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Neutron diffraction by the flux line lattice in YBa2Cu3O7−δ single
. __ l!iB &A&. c
__
ELSEVIER
Neutron
Physica C 282-287
(1997) 2089-2090
diffraction by the flux line lattice in Y13a,Cu,07_~single
crystals G. Brandstatter”, A. Vostne?, Emel’chenko’
H.W. Weber’, T. Chattopadhyayb, R. Cubittb, H. Fischerb, G.A.
“Atominstitut der ijsterreichischen Universitaten Schiittelstrafie 115, A-1020 Wien, Austria bInstitut Laue-Langevin BP 156, F-38042 Grenoble Cedex 9, France ‘Institute of Solid State Physics, RAS 142432, Chernogolovka, Russia
Small angle neutron diffraction was used to image the mixed state in a large twinned superconducting Y-123 single crystal. The integrated intensity I,, of the (lo)-reflection was evaluated as a function of temperature and used to derive h(T) on an absolute scale, which provides us with information on the nature of the pairing mechanism. The results are compared with theoretical predictions calculated within the framework of BCS-theory or other approaches such as d-wave pairing. 1. INTRODUCTION Much interest focused on the nature of the pairing mechanism of the superconducting carriers recently. One way to get information on this matter is to measure the temperature dependence of the magnetic penetration depth h by small angle neutron diffraction. We present data on h(T) obtained on a large YBa,Cu,O,~ single crystal, which will be discussed in terms of theory. 2. EXPERIMENTAL The Y-123 single crystal (V=lOx7x2 mm3, Te=92 K) is of high crystalline quality, but contains a dense twinning pattern. The neutron scattering experiments where carried out at the SANS facility at ILL, Grenoble. The crystallographic c-axis was oriented parallel to both the magnetic field * Financialsupportby the ILL is gratefully acknowledged. 0921-4534/97/$17.00 0 Elscvier Science B.V PI1 SO921-4534(97)01151-g
All rights reserved.
and the incoming monochromatic neutron beam with wave-length h,=l nm. The temperature dependence of the diffracted intensity was obtained after cooling through T, in a certain field and after subtracting the background recorded above T, at the same field. The neutron flux density a, was measured accurately for three different collimations. 3. RESULTS AND DISCUSSION The diffraction patterns show a fourfold symmetry of the flux line lattice at all temperatures and fields, which can be explained by the strong pinning of the flux lines by the twin planes. Rocking curves were taken at several different temperatures, the shape and the width of these curves were found to be temperature independent. Hence, an integration of the diffracted intensity
G. Brandstiitter et al. /Physica C 282-287 (1997) 2089-2090
2090
could be made, which results in the “integrated intensity” of the (lo)-reflection. From the integrated intensity I,,(T), which contains the contributions of all Bragg planes, X can be obtained as follows:
Ilo
= IO[ 1+ $X2(T,12
(1)
with I,=a”,,~,B”V~,“(y/4)‘~(~~), F-1.9131, the flux quantum Q,,, the applied field B, and h(T=O)=h,. Extrapolating I,,(T) to T=O K, we get 144 nm, 142 nm, and 129 nm for 0.4 T, 0.2 T, and 50 mT, respectively, which is in excellent agreement with data reported by other groups [l]. h,,(T) is obtained from Equ. (1) and plotted as (&,/U* vs. reduced temperature in Fig. 1. The large error bars are due to the unavoidable error of the neutron wavelength (10 %o). 3L is directly related to the density of the superconducting and thus provides us with carriers information on the pairing state. The theoretical temperature dependence of h for s-wave pairing [21, d-wave pairing [31, and dirty d-wave pairing [41 is also shown in Fig. 1. As observed previously [51 the slope becomes flat at the lowest temperatures, where the data are close to the d-wave model. We observe a strong increase of the slope at elevated temperatures as predicted by BCS-theory. The s-wave and the dirty dwave model (which is unlikely because high Te single crystals are presumably in the clean limit) describe the data best in this temperature range. The experimental data, therefore, may indicate a mixture of s-wave and d-wave pairing. However, we have not yet included the Debye-Waller factor, which might have a significant influence. In addition, the small differences in the shape of 3Lnh(T) predicted by the various models make a final decision difficult. 4. SUMMARY Neutron diffraction patterns by the flux line lattice in a Y-123 single crystal with fourfold symmetry due to the twin structure
0.6
0.4 ekperimental results d-wave model dirty d-wave model s-wave model - - Iwo-fluid-model
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0.2
-
t
0.0’ 0.0
s
’ 0.2
’
’
’
0.4
’ 0.6
’
’ 0.8
’
N
1.0
TTT,
Fig. 1: Normalized 3Ldeduced from I(T) at 0.4 T and various theoretical models. were observed. h, was extracted from the integrated intensity I,,(T) extrapolated to 0 K. We obtain A,=140 nm in excellent agreement with previously published results. As 1(T) reflects the pairing mechanism, fundamental information on the pairing state can be obtained in principle. However, the differences in X,,(T) predicted by different models are very small. Investigations of & which is much more sensitive to the pairing state, would help to clarify this matter [6]. 5. REFERENCES 1.
2. 3. 4. 5.
6.
P. Zimmermann,H. Keller, S.L. Lee, I.M. Savic, M. Warden, D. Zech, R. Cubitt, E.M. Forgan, E. Kaldis, J. Karpinski,C. Kriiger, Phys. Rev. B 52 (1995) 541. B. Miihlschlegel,Z. Physik 155 (1959) 313. H. Won, K. Maki, Phys. Rev. B 49 (1994) 1397. Y. Sun, K. Maki, Phys. Rev. B 51 (1995) 6059. G. Brand&titter,H.W. Weber, T. Chattopadhyay, R. Cubit&H. Fischer, M. Wylie, G.A. Emelchenko,A. Wiedenmann,to be published in J. Appl. Cry&. (1997). R.A. Klemm, S.H. Liu, Phys. Rev. Lett. 74 (1995) 2343
__
ELSEVIER
Neutron
Physica C 282-287
(1997) 2089-2090
diffraction by the flux line lattice in Y13a,Cu,07_~single
crystals G. Brandstatter”, A. Vostne?, Emel’chenko’
H.W. Weber’, T. Chattopadhyayb, R. Cubittb, H. Fischerb, G.A.
“Atominstitut der ijsterreichischen Universitaten Schiittelstrafie 115, A-1020 Wien, Austria bInstitut Laue-Langevin BP 156, F-38042 Grenoble Cedex 9, France ‘Institute of Solid State Physics, RAS 142432, Chernogolovka, Russia
Small angle neutron diffraction was used to image the mixed state in a large twinned superconducting Y-123 single crystal. The integrated intensity I,, of the (lo)-reflection was evaluated as a function of temperature and used to derive h(T) on an absolute scale, which provides us with information on the nature of the pairing mechanism. The results are compared with theoretical predictions calculated within the framework of BCS-theory or other approaches such as d-wave pairing. 1. INTRODUCTION Much interest focused on the nature of the pairing mechanism of the superconducting carriers recently. One way to get information on this matter is to measure the temperature dependence of the magnetic penetration depth h by small angle neutron diffraction. We present data on h(T) obtained on a large YBa,Cu,O,~ single crystal, which will be discussed in terms of theory. 2. EXPERIMENTAL The Y-123 single crystal (V=lOx7x2 mm3, Te=92 K) is of high crystalline quality, but contains a dense twinning pattern. The neutron scattering experiments where carried out at the SANS facility at ILL, Grenoble. The crystallographic c-axis was oriented parallel to both the magnetic field * Financialsupportby the ILL is gratefully acknowledged. 0921-4534/97/$17.00 0 Elscvier Science B.V PI1 SO921-4534(97)01151-g
All rights reserved.
and the incoming monochromatic neutron beam with wave-length h,=l nm. The temperature dependence of the diffracted intensity was obtained after cooling through T, in a certain field and after subtracting the background recorded above T, at the same field. The neutron flux density a, was measured accurately for three different collimations. 3. RESULTS AND DISCUSSION The diffraction patterns show a fourfold symmetry of the flux line lattice at all temperatures and fields, which can be explained by the strong pinning of the flux lines by the twin planes. Rocking curves were taken at several different temperatures, the shape and the width of these curves were found to be temperature independent. Hence, an integration of the diffracted intensity
G. Brandstiitter et al. /Physica C 282-287 (1997) 2089-2090
2090
could be made, which results in the “integrated intensity” of the (lo)-reflection. From the integrated intensity I,,(T), which contains the contributions of all Bragg planes, X can be obtained as follows:
Ilo
= IO[ 1+ $X2(T,12
(1)
with I,=a”,,~,B”V~,“(y/4)‘~(~~), F-1.9131, the flux quantum Q,,, the applied field B, and h(T=O)=h,. Extrapolating I,,(T) to T=O K, we get 144 nm, 142 nm, and 129 nm for 0.4 T, 0.2 T, and 50 mT, respectively, which is in excellent agreement with data reported by other groups [l]. h,,(T) is obtained from Equ. (1) and plotted as (&,/U* vs. reduced temperature in Fig. 1. The large error bars are due to the unavoidable error of the neutron wavelength (10 %o). 3L is directly related to the density of the superconducting and thus provides us with carriers information on the pairing state. The theoretical temperature dependence of h for s-wave pairing [21, d-wave pairing [31, and dirty d-wave pairing [41 is also shown in Fig. 1. As observed previously [51 the slope becomes flat at the lowest temperatures, where the data are close to the d-wave model. We observe a strong increase of the slope at elevated temperatures as predicted by BCS-theory. The s-wave and the dirty dwave model (which is unlikely because high Te single crystals are presumably in the clean limit) describe the data best in this temperature range. The experimental data, therefore, may indicate a mixture of s-wave and d-wave pairing. However, we have not yet included the Debye-Waller factor, which might have a significant influence. In addition, the small differences in the shape of 3Lnh(T) predicted by the various models make a final decision difficult. 4. SUMMARY Neutron diffraction patterns by the flux line lattice in a Y-123 single crystal with fourfold symmetry due to the twin structure
0.6
0.4 ekperimental results d-wave model dirty d-wave model s-wave model - - Iwo-fluid-model
??
__ -
0.2
-
t
0.0’ 0.0
s
’ 0.2
’
’
’
0.4
’ 0.6
’
’ 0.8
’
N
1.0
TTT,
Fig. 1: Normalized 3Ldeduced from I(T) at 0.4 T and various theoretical models. were observed. h, was extracted from the integrated intensity I,,(T) extrapolated to 0 K. We obtain A,=140 nm in excellent agreement with previously published results. As 1(T) reflects the pairing mechanism, fundamental information on the pairing state can be obtained in principle. However, the differences in X,,(T) predicted by different models are very small. Investigations of & which is much more sensitive to the pairing state, would help to clarify this matter [6]. 5. REFERENCES 1.
2. 3. 4. 5.
6.
P. Zimmermann,H. Keller, S.L. Lee, I.M. Savic, M. Warden, D. Zech, R. Cubitt, E.M. Forgan, E. Kaldis, J. Karpinski,C. Kriiger, Phys. Rev. B 52 (1995) 541. B. Miihlschlegel,Z. Physik 155 (1959) 313. H. Won, K. Maki, Phys. Rev. B 49 (1994) 1397. Y. Sun, K. Maki, Phys. Rev. B 51 (1995) 6059. G. Brand&titter,H.W. Weber, T. Chattopadhyay, R. Cubit&H. Fischer, M. Wylie, G.A. Emelchenko,A. Wiedenmann,to be published in J. Appl. Cry&. (1997). R.A. Klemm, S.H. Liu, Phys. Rev. Lett. 74 (1995) 2343