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Electronic carrier density in doped Bi-based high-Tc superconductors
B
Ph)~ica C 185- 189 (1991) 749-7~;0 North-Holland
ELECTRONIC CARRIER DENSITY IN DOPED BI-BASED HIGH-T~ SUPERCONDUCTORS M, Weber ~, A, A m a t o t, J. Beck s, V,N. Du~intr¢ a, I.A, Gagamov 3, V,G, Grebinnik z, F.N. Gygax ~, S. Kapus~a s, B.F. I~5rillov~, A.B, Lazarev a, H. M a l e t t a ~, V.G. O l s h m ~ k y z, A.V. P i m ~ ~, V.Yuo Pomjak~whiwa, A.N. P o n o m a r e v ~, E. Preisler ~, A. Sehenek t, $.N. Shilov a, V.G. Storchak ~, and V.A. Zhukov a t lnstitut ffir M i t t e l e n ~ e p l k v s i k der E T H Zfirich, CH-fi232 Villigen PS!, S w i t z ~ l a n d lnstitut ffir F e s t k g r p e r f o ~ c h u n g , F o r s e h u n ~ e n t r u m afilieh, D-5170 3filich, G ~ a n y a Joint I n s t i t u t e for N u d e a r Research, P.O. Box 79, Dubna, 10100 Moscow, USSR I.V. K u r e h a t o v I n s t i t u t e of Atomic Energy, Kurchatov sq.1, 123182 Moscow, USSR Institute of Physics, Czechoslovak Aeaden~" of Science, 25068 Rez near Prague, Czechostm'akia Hoeehst AG, D-5030 Hfirth-Knappsaek, G e r m a n y T h e s u p e r c o n d u c t i n g carrier density n , was measured by means of t~+SR spectroscopy in the mixed phase of a series of polyerystalline Bi-based 2212 s u p e r c o n d u c t o ~ with different substitution of Bi 3+ by Pb "~*. In exactly the s a m e samples the effective valence per C u - a t o m V ( C u ) was determined by neutron powder diffraction. We o b s e r v e d that n, a n d V ( C u ) are not proportional to each other in the heavily dopcxt region. This behavior is interpreted as evidence t h a t the carriers b e c o m e more and more locMized with increash~g lead content.
1. INTRODUCTION
2.
The second moment of the induction field distribution F(B) due to the formation of a regular flux fine lattice in the mixed state of a type II superconductor is related to the London magnetic penetration depth A 1. In the special case of highly anisotropic superconductors with unia,xial s,vmmetry, W. Barford and ,I.M.F. Gunn 2 derived < AB 2 >tin = (0.00371)1t2 . q~0/(1.23-~)2
,
(1)
which is valid for polycrystals in the intermediate field r e , me Hcl << Hext << He2- Aab denotes the penetration dep;,h perpendicular to the hard axis (&axis). q'o is the elementary flux quantum. Muon spin rotation ( # S R ) spectroscopy allows to aetermine the field distribution within a sample and therefore i: a technique, which is suited to measure )~b in polycrystalline ),;,,),_T . . . . . . . . . a,,~, . . . . . . . . a;~,, ,. ~, (!). Since )~b is related to the concentration of superconducting carriers ns via A,~, = CMabc~/4rnse 2 ,
EXPEP, IMENTAL DETAILS AND DATA ANALYSIS We have mea.~ured the rouen spin rela~xation in four poly° crystalline Bi2-zPbzSr2Ca('u2Os+,~ samples ( p r ~ s ~ powder) with different substitution of Bi 3+ by Pb 2+ (x=0.C@ 0.15, 0.30, 0.67)in a transw-rse magnetic fidd of 3 kG using the fieId-coolin~ procedure. The exact composition of the samptes was determined by d~ennc~ anatysis. The expe~'ime~t was performed at the Phasotrou of.HNR in Dubua, USSR. In order to account for the asymmetric shape 3 of F~B}, a two component function 2
e: i~(t)
=
S
2 ¢2
Ai.e
~ .cos(~,.t}
~3}
i=1
was fitted to the measured : t S R time spectra. Parameters to be determined were therefore the Larmor aaguIar velocities -:i, the relaxation rates ~, and the amplhudes A,- Assuming the description of the measured tinge spectra by eq. (3) to be perfect, fl-te second mouter, t of the fie':d d{stributiot~ can ~: ~ the time evolution of the rouen poiafiration is given by
(2) < AH 2 >~/~
the determination of < ABz >~/2 within a superconductor in the mixed state also yields information about its electronic properties. M~b is a component of the phenomenological tensor describing the superconductor's anisotropv.
<,.:>
0921-4534/91/$03.50 O 1991 - Elsevier Science ?ubiistters B.V. AH fights r e ~ .
=
=
{
.4, ==l A,~ + A2
.
~ 2 4- ( - ' - -
'
< ,'-' > i2
J
. -~}
M. Weberet al.
750
/
Doped ~i.ba#edhigh-T¢superconductors
Since all fits were excellent, which was reflected i n values of the normalized X~ close to unity, eqs. (4) were used to determine the values of < AB z >t/~.
3, RESULTS A N D DISCUSSION The temperature dependence of < A B 2 >I12 for the four investigated samples is perfectly explained iv the framework of conventional BCS theory in the weak coupling limit. The description by the two-fluid model, which is valid in the strong coupling limit, is significantly worse 7 . The values of < AB 2 >llz (T --* 0) Listed in Table 1 were obtained by a fitof < AB s >1Is (T) = < AB s >tls (0).{Aecs(0)/AScs(T)} 2 (5) to the data points determined with the help of eq. (4). Assuming the phenomenologlcal tensor component M a b to be the same fo." all four investigated samples, the values of < A B 2 >1/2 (0) are proportional to the superconducting carrier concentrat, on < A B 2 >i/2 (0) o: n, ,
(6)
according to eqs. (i) and (2). The Cu(2) bond valence sums V(Cu) also listed in T~ble 1 were obtained by means of neutron diffraction4. Assuming the valencies of the ions of Bi2-=Pb=Sr2CaCu2Os+6 to be Bi3+, Pb 2+, Sr2+, Ca 2+, Cu ~+~ and 0 ~-, the hole concentration per Cu p is represented as p = ~+x/2 . (7)
As expected, V(Cu) scales with p. However, the fact that < AB ~ >~/~ (T --* 0) c¢ n, decreases with increasing hole concentration p is rather surprising 6. This feature of the Bi2-=Pb~Sr~CaCu~Os+a series is displayed in Figure 1. For comparison we also show corresponding results obtained in a series of Bi~Sr2Ca~_~Y~Cu~Os+~ samples with different Y doping5, where n~ scales with p = $ - z / 2 .
3.O :S.
2.5
! zo 1,5
,-^ % to V
O.5
0
l
-0.4
I
I
~.2
i
I
i
0
I
I
0.2
0.4
.
I
,
0.0
X-Z FIGURE I Compilation of < A B 2 >112 (T ~ 0) c( n, for Bi2_~PbxSr2CaCu2Os+s and Bi2Sr2Ca1-~Y, Cu2Os+t plotted against (x-z) c¢ p. The straight llne is a fit to the data points of the Y doped samples. The puzzling behaviour of the lead doped 2212 superconductors may be interpreted as evidence that the carriers become more and more localized with increasing lead content: Localized carriers cannot take part in the formation of Cooper pairs, which leads to a decrease of the effective superconducting carrier density ns. The question, whether this feature is related exclusively to doping with Pb will be subject of further investigations. REFERENCES I. E.H. Brandt, Phys. Rev. B37 (1988) 2349. 2. W. Barford and J.M.F. Gunn, Physica C156 (1988) 515. 3. M. Weber et al.,Measurements of the London Penetration Depth in Bi-based High-Tc Compounds, in: Proceedings of the 5th International Conference on M u o n Spin Rotation, Relaxation and Resonance (J.C. Baltzer AG, Basel, 1990) pp. 93-101. 4. H. Maletta et ~., to be published.
Table 1: Compilation of x,/~, p, V(Cu) and < AB2 >i/2 (0) o¢ n~ (see text for explanation) of the four investigated Bi2-rPb~Sr2CaCuzOs+a samples. x 0100 0.15 0.30 0.67
~ 0.16 O.lO 0.25 0.28
p V(Cu) 0.16 (1) 2.22 (1) 0.18 (1) 2.23 (1) 0.40 (1) 2.29 (1) 0.61 (I) -
< A B ~ >I/2 (0) 2.00 (8) 2.01 (7) 1.78 (6) 1.28 (5)
et ~~,. , i.., S ~DL - S ~. .u. au.y. v~ r _J ^ ~ "~he ~o,,uon Penetration Depth in the High-T: compound~ Bi2Sr2Y~CaI-~Cu20s+~, this volume.
5 . .... ~'~ ~~. r. .~. k. ~ .
6. W e believe that a similar effect was also observed by A. Maeda et al.,Phys. Rev. B41 (1990) 6418. 7. IV[.Weber et al., London Penetration Depth in Bibased High-To Compounds, in: Proceedings of the LT19 Satellite Conference (Adam Hilger, Bristol, 1990) pp. 403-405.
Ph)~ica C 185- 189 (1991) 749-7~;0 North-Holland
ELECTRONIC CARRIER DENSITY IN DOPED BI-BASED HIGH-T~ SUPERCONDUCTORS M, Weber ~, A, A m a t o t, J. Beck s, V,N. Du~intr¢ a, I.A, Gagamov 3, V,G, Grebinnik z, F.N. Gygax ~, S. Kapus~a s, B.F. I~5rillov~, A.B, Lazarev a, H. M a l e t t a ~, V.G. O l s h m ~ k y z, A.V. P i m ~ ~, V.Yuo Pomjak~whiwa, A.N. P o n o m a r e v ~, E. Preisler ~, A. Sehenek t, $.N. Shilov a, V.G. Storchak ~, and V.A. Zhukov a t lnstitut ffir M i t t e l e n ~ e p l k v s i k der E T H Zfirich, CH-fi232 Villigen PS!, S w i t z ~ l a n d lnstitut ffir F e s t k g r p e r f o ~ c h u n g , F o r s e h u n ~ e n t r u m afilieh, D-5170 3filich, G ~ a n y a Joint I n s t i t u t e for N u d e a r Research, P.O. Box 79, Dubna, 10100 Moscow, USSR I.V. K u r e h a t o v I n s t i t u t e of Atomic Energy, Kurchatov sq.1, 123182 Moscow, USSR Institute of Physics, Czechoslovak Aeaden~" of Science, 25068 Rez near Prague, Czechostm'akia Hoeehst AG, D-5030 Hfirth-Knappsaek, G e r m a n y T h e s u p e r c o n d u c t i n g carrier density n , was measured by means of t~+SR spectroscopy in the mixed phase of a series of polyerystalline Bi-based 2212 s u p e r c o n d u c t o ~ with different substitution of Bi 3+ by Pb "~*. In exactly the s a m e samples the effective valence per C u - a t o m V ( C u ) was determined by neutron powder diffraction. We o b s e r v e d that n, a n d V ( C u ) are not proportional to each other in the heavily dopcxt region. This behavior is interpreted as evidence t h a t the carriers b e c o m e more and more locMized with increash~g lead content.
1. INTRODUCTION
2.
The second moment of the induction field distribution F(B) due to the formation of a regular flux fine lattice in the mixed state of a type II superconductor is related to the London magnetic penetration depth A 1. In the special case of highly anisotropic superconductors with unia,xial s,vmmetry, W. Barford and ,I.M.F. Gunn 2 derived < AB 2 >tin = (0.00371)1t2 . q~0/(1.23-~)2
,
(1)
which is valid for polycrystals in the intermediate field r e , me Hcl << Hext << He2- Aab denotes the penetration dep;,h perpendicular to the hard axis (&axis). q'o is the elementary flux quantum. Muon spin rotation ( # S R ) spectroscopy allows to aetermine the field distribution within a sample and therefore i: a technique, which is suited to measure )~b in polycrystalline ),;,,),_T . . . . . . . . . a,,~, . . . . . . . . a;~,, ,. ~, (!). Since )~b is related to the concentration of superconducting carriers ns via A,~, = CMabc~/4rnse 2 ,
EXPEP, IMENTAL DETAILS AND DATA ANALYSIS We have mea.~ured the rouen spin rela~xation in four poly° crystalline Bi2-zPbzSr2Ca('u2Os+,~ samples ( p r ~ s ~ powder) with different substitution of Bi 3+ by Pb 2+ (x=0.C@ 0.15, 0.30, 0.67)in a transw-rse magnetic fidd of 3 kG using the fieId-coolin~ procedure. The exact composition of the samptes was determined by d~ennc~ anatysis. The expe~'ime~t was performed at the Phasotrou of.HNR in Dubua, USSR. In order to account for the asymmetric shape 3 of F~B}, a two component function 2
e: i~(t)
=
S
2 ¢2
Ai.e
~ .cos(~,.t}
~3}
i=1
was fitted to the measured : t S R time spectra. Parameters to be determined were therefore the Larmor aaguIar velocities -:i, the relaxation rates ~, and the amplhudes A,- Assuming the description of the measured tinge spectra by eq. (3) to be perfect, fl-te second mouter, t of the fie':d d{stributiot~ can ~: ~ the time evolution of the rouen poiafiration is given by
(2) < AH 2 >~/~
the determination of < ABz >~/2 within a superconductor in the mixed state also yields information about its electronic properties. M~b is a component of the phenomenological tensor describing the superconductor's anisotropv.
<,.:>
0921-4534/91/$03.50 O 1991 - Elsevier Science ?ubiistters B.V. AH fights r e ~ .
=
=
{
.4, ==l A,~ + A2
.
~ 2 4- ( - ' - -
'
< ,'-' > i2
J
. -~}
M. Weberet al.
750
/
Doped ~i.ba#edhigh-T¢superconductors
Since all fits were excellent, which was reflected i n values of the normalized X~ close to unity, eqs. (4) were used to determine the values of < AB z >t/~.
3, RESULTS A N D DISCUSSION The temperature dependence of < A B 2 >I12 for the four investigated samples is perfectly explained iv the framework of conventional BCS theory in the weak coupling limit. The description by the two-fluid model, which is valid in the strong coupling limit, is significantly worse 7 . The values of < AB 2 >llz (T --* 0) Listed in Table 1 were obtained by a fitof < AB s >1Is (T) = < AB s >tls (0).{Aecs(0)/AScs(T)} 2 (5) to the data points determined with the help of eq. (4). Assuming the phenomenologlcal tensor component M a b to be the same fo." all four investigated samples, the values of < A B 2 >1/2 (0) are proportional to the superconducting carrier concentrat, on < A B 2 >i/2 (0) o: n, ,
(6)
according to eqs. (i) and (2). The Cu(2) bond valence sums V(Cu) also listed in T~ble 1 were obtained by means of neutron diffraction4. Assuming the valencies of the ions of Bi2-=Pb=Sr2CaCu2Os+6 to be Bi3+, Pb 2+, Sr2+, Ca 2+, Cu ~+~ and 0 ~-, the hole concentration per Cu p is represented as p = ~+x/2 . (7)
As expected, V(Cu) scales with p. However, the fact that < AB ~ >~/~ (T --* 0) c¢ n, decreases with increasing hole concentration p is rather surprising 6. This feature of the Bi2-=Pb~Sr~CaCu~Os+a series is displayed in Figure 1. For comparison we also show corresponding results obtained in a series of Bi~Sr2Ca~_~Y~Cu~Os+~ samples with different Y doping5, where n~ scales with p = $ - z / 2 .
3.O :S.
2.5
! zo 1,5
,-^ % to V
O.5
0
l
-0.4
I
I
~.2
i
I
i
0
I
I
0.2
0.4
.
I
,
0.0
X-Z FIGURE I Compilation of < A B 2 >112 (T ~ 0) c( n, for Bi2_~PbxSr2CaCu2Os+s and Bi2Sr2Ca1-~Y, Cu2Os+t plotted against (x-z) c¢ p. The straight llne is a fit to the data points of the Y doped samples. The puzzling behaviour of the lead doped 2212 superconductors may be interpreted as evidence that the carriers become more and more localized with increasing lead content: Localized carriers cannot take part in the formation of Cooper pairs, which leads to a decrease of the effective superconducting carrier density ns. The question, whether this feature is related exclusively to doping with Pb will be subject of further investigations. REFERENCES I. E.H. Brandt, Phys. Rev. B37 (1988) 2349. 2. W. Barford and J.M.F. Gunn, Physica C156 (1988) 515. 3. M. Weber et al.,Measurements of the London Penetration Depth in Bi-based High-Tc Compounds, in: Proceedings of the 5th International Conference on M u o n Spin Rotation, Relaxation and Resonance (J.C. Baltzer AG, Basel, 1990) pp. 93-101. 4. H. Maletta et ~., to be published.
Table 1: Compilation of x,/~, p, V(Cu) and < AB2 >i/2 (0) o¢ n~ (see text for explanation) of the four investigated Bi2-rPb~Sr2CaCuzOs+a samples. x 0100 0.15 0.30 0.67
~ 0.16 O.lO 0.25 0.28
p V(Cu) 0.16 (1) 2.22 (1) 0.18 (1) 2.23 (1) 0.40 (1) 2.29 (1) 0.61 (I) -
< A B ~ >I/2 (0) 2.00 (8) 2.01 (7) 1.78 (6) 1.28 (5)
et ~~,. , i.., S ~DL - S ~. .u. au.y. v~ r _J ^ ~ "~he ~o,,uon Penetration Depth in the High-T: compound~ Bi2Sr2Y~CaI-~Cu20s+~, this volume.
5 . .... ~'~ ~~. r. .~. k. ~ .
6. W e believe that a similar effect was also observed by A. Maeda et al.,Phys. Rev. B41 (1990) 6418. 7. IV[.Weber et al., London Penetration Depth in Bibased High-To Compounds, in: Proceedings of the LT19 Satellite Conference (Adam Hilger, Bristol, 1990) pp. 403-405.