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Variations of normal state resistivity and Cu2+ localized spin moment in the single crystal Bi2Sr2 CaCU2O8 + x
ELSEVIER
Physica C 279 ( 1997) 241-245
Variations of normal state resistivity and Cu*’ localized spin moment in the single crystal Bi,Sr2CaCu20,+x Xiao-Guang Li a,*, Xuefeng Sun a, Wenbin Wu a, Qianwang Chen a, Lei Shi a, Yuheng Zhang a, Y. Kotaka b, K. Kishio b a Structure Research Laboratory, University of Science und Technology of China, Hefei 230026, China ’ Department of Applied Chemistry, University of Tokyo, Tokyo 113, Japan Received 26 February
1997
Abstract The effects of oxygen content on the anisotropic resistivity and Cu2+ localized spin moments have been studied for the single crystals. It was found that the in-plane and out-of-plane resistivities ( pa* and p,), as well as the Bi,Sr,CaCu20,+, electron spin resonance (ESR) signals decrease with increasing oxygen contents from underdoping to overdoping states. We believe that the in-plane resistivity upturn in an underdoped region is closely related to the carrier localization, and the scattering of spin fluctuations plays an important role in the charge transport properties. On the origin of c-axis resistivity, we should take into account the scattering in the ‘barrier’ layer between CuO, ‘cells’ and the scattering or fluctuations in the planes. 0 1997 Elsevier Science B.V. Keyword.sr Bi,Sr,CaCu,Os+,;
Electron spin resonance;
Resistivity;
1. Introduction The layered high-T, oxide materials show a change from antiferromagnetic insulator to normal metal with increasing carrier concentrations, and superconductivity occurs in a relatively narrow range of 0.1-0.2 carriers per CuO, unit carriers which implies an essential relation between the number of carriers and the high-i’, mechanism [l-7]. Some investigators believe that many anomalies in the normal state properties can be explained in terms of AF spin fluctuations of the two-dimensional intierant-electron system which depends on the doping states. The variations of carrier concentration, for
* Corresponding author.
Localized
spin moment
instance, in Bi,Sr,CaCu,O,+, (Bi-22121, have been measured for both polycrystals and single crystals by substituting Ca2+ with Y3+, and annealing at different oxygen pressures. Mandrus et al. [6] found that the temperature dependence of the in-plane resistivity pa,, of the Bi2Sr2Ca, _xY+C~ZOB+x single crystal shows an upturn as well as a metal-insulator transition for Y increasing over 0.4. They explained this phenomenon by using a weak localization and a two-dimensional transition. Such a resistive upturn and metal-‘insulator’ transition were also found for the samples with monotonously reduced T, during decreasing oxygen content, as reported by Briceno et al. [7]. However, Yasuda et al. [8] found that with decreasing oxygen pressure, pab shows only a metallic-like behaviour. This linear temperature dependence of electrical resistivity has been observed for
0921-4534/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO921-4534(97)00141-X
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X.-G. Li et al./Physica
high-T, cuprates [ 10-131. It should be noted that in much of the work on Bi,Sr,CaCu,Os+, single crystals, the oxygen content has remained an ambiguous factor, which may be the reason why the early experimental results on the temperature dependence of resistivity did not agree well with each other [6-91. In this case, at least there are two questions. First, why can an upturn sometimes be observed and sometimes disappears in the Bi,Sr,CaCu,O,+, system? Second, how is the correlation between local spin magnetic moment of Cu2+ and transport properties? Therefore, in order to understand the mechanism of the superconductivity, it is necessary to study the electronic excitation spectrum in the Bi2212 system from underdoping to overdoping states.
2. Experimental The Bi-2212 single crystal with nominal composition Bi2Sr2CaCu20s+x was grown by a floating zone technique. A typical size of the crystal was 5 X 4 X 0.05 mm3. The oxygen content of the samples was controlled by annealing under different oxygen pressures at 400°C for 48 h. The oxygen pressure varied from 1.6 X lo3 to 10m5 Torr by
evacuation of 0, gas. The relatively low annealing temperature is know to be effective in minimizing the decomposition into other phases during annealing. All the annealed crystals checked by X-ray diffraction showed that no phase decompositions took place. For the measurements of out-of-plane resistivity pc, current electrodes are annular rings painted on the ab face (with Ag epoxy). The voltage contacts are spots painted in the centre of the ring. The electron spin resonance (ESR) experiments were carried out at 200 K by a Bruker (ER-2OOD-SRC) reflection x-band-type spectrometer. The frequency and magnetic field were measured by a frequency counter and a proton NMR gaussmeter, respectively.
C 279 (1997) 241-245
1o-6
1o-4
lo’*
IO0
lo*
lo4
P (Tot3 Fig. 1. Variations of superconducting transition temperature T, with oxygen pressure for Bi,Sr,CaCu,O,+, single crystals annealed at 400°C for 48 h in different oxygen pressures.
and out-of-plane ( p,) resistivity curves at 50% recovery of the normal state resistivity, respectively. The transition temperature T, changes with varying oxygen pressure from underdoping to overdoping, and shows a maximum, c - 92 K, around oxygen pressure p = 10 Torr, which could be regarded as an optimized doping state. By using the relation between T, and the hole concentration for a polycrystal derived by Allgerier and Schilling [ 141 the oxygen content can be estimated if one assumes that the value of T, has one-to-one correspondence with the hole concentration. Fig. 2 shows the temperature dependence of the in-plane resistivity pnb for the samples (l-5) with different oxygen pressure p. One can see that the in-plane resistivity decreases with increasing oxygen content. In the underdoped region, pah shows weak localization at lower temperatures, then increases with a nearly linear temperature dependence at higher temperatures. From the optimizing to the overdoping range, pob behaves as a metallic-like. There are only a few models concerning the linear
3. Results and discussion
temperature dependence of the in-plane resistivity of the cuprates. One may exclude the electron-phonon interaction because the electron-phonon coupling constant A estimated from the resistivity in HTSC is
Fig. 1 shows the variation of T, as a function of oxygen pressure. The superconducting transition temperatures are determined from the in-plane ( pob)
very small 1151. Martin et al. [9] fitted a T-linear resistivity in Bi,Sr,CuO, with the Bloch-Gruneisen formula, which gives an unreasonably low Debye temperature of less than 35 K. From the RVB model
X.-G. Li et al./Physica
C 279 (1997) 241-245
243
2.0
1.5 z c: 7 s
. 1.0
ClII
0.5
:_
/ 3
,& .; *. .!
4 5
.. .:
0 50
100
150
I
200
250
2600
300
2800
3000
3400
H (Gs)
T W) Fig. 2. Temperature dependence of the in-plane resistivity five Bi-2212 crystals with different oxygen contents.
I
3200
P(,~ in
proposed by Anderson and Zou 1161, the bosons and fermions are confined to the Cu-0 planes, and the resistivity in the plane is produced by the scattering of the bosom from the fermions, which will follow a linear-temperature dependence. By using the marginal-Fermi-liquid theory by Varma et al. [17] and the nested Fermi liquid by Virosztek and Ruvalds [18], one can also explain the T-linear resistivity. However, it is still an open question if we use the models mentioned above to explain the in-plane resistive upturn at low temperature range in the underdoped region (see Fig. 2). The most plausible candidate model for the normal state transport properties is the scattering due to the spin fluctuations in the CuO, plane [ 19-221. With decreasing charge density from overdoping to underdoping states, a number of the Cu3d electrons are localized. One of the effective methods for determining the localized Cu*+ spin character is to study the variation of electron spin resonance (ESR). It is known that these localized Cu2+ spins will contribute to the ESR signals [23,24]. As shown in Fig. 3, there is a decreasing tendency of the electron spin resonance signals with increasing oxygen contents, which are originated from the decrease of the fraction of the localized Cu2+ spins. Combining the results of both the pob and ESR signals, we believe
Fig. 3. ESR spectra samples.
at 200 K for the five different
Bi-2212
that the spin scattering plays an important role in the charge transport properties in the CuO, planes, and the appearance of the upturn in the p,,(T) curve in the underdoped region is related to the carrier localization [25]. Fig. 4 shows the temperature dependence of the 40fl
50
100
150
200
250
300
T (K) Fig. 4. Temperature in Bi-2212.
dependence
of the out-of-plane
resistivity
p,
X.-G. Li et al./Physica
C 279 (1997) 241-245 I
0.5
50
OL’” 100
150
200
300
250
50
”
1”’
“’
100
150
T WI for the
out-of-plane electrical resistivity p,. In low oxygen pressure, the resistivity has semiconductor-like behaviour and the resistivity upturn is relatively high. With the oxygen content increasing to the overdoped region, pc first shows a metallic-like behaviour, then increases with decreasing temperature and the semiconductor-like upturn decreases. These metallic and semiconductive-like behaviours of p, for Bi,Sr,CaCu20s+, single crystals with different oxygen contents are similar to that reported by Yasuda et al.
Dl. On the origin of pc, several different models, such as the tunnelling of holons from the adjacent layers ( pc a 1/T) proposed by Anderson and Zou [16], an activated hopping [ pc a exp(A/k,T)l by Martin et al. [9], and the coherent interplanar tunnelling between neighbouring layers by Kumar and Iayannavar [26], apparently contradict the complicated temperature behaviours we observed in the
c,, c2, c) and A for samples
Samples
I
c, (0 cm) c2 c, (fi cm K) A (K)
2.75 310 565 151
2 k 0.05 * 5.5 + 7.2 * I.5
200
1,“’ 250
0 300
T (K)
Fig. 5. Variations of or / oob as a function of temperature five Bi-22 12 crystals.
Table I The fitting parameters
‘1,”
E 8 ci”
2.52 51.5 125 I80
f + i *
0.07 IO 0.6 4.5
Fig. 6. Fit of the experimental pc vs. temperature curves with Eq. (1) for the Bi,Sr,CaCu,O,+, single crystals in five different oxidation states with parameters listed in Table I. The solid lines are the fitting results.
Bi-2212 single crystal. In fact, on the one hand, the most important contribution to c-axis transport in the cuprates results from electron scattering in the ‘barrier’ layer between CuO, cells [27], with such a c-axis scattering time [28,29] in the ‘barrier’ expecting to be l/~,a (l/T)exp(A/k,T). On the other hand, as shown in Fig. 5, the variation trends for p, and pob are similar (i.e. p,/p,,) at high temperature range, suggesting that in-plane scattering or fluctuations may dominate c-axis transport in this regime. Considering the scattering in the in-plane and in the ‘barrier’ layer, p, can be written as:
(1)
P, = c1 + % Pab + ‘3
here c,, constants,
c* and cj are temperature independent and c2 measures the effectiveness of pla-
I-5 3
4
I .34 * 0.01
(5.04 * 0.02) x lo1084 k 4.9 (1.11 +0.01)x 10-l 410 + 10
304 * 6.6 10.52 * 0.2 245 & 2
5
’
(2.44iO.Ol)X 1041 f 7.5 (4.12 f 0.01)X 430 i 7.5
IO-’ IO-’
X.-G. Li et al./Physica
nar scattering processes to c-axial. It can be seen from Fig. 6 that Eq. (1) with fitting parameters listed in Table 1 describes our experiment very well. One of me important results is that the gap A (see Table 1) increases gradually from underdoping to overdoping states, and in contrast, the overall magnitude of p, appears to decrease. Although some investigators suggested that the existence of a pseudogap may cause the increase in pc in underdoped samples [10,11,28,30], the origin of the increase of A with oxygen doping still needs further investigation.
4. Conclusions In summary, our experimental results show that the behaviours of poh, p, and ESR signals of Bi,Sr,CaCu,O,+,Y single crystals depend on the changes of the charge density from underdoping to overdoping states. It is evident that the charge density dependence of spin fluctuations of the two-dimensional intierant-electron system plays the central role in the transport and magnetic properties in high temperature superconductors.
Acknowledgements This work was partly supported by the National Natural Science Foundation of China, and the National Center for R&D on Superconductivity. One of the authors (KK) also thanks for the support of the Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and Culture.
References [I] J.B. Torrance, A. Benzigre, A.I. Nazzal, S.S.P. Parkin, Physica C. 162-164 (1989) 291. [2] J.B. Goodenough, Superconduct. Sci. Technol. 3 (1990) 26. [3] Y. Tokura, in: S. Maekawa, M. Sato (Eds.). Physics of High Temperature Superconductors (Springer. Berlin, 19921 p. 191. [4] H.Y. Hwang, B. Batlogg, H. Takagi, H.L. Kao, R.J. Cava, J.J. Krajewski, W.F. Peck Jr., Phys. Rev. Lett. 72 (1994) 2636. [5] K. Kishio, in: G. Deutscher, A. Revcolevschi (Eds.), Coher-
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ence in High Temperature Superconductors (World Scientific, Singapore, 1996) p. 212. t61 D. Mandrus, L. Forro, C. Kendziora, L. Mihaly, Phys. Rev. B 44 (1991) 2418; D. Mandrus, L. Forro, C. Kendziora, L. Mihaly, Phys. Rev. B 45 (1992) 12640; C. Kendziora, L. Forro, D. Mandrus, J. Hartge, P. Stephens, L. Mihaly, R. Reeder, D. Moecher, R. Rivers, S. Sutton, Phys. Rev. B 45 (19921 13025. [71 G. Briceno, A. Zettl, Phys. Rev. B 40 (1989) 11352. l81T. Yasuda, S. Takano, L. Rinderer, Physica C 208 (1993) 385. [PI S. Martin, A.T. Fiory, R.M. Fleming, L.F. Schneemeyer, J.V. Waszczak, Phys. Rev. B 41 (1990) 846. lIO1T. ho, K. Takenaka, S. Uchida, Phys. Rev. Lett. 70 (1993) 3995. [Ill S. Uchida, Jpn. J. Appl. Phys. 32 (1993) 3784. [121 B. Batlogg, H.Y. Hwang, H. Takagi, R.J. Cava, H.L. Kao, J. Kwo, Physica C 235-240 (1994) 130; B. Batlogg, H.Y. Hwang, H. Takagi, H.L. Kao, J. Kwo, R.J. Cava, J. Low Temp. Phys. 95 (1994) 23. (131 X.H. Hou, W.J. Zbu, J.Q. Li, J.W. Li, J.W. Xiong, F. Wu, Y.Z. Huang, 2.X. Zhao, Phys. Rev. B 50 (1994) 496. [I41 C. Allgerier, J.S. Schilling, Physica C 168 (1990) 499. [151 D.B. Tanner, T. Timusk, in: D.M. Ginsberg (Ed.), Physical Properties of High Temperature Superconductors, vol. 3 (World Scientific, Singapore, 1992) p. 416. [161 P.W. Anderson, Z. Zou, Phys. Rev. Lett. 60 (1988) 132. 1171 CM. Varma. P.B. Littlewood, S. Schmitt-Rink, E. Abrahams, A.E. Ruckenstein, Phys. Rev. Lett. 63 (1989) 1996. lts1 A. Virosztek, J. Ruvalds, Phys. Rev. B 42 (1990) 4064. [IPI T. Moriya, Y. Takahasi, K. Ueda, J. Phys. Sot. Jpn. 59 (1990) 2905. [20] A.J. Millis, H. Monien, D. Pines, Phys. Rev. B 42 (1991) 167; H. Monien. D. Pines, M. Takigawa, Phys. Rev. B 43 (1991) 258; H. Monien, P. Monthoux, D. Pines, Phys. Rev. B 49 (1994) 4261; D. Pines, J. Phys. Chem. Solids 56 (1995) 1651. [21] E.J. Nicol, N.M. Plakida. Physica C 185-189 (19891 1637; N.M. Plakida, High Temperature Superconductivity (Springer-Verlag, Berlin, 19951. [22] A.P. Kampf, Phys. Rep. 249 (1994) 219. [23] T. Ishida, K. Koga, S. Nakamura, Y. Lye, K. Kanoda, S. Okui, T. Takahashi, T. Oashi, K. Kumagai, Physica C 176 (1991) 24; T. Ishida, K. Kanoda, T. Takahashi, K. Koga, Physica C 178 (1991) 231. [24] J. Sichelschmidt, B. Elschner, A. Loidl, B.1. Kochelaev, Phys. Rev. B 51 (1995) 9199. [25] Y. Ando, U.S. Boebinger, A. Passner, N.L. Wang, C. Geibel, F. Steglich, Phys. Rev. Lett. 77 (1996) 2065. [26] N. Kumar, A.M. Jayannavar, Phys. Rev. B 45 (19921 5001. [27] Y. Zha, S.L. Cooper, D. Pines, Phys. Rev. B 53 (1996) 8252. [28] Y.F. Yan, P. Mat], J.M. Harris, N.P. Ong, Phys. Rev. B 52 (1995) R751. 1291 G. Balestrino, E. Milani, C. Anna, A.A. Varlamov, Phys. Rev. B 54 (1996) 3628. [30] C.C. Homes, T. Timusk, R. Liang, D.A. Bonn, W.N. Hardy, Phys. Rev. Lett. 71 (1993) 1645.
Physica C 279 ( 1997) 241-245
Variations of normal state resistivity and Cu*’ localized spin moment in the single crystal Bi,Sr2CaCu20,+x Xiao-Guang Li a,*, Xuefeng Sun a, Wenbin Wu a, Qianwang Chen a, Lei Shi a, Yuheng Zhang a, Y. Kotaka b, K. Kishio b a Structure Research Laboratory, University of Science und Technology of China, Hefei 230026, China ’ Department of Applied Chemistry, University of Tokyo, Tokyo 113, Japan Received 26 February
1997
Abstract The effects of oxygen content on the anisotropic resistivity and Cu2+ localized spin moments have been studied for the single crystals. It was found that the in-plane and out-of-plane resistivities ( pa* and p,), as well as the Bi,Sr,CaCu20,+, electron spin resonance (ESR) signals decrease with increasing oxygen contents from underdoping to overdoping states. We believe that the in-plane resistivity upturn in an underdoped region is closely related to the carrier localization, and the scattering of spin fluctuations plays an important role in the charge transport properties. On the origin of c-axis resistivity, we should take into account the scattering in the ‘barrier’ layer between CuO, ‘cells’ and the scattering or fluctuations in the planes. 0 1997 Elsevier Science B.V. Keyword.sr Bi,Sr,CaCu,Os+,;
Electron spin resonance;
Resistivity;
1. Introduction The layered high-T, oxide materials show a change from antiferromagnetic insulator to normal metal with increasing carrier concentrations, and superconductivity occurs in a relatively narrow range of 0.1-0.2 carriers per CuO, unit carriers which implies an essential relation between the number of carriers and the high-i’, mechanism [l-7]. Some investigators believe that many anomalies in the normal state properties can be explained in terms of AF spin fluctuations of the two-dimensional intierant-electron system which depends on the doping states. The variations of carrier concentration, for
* Corresponding author.
Localized
spin moment
instance, in Bi,Sr,CaCu,O,+, (Bi-22121, have been measured for both polycrystals and single crystals by substituting Ca2+ with Y3+, and annealing at different oxygen pressures. Mandrus et al. [6] found that the temperature dependence of the in-plane resistivity pa,, of the Bi2Sr2Ca, _xY+C~ZOB+x single crystal shows an upturn as well as a metal-insulator transition for Y increasing over 0.4. They explained this phenomenon by using a weak localization and a two-dimensional transition. Such a resistive upturn and metal-‘insulator’ transition were also found for the samples with monotonously reduced T, during decreasing oxygen content, as reported by Briceno et al. [7]. However, Yasuda et al. [8] found that with decreasing oxygen pressure, pab shows only a metallic-like behaviour. This linear temperature dependence of electrical resistivity has been observed for
0921-4534/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO921-4534(97)00141-X
242
X.-G. Li et al./Physica
high-T, cuprates [ 10-131. It should be noted that in much of the work on Bi,Sr,CaCu,Os+, single crystals, the oxygen content has remained an ambiguous factor, which may be the reason why the early experimental results on the temperature dependence of resistivity did not agree well with each other [6-91. In this case, at least there are two questions. First, why can an upturn sometimes be observed and sometimes disappears in the Bi,Sr,CaCu,O,+, system? Second, how is the correlation between local spin magnetic moment of Cu2+ and transport properties? Therefore, in order to understand the mechanism of the superconductivity, it is necessary to study the electronic excitation spectrum in the Bi2212 system from underdoping to overdoping states.
2. Experimental The Bi-2212 single crystal with nominal composition Bi2Sr2CaCu20s+x was grown by a floating zone technique. A typical size of the crystal was 5 X 4 X 0.05 mm3. The oxygen content of the samples was controlled by annealing under different oxygen pressures at 400°C for 48 h. The oxygen pressure varied from 1.6 X lo3 to 10m5 Torr by
evacuation of 0, gas. The relatively low annealing temperature is know to be effective in minimizing the decomposition into other phases during annealing. All the annealed crystals checked by X-ray diffraction showed that no phase decompositions took place. For the measurements of out-of-plane resistivity pc, current electrodes are annular rings painted on the ab face (with Ag epoxy). The voltage contacts are spots painted in the centre of the ring. The electron spin resonance (ESR) experiments were carried out at 200 K by a Bruker (ER-2OOD-SRC) reflection x-band-type spectrometer. The frequency and magnetic field were measured by a frequency counter and a proton NMR gaussmeter, respectively.
C 279 (1997) 241-245
1o-6
1o-4
lo’*
IO0
lo*
lo4
P (Tot3 Fig. 1. Variations of superconducting transition temperature T, with oxygen pressure for Bi,Sr,CaCu,O,+, single crystals annealed at 400°C for 48 h in different oxygen pressures.
and out-of-plane ( p,) resistivity curves at 50% recovery of the normal state resistivity, respectively. The transition temperature T, changes with varying oxygen pressure from underdoping to overdoping, and shows a maximum, c - 92 K, around oxygen pressure p = 10 Torr, which could be regarded as an optimized doping state. By using the relation between T, and the hole concentration for a polycrystal derived by Allgerier and Schilling [ 141 the oxygen content can be estimated if one assumes that the value of T, has one-to-one correspondence with the hole concentration. Fig. 2 shows the temperature dependence of the in-plane resistivity pnb for the samples (l-5) with different oxygen pressure p. One can see that the in-plane resistivity decreases with increasing oxygen content. In the underdoped region, pah shows weak localization at lower temperatures, then increases with a nearly linear temperature dependence at higher temperatures. From the optimizing to the overdoping range, pob behaves as a metallic-like. There are only a few models concerning the linear
3. Results and discussion
temperature dependence of the in-plane resistivity of the cuprates. One may exclude the electron-phonon interaction because the electron-phonon coupling constant A estimated from the resistivity in HTSC is
Fig. 1 shows the variation of T, as a function of oxygen pressure. The superconducting transition temperatures are determined from the in-plane ( pob)
very small 1151. Martin et al. [9] fitted a T-linear resistivity in Bi,Sr,CuO, with the Bloch-Gruneisen formula, which gives an unreasonably low Debye temperature of less than 35 K. From the RVB model
X.-G. Li et al./Physica
C 279 (1997) 241-245
243
2.0
1.5 z c: 7 s
. 1.0
ClII
0.5
:_
/ 3
,& .; *. .!
4 5
.. .:
0 50
100
150
I
200
250
2600
300
2800
3000
3400
H (Gs)
T W) Fig. 2. Temperature dependence of the in-plane resistivity five Bi-2212 crystals with different oxygen contents.
I
3200
P(,~ in
proposed by Anderson and Zou 1161, the bosons and fermions are confined to the Cu-0 planes, and the resistivity in the plane is produced by the scattering of the bosom from the fermions, which will follow a linear-temperature dependence. By using the marginal-Fermi-liquid theory by Varma et al. [17] and the nested Fermi liquid by Virosztek and Ruvalds [18], one can also explain the T-linear resistivity. However, it is still an open question if we use the models mentioned above to explain the in-plane resistive upturn at low temperature range in the underdoped region (see Fig. 2). The most plausible candidate model for the normal state transport properties is the scattering due to the spin fluctuations in the CuO, plane [ 19-221. With decreasing charge density from overdoping to underdoping states, a number of the Cu3d electrons are localized. One of the effective methods for determining the localized Cu*+ spin character is to study the variation of electron spin resonance (ESR). It is known that these localized Cu2+ spins will contribute to the ESR signals [23,24]. As shown in Fig. 3, there is a decreasing tendency of the electron spin resonance signals with increasing oxygen contents, which are originated from the decrease of the fraction of the localized Cu2+ spins. Combining the results of both the pob and ESR signals, we believe
Fig. 3. ESR spectra samples.
at 200 K for the five different
Bi-2212
that the spin scattering plays an important role in the charge transport properties in the CuO, planes, and the appearance of the upturn in the p,,(T) curve in the underdoped region is related to the carrier localization [25]. Fig. 4 shows the temperature dependence of the 40fl
50
100
150
200
250
300
T (K) Fig. 4. Temperature in Bi-2212.
dependence
of the out-of-plane
resistivity
p,
X.-G. Li et al./Physica
C 279 (1997) 241-245 I
0.5
50
OL’” 100
150
200
300
250
50
”
1”’
“’
100
150
T WI for the
out-of-plane electrical resistivity p,. In low oxygen pressure, the resistivity has semiconductor-like behaviour and the resistivity upturn is relatively high. With the oxygen content increasing to the overdoped region, pc first shows a metallic-like behaviour, then increases with decreasing temperature and the semiconductor-like upturn decreases. These metallic and semiconductive-like behaviours of p, for Bi,Sr,CaCu20s+, single crystals with different oxygen contents are similar to that reported by Yasuda et al.
Dl. On the origin of pc, several different models, such as the tunnelling of holons from the adjacent layers ( pc a 1/T) proposed by Anderson and Zou [16], an activated hopping [ pc a exp(A/k,T)l by Martin et al. [9], and the coherent interplanar tunnelling between neighbouring layers by Kumar and Iayannavar [26], apparently contradict the complicated temperature behaviours we observed in the
c,, c2, c) and A for samples
Samples
I
c, (0 cm) c2 c, (fi cm K) A (K)
2.75 310 565 151
2 k 0.05 * 5.5 + 7.2 * I.5
200
1,“’ 250
0 300
T (K)
Fig. 5. Variations of or / oob as a function of temperature five Bi-22 12 crystals.
Table I The fitting parameters
‘1,”
E 8 ci”
2.52 51.5 125 I80
f + i *
0.07 IO 0.6 4.5
Fig. 6. Fit of the experimental pc vs. temperature curves with Eq. (1) for the Bi,Sr,CaCu,O,+, single crystals in five different oxidation states with parameters listed in Table I. The solid lines are the fitting results.
Bi-2212 single crystal. In fact, on the one hand, the most important contribution to c-axis transport in the cuprates results from electron scattering in the ‘barrier’ layer between CuO, cells [27], with such a c-axis scattering time [28,29] in the ‘barrier’ expecting to be l/~,a (l/T)exp(A/k,T). On the other hand, as shown in Fig. 5, the variation trends for p, and pob are similar (i.e. p,/p,,) at high temperature range, suggesting that in-plane scattering or fluctuations may dominate c-axis transport in this regime. Considering the scattering in the in-plane and in the ‘barrier’ layer, p, can be written as:
(1)
P, = c1 + % Pab + ‘3
here c,, constants,
c* and cj are temperature independent and c2 measures the effectiveness of pla-
I-5 3
4
I .34 * 0.01
(5.04 * 0.02) x lo1084 k 4.9 (1.11 +0.01)x 10-l 410 + 10
304 * 6.6 10.52 * 0.2 245 & 2
5
’
(2.44iO.Ol)X 1041 f 7.5 (4.12 f 0.01)X 430 i 7.5
IO-’ IO-’
X.-G. Li et al./Physica
nar scattering processes to c-axial. It can be seen from Fig. 6 that Eq. (1) with fitting parameters listed in Table 1 describes our experiment very well. One of me important results is that the gap A (see Table 1) increases gradually from underdoping to overdoping states, and in contrast, the overall magnitude of p, appears to decrease. Although some investigators suggested that the existence of a pseudogap may cause the increase in pc in underdoped samples [10,11,28,30], the origin of the increase of A with oxygen doping still needs further investigation.
4. Conclusions In summary, our experimental results show that the behaviours of poh, p, and ESR signals of Bi,Sr,CaCu,O,+,Y single crystals depend on the changes of the charge density from underdoping to overdoping states. It is evident that the charge density dependence of spin fluctuations of the two-dimensional intierant-electron system plays the central role in the transport and magnetic properties in high temperature superconductors.
Acknowledgements This work was partly supported by the National Natural Science Foundation of China, and the National Center for R&D on Superconductivity. One of the authors (KK) also thanks for the support of the Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science and Culture.
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