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A new high temperature superconductor: Ba2SmCu3O9−x
Solid State Cormnunications, Vol.63,No.6, pp.507-5|0, Printed in Great Britain.
1987.
0038-1098/87 $3.00 + .00 Pergamon Journals Ltd.
A NEW HIGH TEMPERATURE SUPERCONDUCTOR: Ba2SmCu309_x
F. Garcfa-Alvarado, E. Moran, M. Vallet, J.M. Gonz~lez-Calbet and M.A. Alario Departamento de Qul'mica Inorg~nica Facultad de Ciencias Qufmicas. Universidad Complutense. 28040 Madrid SPAIN M.'r. P~rez-Frfas and J.L. Vicent Departamento de Ffsica de la Materia Condensada Facultad de Ciencias Ffsicas. Universidad Complutense. 28040 Madrid SPAIN S. Ferret, E. Garci'a-Michel and M.C. Asensio Departamento de Ffsic8 de la Materia Condensada Facultad de Ciencias. Universidad Aut6noma. Canto Blanco. 28040 Madrid SPAIN
(Received
A p r i l 18, 1987 by
M. Cardona)
A new high temperature superconducting oxide Ba2SmCu309_x (x_~ 2.0) has been synthesized and characterized by means of X-ray and electron diffraction as a single phase with a perovskite related structure (acx acx 3ao ac = perovskite unit cell parameter). The superconducting D.C. transition occurs at Tc = 96.5 K with a transition width (10-90%) of 1.7 K. X-ray photoemission experiments reveal a surface concentration of Cu3+ cations of 36%.
Introduction
accompanied by a slight modification in the Cu(II)/Cu(III) ratio as shown by photoemission studies.
An enormous amount of work has already been done in the so-called H i g h Temperature Superconductors (HTSC) since Bednorz and M~iller1 reported that a phase in the Ba-La-Cu-O system was a superconductor at temperatures much higher than those observed in oxides2, 3. Shortly after, Chu et al 4 and Wu et al 5 confirmed that finding and extended it to another closely related quaternary system: Ba-Y-Cu-O. Those authors observed a new HTSC at temperatures over 77 K. The superconducting phase was however difficult to identify until Cava et al 6 showed that it had a composition Ba2YCu306.9 and a structure related to the perovskite ceil. T h i s constitutes already the so-caNed "second generation" HTSC. In an attempt to find other HTSC materials with higher temperatures and trying to understand the structural and chemical aspects of the problem, we have prepared several new materials based on Ba2YCu309_x by Rare-Earth substitution of the Ytrium cation. Our first choice was Samarium. First of all, Sm is, as Ytrium, exclusively trivalent in oxides, Sm is also of comparable but different ionic size, so that it may introduce distortions in the structure that could modify the material properties. Secondly, as it is a paramagnetic cation, it could be possible to study competition between magnetism and superconductivity. As described below, our results show that Sm does indeed improve the superconducting transition temperature, and this appears to be
Experimental Samples, with average composition Ba2MCu309_x, M being the Rare-Earth element, were prepared by mixing the appropiate amounts of copper nitrate, barium carbonate and a Rare-Earth oxide (Merck R.A.) and heated in air overnight; the process is repeated several times after regr~ding. A finai heat treatment in oxygen at 700-°C appears to increase Tc. Standard D . C . four-probe technique w~s used for resistance measurements. Rectangularshaped samples were cu~ from the sintered pellets. Silver-paint was used for the electrical contacts. Sample current of I0 mA was supplied by a commercial constant current power supply. Commercial temperature controller with calibrated Pt and carbon-glass sensors was used in the experiments. XPS measurements were carried out in a commercial UHV (Ultra High Vacuum) system equipped with an X-ray source and an hemispherical analyzer described in detail previously7. The electron analyzer was operated at a constant pass energy of 50 eV. Results and Discussion X-ray diffraction patterns of the black powder obtained with Sm, indicated an orthorhombic cell similar to that found by Cava et a l 6 . Electron diffraction experiments confirmed this ceil whose 507
508
A NEW HIGH TEMPERATURE
Vol. 63, No. 6
SUPERCONDUCTOR:Ba2SmCu309_ x
parameters appear in Table I, together with those of the Y compound, that we have prepared for comparison.
x :Be 2 y Cu309_ x • :Be 2 Sm Cu309_
Table I 0 0
Lattice parameters, data of the samples.
f r o m X-ray
powder
ri- 0.75 P
Ba2YCu309- x
a=
3.820 (2)~
b= 3.887(2) ~ c= 11.687 (4) ~ V = 173.5 (1) ~3
Ba2SmCu309- x
a=
3.846 (1)
e--
0.50
b= 3.908(1) c= 11.719 (2) V= 176.16 (5) ~3 "O
As expected for the cation size, a small increase is observed in the unit cell dimensions. (~V = 1.5%) Fig. 1 shows the resistance versus temperature
025 0 Z
12 90
95
IOO
Temperature (k)
Fig. 2 Superconducting transitions in Ba2SmCu309_x and Ba2YCu309_ x
Bo 2 Sm CusO9_ X
E ¢.) o cO
n-
I
I
O0
150
200
Temperature (k)
Fig. l Temperature dependence Ba2SmCu309- x
of
resistance in
behaviour of the Ba-Sm-Cu-O sample. Tile sampie shows a clear metaiiic behaviour before the transition. Fig. 2 s h o w s the transition to the zero-resistance state in Ba-Sm-Cu-O together with those of the Ba-Y-Cu-O sampie, plotted for comparison. The midpoint value for the Sin-based sampie is 96.5 K and the transition width (10-90%) is 1.7 K. For the Y-based sample Tc is 93.5 K (midpoint) and the transition width (10-90%) is
1.4 K. Cooling down and heating up the samples through the transitions do not change those values. Hysteresis in the transition temperatures have not been observed within the experimental error. Pure Sm and a lot of Sm-based compounds have localized magnetic moments and some of them present magnetic order at low temperatures. Therefore Ba-Sm-Cu-O could be a good candidate for some kind of re-entrant behaviour8. However the zero-resistance state is observed down to 4.2 K. Perhaps 4.2 K is too high a temperature to observe any re-entrant behaviour. Photoemission experiments were performed in order to investigate the oxidation states of Cu atoms in different samples. Fig. 3 shows the Cu 2P3/2 photoemission lines of the three different samples not subjected to any treatment in UHV. Curve (a) corresponds to the Cu emission in Ba-La-Cu-O. It is centered at a binding energy (BE) of 933.2 eV relative to the Fermi level. This value is in good agreement with the BE corresponding to Cu2+ cations in CuO (933.6 eV)9. The spectrum has been adjusted to one Doniach-Sunjic (DS)I0 curve with a full-width-at-half-maximum(FWHM) of 1.57 eV and a singularity index of 0.07. The adjusted curve (continous line) deviates from the data points at the high BE side due to the shake-up emission characteristic of Cu oxides10 that was not included in the fitting. Spectrum (c) in the figure corresponds to the Ba-Y-Cu-O sample. A small change in BE (932.3 eV) and a noticeable asymmetric broadening are visible in the spectrum comparing with curve ( a ) . The spectrum (c) has been deconvoiuted in two DS functions with the same parameters (FWHM and singularity index) as those of spectrum (a). The intensities and their energy
Vol. 63, No. 6
A NE~' HIGH TEMPEPJ~TURE SUPERCONDUCTOR:Ba2SmCu309_ x
Cu 2p 3/2
...,
hv
(a)
C
O v
r-
t-
(b)
0_ x
~
(c)
I
I
I
I
I
I
940
938
956
954
952
950
Binding
energy
(eV)
Fig. 3 Cu 2P2/3 photoemission lines for different Cu oxides. The experimental data points have been adjusted with Doniach-Sunjic functions (continous lines). Curve (a) corresponds to Ba0.2Lal.8CuO4- x, (b) to Ba2SmCu309_ x and (c) to Ba2YCu309- x separation were adjusted to fit data points. As can be seen in the figure, in addition to the main line that corresponds to Cu 2+ ions, there is another emission separated 2.0 eV in the high BE side.
We interpret it as being due to Cu 3+ cations. From the fit one obtains that the intensity of the Cu3+ emission relative to the total photoemission intensity is 41%. Curve (b) shows the Cu emission for the Ba-Sm-Cu-O sample. It is centered at a BE of 932.8 eV. Deconvolution in DS functions (same parameters as above) reveals a~ain a Cu 3+ emission at 2.0 eV from the main Cu 22- line. The relative intensity of the Cu3+ signal is 36% of the total intensity. Present results show that the substitution of Y(III) by Sm(III) increases the transition temperature in these superconductors. In the asumption that no Cu(1) is present, a result supported by photoemission, the composition of our Sm sample is Ba2SmCU3+l.0 8Cu2+1.9 207.0 4 and its mid-point Tc is 96.5 K. A similary prepared Y sample has a composition Ba2YCu3+I. 2 3Cu2+1.7 707.12 with a mid-point transition temperature of 93.5 K. It is not clear however whether or not there is an oxygen concentration gradient from surface to bulk. In sp~te of the fnct that Tc may depend on several factors, it appears that an increase in the transition temperature is accompanied by a slight decrease in the Cu(III) concentration and a concomitant decrease in oxygen content. However, comparing our Ytrium sample with that described by Cava et al 6, the opposite is true. It is then obvious that a detaiied structura~ analysis including the oxygen sublattice and the oxidation states of the copper ions is essential. This is especially important since we have often observed that non-stoichiometry in perovskites can be accommodated by means of quite elaborated and varied patterns12,13,14. For temperatures close to Tc, measurements of the critical field Hc2 are under way. This kind of measurements will certainly be very interesting to roughly estimate the Hc2(O) value using the WHH11 expression for dirty superconductors. Also measurements of critical field Hc2 anisotropy in single crystals could be, in the future, a good test for dimensionality effects15,16,17 in these compounds. We have been able to successfuily substitute five different Rare-Earth cations in the Y position and obtain HTSC materials in the same range of transition temperatures. These results will be reported in the near future.
Acknowledgements Two of us (M.T.P.F. and J.L.V.) want to thank Instituto de Ffsica de Materiales (CSIC) for allowing us to use their facilities.
References 1. J.G. Bednorz and K.A. Miiller. Z. Phys. B64, 189 (1986) 2. A.W. Sleight, J.L. Gillson and F.G. Bierstedt. Sol. St. Comm. 17, 27 (1975) 3. D.C. Johnston, H. Prakash, W.H. Zachariasen and R. Wiswanathan. Mat. Res. Bull. 8, 777 (1973) 4. C.W. Chu, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang and Y.Q. Wang, Phys. Rev. Lett. 58-4, 405 (1987) 5. M.K. Wu, J.R. Ashburn and C.J. Torng. Phys. Rev. Lett. 58-9, 908 (1987)
509
6. R.J. Cava, B. Battlog, R.B. van Dover, D.W. Murphy, S. Sunshine, J.P. Remika, A.G. Rietman, S. Zaharak and G.P. Espinosa. (preprint) 7. C. Ocal, E. Martinez and S. Ferrer. Surface Sci. 136, 571 (1984) 8. M.B. Maple, W.A. Fertig, A.C. Mota, L.E. Delong, D. Wohlleben and R. Fitzgerald. Sol. St. Comm. ~ 829 (1972) 9. K. Wandelt. Surface Sci. Rep. 2, 1 (1982) I0. S. Doniach and M. Sunjic, J. Phys. C 3, 365 (1970)
510 II.
A NEW HIGH TEMPERATURE SUPERCONDUCTOR:Ba2SmCu309.x
S. Helfond and P.C. H.F. Werthamer, Hohenberg. Phys. Rev. 147, 195 (1966) 12. M. Vallet, J.M. Gonz'~'ez Calbet, J. Verde, M.A. Aiario, J. Sol. State Chem. 57, 197 (i985) 13. J.M. Gonz~lez Calbet, M. Vallet and M.A. Alario. Jour. Sol. State Chem. 60, 326 (1985) 14. J.M. Gonz~lez Calbet, M. Va1!et, M.A. Alario and J.C. Grenier. Mat. Res. Bull. 18, 285 (1983)
Vol. 63, No. 6
15. J.L. Vieent, S.J. Hiilenius and R.V. Coleman. Phys. Rev. Lett. 44, 872 (1986) 16. C.S.L. Chun, O.0. Zheng, J.L. Vieent and I.K. Schuller. Phys. Rev. B29, 4915 (1984) 17. J.D. Jorgensen, H.B. Schuttler, D.G. Hinks, D.W. Capone, H.K. Zhang, M.B. Brodsky and D.J. Scalapino. Phys. Rev. Lett. 58, 1024 (1987)
1987.
0038-1098/87 $3.00 + .00 Pergamon Journals Ltd.
A NEW HIGH TEMPERATURE SUPERCONDUCTOR: Ba2SmCu309_x
F. Garcfa-Alvarado, E. Moran, M. Vallet, J.M. Gonz~lez-Calbet and M.A. Alario Departamento de Qul'mica Inorg~nica Facultad de Ciencias Qufmicas. Universidad Complutense. 28040 Madrid SPAIN M.'r. P~rez-Frfas and J.L. Vicent Departamento de Ffsica de la Materia Condensada Facultad de Ciencias Ffsicas. Universidad Complutense. 28040 Madrid SPAIN S. Ferret, E. Garci'a-Michel and M.C. Asensio Departamento de Ffsic8 de la Materia Condensada Facultad de Ciencias. Universidad Aut6noma. Canto Blanco. 28040 Madrid SPAIN
(Received
A p r i l 18, 1987 by
M. Cardona)
A new high temperature superconducting oxide Ba2SmCu309_x (x_~ 2.0) has been synthesized and characterized by means of X-ray and electron diffraction as a single phase with a perovskite related structure (acx acx 3ao ac = perovskite unit cell parameter). The superconducting D.C. transition occurs at Tc = 96.5 K with a transition width (10-90%) of 1.7 K. X-ray photoemission experiments reveal a surface concentration of Cu3+ cations of 36%.
Introduction
accompanied by a slight modification in the Cu(II)/Cu(III) ratio as shown by photoemission studies.
An enormous amount of work has already been done in the so-called H i g h Temperature Superconductors (HTSC) since Bednorz and M~iller1 reported that a phase in the Ba-La-Cu-O system was a superconductor at temperatures much higher than those observed in oxides2, 3. Shortly after, Chu et al 4 and Wu et al 5 confirmed that finding and extended it to another closely related quaternary system: Ba-Y-Cu-O. Those authors observed a new HTSC at temperatures over 77 K. The superconducting phase was however difficult to identify until Cava et al 6 showed that it had a composition Ba2YCu306.9 and a structure related to the perovskite ceil. T h i s constitutes already the so-caNed "second generation" HTSC. In an attempt to find other HTSC materials with higher temperatures and trying to understand the structural and chemical aspects of the problem, we have prepared several new materials based on Ba2YCu309_x by Rare-Earth substitution of the Ytrium cation. Our first choice was Samarium. First of all, Sm is, as Ytrium, exclusively trivalent in oxides, Sm is also of comparable but different ionic size, so that it may introduce distortions in the structure that could modify the material properties. Secondly, as it is a paramagnetic cation, it could be possible to study competition between magnetism and superconductivity. As described below, our results show that Sm does indeed improve the superconducting transition temperature, and this appears to be
Experimental Samples, with average composition Ba2MCu309_x, M being the Rare-Earth element, were prepared by mixing the appropiate amounts of copper nitrate, barium carbonate and a Rare-Earth oxide (Merck R.A.) and heated in air overnight; the process is repeated several times after regr~ding. A finai heat treatment in oxygen at 700-°C appears to increase Tc. Standard D . C . four-probe technique w~s used for resistance measurements. Rectangularshaped samples were cu~ from the sintered pellets. Silver-paint was used for the electrical contacts. Sample current of I0 mA was supplied by a commercial constant current power supply. Commercial temperature controller with calibrated Pt and carbon-glass sensors was used in the experiments. XPS measurements were carried out in a commercial UHV (Ultra High Vacuum) system equipped with an X-ray source and an hemispherical analyzer described in detail previously7. The electron analyzer was operated at a constant pass energy of 50 eV. Results and Discussion X-ray diffraction patterns of the black powder obtained with Sm, indicated an orthorhombic cell similar to that found by Cava et a l 6 . Electron diffraction experiments confirmed this ceil whose 507
508
A NEW HIGH TEMPERATURE
Vol. 63, No. 6
SUPERCONDUCTOR:Ba2SmCu309_ x
parameters appear in Table I, together with those of the Y compound, that we have prepared for comparison.
x :Be 2 y Cu309_ x • :Be 2 Sm Cu309_
Table I 0 0
Lattice parameters, data of the samples.
f r o m X-ray
powder
ri- 0.75 P
Ba2YCu309- x
a=
3.820 (2)~
b= 3.887(2) ~ c= 11.687 (4) ~ V = 173.5 (1) ~3
Ba2SmCu309- x
a=
3.846 (1)
e--
0.50
b= 3.908(1) c= 11.719 (2) V= 176.16 (5) ~3 "O
As expected for the cation size, a small increase is observed in the unit cell dimensions. (~V = 1.5%) Fig. 1 shows the resistance versus temperature
025 0 Z
12 90
95
IOO
Temperature (k)
Fig. 2 Superconducting transitions in Ba2SmCu309_x and Ba2YCu309_ x
Bo 2 Sm CusO9_ X
E ¢.) o cO
n-
I
I
O0
150
200
Temperature (k)
Fig. l Temperature dependence Ba2SmCu309- x
of
resistance in
behaviour of the Ba-Sm-Cu-O sample. Tile sampie shows a clear metaiiic behaviour before the transition. Fig. 2 s h o w s the transition to the zero-resistance state in Ba-Sm-Cu-O together with those of the Ba-Y-Cu-O sampie, plotted for comparison. The midpoint value for the Sin-based sampie is 96.5 K and the transition width (10-90%) is 1.7 K. For the Y-based sample Tc is 93.5 K (midpoint) and the transition width (10-90%) is
1.4 K. Cooling down and heating up the samples through the transitions do not change those values. Hysteresis in the transition temperatures have not been observed within the experimental error. Pure Sm and a lot of Sm-based compounds have localized magnetic moments and some of them present magnetic order at low temperatures. Therefore Ba-Sm-Cu-O could be a good candidate for some kind of re-entrant behaviour8. However the zero-resistance state is observed down to 4.2 K. Perhaps 4.2 K is too high a temperature to observe any re-entrant behaviour. Photoemission experiments were performed in order to investigate the oxidation states of Cu atoms in different samples. Fig. 3 shows the Cu 2P3/2 photoemission lines of the three different samples not subjected to any treatment in UHV. Curve (a) corresponds to the Cu emission in Ba-La-Cu-O. It is centered at a binding energy (BE) of 933.2 eV relative to the Fermi level. This value is in good agreement with the BE corresponding to Cu2+ cations in CuO (933.6 eV)9. The spectrum has been adjusted to one Doniach-Sunjic (DS)I0 curve with a full-width-at-half-maximum(FWHM) of 1.57 eV and a singularity index of 0.07. The adjusted curve (continous line) deviates from the data points at the high BE side due to the shake-up emission characteristic of Cu oxides10 that was not included in the fitting. Spectrum (c) in the figure corresponds to the Ba-Y-Cu-O sample. A small change in BE (932.3 eV) and a noticeable asymmetric broadening are visible in the spectrum comparing with curve ( a ) . The spectrum (c) has been deconvoiuted in two DS functions with the same parameters (FWHM and singularity index) as those of spectrum (a). The intensities and their energy
Vol. 63, No. 6
A NE~' HIGH TEMPEPJ~TURE SUPERCONDUCTOR:Ba2SmCu309_ x
Cu 2p 3/2
...,
hv
(a)
C
O v
r-
t-
(b)
0_ x
~
(c)
I
I
I
I
I
I
940
938
956
954
952
950
Binding
energy
(eV)
Fig. 3 Cu 2P2/3 photoemission lines for different Cu oxides. The experimental data points have been adjusted with Doniach-Sunjic functions (continous lines). Curve (a) corresponds to Ba0.2Lal.8CuO4- x, (b) to Ba2SmCu309_ x and (c) to Ba2YCu309- x separation were adjusted to fit data points. As can be seen in the figure, in addition to the main line that corresponds to Cu 2+ ions, there is another emission separated 2.0 eV in the high BE side.
We interpret it as being due to Cu 3+ cations. From the fit one obtains that the intensity of the Cu3+ emission relative to the total photoemission intensity is 41%. Curve (b) shows the Cu emission for the Ba-Sm-Cu-O sample. It is centered at a BE of 932.8 eV. Deconvolution in DS functions (same parameters as above) reveals a~ain a Cu 3+ emission at 2.0 eV from the main Cu 22- line. The relative intensity of the Cu3+ signal is 36% of the total intensity. Present results show that the substitution of Y(III) by Sm(III) increases the transition temperature in these superconductors. In the asumption that no Cu(1) is present, a result supported by photoemission, the composition of our Sm sample is Ba2SmCU3+l.0 8Cu2+1.9 207.0 4 and its mid-point Tc is 96.5 K. A similary prepared Y sample has a composition Ba2YCu3+I. 2 3Cu2+1.7 707.12 with a mid-point transition temperature of 93.5 K. It is not clear however whether or not there is an oxygen concentration gradient from surface to bulk. In sp~te of the fnct that Tc may depend on several factors, it appears that an increase in the transition temperature is accompanied by a slight decrease in the Cu(III) concentration and a concomitant decrease in oxygen content. However, comparing our Ytrium sample with that described by Cava et al 6, the opposite is true. It is then obvious that a detaiied structura~ analysis including the oxygen sublattice and the oxidation states of the copper ions is essential. This is especially important since we have often observed that non-stoichiometry in perovskites can be accommodated by means of quite elaborated and varied patterns12,13,14. For temperatures close to Tc, measurements of the critical field Hc2 are under way. This kind of measurements will certainly be very interesting to roughly estimate the Hc2(O) value using the WHH11 expression for dirty superconductors. Also measurements of critical field Hc2 anisotropy in single crystals could be, in the future, a good test for dimensionality effects15,16,17 in these compounds. We have been able to successfuily substitute five different Rare-Earth cations in the Y position and obtain HTSC materials in the same range of transition temperatures. These results will be reported in the near future.
Acknowledgements Two of us (M.T.P.F. and J.L.V.) want to thank Instituto de Ffsica de Materiales (CSIC) for allowing us to use their facilities.
References 1. J.G. Bednorz and K.A. Miiller. Z. Phys. B64, 189 (1986) 2. A.W. Sleight, J.L. Gillson and F.G. Bierstedt. Sol. St. Comm. 17, 27 (1975) 3. D.C. Johnston, H. Prakash, W.H. Zachariasen and R. Wiswanathan. Mat. Res. Bull. 8, 777 (1973) 4. C.W. Chu, P.H. Hor, R.L. Meng, L. Gao, Z.J. Huang and Y.Q. Wang, Phys. Rev. Lett. 58-4, 405 (1987) 5. M.K. Wu, J.R. Ashburn and C.J. Torng. Phys. Rev. Lett. 58-9, 908 (1987)
509
6. R.J. Cava, B. Battlog, R.B. van Dover, D.W. Murphy, S. Sunshine, J.P. Remika, A.G. Rietman, S. Zaharak and G.P. Espinosa. (preprint) 7. C. Ocal, E. Martinez and S. Ferrer. Surface Sci. 136, 571 (1984) 8. M.B. Maple, W.A. Fertig, A.C. Mota, L.E. Delong, D. Wohlleben and R. Fitzgerald. Sol. St. Comm. ~ 829 (1972) 9. K. Wandelt. Surface Sci. Rep. 2, 1 (1982) I0. S. Doniach and M. Sunjic, J. Phys. C 3, 365 (1970)
510 II.
A NEW HIGH TEMPERATURE SUPERCONDUCTOR:Ba2SmCu309.x
S. Helfond and P.C. H.F. Werthamer, Hohenberg. Phys. Rev. 147, 195 (1966) 12. M. Vallet, J.M. Gonz'~'ez Calbet, J. Verde, M.A. Aiario, J. Sol. State Chem. 57, 197 (i985) 13. J.M. Gonz~lez Calbet, M. Vallet and M.A. Alario. Jour. Sol. State Chem. 60, 326 (1985) 14. J.M. Gonz~lez Calbet, M. Va1!et, M.A. Alario and J.C. Grenier. Mat. Res. Bull. 18, 285 (1983)
Vol. 63, No. 6
15. J.L. Vieent, S.J. Hiilenius and R.V. Coleman. Phys. Rev. Lett. 44, 872 (1986) 16. C.S.L. Chun, O.0. Zheng, J.L. Vieent and I.K. Schuller. Phys. Rev. B29, 4915 (1984) 17. J.D. Jorgensen, H.B. Schuttler, D.G. Hinks, D.W. Capone, H.K. Zhang, M.B. Brodsky and D.J. Scalapino. Phys. Rev. Lett. 58, 1024 (1987)