong pinning

rpxy . Ikeda [30] proposed that in the scenario of vor-

tex-glass fluctuation, the sign of the rpxy depended

44 Z. Wang et al. / Physica C 422 (2005) 41–45

on the dimension of the pinning; for nearly three-

dimensionality (two-dimensionality) systems with

disordered point-like (line-like) pinning sites, rpxy

had the same (different) sign as rfxy . The second

sign reversal can be attributed to the line-like pin-ning sites parallel to the twin-boundary planes of

the film when B is perpendicular to the ab-plane.

Lang [28] et al. found that the second sign reversal

can be suppressed by high current density when

the current reduces the strong pinning and by the

oblique magnetic field when the oblique field de-

stroys the line-like disorder pinned on the twin-

boundary planes.Figure 3 shows the resistivity dependence of the

absolute values of qxy for several fixed fields in the

log–log scale. The deep dips of these curves indi-

cate the sign reversals of the qxy. In the low qxxportions of Fig. 3, each jqxyj(qxx) curve linearly de-

creases with decreasing qxx in the plot. This implies

a scaling law for 1.0 6 B 6 10 T. The plot regres-

sions (as presented by the straight lines in thefigure) show that jqxy j � Aqb

xx in the region, where

A is a magnetic-field-dependent factor and b =

1.7 ± 0.1.

Luo, Orlando and Graybeal [14] first discovered

the scaling law qxy / qbxx (with b = 1.7 ± 0.2) in the

region of negative Hall resistivity of Y-123 thin

films and they explained it by the vortex-glass the-

ory proposed by Dorsey and Fisher [32]. Based onthe calculation of the weak flux pinning effect, Vin-

Fig. 3. The resistivity dependence of the absolute values of Hall

resistivity for fixed fields. The inset shows the case for

B = 0.25 T.

okur, Geshkenbein, Feigel�man and Blatter [18]

(VGFB) obtained a universal scaling qxy / q2xx,

which is independent of specific vortex structure.

The similar result was also obtained by Wang

et al. [31] who considered that pinning, togetherwith thermal fluctuation, yields the scaling law.

The scaling law was confirmed by the study of

Y-123 thin film with b = 1.7 ± 0.2 as mentioned

above, work of Budhani et al. [16] on Tl-2223 films

with b = 1.85 ± 0.1 and Samoilov�s work on Bi-

2212 [15] and Tl-2212 films [17] with b = 2.0 ±

0.1. Here, our study of the Y0.8Ca0.2Ba2Cu3O7�d

thin film also gives a support to the scaling law.It seems that the decrease of the b value in different

superconductor systems can relate to the increas-

ing three-dimensional (3D) characteristics, as Y-

123 shows relatively strong 3D characteristics

and a relatively small b value among these HTSCs.

The scaling law with b = 1.7 ± 0.1 is not valid in

the field of B = 0.25 T, which can be seen in the in-

set of Fig. 3. As Kopnin and Vinokur [29] pointedout, the Hall resistivity qxy scales as q2

xx only for

weak pinning and a strong pinning can break the

scaling law and can even result in a sign reversal

again. The scaling law is valid in a limited field

range because of the weak pinning. In this case,

the pinning is probably relatively strong for

B = 0.25 T in which the scaling law breaks down.

Another interesting point is the validity of thescaling law with b = 1.7 ± 0.1 for B = 10.0 T,

where the sign reversal disappears. It seems that

the phenomenon supported the scenario of the

sum of two contributions rxy ¼ rnxy þ rf

xy , where

jrnxy j > jrf

xy j for B = 10.0 T. This is also another

support to the conclusion that the sign anomaly

and the scaling law may have no close connection

with each other.

4. Conclusion

We measured longitudinal and Hall resistivity

of overdoped Y0.8Ca0.2Ba2Cu3O7�d thin film in

different magnetic fields. Sign reversals were ob-

served in a limited magnetic field range. A secondsign reversal was found in the field of 0.25 T. A

scaling law between Hall resistivity and longitudi-

nal resistivity qxy / qbxx with b = 1.7 ± 0.1 was

Z. Wang et al. / Physica C 422 (2005) 41–45 45

obtained in the low longitudinal resistance por-

tions for magnetic field above 1.0 T. The sign

reversal can be attributed to the competition of

the two terms of the Hall conductance arising from

the motion of quasiparticles and vortices. The sec-ond sign reversal can be explained by the flux pin-

ning on the twin-boundary. Our result indicates

that the sign anomaly and the scaling law may

have no close connection with each other.

Acknowledgments

This work has been financially supported by

National Natural Science Foundation of China,

the Ministry of Science and Technology of China

and the Chinese Academy of Sciences. We thank

Prof. Z. D. Wang for fruitful discussions.

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