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Complete Fermi surface mapping of Bi-cuprates
J. Phvs. Chem. Soliak Vol. 56. No. 12. DD. 1845-1847.
1995 Copyrighi @ 199; kkevier Scien& Ltd Printed in Great Britain. All rights reserved 0022-3697195 j9.50 + 0.00
Pergamon
0022-3697(95)00223-5
COMPLETE FERMI SURFACE MAPPING OF Bi-CUPRATES P. AEBI, * J. OSTERWALDER, t P. SCHWALLER, + H. BERGER, * C. BEELI 5 and L. SCHLAPBACH * * Institut de Physique, Universitd de Fribourg, CH-1700 Fribourg, Switzerland 1 Physik-Institut, UniversitHt Ziirich-Irchel, CH-8057 Zurich, Switzerland * Institut de Physique Appliquee, EPFL, CH-1015 Iausanne, Switzerland g Centre Interdepartemental de Microscopic Electronique, EPFL, CH-1015 Lausanne, Switzerland
Abstract-We review recent angle-scanned photoemission experiments on BizSrzCaCuzOs+X. The Fermi surface has been mapped completely revealing previously unobserved “shadow bands” interpreted as due to antiferromagnetic correlations. Since BizSrzCaCuzOs+, exhibits a relatively complicated incommensurate lattice modulation new measurements on a Pb-doped, unmodulated Bi-cuprate are presented for comparison. Keyworuk Angle-scanned photoemission,
Fermi surface mapping, High-temperature
1. INTRODUCI’ION A new mode of angle-resolved photoemission has recently been applied to map the Fermi surface (FS) of BizSr2CaCu20s+x (Ei2212) completely (11. The validity
of this method has been proven by the mapping of sections through the bulk FS of Cu 12). While the traditional procedure for measuring FS transitions relies critically on photoemission line shapes near the Fermi level, this new approach takes the absolute photoemission intensity at the Fermi level directly as indicator for the FS transition. The present method probes instead of the conventional band structure E(k) its inverse function k(E),therefore being complementary to the traditional approach. Using motorized sequential angle scanning data acquisition [3], a full FS mapping typically consists of 6000 intensity measurements uniformly distributed over the full first and part of the second two-dimensional Brillouin zones of the compound under investigation. This high sampling density of the parallel component of the wave vector (kll) does not miss any direct transitions crossing the Fermi level (En). As a matter of fact, this method revealed previously unobserved features, so called “shadow bands” (SB), on the FS of Bi2212 [l]. Since Bi2212 has a relatively complicated incommensurate lattice modulation, measurements on a Pb-doped, unmodulated crystal are presented for comparison.
2. RESULTS AND DISCUSSION Figure l(a) shows the Bi2212 kll mapping of the intensity of He I excited photoelectrons collected within an energy window of about 30 meV centered at En. [l] High intensities result at kll locations where transitions move through Er. These locations present themselves as relatively fine, well defined lines. A sketch of the measurement is shown in Fig.
superconductor
l(b). For a truly two-dimensional system the high symmetry points T and Z would be equivalent. Points X and Y correspond to (n/a, r-r/a) with respect to the Cu-0 planes and are not equivalent because of a slightly different lattice constant of the a and b axis (the b axis going along T Y) and because of the lattice modulation along the b axis. Transmission electron microscopy and low energy electron diffraction are characteristic for an incommensurate “5x1” superstructure along the crystal b axis (not shown). We observe different features in Fig. l(a). First, there is a strong set of lines drawn as strong solid lines in Fig. l(b). No pronounced nesting is observed among these lines. [l] Second, there is a weaker set of lines corresponding to SB, appearing as dashed lines in Fig. l(b). The third feature, plotted as pieces of fine solid lines, occurs near the T and Z points with a banana-like shape. If we take a copy of the stronger set of lines centered at T and center it at X or Y, it covers the weaker set of lines. The weaker set thus seems to behave around Y or X just as the main set of lines around T This behavior is further confirmed by the dispersion observed in constant energy maps for different binding energies, where the strong lines close in towards T and the weaker lines towards X or Y [ 1,4]. X and Y points acting like T points, in a simplified picture, corresponds to a reduction of the Brillouin zone and in real space to a larger unit cell. This is the case if the Cn lattice is occupied with antiferromagnetically (AF) correlated spins. The fine lines observed on the FS also coincide with SB predicted for AF correlated metals by Kampf and Schrieffer [5] and are compatible with the result of an analysis of this model by Haas, Moreo and Dagotto [6] using Monte Carlo and exact diagonalisation techniques. However, also a reconstruction of the atomic structure with the same change of the unit cell is expected to have the same consequences on the FS. Note that our experiment does not specifically detect the magnetism and there-
1845
1846
p. AEJBIet al.
fore cannot distinguish between the two effects. Truly magnetic measurements are necessary or experiments on compounds with well known structures without modulation related complications. The banana-like features near T and 2 have been identified in Ref. [4] as due to the incommensurate “5x1” lattice modulation along the crystal b axis. This can be understood as follows: Changing the periodicity in real space will influence the repeat period of features in reciprocal space ao cordingly. The modulation therefore induces replicas of the FS displaced corresponding to the new periodic@. Then, the banana-like features can be understood as the appearance of such replicas of the main FS. [4] We have carried out FS mapping experiments on leaddoped samples with a Pb to Bi ratio of 0.421.73 and a T, of 83K. [7] These crystals are modulation-free and the idea was to obtain a structurally simplified situation and through this clarity on the influence of the modulation on the SB. Figure l(c) displays the FS mapping on such a crystal. Clearly, the shadow bands are still present whereas the modulation related banana-like features do not appear. Transmission electron microscopy and low energy electron diffraction measurements (not shown) on these Pb doped samples show no indication of modulation related superlattice spots. However, faint diffraction spots occur corresponding to a larger real space layer unit cell with a lattice constant of about 5.4 A. Such a layer unit cell is identical to the one assumed in the model of AF correlations. Thus, the Pb doping provides the intended elimination of the modulation but it also introduces a larger layer unit cell than the primitive, Cu-0 plane related one with a lattice constant of about 3.8 A. Therefore, there are also arguments for a structural origin of SB in these crystals and the situation is not clear-cut. If all layers in the crystal have the larger unit cell, main bands and SB on the FS should exhibit almost identical intensities. This is clearly not the case. More structural information is needed to determine the atomic arrangement in this Pbdoped unmodulated high T, superconductor. While there is evidence for a larger layer unit cell somewhere in the three-dimensional unit cell AF spin correlations remain a probable origin of the SB.
W
C
Fig. 1. (a) Bi2212 PI1 mapping of the He1 (21.2 eV) excited photoelectrons collected within an energy window of about 30 meV 3. CONCLUSIONS Essential findings of our angle-scanned photoemission experiments [l] are: (i) no pronounced nesting is observed, (ii) the observation of a weak superstructure on the FS which coincides with SB predicted by Kampf and Schrieffer [S] based on the presence of AF spin fluctuations in the metallic state, and (iii) the identification of a second superstructure on the FS as due to the incommensurate lattice modulation present in the Bi-cuprates [4]. Measurements on Pbdoped, modulation free crystals also exhibit the SB. These crystals, however, exhibit weak diffraction spots corresponding to a layer unit cell identical
centered at &. A logarithmic intensity scale is used to enhance weaker features. (b) Outline of (a) indicating highqmmetry points and different sets of lines. (c) game as (a) but for a modulation-free lead-doped sample (see text).
to the one for a model with AF correlated spins. While this does not rule out AF correlations in the Cu-0 planes it does not clarify the situation. More structural information is required, truly magnetic measurements and/or FS maps on samples not presenting structural di5culties.
Acknowledgements- We wish to thank R. Fasel, R. Agostino, T.
Fermi surface mapping Kreutz and G. Margaritondo for stimulating discussions, D. Zech for the Te measurements and P Buerri and G. ‘Bolliet for the chemical analysis. Skillful technical assistance was provided by E. Mooser, 0. Raetzo, F. Bourqui and H. Tschopp. This work has been supported by the Swiss National Foundation and the NFP30.
RETERENcE3
1. Aebi P, Osterwalder J., Schwaller P., Schlapbach L., Shimoda M., Mochiku T. and Kadowaki K., Phys. Rev. Lett. 72,2757 (1994); Comment by Chakravarty S., Phys. Rev. Lett. 74,1885 (1995); Reply by P. Aebi, J. Osterwalder, P. Schwaller, L. Schlapbach, M. Shimoda, T Mochiku, K. Kadowaki, Phys. Rev. I&t. 74, 1886 (1995).
1847
2. Aebi P., Osterwalder J., Fasel R., Naumovioc D. and Schlapbach L., Surf: Sci. 307-309,917 (1994). 3. Osterwalder J., Greber T., Stuck A. and Schlapbach L., Phys. Rev. B 44, 13764 (1991); Namnovioc D., Stuck A., Greber T., Osterwalder J. and Schlapbach L., Phys. Rev. B 47, 7462 (1993). 4. Osterwalder 1, Aebi P.,Schwaller P., Schlapbach L., Shimoda M., Mochiku T. and Kadowaki K., Appl. Phys. A 60, 247 (1995). 5. Kampf A.P and Schrieffer JR., Phys. Rev. B 42, 7967 (1990); Phyx Rev. B 41, 6399 (1990). 6. Haas S., Moreo A. and Dagotto E., Phys. Rev. Left. 74, 4281 (1995). 7. Schwaller P., Aebi P., Beeli C., Osterwalder J., Berger H., Fasel R., Kreutz T.J. and Schlapbach L., in preparation.
1995 Copyrighi @ 199; kkevier Scien& Ltd Printed in Great Britain. All rights reserved 0022-3697195 j9.50 + 0.00
Pergamon
0022-3697(95)00223-5
COMPLETE FERMI SURFACE MAPPING OF Bi-CUPRATES P. AEBI, * J. OSTERWALDER, t P. SCHWALLER, + H. BERGER, * C. BEELI 5 and L. SCHLAPBACH * * Institut de Physique, Universitd de Fribourg, CH-1700 Fribourg, Switzerland 1 Physik-Institut, UniversitHt Ziirich-Irchel, CH-8057 Zurich, Switzerland * Institut de Physique Appliquee, EPFL, CH-1015 Iausanne, Switzerland g Centre Interdepartemental de Microscopic Electronique, EPFL, CH-1015 Lausanne, Switzerland
Abstract-We review recent angle-scanned photoemission experiments on BizSrzCaCuzOs+X. The Fermi surface has been mapped completely revealing previously unobserved “shadow bands” interpreted as due to antiferromagnetic correlations. Since BizSrzCaCuzOs+, exhibits a relatively complicated incommensurate lattice modulation new measurements on a Pb-doped, unmodulated Bi-cuprate are presented for comparison. Keyworuk Angle-scanned photoemission,
Fermi surface mapping, High-temperature
1. INTRODUCI’ION A new mode of angle-resolved photoemission has recently been applied to map the Fermi surface (FS) of BizSr2CaCu20s+x (Ei2212) completely (11. The validity
of this method has been proven by the mapping of sections through the bulk FS of Cu 12). While the traditional procedure for measuring FS transitions relies critically on photoemission line shapes near the Fermi level, this new approach takes the absolute photoemission intensity at the Fermi level directly as indicator for the FS transition. The present method probes instead of the conventional band structure E(k) its inverse function k(E),therefore being complementary to the traditional approach. Using motorized sequential angle scanning data acquisition [3], a full FS mapping typically consists of 6000 intensity measurements uniformly distributed over the full first and part of the second two-dimensional Brillouin zones of the compound under investigation. This high sampling density of the parallel component of the wave vector (kll) does not miss any direct transitions crossing the Fermi level (En). As a matter of fact, this method revealed previously unobserved features, so called “shadow bands” (SB), on the FS of Bi2212 [l]. Since Bi2212 has a relatively complicated incommensurate lattice modulation, measurements on a Pb-doped, unmodulated crystal are presented for comparison.
2. RESULTS AND DISCUSSION Figure l(a) shows the Bi2212 kll mapping of the intensity of He I excited photoelectrons collected within an energy window of about 30 meV centered at En. [l] High intensities result at kll locations where transitions move through Er. These locations present themselves as relatively fine, well defined lines. A sketch of the measurement is shown in Fig.
superconductor
l(b). For a truly two-dimensional system the high symmetry points T and Z would be equivalent. Points X and Y correspond to (n/a, r-r/a) with respect to the Cu-0 planes and are not equivalent because of a slightly different lattice constant of the a and b axis (the b axis going along T Y) and because of the lattice modulation along the b axis. Transmission electron microscopy and low energy electron diffraction are characteristic for an incommensurate “5x1” superstructure along the crystal b axis (not shown). We observe different features in Fig. l(a). First, there is a strong set of lines drawn as strong solid lines in Fig. l(b). No pronounced nesting is observed among these lines. [l] Second, there is a weaker set of lines corresponding to SB, appearing as dashed lines in Fig. l(b). The third feature, plotted as pieces of fine solid lines, occurs near the T and Z points with a banana-like shape. If we take a copy of the stronger set of lines centered at T and center it at X or Y, it covers the weaker set of lines. The weaker set thus seems to behave around Y or X just as the main set of lines around T This behavior is further confirmed by the dispersion observed in constant energy maps for different binding energies, where the strong lines close in towards T and the weaker lines towards X or Y [ 1,4]. X and Y points acting like T points, in a simplified picture, corresponds to a reduction of the Brillouin zone and in real space to a larger unit cell. This is the case if the Cn lattice is occupied with antiferromagnetically (AF) correlated spins. The fine lines observed on the FS also coincide with SB predicted for AF correlated metals by Kampf and Schrieffer [5] and are compatible with the result of an analysis of this model by Haas, Moreo and Dagotto [6] using Monte Carlo and exact diagonalisation techniques. However, also a reconstruction of the atomic structure with the same change of the unit cell is expected to have the same consequences on the FS. Note that our experiment does not specifically detect the magnetism and there-
1845
1846
p. AEJBIet al.
fore cannot distinguish between the two effects. Truly magnetic measurements are necessary or experiments on compounds with well known structures without modulation related complications. The banana-like features near T and 2 have been identified in Ref. [4] as due to the incommensurate “5x1” lattice modulation along the crystal b axis. This can be understood as follows: Changing the periodicity in real space will influence the repeat period of features in reciprocal space ao cordingly. The modulation therefore induces replicas of the FS displaced corresponding to the new periodic@. Then, the banana-like features can be understood as the appearance of such replicas of the main FS. [4] We have carried out FS mapping experiments on leaddoped samples with a Pb to Bi ratio of 0.421.73 and a T, of 83K. [7] These crystals are modulation-free and the idea was to obtain a structurally simplified situation and through this clarity on the influence of the modulation on the SB. Figure l(c) displays the FS mapping on such a crystal. Clearly, the shadow bands are still present whereas the modulation related banana-like features do not appear. Transmission electron microscopy and low energy electron diffraction measurements (not shown) on these Pb doped samples show no indication of modulation related superlattice spots. However, faint diffraction spots occur corresponding to a larger real space layer unit cell with a lattice constant of about 5.4 A. Such a layer unit cell is identical to the one assumed in the model of AF correlations. Thus, the Pb doping provides the intended elimination of the modulation but it also introduces a larger layer unit cell than the primitive, Cu-0 plane related one with a lattice constant of about 3.8 A. Therefore, there are also arguments for a structural origin of SB in these crystals and the situation is not clear-cut. If all layers in the crystal have the larger unit cell, main bands and SB on the FS should exhibit almost identical intensities. This is clearly not the case. More structural information is needed to determine the atomic arrangement in this Pbdoped unmodulated high T, superconductor. While there is evidence for a larger layer unit cell somewhere in the three-dimensional unit cell AF spin correlations remain a probable origin of the SB.
W
C
Fig. 1. (a) Bi2212 PI1 mapping of the He1 (21.2 eV) excited photoelectrons collected within an energy window of about 30 meV 3. CONCLUSIONS Essential findings of our angle-scanned photoemission experiments [l] are: (i) no pronounced nesting is observed, (ii) the observation of a weak superstructure on the FS which coincides with SB predicted by Kampf and Schrieffer [S] based on the presence of AF spin fluctuations in the metallic state, and (iii) the identification of a second superstructure on the FS as due to the incommensurate lattice modulation present in the Bi-cuprates [4]. Measurements on Pbdoped, modulation free crystals also exhibit the SB. These crystals, however, exhibit weak diffraction spots corresponding to a layer unit cell identical
centered at &. A logarithmic intensity scale is used to enhance weaker features. (b) Outline of (a) indicating highqmmetry points and different sets of lines. (c) game as (a) but for a modulation-free lead-doped sample (see text).
to the one for a model with AF correlated spins. While this does not rule out AF correlations in the Cu-0 planes it does not clarify the situation. More structural information is required, truly magnetic measurements and/or FS maps on samples not presenting structural di5culties.
Acknowledgements- We wish to thank R. Fasel, R. Agostino, T.
Fermi surface mapping Kreutz and G. Margaritondo for stimulating discussions, D. Zech for the Te measurements and P Buerri and G. ‘Bolliet for the chemical analysis. Skillful technical assistance was provided by E. Mooser, 0. Raetzo, F. Bourqui and H. Tschopp. This work has been supported by the Swiss National Foundation and the NFP30.
RETERENcE3
1. Aebi P, Osterwalder J., Schwaller P., Schlapbach L., Shimoda M., Mochiku T. and Kadowaki K., Phys. Rev. Lett. 72,2757 (1994); Comment by Chakravarty S., Phys. Rev. Lett. 74,1885 (1995); Reply by P. Aebi, J. Osterwalder, P. Schwaller, L. Schlapbach, M. Shimoda, T Mochiku, K. Kadowaki, Phys. Rev. I&t. 74, 1886 (1995).
1847
2. Aebi P., Osterwalder J., Fasel R., Naumovioc D. and Schlapbach L., Surf: Sci. 307-309,917 (1994). 3. Osterwalder J., Greber T., Stuck A. and Schlapbach L., Phys. Rev. B 44, 13764 (1991); Namnovioc D., Stuck A., Greber T., Osterwalder J. and Schlapbach L., Phys. Rev. B 47, 7462 (1993). 4. Osterwalder 1, Aebi P.,Schwaller P., Schlapbach L., Shimoda M., Mochiku T. and Kadowaki K., Appl. Phys. A 60, 247 (1995). 5. Kampf A.P and Schrieffer JR., Phys. Rev. B 42, 7967 (1990); Phyx Rev. B 41, 6399 (1990). 6. Haas S., Moreo A. and Dagotto E., Phys. Rev. Left. 74, 4281 (1995). 7. Schwaller P., Aebi P., Beeli C., Osterwalder J., Berger H., Fasel R., Kreutz T.J. and Schlapbach L., in preparation.