Electron-positron P- and K-space densities in YBa2Cu3O7-δ

J. Phys. Chem. SolidsVol. 52, No. ll/lZ. Printed in Great Britain.

OOZZ-3697/91 93.M) + 0.00 PergamonPressplc

pp. 1535-1540, 1991

ELECTRON-POSITRON P- AND K-SPACE DENSITIES IN YBa2Cu307_8 H. HAGHIGHI, J. H. KAISER, S. RAYNER and R. N. WEST University of Texas at Arlington, Arlington, Texas 76019

J. 2. LIU and R. SHELTON University of California at Davis, Davis, California

95616

R. H. HOWELL, F. SOLAL, P.A. STERNE, and M. J. FLUSS LawrenceLivermom Abstract-

National Laboratory, Livermore, California

Wehaveperformedanultra-highprecisionmeasurrmurt(5x

94550

108coincidencecountr)ofthebasal-planeelectron-

positron momentum density (MD) in well oxygenated. twin-free, single crystals of YBa$u307_&

The anisotrcpies of the

raw and processed MD spectra and LCW-transformed spectra (k-space densities) not only show the h priate to the untwitmed crystals but, more imponantly, unambiguously

symmetry appro-

show a clear image of a major Fermi surface sheet.

‘IIe form of the FS image is in substantial agreement with theoretical predictions of a T-X electron ridge section associated with states in the Cu-0 chains.

Keywords: superconductivity,

eleckron-positron momentum distributions. Fermi surface, YBa$u307_6.

INTRODUCTION Since the discovery of high temperature superconductors, concentrated scientific effort has been directed at the elucidation of the nature of the electronic ground state and of the elementary excitations in those materials. Since present theories of high temperature superconductivity can be classified according to whether or not they require the existence of Fermi surface (FS), direct experimental observation of FS in these materials would impose a severe constraint on the acceptability of any such theory. There are only three experimental techniques which can presently provide the necessary details of the electronic structure at useful resolutions. These are angle resolved photoemission spectroscopy (ARPES), the de Haas-van Alphen technique (dHvA) and angular correlation of positron annihilation radiation (ACAR). ARPES measurements have provided evidence for a variety of FS sections in twinned YBa$u307_6

(YBCO) (Tobin et al, unpublished) and Bi&CaCu208

(Olsen et al,1990)

but only at specific sampling momenta. Novel dHvA studies in oriented polycrystalline samples of YBCO (Mueller et al, unpublished) have disclosed frequencies consistent with a small closedFS orbit predicted by band calculations and associated with states predominantly on the Cu-0 chains. The ACAR technique has a much higher momentum resolution and is much less sensitive to surface effects than is ARPES and can, in principle, expose

an overall FS topology in a single spectrum measurement However, the interpretation of the ACAR results

has, thus far, been complicated by the limited statistical precision of much of the data and, in YBCO, by the use of twinned crystals. The results (Smedskjaer et al, 1988; Peter, Hoffman and Manuel, 1988; Peter and Manual, 1989; Tanigawa, 1989; Haghighi et al, 1990; Sferlazzo et al, unpublished) have been in reasonable agreement in regard to the grosser features of the experimental spectra but have differed markedly in respect of the identification of finer structures in the processed spectra and their interpretation. This paper reports an ultra-high precision ACAR study of essentially twin-free YBCO crystals with a spectnun which provides one of the clearest displays by this technique of a major FS section in an electronically complex system. 1535

1536

H.

HACHIGHI

et al.

EXPERIMENTAL The measurements were performed with the new University of Texas at Arlington 2D-ACAR spectrometer on a planar assembly of six twin-free single crystals of YBCO. The crystals, prepared by the Lawrence Liver-more National Laboratory program at the University of California at Davis, were rendered essentiaIly twin-free by annealing under compression along the a direction (Liu et al.1990). This resulted in crystals that were twin-free over more than 90% of their area. Measurement of the DC magnetic susceptibility showed that all of the crystals had an onset of superconductivity above 92K. Two of the crystals had transitions significantly broader than the rest with mid-points at 85K. These data indicate that the level of oxygenation was high (6 - 6.9). The six crystals were attached by epoxy to a mesh of eight 25 p

diameter W wires. The crystals were brought into common

alignment to within 0.5 degrees by Laue back reflection X-ray photography. This assembly was then mounted so that the c axis of the samples was along the line connecting the detector centers and thea and b axes were along the x and y data axes respectively. The spectra were collected in a 256 by 256 channel matrix with a bin area of (0.143 mmd)2, at an instrumental angular resolution of 0.72 mrad (to 0.76 - 0.80 mrad when the effect of positron motion is included), and with the specimens at 300 K under a vacuum of 10-6 torr. The spectra were dumped every 2 x lo7 counts and, after individual analysis to verify the stability of the detection system, were later summed to form a consolidated raw spectrum of 2.5 x 108 counts (Set 1). In order to ensure the independence of all spectral features from the detection system, the sample-detector alignment was rotated by 90” and the same measurement procedure was repeated with x and y axes exchanged (Set 2). These raw spectra were then corrected for the efficiency function of the detector system and the isotropic portion of each spectrum was subtracted to produce anisotropic residuals for each of Sets 1 and 2 (Fig. la and lb respectively). Both of these residuals clearly show D2 symmetry in alignment with the crystalline axes as would be expected from contributions related to the Cu0 chains in untwinned YBCO crystals. Therefore, the data of each set was folded about the two major axes to provide two fully symmetrized correctedspectraeach equivalent to a distribution of lo9 counts. These two spectra were then rotated to the same orientation and summed to produce a final distribution containing 2 x lo9 counts.

-18

-12

-6

[lOOI

0

6

12 18 (mrad)

-12 -6 [OlOl

0

6

12 18 (mrad)

Figure l.- gray scale plot of the anisotropic residuals of the consolidated and corrected Set 1 (a) and Set 2 (b) spectra. White is high, black is low. The circle defines the outer limit of the isotropic subtraction processes.

Electron-positron

momentum densities in YBa$Tu&

1537

DISCUSSION Throughout the processing two main types of structure, already apparent in all the anisotropic residuals of the experimental spectra,became more clearand regular in the progressively more precise intermediate (figure 1) and final (figure 2) images. The first of these, the large closed regions of significant positive and negative excursion, often appear in this type of presentation. These structures are, as can be easily verified by forcing D4 symmetry on any of the spectra, fully consistent with those observed in our and others earlier studies of twinned specimens, and bear a similar in~~~~on in terms of wavefunction effects (Haghighi et al, 1990). The second and more remarkable of these was not seen in these earlier studies. This structure consists of two clot-~s~ght line discontinuities running parallel to the G-X direction and syrnrne~~~y ~sition~ at py = + (4@b + E). These structures were apparent in all of the partial spectra and very clear in the intermediate, consolidated spectra, In the final, fully symmetrized and corrected spectrum the equivalent discontinuity is sharp and statistically significant (> 3cr)throughout the range -8 mrad < px c +8 mrad, The sharpness of the break, the continuity over a range of c 24 mrad, and the symmetrical disposition in the original unsymmetrized spectra all point to a FS. Ail these features are quite remote from those expected of wavefunction effects.

18 12 6

-6

-18 18

-12

-6

0

py along [OIO]

6

12 18 (mrad)

Figure 2.- gray scale plot with contour overlay of the anisotropic residual of the corrected and s~rne~z~

final specwm. White is high, black is low. The circle defines the outer limit of the isotropic subtraction processes.

That these breaks mark a FS supports the results of numerous electronic structure calculations {Yu et al, 1987; Picket, Krakauer and Cohen, 1988; Bansil et a&1988;Bans& Mijnarends and Smedskjaer, 1990,199l; Picket, Cohen and Krakauer, 1990;Singh et al, 1990). These and our own LMTO calculations (figure 3) predict a quasitwo dimensional FS consisting of: two large ‘“barml”hole sections centered on S (arising from bands associated pr~omin~~y with the Cu-Oplanes),amuchsmaller holepocketats ~a~wo~nel~~“~dge”~n~r~ on and running roughly parallel to the T-X direction (both of which are due to bands associated with the Cu-0

1538

H. HACHIGHI et

al.

chains). Calculations of the corresponding electron-positron momentum density (Bansil et alJ988; Bansil, Mijnarends and Smedskjaer, 1990) and of the related electron-positronk-space density (Singh et al, 1990; Bans& Mijnarends and Smedskjaer, 199 1) are also in substantial agreement. On the one hand, they predictpoor definition of the barrel sections (because the positron resides predominantly on the chains) and the small closed S-pocket (because that section is small and may not even exist at small levels of oxygen depletion). On the other hand, they concur in their prediction of a well-defined manifestation of the ridge surface in the measured spectra.

Ourexperimental results are consistent with this overall theoretical picture. The major anisotropies are in close agreement with those predicted by Bansil et al (1990) and can be attributed to wavefunction effects. More importantly the line discontinuities visible in the anisotropic residuals of figures 1 and 2 are of the same form and are at almost exactly the same position as those arising from the FS ridge that appear at py = + (4x/b + E) in all the relevant sections of the theoretical momentum density (this discovery has been confirmed, see Smedskjaer et al (1991) in this volume). These d&continuities are particularly clear because they occur in outlying regions of the momentum density where wavefunction anisotropies are small. But other manifestations of the same FS section at lower momenta can also be found close to the lines py = 0 and py = + 2x/b. Figure 4 presents cross sections through the final spectrum for fixed values of px and demonstratesthe good correspondence with the more obvious of the corresponding discontinuities in the published theoretical sections (Bansil et al,1990).

X

-A-III_ Figure 3.- LMTO calculations of the basal-plane projected sheets of the Fermi surface of YBCO. The high symmetry points are marked in the top right quarter. We have found a clear image of the electron ridge but we have found no evidence of the other predicted FS SeCtiOnS in any of our raw or symmetrized momentum spectra. So clear an image of FS is nevertheless rare in essentially unprocessed momentum data and is more usually found only after that data has been transformed into a k-space density by the LCW procedure (Lock, Crisp and West, 1973). We applied that transformation to the final COrRCted and symmetrized data set after first subtracting the isotropic substrate(wire + epoxy) spectrum whose form and intensity (20%) had been determined in a subsidiaryexperiment. The essential results (Figure 5) are the expected

Electron-positron

momentum densities in YBa,Cu30,_,

1539

reinforcement of the original p-space discontinuities due to the electron FS ridge and the emergence of a major depression centered on S. The image of the electron ridge has a FWHM (marked by the extremities of the white region) - 1.3 mrad, a profile consistent with the resolution and is in good agreement with theoretical predictions of this FS feature (figure 3). An interpretation of the remaining depression around S as simply the smeared, composite image of the remaining three FS hole sections is tempting. But that interpretation cannot be entirely justified because: (i) there is no evidence of the sharper discontinuities already found for the ridge and (ii) roughly similar depressions also result when an angular averageof the same momentum density is identically transformed. On the other hand, the general form of the LCW distribution is compatible with theoretical predictions (Singh et al, 1990; Bans& Mijnarends and Smedskjaer, 1991) when the effects of wavefunctions, of oxygenation, and of resolution am taken into account.

r/a

W2a

!x/a -4x/b

-2lVb

0

Figure 4.- Integrated (over 5 channels or 0.74 mrad) sections through the anisotropy spectrum of figure 2. The positionsof theprincipaldiscontinuitiespredictedby arrows.

Bansiletal(l990)for

theFS ridgeare markedby thevertical

H. HACHIGHI et al.

1540

ACKNOWLEDGMENTS

This work was performed under the auspices of the US Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405ENG-48 and, at the University of Texas at Arlington, with the support of the Robert A. Welch Foundation (Grant No. Y- 1135) and the Texas AdvancedResearch Program (GrantNo. 003656133).

-6 -6

-4

Figure 5.- Electron-positronk-space

-2

0 (mrad)

2

4

6

density. White is high, blackislow. The high symmetry points are indicated

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