PHYSICAL REVIEW B VOLUME 40, NUMBER 16

phonon density of states in pb2Sr2(Ca, Y) Cu30g

1 DECEMBER 1989

R. Currat and A. J. DianouxInstitut Laue-Langevin, 156X avenue des Martyrs, 38042 Grenoble CEDEX, France

P. MonceauCentre de Recherches sur les Tres Basses Temperatures Centr-e National de la Recherche Scientigque,

166X avenue des Martyrs, 38042 Grenoble CEDEX, France

J. J. CapponiLaboratoire de Cristallographie, Centre National de la Recherche Scientigque,

166X avenue des Martyrs, 38042 Grenoble CEDEX, France(Received 15 August 1989)

The phonon density of states of the high-T, superconductor Pb2Sr2Ca0. 5Y0.5Cu308 has beenmeasured by the neutron time-of-flight technique. Comparison with the undoped nonsupercon-ducting compound Pb2Sr2 YCu308 shows small difrerences near 35 and 67 meV. Availablelattice-dynamical results suggest that the relevant spectral regions correspond to Sr and O(3)bond-bending modes in the first case, and O(1), O(2) bond-stretching modes in the second case.The results are discussed in the light of comparable results on other high-T, superconductors.

The lattice-dynamical characterization of the copper-based superconducting oxides is essential in order to assessthe role played by phonons and conventional electron-phonon coupling in the mechanism for high-T, supercon-ductivity.

A number of oxide compounds have been investigated,in both polycrystalline and single-crystal forms, using Ra-man and infrared spectroscopy and inelastic neutronscattering. Phonon anomalies have been observed inLa2Ni04 and La2Ni„Cui —„04 single crystals, which giveevidence for a large electron-phonon coupling strength lo-calized on the high-frequency oxygen "breathing" modes.

The phonon density of states (PDOS) of compounds inthe La2Cu04 and (Y,R)Ba2(Cu, M)sOs+s (R is a rareearth and M a metal) families has been extensively stud-ied as a function of temperature, oxygen, and/or dopantconcentration. ' Such studies are best performed in acomparative way, using the neutron time-of-Aight tech-nique with polycrystalline samples of superconducting andnonsuperconducting reference compounds.

So far no direct correlation is observed between the T,value and any unique feature in the PDOS of the corre-sponding compound. Varying the oxygen concentrationbetween Oz and 06 in YBa2Cu306+~ induces an upwardshift of the high-frequency cutoA' by —10 meV togetherwith a major loss of spectral weight in the 40-65-meV re-gion. ' ' These changes are too drastic to be associatedsimply with the removal of one of the oxygen atoms. Theyare thus believed to reAect changes in the electronic struc-ture of the Cu02 planes. This interpretation is supportedby results on doped (R Pr; M Co, Zn) nonsupercon-ducting samples ~here qualitatively similar, albeit moremodest, changes are observed. ' '

In this Rapid Communication we report on PDOS mea-surements on the recently discovered, ' lead-based super-conductors: PbzSr2Ca„Ri „Cu30s~s (R-Y, Eu, Sm,Pr). The structure of these compounds' ' is sketched in

Fig. 1. It is closely related to that of the other layered su-perconductors such as YBa2Cu306+~ and Bi2CaSr2Cu2-Os+s. It consists of the following: (a) a pair of pyramidalCu02 planes separated by an oxygen-free rare-earth planeand (b) a block of SrO-PbO-Cu-PbO-SrO planes. Due to

(3 Sr

Q} R, Ca

Q~ pb

0 (:u(1)

~ (u {2)

9 Q{1)

Q(2)

O Q(~)

FIG. 1. Tetragonal pseudocell of P12Sr2Ca R &—~Cu308.

The actual structure is based-centered orthorhombic with prin-cipal axes rotated by 45 in the basal plane.

~4 11 362 1989 The American Physical Society

PHONON DENSITY OF STATES IN Pb2Sr2(Ca, Y)Cu30s 1 1 363

G(a)) -e ' 2P sinh(P/2)S ) (g, ro)/a,

where S& (Q, ro) is the symmetrized one-phonon scatteringlaw and e is the Debye-Wailer attenuation factor.The dimensionless quantities a and P are related to themomentum and energy transfer variables through

g A toa2MkT kT

where M is an average atomic mass. Approximate analy-tic procedures to perform the Debye-Wailer and multi-phonon corrections in a self-consistent way have beendeveloped and are described elsewhere. The contribu-tion of the instrumental background and multiphononprocesses to the measured intensities is shown in Fig. 2.

The quantity plotted is

(2)

a slight orthorhombic distortion, the true unit cell is base-centered orthorhombic ' (Cmmm; Z =2), with crystallo-graphic axes rotated 45 from those shown in Fig. 1 . For

0 the excess oxygen atoms are accommodated in theCu(1) planes, which thus play the same role as the "chainsites" in YBa2Cu 306+q. However, due to the larger sepa-ration between Cu(1) and Cu02 planes, the oxygen con-centration 8 does not influence the hole carrier concentra-tion in the Cu02 planes, which is known to determine thesuperconducting properties of the compounds. Instead,the carrier concentration, and hence the value of T„ isdirectly correlated with the value of the divalent dopantconcentration, x.

Two compounds have been investigated, correspondingto R =Y, 8=0, x =0, and x =0.5. The samples wereprepared in powdered form according to the procedure de-scribed by Cava et al. ' The oxygen content was checkedby thermogravimetric analysis for the pure- Y sample.The Ca-doped sample showed weak additional powder-diN'raction lines corresponding to —5% of minorityphases. Due to this eA'ect and to the low stability of theCa-doped compound, the oxygen content could not bechecked by thermogravimetric analysis. However, lat-tice-parameter measurements indicate 6' =0, by compar-ison with the results of Gallagher et al. ' The Ca-dopedcompound is superconducting with an onset temperaturenear 78 K and a superconducting volume fraction of—20% at 20 K. This last result is deduced from ac mag-netic measurements and is very similar to that quoted inRef. 14.

The neutron time-of-flight (TOF) measurements wereperformed at the Institut Laue-Langevin using the IN6spectrometer in the up-scattering mode with an incidentneutron energy of 3.1 2 meV. The TOF spectra were col-lected over the full range of scattering angles (10-115 )and summed. Within the framework of the incoherentapproximation, ' a generalized or "neutron-weighted"PDOS is obtained after correcting for instrumental back-ground and multiphonon contributions:

2 ~ 0

V)

JD

1 ~ 0 » »

»»»»»x» »»»X

X»»

X» »X»1»»»» X»

0.0 1 00ENERGY {+eVj

200

spectral distribution P~(a,p) through

G(ro) =e'~ P)(a, P) (4)

and is shown in Fig. 3 for the x =0.5 sample at two tem-peratures: 300 and 480 K. The close agreement betweenthe two sets of data at large energy transfers (40 meV andabove) is indicative of the correctness of the data-reduction procedure, including Debye-Wailer and multi-phonon corrections.

The PDOS curves shown in Figs. 3 and 4 are not decon-voluted for finite instrumental energy resolution. Thelatter varies from 0.1 meV at 1 meV to 17 meV (FWHM)at 80 meV energy transfer. The smooth high-energy tailis thus, to some extent, due to instrumental broadening.From lattice-dynamical calculations, ' one expects ahigh -energy cutoA near 80 meV. It is clear, however, thatsuch a value is not consistent with the data in Fig. 3. Bynumerical convolution with our known resolution func-tion, we find that any reasonable PDOS curve must ex-

X102.4

FIG. 2. Measured spectral distribution P(a,p) for Pb2Sf�-2Cap�5,5Cu308 at 300 K. The data (+ with error bars) must becorrected for instrumental background (taken as constant inTOF units; solid line), multiphonon contributions (x ), andDebye-Wailer attenuation.

P(a,P) =2P sinh(P/2)

a0.0 6 0

ENERGY I fneV )

1 20

where S(g, ro) is the uncorrected symmetrized scatteringlaw. The generalized PDOS is derived from the corrected

FIG. 3. Generalized phonon density of states for Pb2Sr2-Cap 5Yp gCu308 at 480 K (solid line) and 300 K (+ ).

11 364 CURRAT, DIANOUX, MONCEAU, AND CAPPONI

tend at least up to 100 meV in order to reproduce our ex-perimental curves.

A similar difficulty has been encountered in the analysisof the YBa2Cu306+b spectra where a high-energy tail isobserved for all oxygen concentrations 0&8& 1. Thepossibility of an experimental artifact (multiple scatter-ing, inadequate multiphonon correction, etc.) is undercurrent investigation. No such difficulties arise for testsystems such as vanadium, aluminum, and insulatingperovskites (KTa03, BaTi03). In these cases, the intensi-ty observed above the known PDOS high-frequency cutoA'can be accounted for by the combined effect of resolutionbroadening, instrumental background, and multiphononcontributions.

Figure 4 shows a comparison of the experimentalPDOS curves for the x =0.0 and x=0.5 samples. Bothdata sets were measured at 300 K, in a vacuum tight fur-nace, after in'situ annealing at 480 K, for 4 h, under vacu-um. This procedure guarantees that the samples are freefrom moisture, even in small amounts.

Once normalized to the same area, the two curves arevery similar. This result is reminiscent of the rather mod-est diA'erences found ' between doped and undoped corn-pounds in the La2CuO4 family and contrasts with the verylarge diA'erences observed as a function of oxygen concen-tration in the 1:2:3 compounds. The regions where thetwo curves in Fig. 4 diA'er in shape are located near 35 and67 meV. It is tempting to try and ascribe these diA'erencesto particular modes, although the only lattice-dynamicalmodel available for Pb2Sr2YCu308 has only been used topredict the zone-center optical frequencies. '

The region from 30 to 40 meV appears to correspond tothe lowest frequency oxygen O(3) (bond bending) vibra-tions. Kress eE aI. ' found the following: an A~g mode at249 cm ' (3l meV) involving in-phase Sr, and O(3),displacements; a 82„mode at 281 cm ' (35 meV) involv-

ing O(3), displacements only; and the corresponding 8~+mode at 336 cm ' (42 meV). This last mode has beendefinitely identified by Raman scattering at 325 cm(40.5 meV).

The region from 60 to 74 (480 to 590 cm ') appears toinvolve mostly O(1) and O(2) bond-stretching vibrations.From the same work ' we note the following zone-centerfrequencies: an A ~~ mode at 483 cm involving primari-ly O(1), vibrations; the corresponding TO-LO A2„pair at469 and 487 cm '; similar modes polarized in the basalplane (Eg+E„) in the range from 490 to 510 cm '; andfour modes between 560 and 590 cm involving primari-ly a vibration of O(2) either along z (A ~g+A2„) or in thebasal plane (Es+E, ).

In the 1:2:3 family, the region from 40 to 60 meV isstrongly enhanced for the superconducting member. Thisregion is dominated by bond-bending vibrations involvingthe oxygens in the Cu02 planes [oxygen O(3)]. These vi-brations are found to have very similar frequencies here.In particular, there is a set of four modes between 375 and465 cm ' (A~+, A2„,E„,Ez), which, at least for the A~g

x102.4-

TI

QJE:12

L3

V

C3C3CL

0.0 60

E NERGY (meV j

120

FIG. 4. Generalized phonon density of states for Pb2-Sr2Ca, Y~ — Cu308 at 300 K: x O.S (solid line); x 0.0 (x).

member, involve a bond-bending O(3) vibration. It isnoteworthy that the two curves in Fig. 4 coincide in thisfrequency region, indicating that these vibrations are notaA'ected by doping in the present case. A similar remarkmay be formulated concerning the upper end of the spec-trum which includes the bond-stretching O(3) "breath-ing" modes. These vibrations have been shown to play animportant role in the La2Cu04 family, based on polycrys-talline ' and single-crystal neutron measurements. Oneis thus led to conclude that the electron-phonon couplingmechanism in the various superconducting oxides is notconcentrated on a single type of lattice vibration. The ob-served phonon "anomalies" tend to affect the upper fre-quency part of the PDOS distribution, which establishesthat, in all cases, oxygen vibrations are involved. Howev-er, diA'erent types of oxygen vibrations seem to be aA'ectedin each case. At most one may note a correlation betweenthe frequency range of the possible anomalies and the T,value of the superconducting member: 80 to 90 meV inLa~ s5SI'p ~5Cu04 (T, =38 K); (mostly) 60 to 75 meV inthe Pb-based compound (T, =78 K); and 40 to 60 meV inYBa2Cu07 (T, =92 K).

Finally, one should stress that the mode assignmentsare performed on the basis of calculated zone-center fre-quencies. These calculations appear to be in good generalagreement with available optical results. However, someof the phonon branches can be highly dispersive and an-isotropic when going away from the Brillouin-zone center.This is a well-known feature in ionic or partly ionic sys-tems where large cancellation eA'ects occur between theCoulomb and short-range overlap forces. Thus, if the im-portant electron-phonon mechanisms affect primarilymodes with finite wave vectors, as recently suggested, "'the character of such modes may be very different fromthat of the zone-center modes which happen to lie in thesame frequency range.

PHONON DENSITY OF STATES IN P12Sr2(Ca, Y)Cu30s 11 365

'For a recent survey, see, e.g. , Proceedings of the InternationalConference on Materials and Mechanisms of Superconductr'vity and High Temperature Superconductors, edited by J.Muller and J. L. Olsen [Physica C 153-155 (1989)].

zC. Thomsen and M. Cardona, in The Physical Properties ofHigh T, S-uperconductors, edited by D. M. Ginsberg (WorldScientific, Singapore, 1989).

H. Rietschel, J. Fink, E. Gering, F. Gompf, N. Nucker, L.Pintschovius, B. Renker, W. Reichardt, H. Schmidt, and W.Weber, in Ref. 1, p. 1067.

L. Pintschovius, J. M. Bassat, P. Odier, F. Gervais, B. Hennion,and W. Reichardt, Europhys. Lett. 5, 247 (1988); in Ref. 1, p.276.

5B. Renker, F. Gompf, E. Gering, N. Nucker, D. Ewert, W.Reichardt, and H. Rietschel, Z. Phys. 8 67, 15 (1987).

A. P. Ramirez, B. Batlogg, and G. Aeppli, Phys. Rev. B 36,8833 (1987).

7M. J. Rosseinsky, K. Prassides, P. Day, and A. J. Dianoux,Phys. Rev. 8 37, 2231 (1988).

A. V. Belushkin, E. A. Goremychkin, I. Natkaniec, I. L.Sashin, and W. Zajac, Physica C 156-157, 906 (1989).

F. Gompf, B. Renker, and E. Gering, in Ref. 1, p. 274.'OP. Strobel, P. Monceau, J. L. Tholence, R. Currat, A. J. Di-

anoux, J. J. Capponi, and J. G. Bednorz, in Ref. 1, p. 282.I. Natkaniec, A. V. Belushkin, J. Mayer, R. K. Nikolaev, V.K. Fedotov, E. A. Goremychkin, E. G. Ponyatovski, I. L.Sashin, and N. S. Sidorov, Pis'ma Zh. Eksp. Teor. Fiz. 48,152 (1988) [JETP Lett. 4$, 166 (1988)l.

' B. Renker, F. Gompf, E. Gering, G. Roth, W. Reichardt, D.Ewert, H. Rietschel, and H. Mutka, Z. Phys. B 71, 437(1988).

' B. Renker, F. Gompf, E. Gering, D. Ewert, H. Rietschel, andA. J. Dianoux, Z. Phys. 8 73, 309 (1988).

'4R. J. Cava, B. Batlogg, J. J. Krajewski, L. W. Rupp, L. F.Schneemeyer, T. Seigrist, R. B. van Dover, P. Marsh, W. F.Peck, Jr., P. K. Gallagher, S. H. Gharum, J. H. Marshall, R.C. Farrow, J. V. Waszczak, R. Hull, and P. Trevor, Nature(London) 336, 211 (1988).

'~R. J. Cava, M. Marezio, J. J. Krajewski, W. F. Peck, A. San-toro, and F. Beech, Physica C 157, 272 (1989).

~6E. A. Hewat, J. J. Capponi, R. J. Cava, C. Chaillout, M.Marezio, and J. L. Tholence, Physica C 157, 509 (1989).

' L. F. Matheiss and D. R. Hamman, Phys. Rev. B 39, 4780(1989).

~ P. K. Gallagher, H. M. O'Bryan, R. J. Cava, A. C. W. P.James, D. W. Murphy, W. W. Rhodes, J. J. Krajewski, W. F.Peck, and J. V. Waszczak, Chem. Mater. 1, 277 (1989).

' P. A. EgelstaA' and P. Schofield, Nucl. Sci. Eng. 12, 260(1962).

A. J. Dianoux and R. Currat (unpublished).'W. Kress, J. Prade, U. Schroder, A. D. Kulkarni, and F. W.

De Wette (unpublished).R. Liu, M. Cardona, B. Gegenheimer, E. T. Heyen, and C.Thomsen (unpublished).C. H. Perry, R. Currat, H. Buhay, R. M. Migoni, W. G. Stir-ling, and J. D. Axe, Phys. kev. 8 39, 8666 (1989).

24M. Tachiki and S. Takahashi, Phys. Rev. 8 38, 218 (1988).25Y. Fukuda, M. Nagoshi, T. Suzuki, Y. Namba, Y. Syono, and

M. Tachiki, Phys. Rev. 8 39, 2760 (1989).