negative out-of-plane magnetoresistance of bi2(sr,la)2cuo6+δ single crystals

ELSEVIER Physica C 271 (1996) 171-180

PHY$ A®

Negative out-of-plane magnetoresistance of Bi2(Sr,La)2CuO6÷ single crystals

R. Yoshizaki *, H. Ikeda Institute of Applied Physics and Cryogenics Center, University of Tsukuba, Tsukuba, lbaraki 305, Japan

Received 26 June 1996; revised manuscript received 11 September 1996

Abstract

Lorentz-force independent magnetoresistance was observed below 200 K in slightly underdoped Bi2(Sr,La)2CuO6+ crystals. The positive out-of-plane magnetoresistance at 200 K is decreased as the temperature is lowered and turns to negative at about 50 K. The out-of-plane resistance shows log T dependence in zero magnetic field, and the divergent profile is suppressed in intense magnetic field. These results indicate the responsibility of spin correlation for the c-axis transport and are discussed from a view point of a possible pseudo-spin-gap formation in this one CuO 2 layer system.

PACS: 74.25.-q; 74.25.Fy; 74.72.-h; 74.72.Hs; 72.15.Gd Keywords: Bi-2201; Negative magnetoresistance; Out-of-plane resistance; Magneto-transport; Spin gap

1. Introduct ion

Recently, the out-of-plane (c-axis) transport phenomena have attracted interest in the cuprate superconductors from the view point of the carrier confinement [1-5] with the relevance to the number of the CuO 2 planes [6]. In the two-layer system, typi- cally in YBa2Cu307 (YBCO), there is a great deal of experimental evidence for the spin-gap opening at low temperature and the carrier confinement effect [7-11]. In the one-layer system of (La,Sr)2CuO 4 (LSCO), in contrast, the presence of the spin gap has not been confirmed until now [12], although there are many experimental results suggesting the presence of

* Corresponding author. Fax: + 81 298 53 2482; e-mail: yoshizak@ bk.tsukuba.ac.jp.

the spin gap [13,14]. Then the interlayer coupling is proposed to be essential for the appearance of the high-T~ superconductivity [15].

The influence of antiferromagnetic spin correlation onto the in-plane transport phenomena was demonstrated in YBCO as the decrease of the in-plane carrier scattering by Ito et al. [16], and as the impu- rity effect upon the carrier scattering by Kitaoka et al. [17]. Concerning the influence on the interplane phenomena, the charge dynamics was studied by c-axis optical and Hall measurements with doping holes in LSCO by Tamasaku et al. [14], suggesting the carrier confinement in CuO 2 plane. Recently, the behavior of the in-plane and the out-of-plane resistivities at low temperature are measured by Ando et al. [18] for LSCO in intense magnetic field, attempting to clarify the carrier confinement effect at T ~ 0, and the divergent profiles are obtained for the both

0921-4534/96/$15.00 Copyright © 1996 Published by Elsevier Science B.V. All rights reserved PII S 0 9 2 1 - 4 5 3 4 ( 9 6 ) 0 0 5 5 5 - 2

172 R. Yoshizaki, H. Ikeda / Physica C 271 (1996) 171-180

resistivities at low temperature as low as T / T c

0.04, suggesting an unusual three-dimensional insulator.

As for the magnetoresistance (MR) measurement in the normal state of the high-T c superconductors [19-22], Nakao et al. [19,20] have observed negative out-of-plane MR around the critical temperature T c of 79 K for Bi2Sr2CaCu208 (Bi-2212) single crystals, and the behavior was explained by a fluctuation conductivity including the density-of-states term in addition to the Aslamazov-Larkin term. Similar measurements have been done for the two-layer system of Bi-2212 and YBCO single crystals by Yan et al. [22] in a wide range of temperatures. They interpreted the negative MR in terms of a pseudogap in the spin system that was slightly reduced by magnetic field. Recently, extensive studies have been done by Kimura et al. [23] for the in-plane and the out-of-plane MR measurement with varying hole densities from the underdoped regime to the overdoped regime in the one layer system of LSCO. They observed isotropic negative MR in the out-of- plane resistivity only for the underdoped samples which showed strong semiconductor-like behavior in the temperature dependence of the out-of-plane resistivity.

The magnetic and transport properties of Bi-2201 single crystals have the characteristic features of high-T c superconductors although T~ is much lower than them [24,25]: T-linear normal-state resistivity is observed for the in-plane current as well as fun-like transition broadening under the magnetic field. In contrast, the semiconductor-like behavior and the enhancement of the resistivity below T c under the magnetic field are observed for the out-of-plane current. The mixed state is composed of a narrow region of the irreversible flux state and a wide range of the fluctuation superconductivity. A broad spin correlation peak is observed in the static magnetic suscepti- bility of the normal state, and the shift of the peak towards the lower temperature side with the doping of holes is confirmed to be observed [26].

In this paper, we report the MR for the one-layer system of Bi2(Sr,La)2CuO6+ d (Bi-2201) single crystals. In the whole range of the measured temperature below 200 K, the MR is proportional to H 2 and written by A p / p o - [ p ( H ) - p ( O ) ] / p ( O ) = B H 2 to a good approximation. The coefficient B is almost

independent of the transverse or longitudinal configurations not only for the out-of-plane current but also for the in-plane current. The magnitude of B for the out-of-plane current is about five times larger than the case of the in-plane current at the temperatures at 200 K. However, the reduction of B for the out-of- plane current started as lowering the temperature and became negative at a temperature lower than 50 K. Those results imply that the spin correlation plays an essential role in the out-of-plane transport phenomena, and the negative MR is discussed from a model based on formation of the pseudo spin-gap.

2. Experimental

The samples were prepared by a floating zone method with using a single ellipsoidal-mirror optical furnace. The carrier density was controlled by doping of La, and the atomic ratio of the cations was measured by an electron-probe microscope analysis (EPMA) for each sample. A dome-shaped T c versus hole density relation is observed for the single crystals in the wide range of La content [24]. The maximal T c of 28.7 K defined by a zero-resistance temperature is obtained for the optimally doped sample. The T c values of the present samples are in the range of 24-25 K and confirmed to be in the slightly underdope side from EPMA. The typical sample size is 4 x 3 X 0.1 mm 3. The MR was measured in the magnetic field up to 17 T, and all of the MR results were corrected for the field dependence of the ther- mometer of cernox (Lakeshore 1050) by using a capacitance sensor calibrated in each cool down process.

3. Results and discussion

Fig. 1 shows the resistive transition broadening under the magnetic field for the out-of-plane current (z II c-axis) in (a) longitudinal (H II I) and (b) transverse (H _L I, H II ab-plane) configurations. The out- of-plane resistivity is monotonically decreasing with increasing temperatures up to the measured temperature of 300 K as shown in the inset of Fig. I a, which is consistent with the slightly underdoped samples. The negative MR is clearly observed in the Lorentz-

R. Yoshizaki, H. Ikeda / Physica C 271 (1996) 171-180 173

force free configuration (Fig. 1 a). The in-plane resistive transition broadening in intense magnetic field is shown in Fig. 2. It is difficult to identify the in-plane MR of the normal state around T~ because of the field-dependent fluctuation superconductivity.

The out-of-plane MR, A P/Po, at a constant temperature in the longitudinal configuration is plotted in Fig. 3 as functions of (a) magnetic field and (b) the square of the field. In the other case of the transverse configuration, A P/Po is plotted in Fig. 4

60

E

0..

!

40

20

i i

j i ' ' ' I ' ' ' I ' ' ' I ' ' '

6o . . . . . . . . . . . . . . . . . . . . . . . . H=17 T B i - 2 2 0 1 14

40 .,,;: 1

Bi-2201 H//c I / /c (a)

0 l l I J I l I I i i I i i i

0 20 40 60 80 100 T (K)

60 . . . . , . . . . I 4 . . . . I . . . . I . . . .

Bi-2201 H//ab t lllc 1

' 14 11

~ 20

o , 0 10 2O 30 40 5O

T (K) Fig. 1. Temperature dependence of the out-of-plane resistivity (1 II c axis) around the superconducting transition in the (a) longitudinal ( n II 1) and (b) transverse (H ± 1) configurations. The magnetic field is varied from 0 to 17 T as indicated in the figure (from right to left at the vertical transitions).

174 R. Yoshizaki, H. lkeda / Physica C 271 (1996) 171-180

as functions of (a) H and (b) n 2. Similarly, the in-plane MR (1 II ab-plane) is obtained in the longitudinal (H II I) and transverse (H It c-axis) configurations as shown in Figs. 5 and 6, respectively, where the insets show the H 2 plots of A P/Po" All of the data in Figs. 3-5 indicate that the MR is quadratic of the magnetic field in the wide range of the magnetic field up to 14 T. Then, the coefficient B obtained at H ~ 0 is plotted as a function of temperature in Fig. 7, where the B values below 34 K are estimated from the MR data only in the high magnetic field because of the presence of the fluctuation superconductivity at low magnetic field.

As for the positive MR in the high temperature regime (higher than 100 K), there are two prominent features. One is the little difference of B between the longitudinal and transverse configurations both in the out-of-plane and in-plane MR. This Lorentz- force-independent property solely indicates the spin dominated origin of the MR, whereas the orbital effect is estimated to be less than 10 -5 for both

cases. The other is the different magnitude of B by the current directions. The out-of-plane MR is about five times larger than the in-plane one at 200 K. This implies that the out-of-plane transport mass is heav- ier than the in-plane transport mass as discussed for the similar results observed in LSCO [23]. In the low temperature regime (below 100 K), the situation becomes different. The out-of-plane MR decreases rapidly as the temperature is lowered and changes sign from positive to negative at T = T * (T* = 43.3 K was obtained for H II ! II c-axis [27]).

The temperature dependence of B for H [I I II c- axis below 100 K is so sharp especially in the range of the negative values. In fact the negative MR suppresses the divergent profile of the normal-state resistivity when the temperature is lowered [28]. The temperature dependence of the normal-state out-of- plane resistivity at zero magnetic field fits on p(T) = - a log T+ /3 , (T c < T < 120 K) quite well below 120 K as shown in Fig. 8, where a and /3 are constant parameters [28]. When the magnetic field is

0.4 ' ' ' ' I . . . . I ' ' ' ' I . . . . I

Bi -2201 ~ " Hllc

0.3 I / / ab , ~ ,,,~ ~ / " / / " H=17 T

0.2 .:"/.//~" / / ,#[[':': 7 C= • o . . ' . - ¢ # ] ] :

• " • , @ .~ ¢ Z

h"i- i// / i / I o.1 ~:'.; : / /I I " n

; 1 : : ' # , , , , ,. + . - ;I;,'/. / / , [ / ] 0.01

i / f I " o o dl i ._t~ , ~ , , ~ , , , , : , , . . . . , . . . .

0 I0 20 30 40 50

T (K) Fig. 2 . Temperature dependence of the in-plane resistivity (/II ab plane) around the superconducting transition in various magnetic fields. The field is 0 to 17 from right to left at the transition.

R. Yoshizaki, H. lkeda /Physica C 271 (1996) 171-180 175

applied, the divergent profiles near T c increase in weak field up to 3 T and then turn to decrease in the higher field. The temperature dependence of the

normal-state resistivity at 17 T, for example, can be well approximated by p ( T ) = - ot log T - c / T +

which is an approximation form of Eq. (7) in Ref.

o Q_

O_ <

0.020

0.015

0.010

0.005

0.000

-0.005

-0.010

-0.01 5

-0.020 0

i I I I I I i I I I I I I I ] i I I i

T=83 K B i - 2 2 0 1 7s K-

H//c / / 70K

60 K.

49 K

41 K_

35K , , , , I , , , , I , , , , I , , L ,

5 10 15 20

H (T)

o c)..

c).. <

0.020

0.01 5

0.010

0.005

0.000

-0.005

-0.01 0

-0.01 5

-0.020

/ ~ T=83 K: B i - 2 2 0 1 7s K -~

H I I c 7o K i I / / c

60 K-

49 K!

(b) 41 Ki

37

0 50 1 00 1 50 200 250 300 350 H 2 (T 2)

Fig. 3. The out-of-plane magnetoresistance plotted as functions of (a) H and (b) H 2 at several temperatures in the longitudinal (H II t) configuration.

176 R. Yoshizaki, H. Ikeda /Physica C 271 (1996) 171-180

[27], where c is a positive parameter. The fit result is shown by a dashed line in Fig. 8. The positive value of c suggests the suppression of the divergence of the out-of-plane resistivity at T ~ 0. Recently, how-

ever Ando et al. claimed that both in-plane and out-of-plane resistivities diverged logarithmically as T / T c ~ 0 in the one-layer system of LSCO [18].

As the system where the resistivity shows log T

O

Q_ <1

0.020

0.015

0.O10

0.005

0.O00

-0.005

-0.01 0

-0.01 5

I ' ' ' '20,1 . . . . , . . . . , . . . . B i -2 b , ~ j T=83K

60K

49K

. . . . . I i - _ _ 4 1 K

~ ' ~ ~ ' ~ ' ~ ' ° ~ ' ~ ' ~ ~ 35 K

(a)

I I I I I t ' ' I I ' ' ' l I

0 5 10 15

H (T)

I I I I

20

0.020 . . . . j . . . . I . . . . I . . . . I . . . . I . . . . I . . . .

O Q.

CL <I

0.015

O.010

O.O05

0.O00

-0.005

-O.O1 0

-0.01 5

B i - 2 2 0 1 .~0 T=83K. H//ab _ ~ ~ 75K

I / / c 60,: ~ 49K

41K

(b) 35K

i i , , I , , , , I , , , , I , , , , [ , , , , I , , , , I , , , ~

0 50 I00 150 200 250 300 350 H z (T z)

Fig. 4. The out-of-plane magnetoresistance plotted as functions of (a) H and (b) H z at several temperatures in the transverse (H A_/) configuration.

R. Yoshizaki, H. lkeda / Physica C 271 (1996) 171-180 177

0.010 . . . . I . . . . I . . . . I . . . .

o o_

Q. <I

0.005

0 . 0 0 0

-0.005

B i - 2 2 0 1 T=IO0 K H / l a b T=I 50 K ~ , ~ _

I / l a b

~ . 0 1 0 - - . , . . . . . . . . . . . . . . . . . . . . .

- B i - Z 2 0 1 H / l a b - " . ~ - " O.OOS . " " . ~ "

~0.000

- 0 . 0 0 5

T = 1 0 0 K

T = 1 5 0 K

T = 2 0 0 K

- 0 . 0 1 0 " ' ' ' . . . . ' . . . . ' . . . . ' . . . . ' . . . . o so loo 1so zoo zso 3oo

H 2 (T z) i i i l | l i i i -0.010 . . . . i . . . . ,

0 5 10 15 20 H (T)

Fig. 5. The in-plane magnetoresistance plotted as a function of H at the three representative temperatures in the longitudinal (H II t) configuration. The inset shows the plot against H 2.

temperature dependence and negative MR experi- mentally, there are mixed-valent compounds and 2D weak localization system as far as we know. In the

mixed valent TmSe, for example, log T dependence of the resistivity is observed below the N~el temperature T N ( ~ 3 K) down to the onset of the residual

o o_ cL -<3

0.010

0.005

0.000

-0.005

-0.01 0

' ' ' ' I ' ' ' ' I ' ' ' ' I ' '

B i - 2 2 0 1 T=IO0 K ...,.,-,~ H / / c T=150 K . , m ~ ~ I / / ab T=200 K _ , , ~ - ~ - , ~ "

_ . . a # : B i - 2 2 0 1

. . . , , . ~ _ ~ : 0 . 0 0 5 ~ "

-~ o.ooc ~ ~ "

- 0 . 0 0 5

- 0 . 0 1 0

. . . . I . . . . I ,

0 5 10 15 H (T)

T : I 0 0 K

T = 1 5 0 K

T = 2 0 0 K

. . . . , . . . . i . . . . , . . . . , . . . . , . . ,

50 100 150 zoo zso 300 H 2 (T z)

i t i I i l i i

2 0

Fig. 6. The in-plane magnetoresistance plotted as a function of H at the three representative temperatures in the transverse ( H ± 1) configuration. The inset shows the plot against H 2.

178 R. Yoshizaki. H. lkeda /Physica C 271 (1996) 171-180

resistivity (below 50 mK), and the negative MR is observed at low temperature [29]. In this system the interaction between the itinerant 5d electrons and the localized 4f electrons is significant at low temperature. The situation is a little different from the present case because of the existence of a static antifer- romagentic order in the TmSe case. In the present system of Bi-2201, it is noted that the out-of-plane resistivity exhibits log T dependence below about 120 K and below that temperature the negative MR turns out to be pronounced. When we compare the two systems, T N may be compared to T o in Ref. [30], if we assume the spin gap formation below T o in Bi-2201. In the case of weak localization, on the other hand, the temperature dependence of the out- of-layer resistivity in a metal/insulator multilayer system is unclear, although the in-plane resistivity shows log T dependence [31].

Although the in-plane transport properties are discussed from the viewpoint of the spin fluctuation effect based on the mode-mode coupling theory, the out-of-plane properties are still beyond reach [32]. A basic concept for the out-of-plane conductivity is due

to tunneling of electrons between the adjacent C u O 2

layers for highly anisotropic crystals. According to the theories of Refs. [33-35], the out-of-plane resistivity is relevant to or stimulated by the in-plane resistivity. Then the large negative MR observed in the out-of-plane resistivity should be reflected in the in-plane one and vice versa. In the experiment, however, such a correlation is not apparent, and it is difficult to extract from the results of Figs. 1 and 2. From the experimental point of view the theories are required to explain the present results of almost the same negative MR in the two configurations, H II c- axis and H 11 ab-plane, in Fig. 7.

The other theoretical pictures are based on a non-Fermi liquid model [36,37]. The observed properties of the out-of-plane MR are interpreted by a gauge theory based on a t - J model [30,38]. Accord- ing to the theory, spin gap in a spinon system plays a strong role in the out-of-plane transport phenomena for the underdoped samples, and the out-of-plane resistivity is expected to be proportional to e x p ( A / T ) if the spinon paring is s-wave, and to 1 / T if the paring is d-wave, where A is a spin gap. In this case,

I-'-

O

DC)

1.0

0.5

-0.5

-I .0

m•O

~m A

~m

I ' ' ' ' l ' ' ' ' I ' ' ' '

Bi-2201

• Hllc lllc A H/lab ll/c [] HIIc I/lab • H/lab I/lab

, , , * I I I i A i i I i i i i I i i i i

-1.5 0 50 100 150 200 250

T (K) Fig. 7. Temperature dependence of the coefficient B of the magnetoresistance in the out-of-plane resistivity (1 I[ c-axis) denoted by • for the longitudinal configuration and by zx for the transverse one and in the in-plane resistivity (1 II ab-plane) denoted by [] for the transverse configuration and by • for the longitudinal one.

R. Yoshizaki, H. lkeda / Physica C 271 (1996) 171-180 179

60

40 E 0

v

to 20

/ ? o° ,~ . . :

' " ° ' <:: : 2

' j g j

~ g

+, ~ ? g • S "J #

Bi-2201 H//c, I//c

1.5 10 100

OT 0.01 1 3 5 7 9 11 14 17

T (K) Fig. 8. Temperature dependence of the out-of-plane resistivity in Fig. 1 is re-plotted as a function of log T. The solid line is a fitting curve for H = 0 ; p ( T ) = - c t log T + f l ( a = 4 2 . 0 7 and f l = 100.77), and the dashed line for H = 17 T; p ( T ) = - a log T - c / T + ~ (or = 42.85, fl = 104, and c = 95) with the units of p in f l cm and T in K.

the in-plane resistivity is not affected by the spin gap but the out-of-plane resistivity is affected by it, showing semiconductor-like temperature dependence. Since the spin gap is reduced by the magnetic field, negative MR is expected in the out-of-plane resistivity, which is qualitatively consistent with the present results. It is noted that the temperature dependence of the out-of-plane resistivity predicted by the theory is strongly divergent with respect to the observed log T at T ~ 0. In this respect, however, the present results suggest the possibility that the normal-state out-of-plane resistivity below 30 K in zero magnetic field will be more insulating than log T temperature dependence as shown in Fig. 8 if we kill the superconductivity without applying magnetic field.

A slight difference between the two geometries was observed in B below 50 K: B in Lorentz-force active geometry is a little larger than the values in Lorentz-force free geometry at the same temperature (Fig. 7). This difference is not induced by the fluctuation superconductivity but is substantial in normal- state conductivity. In fact, the MR at 41 K shows

slightly positive for the Lorentz-force active geometry (Fig. 4) and in contrast negative for the Lorentz- force free one (Fig. 3), even in strong magnetic field where the fluctuation conductivity is believed to be fully suppressed. A possibility is the appearance of an orbital effect due to the decrease of the magnitude of the spin-dependent MR.

4. Summary

In conclusion, we measured the MR in the in-plane and the out-of-plane resistivity for the one-layer superconductivity of Bi-2201 single crystals. The MR is almost independent of the magnetic field direction with respect to the current direction, which indicates the spin-dominated MR effect. The magnitude of the out-of-plane MR is about five times larger than the in-plane one in the high temperature regime ( > 100 K), suggesting the mass anisotropy as pointed out by Kimura et al. [22]. We observed the reduction of the out-of-plane MR in the low temperature regime ( < 100 K) accompanied by a sign rever-

180 R. Yoshizaki, H. lkeda / Physica C 271 (1996) 171-180

sal below about 50 K. The negative MR suppresses the divergent profile of the normal-state out-of-plane resistivity at T ~ 0. Those facts indicate the substantial participation of antiferromagnetic spin correlation in the normal state resistivity and suggest possible spin-gap formation at low temperatures.

Acknowledgments

The authors acknowledge a very useful discussion with N. Nagaosa. Part of this work was supported by a Grand-in-Aid from the Ministry of Education, Cul- ture, Sports and Science.

Note added in proof. Recently, Ando et al. re- ported the divergent out-of-plane resistivity at a temperature down to 0.6 K in an intense magnetic field of 60 T for the Bi-2201 single crystals [Y. Ando, G.S. Boebinger, A. Passner, N.L. Wang, C. Geibei and F. Steglich, Czech. J. Phys. 46 (1996) 1397, Suppl. $3; Y. Ando, G.S. Boebinger, A. Passner, N.L. Wang, C. Geibel and F. Steglich, Phys. Rev. Lett. (preprint)]. It is noted, however, that their crystals are slightly overdoped with T~ of 13 K (mid point), contrary to the present underdoped samples with T~ of 24-25 K (zero resistance).

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negative out-of-plane magnetoresistance of bi2(sr,la)2cuo6+δ single crystals

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