ELSEVIER PhysicaC222 (1994) 233-240

Study of Hall effect, electrical resistivity and magnetoresistance in BiESrE_xGdxCalCU208+ (x=0.00-0.65) systems

S a n d e e p Singh Department of Physics, Indian Institute of Technology, Kanpur 208016, India

D . C . K h a n

Illinois Wesleyan University, Bloomington, IL 61702, USA

Received 14 October 1993; revised manuscript received 25 January 1994

Abstract

The present work reports a detailed experimental study of lattice parameters, Hall effect, electrical resistivity and magnetores- istance of the Bi2Sr2_xGdxCatCu2Os+6 system. Hail and resistivity data show that the suppression of superconductivity is due to a combined effect of disorder and hole filling. The high-gadolinium-concentration samples at low temperature satisfy the condition of variable range hopping for conductivity. The best agreement of the resistivity data for these samples has been achieved with the Ortuno and Pollak model. This model has the interesting feature that the density of states near EF is concave in nature. The magnetoresistance of a low-gadolinium-concentration sample in low field indicated the existence of temperature- dependent activation energy for the flow of flux lines.

1. Introduction

One of the interesting problems in oxide supercon- ductors is the destruction of superconductivity due to the presence of impurities. There are a number of experimental results on this phenomenon and asso- dated physical properties. However, no consensus on the issue has emerged yet. For example, both mag- netic and non-magnetic impurities a t Cu sites in the LaLssSro.15CuO4 system generated local magnetic moments in Cu-O planes, which induced pair break- ing effect leading to the destruction of superconduc- tivity [1]. On the other hand in the Yt -xRexBa2Cu307_a (Re = trivalent rare earth) sys-

permanent address: Dept. of Physics, Indian Institute of Tech- nology, Kanpur 208016, India.

tem, the transition temperature remains unchanged even with complete substitution of Y by Re except in the case o fPr [ 2 ]. It is suggested that a strong hybrid- ization between Pr 4f states and conduction band is responsible for depairing [3,4]. Again, the suppres- sion of superconductivity in YiBa2Cu3_xZnxO7_6 and Bi2Sr2Cat_xYxCu2Os+6 systems has been inter- preted as being due to pair breaking caused by non- magnetic disorder [ 5 ]. It is evident that there is no single generally accepted mechanism at present. Even for a single system Bi2Sr2Cal _xGdxCu2Os+ a two dif- ferent mechanisms for the destruction of supercon- ductivity have been proposed. Rev. [ 6 ] proposes in- creased Coulomb interaction whereas ref . [7] proposes disruption of Cu 3d-O 2p hybridization as the basic reason for depression of To. We have carried out a detailed study on this system (Gd-doped

0921-4534/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD10921-4534 (93)E090 I-C

2 3 4 S. Singh, D.C. Khan/Physica C 222 (1994)233-240

Bi2Sr2CaCu2Og+j (2:2: I : 2) ) to get more insight into the issue.

In Bi2Sr2CaCu2Os+6 the crystallographic site of Sr is identical to that of La in La2CuO 4 (2: 0: 1 ) [ 8 ]. Hence by analogy with the substitution of La by Sr in 2:0:1 system, Sr can be replaced by rare earth ele- ments in the 2: 2: 1 : 2 system. The consequences of Gd a+ doping in the 2 :2 :1 :2 system are studied by experiments on lattice parameter, Hall effect, tem- perature dependence of electrical resistivity and magnetoresistance. Hall effect and magnetoresist- ance are reported for the first time for this system. The electrical properties in the insulating phase are interpreted by Ortuno-Pollak model [ 9 ] of hopping transport. The suppression of superconductivity is explained as due to combined effect of disorder and reduction in charge carrier density.

2. Experiment

The samples Bi2Sr2_xGdxCatCu2Os+a (x=0 .0 0 - 0,65) were prepared by the solid state reaction method. Stoichiometric amounts of Bi203, SrCO3, Gd203, CaCO3 and CuO, all 99.99% pure, were ground in mor tar and pestle for 2-3 h. The powder was calcined in air at 700 ° C for 2 h and then at 800 ° C for 12 h. The product was reground, pressed into pel- lets and sintered for 40 h. The sintering temperature was increased from 860°C (for x = 0 ) to 880°C (for x=0 .65) with increasing value ofx . Powder diffrac- tion measurements of all samples were done on a Sie- fert X-ray diffractometer using Cu Ks radiation. The DC resistivity of the samples was measured in an APD closed-cycle Helium refrigerator using the van der Pauw four-probe technique. Low-resistive electrical contacts were made by applying silver paint on cleaned surface of the samples and fn'ing at 550°C for 30 rain. Thin copper wires were indium soldered on these silver pads. A small current (0.5-1 mA) was used in resistivity measurements to avoid heating ef- fects at contacts although the I - V curve was linear even upto 70 mA. The Hall effect measurement was done at 40 mA of sample current and 3.5 kG of exter- nal magnetic field. In order to cancel the thermal EMF and misalignment voltages, the data were taken for both polarities of the current and magnetic field.

3. Results and discussion

3. I. Crystal structure

X-ray measurements showed all samples, Bi2Sr2_xGdxCalCu2Os+y (x=0.00-0.65) to have single-phase tetragonal structure. Fig. 1 shows the variation of the lattice constants a and c with doping concentration x. We note that the c-axis shows a lin- ear decrease as x increases and interpret the contrac- tion in c-axis as due to replacement of a bigger Sr 2+ ion (ionic radius r= 1.10 A) by a smaller Gd 3+ ion (r=0.938 A). A similar trend was observed in com- pounds derived from substitution of yttrium for cal- cium in Bi2Sr2CalCu2Os+y (2 :2 :1 :2 ) [10]. How- ever, the contraction in c-axis in the present system (dc /dx= - 1.17) is more than in the yttrium-doped 2: 2: 1 : 2 system (d c /d x = - 0.75), consistent with a larger ionic radii difference of Gd 3+ and Sr 2+ ions. The lattice constant "a" shows an increase on dop- ing. This probably is caused by the decrease in formal valence of Cu which weakens the Cu-O bond.

3.2. Transition temperature and hole concentration

Figs. 2(a) and 2(b) show the variation of carrier concentration (nil) obtained from Hall measure- ments and transition temperature (To) obtained from 5,65~~.~ r s . s s l - °

5./J.

~ Q

5.3~ i

" I Oo O o o o

I 0.0 0.4

X

Fig. 1. V a r i a t i o n o f la t t ice p a r a m e t e r s a a n d c wi th d o p a n t con-

centration x in Bi2Sr2_xGdxCaiCu2Os+6 systems. The solid lines are linear fits to data points.

31

o --30

u

o_

29 0.8

S. Singh, D.C Khan / Physica C 222 (1994) 233-240 235

v

to) +

0 2

I 0.2

Ibl S O -

0 0 0 0

t c

0 0

¢ o I I

O.t. 0 .6 X

0 0

0

0

0-2 0-4 0.6 X

0.8

0.8

Fig. 2. Variation of (a) hole concentration (nil) and (b) transi- tion temperature (To) with Gd concentration x in the Bi2Sr2_xGdxCatCu2Os+a system.

resistivity vs. temperature curves (see next section) with gadolinium concentration (x) respectively, n H shows a rapid decrease with x. The sign of the Hall coefficient showed that the charge carriers were holes. We note that T¢ increases to a maximum value at x=0 .10 and then decreases to zero at x~0 .6 . The parabolic dependence of T¢ on x has been observed in Laz_~SrxCuO4 [ 11,12 ] and Bi2SrzCa~_xYxCu2Os+6 [13,14] systems also and appears to be a typical characteristic of doped high- temperature superconductors.

In the YmBa2Cu30~+y ( 1 : 2: 3) system the holes are distributed over the CuO2 planes and CuOv chains. In 2: 2: 1 : 2 the holes are confined to the CuO2 planes only. Hence, the hole concentration determined from Hall effect measurements in 2: 2: 1 : 2 is the same as that determined from chemical methods [15] whereas in 1 : 2: 3 they are different. In our samples the addition of Gd 3+ fills the holes causing the de- crease of nh with x.

Our samples were processed in air which has an ox- ygen pressure well above the optimum partial pres- sure that produces the optimum hole concentration

for maximum Tc [16]. So the x=O sample has too much oxygen (~) i.e. excess holes with a depressed To. The addition of Gd 3+ i.e. the increase of x, fills excess holes which results in the hole concentration being closer to the optimum value and hence T¢ goes up. Further hole filling depresses Tc again.

3.3. Resistivity data

Figs. 3 (a), ( b ) and (c) show the variation of elec- trical resistivity with temperature for the Bi2Sr:_xGdxCa~Cu2Os+y (x = 0.00-0.65) system. The resistivity behaviour of samples is divided into three categories:

(A) Samples with x = 0.00-0.45 show metallic be- haviour at high temperature followed by supercon- ducting transition as the temperature is lowered. The resistivity data between 200 and 300 K may be fitted to p (T ) =p (0 ) +pT. Residual resistivity p(0) and slope # show an exponential increase with x as shown in Fig. 4. p (0) increases by two orders of magnitude whereas the slope increases four times only.

(B) As x is increased beyond 0.50, an upturn in resistivity is observed as the temperature is lowered which is a characteristic of electron localization. x=0 .50 shows a shallow minimum in resistivity at around 95 K. This minimum becomes more promi- nent at x=0.55, 0.56 and 0.57. The temperature (Tmi,) at which the minimum in resistivity occurs increases as x changes from 0.50 to 0.57. Above Tmi~ all samples show metallic behaviour (poc T) while below Tram they show semiconducting behaviour fol- lowed by transition to the superconducting state. The x = 0.57 sample shows an increase in resistivity to the lowest temperature ( 14 K) measured by us. We in- terpret the upturn in resistivity being caused by dis- order (due to random distribution of Gd at Sr sites) giving rise to a two-dimensional 2D weak localiza- tion effect. This leads to a logarithmic correction in the conductivity as shown in Fig. 5 producing an ap- parent metal to semiconductor transition [ 17 ].

(C) At x = 0.60 superconductivity disappears and transition to an insulating state occurs. One expects that by introduction of a magnetic impurity like Gd 3 + superconductivity should vanish due to the Abriko- sov-Gor'kov mechanism [18] which involves ex- change interaction between spins of an electron and that of an impurity atom. The interaction inhibits the

236 S. Singh, D.C Khan/Physica C 222 (1994)233-240

{o) 6 -

4 0-3

e,, 2

" 1 o ° ° oOOO oOOOo --o//joooo O.: . . . . . . . . . O o

o o o o o o o o o o o O O o u G o o o a O

0 100 200 300 T(K]

2(;I_ (b]

Y _ o.56

E

"; IC - ~ 0 . 5 0

0 . 5 5

" ~ I I I I i I 0 100 200

T(K) 0.6

3 0 0

u

w

(c}

6

b

100 200 300 T (K )

Fig. 3. Temperature dependence o f electrical resistivity for var- ious Gd concentrations x in the Bi2Sr2_xGdxCatCu20s+ a system as shown in (a) , ( b ) a n d (c).

(a }

~ 1.5 *

E

o. 1.0

¢

0 " ° I Ibl

v 3 - E u i

~ 2

0.0 0.2 0.4 0.6 x

Fig. 4. Dependence of (a) residual resistivity ( p ( 0 ) ) a n d (b) slope (p) on Gd concentration x in the Bi2Sr2_xGd=CaiCu2Os+~ system.

'7

*

"o

o= t.J

64.0

56.C

4 8 . 0 ~ I i I i 3.6 4.0 4.4 4.8

In [T]

Fig. 5. Plot of conductivity vs. In(T) for sample x = 0 . 5 6 in the temperature region 50-115 K showing logarithmic correction to conductivity.

appearance of the superconducting correlation and decreases the transition temperature. Evidently, suppression of Tc will be larger for the impurity atom having higher magnetic moment. However by substi- tution of Nd for Sr in 2: 2: 1 : 2, in ref. [ 19 ] supercon-

S. Singh, D.C Khan/Physica C222 (1994) 233-240 237

ductivity disappears at nearly the same concentra- tion as for Gd 3+ substitution. This suggests the involvement of a different mechanism in suppres- sion of superconductivity in the present system.

Polycrystalline Bi2Sr2CatCu2Os+a can be mo- delled as consisting of grains of ideal crystalline su- perconductors which are weakly coupled to each other. These grains consist of a stack of supercon- ducting Cu-O bilayers separated by BiO or SrO planes acting as weak link or insulator. The bilayers are con- netted by Josephson couplings which lead to the ob- servation of superconductivity perpendicular to the Cu-O plane [ 20 ]. Since the a-b i.e. Cu-O plane con- ductivity in an ideal crystallite is five orders of mag- nitude larger than the c-axis conductivity [ 21 ], the dominant mechanisms responsible for the destruc- tion of superconductivity, and suppression of T¢, are those which affect charge carriers in this (i.e. Cu-O) plane. As per the results of our Hall measurements, one of the mechanisms is hole filling. Evidently, the other mechanism is disorder, which has been dis- cussed in connection with the upturn in resistivity below T< Tmm. For lower concentration a major role in suppression of T~ is played by the reduction in hole concentration. As the Gd concentration increases the localization effect becomes evident. The supercon- ductivity is destroyed completely due to disorder when all the charge carriers become localized and conductivity due to variable range hopping is observed.

The conductivity in the insulating state of our sam- ples can be described by the variable range hopping (VRH) formula [22 ]

~=~o e x p [ - (To/T) n+ ' ] , (1)

where n determines the dimensionality of the hop- ping mechanism involved. For the 3D (n = 3) VRH ease the localization length ( a -~) can be deduced from [ 23 ]

16ot 3 To= kN(EF) ' (2)

where N(Er) is the density of states at the Fermi level. There are different views on the pre-exponential fac- tor Uo. Brodsky and Gambiono [24 ] assume a con- stant density of states near the Fermi level and obtain

_t/2 { 3e2v'~ (N(EF)'~ 1/2 ao = (2~) ~---~--] \ ~ ] , (3)

where g is phonon frequency and k is Boltzmann con- stant. However, assuming a concave density of states near the Fermi level, Ortuno and Pollak obtained fol- lowing expression [ 9 ]:

Uo = 1.7e2vN(EF) °58(oQ-°74(kT)-042. (4)

We calculate N(EF) by using Eqs. (2), (3) and Eqs. (2), (4). In Fig. 6 we plot In (aT ~42) vs. (T) -1/4 curves for samples x=0 .60 and x=0.65. A linear fit is observed in two temperature regions: from 14 to 32 K and then up to 110 K. A knee in the fit separates these regions. We used region below 32 K to calculate parameters. Values of ao and To thus obtained are 5.06×103 ( ~ cm) -1 and 1.75×104 K for sample x=0.60 while for x=0.65 these are 8.96× 103 (f~ cm) - 1 and 4.05 × 104 K respectively. By using these values of ao and To, and Eqs. ( 1 ) and (3) gives

8.45 × 1060 N ( E r ) = v3 states/eVcm 3 f o r x = 0 . 6 0 ,

8.75 × 1061 - - / / 3 states/eV cm 3 for x = 0.65.

Taking u ~, 10 ~3 Hz and considering uncertainty in u, N(EF) thus obtained for both the samples are in close agreement with that obtained for 2: 2: 1 : 2 by

6

%

Y

c i i t [ ~ I i 0.2 0-3 O-t 0.5 0,6

T-I/t

Fig. 6. Plot o f In (o / ° '42 ) as a func~on o f ( T ) - v 4 for samp]es x = 0 . 6 0 and 0.65. The sofid LLucs are I b ~ fits in two separate temperature regions: 14 K ~ T< 32 K and 32 K < T~ 110 K.

238 S. Singh, D.C. Khan /Physica C 222 (1994) 233-240

specific heat measurement [25,26] i.e. (2.0- 3.4) X 1022 states/eV cm 3. However, N(EF) derived from ln(ax/CT) v e r s u s (T) -1/4 curves obtained by assuming a constant density of states near EF, and Eqs. (2), (3) are two orders of magnitude smaller than the experimental value. These results suggest that the Ortuno and Pollak model gives the best fit to our data and hence the density of states near Fermi en- ergy is concave in nature. The suggestion is sup- ported by the observation of a slight upward trend in Fig. 6 at low temperature i.e. below the knee. This trend is predicted by the theory of Ortuno and Pollak which takes into account the concavity of density of states near Fermi energy.

At high temperature, conductivity data of samples x=0.60 and 0.65 follow

o__,oxo(,o:,) This suggests a thermally activated conduction by transport of carriers beyond the mobility edges into nonlocalized states.

3.4. Magnetoresistance

x=0.10 which lies on the maximum in the To vs. x curve, Fig. 2(b), was chosen for the study of the broadening of resistive transition. Fig. 7 displays the variation of the resistivity of the x= 0.10 sample with

1.0

0.8 oXd7 A ott

0.6

~-~.~_ j ~ : X 0-00 kOe 0.z, A 0.128 '"

o 0.~60 '" ,~ v 1.10 "

0.2

I I ~ I I [ 50 70 90 11o 13o

T(K) Fig. 7. Temperature dependence o f resistivity for x = 0 . 1 0 in the presence o f low external magnetic fields.

temperature in the presence of external magnetic fields of 0, 0.128, 0.560 and 1.1 kOe. As we notice the broadening occurs below the mean field transi- tion temperature T~o= 85.8 K of the present system. T~o was obtained by applying the Aslamasov-Larkin theory of fluctuation conductivity in 2D systems above T~o [27,28 ]. Since the conductivity in 2: 2:1 : 2 is mostly 2D due to the large anisotropy ratio of the c-axis and a-b-plane conductivity [21 ] the above theory could be applied.

The resistivity below T~o can be described by the thermally activated motion of flux lines with the temperature-dependent activation energy. The esti- mate of the activation energy U0 which must be over- come to allow flux motion, can be written as [29]

H~o Uo= ---if-, (5)

where ~ is the coherence length, He is the thermody- namic critical field, B is the flux density in the sample and ~o = hc/2e is the superconducting flux quantum. An explicit expression for the temperature depen- dence of U0 is obtained by using results of the Ginz- burg-Landau theory:

(Tc°-- T~ -1/2 , (6) ~ ( T ) = ~ ( 0 ) \ Too ]

where T~o is the mean field transition temperature. The thermodynamic critical field Ho(T) can be ex- pressed in terms of the upper critical field Ho2 as

He(T)----Ho2/N//2)~ w h e r e X is the Ginzburg-Landau parameter which is temperature independent. More- over, Ho2(T)=~o/2rc~2(T). All these expressions combine to give

( Too -- T~ 3 / 2 Uo(T)fUo(O)\ Too ] (7)

where Uo(0)--¢]/8n2X~3(0)B. Thermally activated resistivity can now be written as p (T) = p (0) exp [ - Uo (T) / kT] with Uo (T) as given above.

Fig. 8 shows the fitting represented by the solid curve, using Eq. (7). Uo(0)decreases with increas- ing magnetic field. The dissipation in the present sys- tem involves temperature-dependent activation en- ergy due to the temperature dependence of the coherence length.

S. Singh, D.C. Khan/Physica C 222 (1994) 233-240 239

I -0

x 0 .128 kOe A 0. 560 "" o 1,10

0.E

5 m

E w > ,

>

r , ,

0-,~

0.2

I

50 60 100

X ° ° ° ° ° ,o

6

70 80 90

T(K )

Fig. 8. Temperature dependence of resistivity for x=0.10 in low external magnetic fields. The solid lines are fitted curves by using Eq. (7) in the text. Symbols represent the experimental data points.

4. Conclusions

We prepared Bi2Sr2_xGdxCalCu2Os+y ( x = 0 . 0 0 - 0.65 ) samples and studied the results of X-ray, elec- trical resistivity, Hall effect and magnetoresistance measurements. With increasing doping concentra- tion (x) , lattice parameter "c" decreases while "a" increases. The transition temperature shows an ini- tial rise with x followed by a decrease in the value until superconductivity is destroyed. The suppres- sion of superconductivity occurs due to a combined effect of disorder, and reduction in the charge carder density. The high-gadolinium-concentrations sam- ples at low temperature satisfy the condition of 3D variable range hopping for conductivity. The resis- tivity data for these samples are in best agreement with the Ortuno and PoUak model. This model has the interesting feature that the density of states near Ev is concave in nature. The magnetoresistance mea- surement of a low-gadolinium sample indicated the existence of temperature-dependent activation en- ergy for the flow of flux lines.

Acknowledgements

One of the authors (DCK) expresses his thanks to N.K. Jaggi for his keen interest in the work and for

helpful discussions. The authors are thankful to the Department of Science and Technology, Govern- merit of India, for partial support of the facilities used in the work.

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