PHYSICAL REVIE%' 8 VOLUME 48, NUMBER 1 1 JULY 1993-I

Phonon density of states in R 2Cu04 and superconducting R t s5 Ceo t 5Cu04 (R =Nd, Pr)

I. W. Sumarlin and J. W. LynnDepartment ofPhysics, Center for Superconductiuity Research, Uniuersity ofMaryland, College Park, Maryland 20742

and Reactor Radiation Division, National Institute ofStandards and Technology, Gaithersburg, Maryland 20899

D. A. Neumann and J. J. RushReactor Radiation Diuision, National Institute ofStandards and Technology, Gaithersburg, Maryland 20899

C-K. LoongIntense Pulsed Neutron Source, Argonne National Laboratory, Argonne, Illl'nois 60439

J. L. Peng and Z. Y. LiCenter for Superconductiuity Research, Department ofPhysics, Uniuersity ofMaryland, College Park, Maryland 20742

(Received 13 November 1992)

Inelastic-neutron-scattering measurements of the generalized phonon density of states (GDOS) for theelectron-doped superconductors Nd& g5Ceo»Cu04 and Pr, ~&Ceo»Cu04 have been carried out with theuse of both a filter-detector method and time-of-Aight spectroscopy. A measurement of the GDOS forthe insulating Pr2Cu04 was also done for comparison with that of Pr&»Ceo»Cu04, while a more limitedset of data was obtained for Nd2Cu04. Comparison between the GDOS spectrum of theNd, 85Ceo»Cu04 with that of Pr, 85Ceo»Cu04 shows differences in the shape of some structures in theGDOS spectrum. Furthermore, there are substantial changes in the GDOS spectrum ofPr, 85Ceo»Cu04 as compared to that of Pr2Cu04, particularly in the energy regime between 33 and 63meV. In the Nd&»Ceo»Cu04 system, where electron-tunneling measurements have been performed,there are similarities between the GDOS spectrum and the Eliashberg-coupling function a F(co) ob-tained from the tunneling data in the energy regions where comparisons can be made. To the extent thatthis comparison is valid, it suggests that phonons are to some extent involved in the electron-pairingmechanism in these electron-doped superconductor systems. We have also determined the ground-statecrystal-field excitations associated with the rare-earth ions (Nd', Pr' ). The Nd'+ crystal-field levelsare observed at energies of 13, 20.7, 26.4, and 93 meV in superconducting Nd& 85Ceo»Cu04. For thePr2Cu04 system, the Pr'+ crystal-field excitations are found at 18.6 and 87.9 meV. These peaks broadenand split when doped to form superconducting Pr& 85Ceo»CuO&. The observed crystal-field levels in theabove systems are in good agreement with those reported by other groups.

I. INTRODUCTION

The role of phonons in the mechanism of superconduc-tivity for the high-T, oxide superconductors is stilllargely an open issue. Historically, one indication for theelectron-phonon mechanism in conventional supercon-ductors has been the isotope effect ( T, 0- M ), wherethe BCS value for the isotope exponent is a= —,'. For thecopper-oxide superconductors, the oxygen exponent ahas been found to depend on the carrier concentrationand T, . In fact, for hole-doped superconductors thevalue of a has a decreasing trend with increasing T, andwith increasing number of CuO layers, n, with the excep-tion of YBa2 „Sr„Cu307. In the electron-doped super-conductors such as Nd, s~Ceo &sCuO4 (T, —=25 K)," a hasbeen found to be very small (a ~0.05). The absence ofan isotope efFect by itself, of course, does not rule out aphonon-mediated pairing mechanism. Indeed, there issubstantial evidence from inelastic neutron scatteringthat the phonons are involved in the superconductingstate, both in the present moderate-T, electron supercon-

ductors, as well as the high-T, materials YBa2Cu307(Ref. 8) and Bi2Sr2CaCu208.

One of the most direct experimental probes of theelectron-phonon coupling in superconductors is a corn-parison of the electron-phonon spectral function a F(to)determined by electron-tunneling measurements withphonon density-of-states spectra measured by neutronscattering. ' This approach has been used in theBa, K„Bi03 system" (T, =—30 K, et=0. 41)„' wherereasonably good agreement was found between the tun-neling and neutron data. ' Electron-tunneling measure-ments have also been made on single crystals ofNd, 85Ce0, 5CuOz grown in our laboratory, "and as a re-sult we embarked on a determination of the phonon den-sity of states in these systems to compare with the tunnel-ing data. We have measured the generalized phonondensity of states (GDOS) on polycrystalline samples ofsuperconducting Nd& 85Ceo &5Cu04 and Pr& 85Ceo &5CuO4,as well as on insulating Pr2CuO4. We have also obtaineda limited set of data for Nd2Cu04. For theNd& ~5Ceo &5Cu04 material where tunneling data have

0163-1829/93/48(1)/473(10)/$06. 00 473 1993 The American Physical Society

SUMARLIN, LYNN, NEUMANN, RUSH, LOONG, PENG, AND LI 48

been obtained, we And that there are indeed some similar-ities between the two sets of data. Of course, in the an-isotropic copper-oxide systems tunneling experiments ac-curate enough to extract a F(co) are generally verydifficult to perform due to the short coherence lengths, '

and any observed similarities between a F(co) and theG-DOS have to be viewed with some reservations. Mea-surements of the phonon density of states, on the otherhand, are less difficult to make, although in the presentsystems separating the magnetic (crystal-field) excitationsfrom phonon scattering also presents some challenges.Nevertheless, the present GDOS measurements shouldserve for comparison purposes as more refined tunnelingdata become available.

In principle, there are two methods to determine thephonon density of states via inelastic neutron scattering.One method is to make extensive measurements of thephonon dispersion relations, generally along high-symmetry directions in reciprocal space, at as many re-duced wave vectors as possible. Large, high-quality sin-gle crystals, of both the parent insulating systems and thedoped superconducting materials, are needed for thesetypes of measurements. Ideally, these measurements canthen be compared with model calculations of the disper-sion relations, and the model parameters are then adjust-ed to achieve a reasonable description of the dispersionrelations. The model is then used to obtain an estimate ofthe phonon density of states. However, in the presentsystems where there are many phonon modes (21 in thepresent case), the model calculations play a much moreimportant role in that they generally must be used to as-sign each measured phonon group to a specific phonondispersion relation. The phonon energy and intensity in-formation is then fed back into the model to make newpredictions, and this type of iterative process is used toboth conduct measurements and interpret data. Cxeneral-

ly, this is not a straightforward procedure, and moreoverthe model must be simplified for calculational purposes.In the Anal analysis there are typically significantdiscrepancies between the calculated and observed ener-gies along the high-symmetry directions. ' ' To accu-rately calculate the phonon density of states, however,one must rely on the model to generate the correct pho-non energies at all q values, not only along the high-symmetry directions, but also throughout the Brillouinzone. In the case of the doped Nd&»Ceo, ~Cu04 andPr, »Ceo»Cu04 alloys of primary interest, it is not clearhow well the partial, random substitution of Nd by Cecan be modeled by lattice dynamical calculations. There-fore the reliability of the density of states obtained withthis method is difficult to assess in these complicated ma-terials.

The second method is to directly measure the general-ized phonon density of states via inelastic neutronscattering from polycrystalline materials, which has thedistinct advantage that a model-independent determina-tion can be made. For a single-component system (suchas Pb), a measurement of the GDOS would in fact reAectthe true phonon density of states. In a multicomponentsystem such as the present materials, on the other hand,this method has the drawback that the data are weighted

by (cr; /m; ), where a; is the nuclear scattering cross sec-tion and m; is the mass of the ith ion, hence the term"generalized" phonon density of states. It is important tokeep in mind when comparing the tunneling and neutrondata that in fact neither technique directly measures thephonon density of states F(co); the tunneling data areweighted by the electron-phonon coupling a . Hence, forthese multicomponent oxide systems, we cannot expectthe detailed correspondence that can be obtained for sim-ple systems such as lead.

The presence of magnetic rare-earth ions (Nd +,Pr +)in these electron-superconductor systems and the mag-netic Cu + spins means that there are also magnetic con-tributions to the scattering. ' ' The rare-earth spins or-der at very low temperatures (Tz ~2 K), ' ' while theCu spins order at high temperatures ( T&-250 K) in theinsulating compounds. ' ' In the present materials theCu ions have a small moment and thus scatter weakly.Moreover, this magnetic scattering is spread over a widerange in energy, and indeed it is the large energy scaleassociated with this magnetism that has supported thespeculation that it is directly connected with Cooperpairing. It is unlikely that the inelastic magnetic scatter-ing from the Cu spins can be observed at all in these poly-crystalline samples —single crystals are required to ob-serve this.

The rare-earth —rare-earth interactions, on the otherhand, are very weak, giving rise to ordering temperaturesof a few degrees K or less. Hence the crystal-field excita-tions have little dispersion and thus give rise to sharp, Q-independent peaks in the inelastic spectra. Most of thesepeaks are very strong due to the large rare-earth mo-ments and are easily identi6ed. %'e note that the crystal-field excitations we have observed are in good agreementwith those reported by other groups, ' but in somecases we have been able to take data with better resolu-tion than previous measurements. At the energies wherethese crystal-field excitations occur, however, it is notpossible to separate the magnetic from phonon scattering.Furthermore, at elevated temperatures additionalcrystal-6eld transitions can be observed via the thermalpopulation of excited states, while the crystal-6eld transi-tions tend to broaden. This makes temperature-dependent measurements of the GDOS very difficult.Fortunately, the temperature region of interest is at andbelow T, (-25 K), and consequently we have restrictedour measurements to low temperatures. We note thatpreliminary reports of our measurements have alreadybeen presented. '

II. KXPKRIMENTAI. PROCEDURES

For coherent scatterers with vibrational energy Ace, theone-phonon cross section in the incoherent approxima-tion is given by

0 kfdQd k,

with

PHONON DENSITY OF STATES IN R2Cu04 AND. . .

Pl~ CO

(2)

where c, o, m, e, 8' (Q), and F are the concentra-tion, total coherent scattering cross section, mass, pho-non unit-polarization vector, Debye-Wailer factor, anddensity of states, respectively, for the jth atom. k, and

kf are the incident and final neutron wave vectors, fiQ isthe momentum transfer, and n (co) is the Bose thermal oc-cupational factor. At low temperatures the thermal fac-tor n(co)+1 = 1, and the effect by the Debye-Wailer fac-tor is assumed to be small for each ion. The quantitywithin the angular bracket ( . ) is averaged over allmodes with energy Ace, and this also includes averagingover all Q directions for polycrystalline materials. Theabove equation contains the generalized phonon densityof states p

p=g ' ' ((Q e, )'e ')+, (~) .j j

(3)

The incoherent approximation is best realized under ex-perimental conditions with large values of Q. However,for moderate Q values, it has been shown that a reliableGDOS can be obtained by averaging over a range ofscattering angles. The contribution to the GDOS fromeach F~(co) is weighted mainly by o,. /m, , which for Nd,Pr, Ce, Cu, and 0 are, respectively, 0.11, 0.15, 0.02, 0.12,and 0.26 b/amu. The phonon cross sections are thereforeparticularly sensitive to scattering from oxygen vibra-tions.

The main technique we used to measure the GDOS isthe filter-detector technique. These data were collectedat the BT-4 spectrometer at the National Institute ofStandards and Technology Research Reactor. The pri-mary experimental advantage of this technique is that itprovides excellent signal to noise while maintaining goodenergy resolution. The technique employs a thick poly-crystalline block of Be in front of the detector, whichtransmits only neutrons with a final energy Ef ~5 meV.The scattering intensity as a function of energy is thenobtained by varying the incident neutron energy. Im-proved energy resolution can be obtained with this sametechnique by using a combination of polycrystalline Beand powder graphite, which restricts Ef to ~1.8 meV.Since Ef is quite small, we have that Q =k, , and we seethat the wave vector and energy transfer are directly cou-pled. This also means that Q /co is a constant in Eq. (2),and hence to a good approximation the observed intensi-ty is directly related to the GDOS. With this technique apyrolytic graphite PG(002) monochromator was em-ployed for energy transfers ~40 meV, and we used col-limations of 20'-20' before and after the monochromator.For the range of higher-energy transfers (34—120 MeV),a Cu(220) monochromator was employed, with 40'-40'collimation. In the low-energy regime (0—20 me V),where the measured Q becomes small for the filter-detector technique, we supplemented these data with datataken with the conventional triple-axis technique. In the

triple-axis arrangement, Ef was fixed to 28 meV by use ofa graphite analyzer, and measurements were made by theconstant-Q technique for 3 & Q &6 A ' (see Table I).The procedure for determining the GDOS by the triple-axis method includes averaging the data taken withdifferent Q values to average out any coherency effects.The data were also corrected for A, /2 contamination inthe incident beam. The triple-axis measurements weretaken on the BT-2 and BT-4 triple-axis spectrometers atNIST, with collimations of 60'-40'-20'-40' with a Cu(220)monochromator or 40'-40'-40'-40' with a PG(002) mono-chromator.

In order to identify possible weak crystal-field peaks inthe scattering spectrum, we supplemented the filter-detector method with the time-of-fiight (TOF) technique,where the Q dependence of the scattering can be used todifferentiate phonon scattering ( ~ Q ) from the magneticscattering which is proportional to the square of the mag-netic form factor f(Q). The time-of-flight data were ob-tained with the low-resolution-medium-energy chopperspectrometer (LRMECS) at the Intense Pulsed NeutronSource (IPNS) at Argonne National Laboratory. In theTOF technique, monochromatic neutrons are incident onthe sample and the scattering at various energy transfersare obtained through their time of flight from the sampleposition to the 28 detector groups which span a rangefrom —7' to 117' with respect to the incident beam. Cali-bration of the He detectors was made using scatteringfrom a vanadium standard. The data reduction pro-cedure involves averaging over a range of Q values, againto average out any coherency effects. For energytransfers ~ 40 meV, neutrons with incident energyE, =50 meV were used, while for higher-energy transfersneutrons with incident energy E, =130 meV were em-

ployed. The various instrumental configurations aresummarized in Table I along with some typical energyresolutions.

Data were obtained on polycrystalline samples ofNd &. 8sCeo &5CuO&, Nd2Cu04, Pr2Cu04, andPr& 85Ceo &5CuO~ weighing -47, —10, -40, and -40 g,respectively. All the samples were prepared by the usualmethods. ' The samples were encased in a rectangularAl can with dimensions 10X5 XO. 11 cm for the TOF ex-periments, whereas a sample can of size 4.5X4.5X0.69cm was used for the filter-detector method experiments.Measurements were made at a temperature of 18 K atIPNS using a closed-cycle helium displex refrigerator andat a temperature of 4.2 K at NIST with a He cryostat.Low temperatures were necessary to avoid scatteringoriginating from transitions between crystal-field excitedstates. For both methods, corresponding backgroundruns were taken with an empty A1 can at the sample posi-tion. In addition to the background correction, datawere also corrected for multiphonon contributions whichwere approximated by self-con voluting the phononfeatures in the spectrum. The result of this convolutionis a featureless profile which increases approximatelylinearly up to an energy transfer well above the phononcutoff frequency. Thus correction for the multiphononcontribution was made by subtracting from thebackground-corrected data a linear function which is ex-

SUMARLIN, LYNN, NEUMANN, RUSH, LOONG, PENG, AND LI

TABLE I. Instrumental configurations used for the inelastic-neutron-scattering experiments and thecorresponding resolutions. TOF, time of flight; Be, Be-graphite-Be filter; T, triple axis; PG, pyrolyticgraphite (002) monochromator; Cu, Cu(220) monochromator.

No. Mode

TOFTOF

Be-PGBe-CuT-PGT-Cu

Collimations

20'-20'40'-40'

40'-40'-40'-40'60'-40'-20'-40'

(meV)

50130

(meV)

—1

28'28'

Energy resolutions(meV)

2.5 at E=36 meV3.2 at E=93 meV1.7 at E=18 meV4.3 at E=93 meV3.3 at E=10 meV1.7 at E=10 meV

'PG(002) analyzer.

trapolated from scattering at an energy well above thephonon cutoff frequency.

III. RESULTS AND DISCUSSIQN

The spectra obtained with the filter-detector methodare shown in Fig. 1, with an expanded view displayed inFig. 2, for the Nd, s~Ceo»Cu04 (top), Pr, s5Ceo»Cu04(middle), and Pr2Cu0~ (bottom) systems. All the datashown were corrected for background and multiphononcontributions as explained in the previous section. Thepeaks that are readily observed in Fig. 1 are those origi-nating from ground-state crystal-field excitations. Forthe Nd& 8~Ceo»Cu04 spectrum, a sharp crystal-field peakat 20.7 meV and another broader excitation at 26.4 meVcan be clearly seen in the top of Fig. 1. We have also tak-en a limited set of measurements on Nd2Cu04, where wefound that these two crystal-field peaks are shifted by lessthan 1 meV to higher energies. The crystal-field peak at-26 meV in the Nd& 85Ceo»Cu04 system has a widththat is considerably broader than the width of the samepeak in the parent Nd2Cu04 system, and this broadeningis likely caused by the random substitution of Ce,affecting the crystal-field environment. There are alsocrystal-field levels at energies 93 and 13 meV, which canbe seen in the top of Fig. 2. Both these peaks have widthsthat are somewhat 1arger than the instrumental energyresolution. There is no single-phonon GDOS scatteringabove 83 meV, and therefore the peak at -93 meV is dueto purely magnetic scattering. The peak at 13 meV, onthe other hand, has both magnetic and phonon contribu-tions as we will show below when we present the TOFdata.

For the PrzCu04 system, two crystal-field peaks areeasily observed at 18.6 meV (bottom of Fig. 1) and at 87.9meV (bottom of Fig. 2), in agreement with previous re-ported results. ' However, these data have been takenwith higher resolution than previous measurements. Thepeak at 18.6 rneV has a resolution-limited width of 1.5meV, and we note that it is much stronger than the peakat 87.9 meV. Recalling that Q varies with b,E for thefilter-detector method, we anticipate a reduction in inten-sity at the higher energies due to the decreasing magneticform factor, but this only accounts for a factor of 3 inthis case. We also note a small shoulder at -22 meV,

which originates from the -88-meV crystal-field excita-tion via k/2 contamination of the incident beam at thisenergy. We remark that generally A, /2 contamination isonly a problem for energy transfers below ~ 30 meV andthen only in cases where there is a strong excitation athigh energies.

It can be seen from the figures that the crystal-fieldpeaks in the Pr2Cu04 system undergo broadening andsplitting when the system is doped with Ce to formPr& 8~Ceo»Cu04. The peak at 18.6 meV broadens andsplits into peaks at 15 and 17.9 meV, and the peak at—88 rneV appears to split into two peaks at 81 and —88meV (middle of Fig. 2). All of the observed crystal-fieldpeaks in our data are summarized in Table II and are ingood agreement with those reported by othergroups. ' Although various groups agree on the ob-served crystal-field excitations, the proposed detailedcrystal-field level schemes are subject to different inter-pretations.

Figure 2, which is an enlargement of Fig. 1, illustratesthe phonon scattering of interest. The phonon spectrumis rich in structure, as might be expected since these sys-tems contain a large number of branches (21). There hasalso been substantial dispersion observed in many phononbranches, as, for example, in NdzCu04 where the disper-sion relations have been measured in considerable de-tail. ' Indeed, we note that there is little correspondencebetween the observed peaks in the GDOS and the excita-tions observed via Raman scattering or IR absorption.In the top figure, the Nd, 8~Ceo»Cu04 phonon density ofstates is seen to extend up to an energy of 83 meV, fol-lowed by a broad crystal-field peak at -93 meV. In theenergy region from —17 to 30 meV, the phonon scatter-ing is masked by the strong crystal-field peaks. Outsidethis region, the spectrum contains obvious peaks at ener-gies —13 and -36 meV. We remark that we observed abackground peak at —36 meV due to the Al phonon den-sity of states from the sample holder, and we have takencare to avoid "overcorrecting" this contribution by tak-ing into account the sample absorption factor at this en-ergy. The rest of the GDOS spectrum contains smallpeaks at -42 and 52 rneV, which sit on top of a broaderpeak, followed by another broad peak around 64 meV.There are shoulders at energies -72 and -78 meV be-fore reaching the cutoff frequency.

PHONON DENSITY OF STATES IN R2Cu04 AND. . . 477

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Energy (meV)FIG. 1. Top portion of the figure shows the magnetic Nd'+

crystal-field scattering for the Nd&»Cep»Cu04 system at ener-gies of 20.7 and 26.4 meV. The bottom portion of the figureshows the Pr + crystal-field peaks at 18.6 and 87.9 meV for thePr2Cu04 system. These peaks split and broaden as the system isdoped to form superconducting Pr&»Cep»Cu04 (middle). Allof the above spectra were taken using the filter-detector methodand have been corrected for background and multiphonon con-tributions.

The GDOS spectrum for the Pr, 85Cep»Cu04 systemshown in the middle of Fig. 2 appears to be somewhatdifferent than the Nd& 85Cep»Cu04 system despite theirbeing isostructural. These differences cannot be attribut-ed to the change in the scattering length for the rare-earth alloys as most of the rare-earth vibrational modesoccur in the region below 30 meV owing to the heavymasses of the rare-earth ions. ' The difference betweenthe two GDOS spectra consists primarily in changes ofthe intensities of some structures, without apparent shiftsin the energies. The peaks at 36 and 42 me V inPr, 85Cep»Cu04 have difFerent relative intensities com-pared to the corresponding peaks observed in theNd

& 85Cep»Cu04 spectrum. The broad feature at —52meV observed in the Nd& 85Cep»Cu04 spectrum becomesa relatively sharp peak in the Pr& 85Cep»Cu04 spectrum.In the energy range of 58—76 meV, the two spectra are ingeneral agreement. The precise phonon cutoff frequency

FIG. 2. Same data as in Fig. 1, plotted on a scale where thegeneralized phonon density of states (GDOS) can be observed.The peaks at -93 meV in the top figure and at —88 meV in themiddle and bottom are magnetic crystal-field peaks. The peakat 13 meV in the Nd& g,Cep»Cu04 spectrum contains contribu-tions from both magnetic and phonon scattering.

in the Pr& 85Cep ~5Cu04 cannot be determined sincescattering above -76 meV is dominated by the neighbor-ing crystal-field peak.

For the Pr2Cu04 system, we observe a phonon peak at-30 meV. The observation of this feature is only possi-ble due to the sharpness of the crystal-field peak at —18meV; it is not possible to observe this feature in thePri 85Cep»Cu0& sample. On the other hand, the relative

Nd) g5Cep»Cu04E.„, (meV)

13.0+0.420.7+0.226.4+0.293.1+0.4

Pr)»Cep»Cu04Epbs (meV)

15.0+0.417.9+0.481.0+1.087.9+0.4

Pr2Cu04E,b, (meV)

18.6+0.2

87.9+0.4

TABLE II. Observed energies for the crystal-field peaks inNd& g&Cep»Cu04, Pr& g5Cep»Cu04, and Pr2Cu04 measured at atemperature of 4.2 K.

478 SUMARLIN, LYNN, NEUMANN, RUSH, LOONG, PENG, AND LI

intensities of the various structures of the GDOS spec-trum in Pr, 85Ceo»Cu04 change substantially in intensi-ty, particularly in the energy region of 33—63 meV; thereare no dramatic shifts in the energies of phonon struc-tures between the two spectra. In the Pr2Cu04 spectrum,the peak around 52 meV is broader (and perhaps split)than the corresponding peak in the Pr, 85Ceo»CuO~spectrum. The peaks at 36 and 42 meV have higher in-tensities relative to the peak intensity at 52 meV inPr2CuO4, whereas in the Pr& 85Ceo»Cu04 spectrum thepeaks at 36, 42, and 52 meV have comparable peak inten-sities. Interestingly enough, the peak at 36 meV in thePr2Cu04 spectrum has an intensity which is greater thanany of the density-of-states features and is in fact compa-rable to the 88-meV crystal-field peak. This raises thequestion of whether this peak has a magnetic contribu-tion, but we will see below that the TOF data rule outthis possibility. Hence this scattering likely originatesfrom oxygen vibrations.

The GDOS spectra obtained by TOF spectroscopy inthe energy region 30—100 meV are shown in Fig. 3. Theopen circles are the TOF results, and the solid circles arethe data obtained with the filter-detector method, shownfor comparison. The top part of the figure represents the

0.4 — Pr, „Ceo.15CU

0.3

0.2

0.1 oo

0 i I i i ~I

II I I ~

f~ I I

il

Nd, „Ce, „CUO~

0.05—

030 40 50 60 70

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80 90 100

Energy (meV)

FIG. 3. Comparison of the generalized phonon density-of-states (GDOS) spectra taken by employing the filter-detectormethod (solid circles) with that taken using the time-of-flightspectrometer (open circles) for Pr&,5Ceo»Cu04 (top) andNd& 8&Ceo»Cu04 (bottom). The data for the time-of-Qightmethod and the filter method were taken using instrumentalconfiguration Nos. 2 and 4 from Table I, respectively. There isgeneral agreement between the two methods except at 52 meVin the Pr, »Ceo»Cu04 spectrum and in the lower-energy regionin the Nd& 85Ceo»Cu04 spectrum (see text).

Pr& 85Ceo»Cu04 data, and the bottom part represents thedata for Ndi 85Ceo»Cu04. These TOF data were takenwith an incident energy E;=130 meV and have beenaveraged over a series of scans with Q values rangingfrom 5 to 10 A '. In normalizing the averaged TOFscans to the filter data, we made use of the integrated in-tensities of the crystal-field peaks at the high end of thespectra after adjusting the factor f (Q) to the value ex-pected at the corresponding measured Q in the filter-detector data. It is important to note that in the TOFspectra the energy resolution coarsens as one measurestoward lower energy, going from a resolution AE—=3.2meV at 93 meV to AE -=9.6 meV at 36 meV. In the caseof the filter-detector spectra, on the other hand, the reso-lution gets better, going from kE =—4.2 meV at 93 meV toAE —= 1.8 meV at 36 meV. There is general agreement be-tween the two sets of data for the Pr& 85Ceo»Cu04 spec-trum, with the exception of the peak at 52 meV. Thispeak is clearly observed in the filter data, but not in theTOF data. The discrepancy at 52 meV may be due inpart to the fact that the filter-detector method has -3times better resolution at this energy than the data takenby the TOF method. However, it may also be related to"coherency effects"; i.e., the data for the filter-detectormethod may not be averaging over a large enough rangein Q. This effect would give rise to variations in the peakintensities as a function of Q, therefore affecting the rela-tive intensities of the observed peaks in the filter data.Coherency effects are greatly reduced in the TOF tech-nique since the data shown were obtained by averagingover a large range of Q. In the filter-detector method, themeasured value for Q at 52 meV is 5.1 A and decreasesdown to Q =4.2 A ' at 32 meV, which is still substan-tially larger than the size of the Brillouin zone ( —2 A ),yet the coherency effects may still be significant. The bot-tom of Fig. 3 compares the spectrum forNd ] 85Ceo»Cu04 between the TOF data and the filterdata. Apart from the general agreement between the twospectra for energies ~ 55 meV, there also appears to be aconsiderable difference in intensities between the twospectra for lower energies. For energies ~ 55 meV,features in the TOF spectrum have intensities larger thanthose observed in the filter data. This difference in inten-sities cannot be explained on the basis of energy resolu-tions alone in this energy range, as this would only meanthat features seen in the filter data would not be wellresolved in the TOF data. The investigation of the Qdependence of the scattering in the TOF method confirmsthe existence of phonon peaks at —36 and -42 meV aswe will next show.

Figure 4 illustrates the variation of the integrated in-tensity as a function of Q obtained through the TOFmethod for peaks at energies of 13, 20.7, 26.4, and -93meV in the Nd& 8~Ceo»Cu04 spectrum. The solid curveis a plot of the square of the form factor f (Q) for theNd + ion. ' All the integrated intensities in Fig. 4 arescaled to unity at Q =0 for comparison purposes. It canbe seen from the figure that the 20.7-, 26.4-, and 93-meVpeaks are indeed crystal-field peaks since they conformclosely to f (Q). At the highest Q values ()9.25 A '),the intensity of the 93-me V peak has decreased

48 PHONON DENSITY OF STATES IN R2Cu04 AND. . . 479

1.2

() c) c&1.0 ~ ()

85ep g5CUO~

%3.0 meV

2.5

2.0-

1.5

13-meV peak

= ff(H)I Df Nd '

0.6—

0.4—

20.7 meV

26.4 meV

93.t meV

C/)

0.5

0

2.0—

1.5

1.0

2 4 6 8 10 00

FIG. 4. Q dependence of the magnetic crystal-field integratedintensities for the Nd&»Ceo»Cu04 system. For the crystal-fieldpeaks at 20.7 meV ( ), 26.4 meV (6 ), and 93.1 meV (~ ), the Qdependence of their intensities agrees well with the square of themagnetic form factor f ( Q ) for Nd' (solid curve). However,the peak at 13 meV ( 0 ) increases in intensity with increasing Q,demonstrating that there is a phonon contribution at this ener-

FIG. 5. Top portion of the figure shows the scattering inten-

sity vs Q for 13-meV scattering in Nd, „Ceo»CuO~. Thisscattering can be separated into a magnetic component at small

Q, which follows the square of the Nd3+ magnetic form factor(dot-dashed curve), and a phonon contribution which varies as

Q . The bottom portion of the figure shows the remainder ofthe scattering with the magnetic contribution removed andwhere we see that it follows the Q' dependence (solid curve)quite well.

significantly, allowing the determination andconfirmation of the phonon cutoff frequency, which is at-83 meV. Unfortunately, the intensities of the two oth-er crystal-field peaks still dominate the scattering in the18—32-meV region even at the highest measured Qvalues, prohibiting the determination of the phonon spec-trum in this particular energy region.

For the case of the peak at 13 meV, it can be seen fromthe figure that its intensity has an upward trend with in-creasing Q, which is better illustrated in the top of Fig. 5,where the Q dependence of the integrated intensity isplotted for the 13-meV peak only. Also plotted on thetop of Fig. 5 is f (Q ) (dot-dashed curve) for Nd +. It isclear that this peak contains both magnetic and phononscattering. At small Q the magnetic scattering is strong-est, while the phonon scattering ( ~ Q ) dominates themagnetic part for high values of Q. This is better illus-trated in the bottom of Fig. 5 where the contributionfrom the magnetic scattering, which is approximated byf (Q) in the top of Fig. 5, has been subtracted from thetotal peak intensity, giving a result of a plot of only pho-non intensity versus Q. We see that we obtain a nice sep-aration of the magnetic and phonon scattering; the pho-non character of the scattering at 13 meV is confirmed bythe fact that the subtracted intensity conforms to the Qbehavior, which is depicted as the solid curve in the bot-

tom of Fig. 5.Figure 6 shows a plot of the scattering function

S(Q, co) versus energy for three values of Q, in the energyregion around 36 meV. All the data shown have beencorrected for background contributions. The top figure isscattering associated with Q =2.73 A, and in this ener-

gy region obviously the spectrum is Oat; the extra scatter-ing around 31 meV comes from the shoulder of the neigh-boring crystal-field peak. In the middle figure wherescattering is shown for Q =5.23 A, increases in intensi-ties can be seen in the 33—38-meV region developing intosome structure. The structure eventually develops into apeak around 36 meV, which is observed in the highest-angle (and therefore highest-Q) detectors, as shown in thebottom figure for Q =6.34 A . Thus in spite of the factthat the 36-meV peak is only observed for the few highestQ values, the increasing trend in intensities isconfirmation of a peak in the GDOS at this energy. Wehave also confirmed the presence of a phonon peak at 42meV by the same analysis. In fact, the same observationshave been done on other parts of the spectrum with theresult that the energy region below 18 meV and from 30meV up to the phonon cutoff frequency the scattering islattice dynamical in origin. We cannot establish thecharacter of the small peak at -52 meV seen in the filter

480 SUMARLIN, LYNN, NEUMANN, RUSH, LOONG, PENG, AND LI 48

0 ' 4

0.3

0.2

0. 1

0 ' 3

0 2

0.1—

g &$Ig5lll(

Gl=2. /3I I I I

II

II

y &(&)(j

@=5.23

1.Q

O. B

0.6—

O. a—

& 17.9 meV Pr ~.a5CeQ f5CuO„-

87.9 meV Pr «5CeQ f5CuO,

a iB.6 meV Pr ~CuO,

Ds — &&

I I I I I I

I II

II

II

I

0.2—

0.2

0 1

G=6.34

30I I I I I I I I

32 34 36 38

Energy (meV)40

data by this means since it is not observable in the TOFdata. However, neutron-scattering' and infrared mea-surements reveal the existence of a zone-center modeenergy at -52 meV, which suggest that the observedpeak at this energy in the filter data might be a phononpeak.

For the Pr& s5CeD, ~CuO4 and PrzCuO~ samples, the Qdependence of the integrated intensities of the crystal-field peaks are shown in Fig. 7 for peaks at energies 18and -88 meV. The behavior of these intensities with Qconfirms that these peaks are indeed Pr + crystal-fieldpeaks since the data yields good agreement with f (Q)for Pr~+ ious. s~ Unfortunately, even for the highest Qmeasured, the peak around 88 meV in both samples stillcontains substantial magnetic intensity, preventing agood determination of the phonon cutoff frequency.However, in analogy with the Nd, 8~Ce() &5Cu04 densityof states, we expect that the phonon cutoff frequency tobe somewhere between 80 and 90 meV.

To identify the origin of the peak at 36 meV inPrzCuO~, we analyzed the Q dependence of its intensityas depicted in the top of Fig. 8, while the same analysisfor the 30-meV peak is illustrated in the bottom of Fig. 8for 3.5&Q &7 A '. The solid curves shown are func-tions proportional to Q, and this describes the generalbehavior of both peak intensities as a function of Q,showing that both peaks contain scattering which origi-nates mainly from phonons. We have also determinedthe existence of these two phonon peaks in superconduct-ing Pr& 85Ce(),5CuO4 through the same procedure. The

FIG. 6. TOF data showing the Q dependence of the scatter-ing at 36 meV for the Nd&»Cep»CuO4 system. The increase inscattering with increasing Q demonstrates that this is phononscattering.

0

P 2 4 6 B

g (A~)10 12

FIG. 7. Q dependence of the integrated intensities for thecrystal-field transitions in the Pr&»Ce()»Cu04 system. Thedata symbolized by (0 ) and (~ ) represent the peaks at 17.9 and87.9 meV, respectively, while the data symbolized by (0) and(6 ) represent the 18.6-meV peak for the Pr2Cu04 system. TheQ dependence of the intensities of these peaks are in very goodagreement with the square of the magnetic form factor for thePr'+ ions (solid curve).

2.5

2 ~0—

36-meV peak Pr ~Cubi,

1.5

()()

() ( " ()() ()0

2.0—O-mev peak Pr, CuQ„

1.5

1.0

0.5—

03.5 4.5

I I

5.5

Q (~')6.5 7.5

FIG. 8. Q dependence of the integrated intensities for pho-non peaks at energies 36 meV (top) and 30 meV (bottom) for thePrzCu04 system. The solid curves are proportional to Q'.

PHONON DENSITY OF STATES IN R2Cu04 AND. . . 481

I I I ~I

I I $ ~I

~ I I II

I I ~ I I I I 1 II I I I I

II 0 I ~

I~ I I ~1 2

1.0

0.8

0.6

Q

No. I—

0.0

Q 2 s s ~ ~ I ~ a ~ i I I & ~ i I~ ~ I I ~ I ~ I I II

t'I

~ i ~ I s ~ i s I aI I I ~ I I

a s ~ I~ I I

II

No. 2

s ~ I ~ s ~ sI I I

II I I I

300—

200—

100—

0 a «a I ~

0 10 20 30 40 50 60 70 BO

Energy WM (rneV)

FIG. 9. Comparison of tunneling measurements of u I'(co)(top) for two samples of Nd& 8,Ceo»Cu04 (Ref. 11) with thegeneralized phonon density of states (bottom}. There are sub-stantial similarities between the two spectra at lower energies,as indicated by the presence of peaks at —14, 36, and -42 rneVin both spectra.

scattering in the region of 52 meV may also be phonon inorigin, but there is no clear peak observed in the TOFdata. We note that infrared reQectivity measurements re-veal a zone-center mode at this energy.

Finally, we address the question of whether phononsmay play a role in the electron-pairing mechanism inthese materials by comparing the Eliashberg-couplingfunction a F(co) extracted from tunneling measurementswith the GDOS. Figure 9 displays the spectra of ct F(co)for two samples (to convey the repeatability of the data)of Nd& 85Ceo»Cu04 obtained from tunneling measure-ments, " while the bottom part of the figure shows thephonon density-of-states GDOS for Nd, 85Ceo»Cu04taken with the filter method. The peak at —14 meV is ingood agreement with the GDOS, as are the peaks at -35and -40 meV. The correspondence with the neutrondata at higher energies is not particularly good, but nei-ther is the repeatability of the tunneling data, and indeedthis is not surprising as the tunneling measurements areknown to become less reliable with increasing energy.To the extent that the comparison between the GDOSspectrum of Nd, 85Ceo»Cu04 and the correspondingtunneling spectrum is correct, this suggests that phonons

are to some extent involved in the electron-pairing mech-anism in these electron-doped superconductor systems.Since the measured GDOS in the Pr, 85Ceo»Cu04 sys-tem reveals a different shape in some of the structuresthan that of the Nd, 85Ceo»Cu04 system, it would be in-

teresting to see how the GDOS of Pr, 8~Ceo»Cu04 com-pares with the tunneling spectrum a F(co) of thePr ] 8gCeo»Cu04 system. Of course, the possibility thatother excitations are also playing a role in the pairingcannot be ruled out.

In conventional superconductors the observation ofsubstantial phonon softening, which is a shifting of thephonon modes toward lower energies, as the system goesinto the superconducting state is taken as evidence ofphonon involvement in the formation of superconductivi-ty. Measurements of the GDOS in the related systemI.a2 „Sr„Cu04 have indicated some phonon softeningwhen going into the superconducting state. The soften-ing occurs in the energy region of the oxygen-vibrationalmodes, yet the effect is believed to be too small to accountfor the high T, values if conventional electron-phononmodels are employed. In our data, the comparison ofthe GDOS between the parent insulating Pr2Cu04 andthe superconducting Pr, 85Ceo»Cu04 from Fig. 2 revealsno appreciable softening. Instead, as the system goesfrom Pr, 85Ceo»Cu04 to Pr2Cu04, substantial increasesin intensities occur between the 33 and 63 meV. Thesechanges likely entail a number of phonon branches andcertainly in part result from the change in the screeningin going from insulator to conductor. There may also bea magnetovibrational contribution to the scattering inthe insulating phase, where the Cu spins are ordered.This might affect the relative intensities of thephonon peaks. As for the differences in the shape ofthe GDOS spectrum between Pr, 8~Ceo, ~Cu04 andNd& 85Ceo»Cu04 below 60 meV, we can only speculateas to whether or not any phonon modes in this energy re-gion are affected by the decrease in the stability of the T'structure as the rare-earth radius increases from Nd toPr. It would be useful to compare the GDOS with oth-er R»5Ceo»Cu04 systems for R =Sm, Gd, but thesemeasurements are dificult to carry out due to the highneutron absorption cross section of these rare-earth ions.

ACKNOWLEDGMENTS

We would like to acknowledge helpful discussions withR. L. Greene and K. E. Gray. Two of us (I.W.S. andJ.W.L.) would like to thank the staff of IPNS for theirhospitality during our stay at Argonne. The research atMaryland is supported by the NSF, DMR Grant No. 89-21878, and by the Electric Power Research Institute andBaltimore Gas 8c Electric Co. Work performed at Ar-gonne is supported by the U.S. DOE, Basic Energy Sci-ences under Contract No. W-31-109-ENG-38.

~For a general review of the oxide superconductors, see HighTemperature Superconducti Uity, edited by J. W. Lynn(Springer-Verlag, New York, 1990).

For a general review of phonon effects in superconductors, see

P. B. Allen, in Dynamical Properties of Solids, edited by Cx. K.Horton and A. A. Maradudin (North-Holland, Amsterdam,1980), Vol. 3.

H. J. Bournemann, D. E. Morris, and H. B.Liu, Physica C 182,

482 SUMARLIN, LYNN, NEUMANN, RUSH, LOONG, PENG, AND LI 48

132 (1991).4Y. Tokura, H. Takagi, and S. Uchida, Nature 337, 334 (1989).5B. Batlogg, S.-W. Cheong, G. A. Thomas, S. L. Cooper, L. W.

Rupp, Jr., D. H. Rapkine, and A. S. Cooper, Physica C 185-189, 1385 (1991).

Ru and Zr are examples of conventional superconductors withno isotope effect; see C. Kittel, Introduction to Solid StatePhysics, 6th ed. (Wiley, New York, 1986), p. 330. Also see J.W. Garland, Jr., Phys. Rev. Lett. 11, 111 (1963); 11, 114(1963).

7J. W. Lynn, I. W. Sumarlin, D. A. Neumann, J. J. Rush, J. L.Peng, and Z. Y. Li, Phys. Rev. Lett. 66, 919 (1991).

8M. Arai, K'. Yamada, Y. Hidaka, S. Itoh, Z. A. Bowden, A. D.Taylor, and Y. Endoh, Phys. Rev. Lett. 69, 359 (1992).

H. A. Mook, B. C. Chakoumakos, M. Mostoller, A. T.Boothroyd, and D. McK. Paul, Phys. Rev. Lett. 69, 2272(1992).For a review of tunneling data in the oxide systems, see J. R.Kirtley, Int. J. Mod. Phys. 4, 201 (1990).

~'Q. Huang, J. F. Zasadzinski, N. Tralshawala, K. E. Gray, D.G. Hinks, J. L. Peng, and R. L. Greene, Nature 347, 369(1990).D. G. Hinks, D. R. Richards, B. Dabrowski, D. T. Marx, andA. W. Mitchell, Nature 335, 419 (1988).C.-K. Loong, P. Vashishta, R. K. Kalia, M. H. Degani, D. L.Price, J. D. Jorgensen, D. G. Hinks, B. Dabrowski, A. W.Mitchell, D. R. Richards, and Y. Zheng, Phys. Rev. Lett. 62,2628 (1989);C.-K. Loong, P. Vashishta, R. K. Kalia, Wei Jin,M. H. Degani, D. G. Hinks, D. L. Price, J. D. Jorgensen, B.Dabrowski, A. W. Mitchell, D. R. Richards, and Y. Zheng,Phys. Rev. B 45, 8052 (1992).L. Pintschovius, N. Pyka, W. Reichardt, A. Yu. Rumiantsev,N. L. Mitrofanov, A. S. Ivanov, G. Collin, and P. Bourges,Physica C 185-189, 156 (1991).A. S. Ivanov, N. L. Mitranov, A. Yu. Rumiantsev, L.Pintschovius, N. Pyka, and W. Reichardt, Fiz. Nizk. Temp.[Sov. J. Low Temp. Phys. 17, 693 (1991)].J. W. Lynn, I. W. Sumarlin, S. Skanthakumar, W.-H. Li, R.N. Shelton, J. L. Peng, Z. Fisk, and S.-W. Cheong, Phys. Rev.B 41, 2569 (1990).M. Matsuda, K. Yamada, K. Kakurai, H. Kadowaki, T. R.Thurston, Y. Endoh, Y. Hidaka, R. J. Birgeneau, M. A.Kastner, P. M. Gehring, A. H. Moudden, and G. Shirane,Phys. Rev. B 42, 10098 (1990).S. Skanthakumar, J. W. Lynn, J. L. Peng, and Z. Y. Li, J.

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2 The spin-wave velocity has recently been measured to be0-700 meV A in PrzCu04', see I. W. Sumarlin, J. W. Lynn, T.

Chattopadhyay, S. N. Barilo, and D. I. Zhigunov (privatecommunication).A. T. Boothroyd, S. M. Doyle, D. McK. Paul, and R. Osborn,Phys. Rev. B 45, 10075 (1992), and references therein.P. Allenspach, A. Furrer, R. Osborn, and A. D. Taylor, Z.Phys. B 85, 301 (1991).P. Hoffmann, M. Loewenhaupt, S. Horn, P. v. Aaken, andH.-D. Jostarndt, Physica B 163, 271 (1990);V. Nekvasil, Phy-sica C 170, 469 (1990).I. W. Sumarlin, J. W. Lynn, D. A. Neumann, J. J. Rush, J. L.Peng, Z. Y. Li, and S. J. Hagen, Physica C 185-189, 2571(1991).P. F. Miceli, S. E. Youngquist, D. A. Neumann, and H. Zabel,Phys. Rev. B 34, 8977 (1986); see also V. S. Oskotskii, Fiz.Tverd. Tela (Leningrad) [Sov. Phys. Solid State 9, 420 (1967)].F. Gompf, H. Lau, W. Reichardt, and J. Salagado, in Proceed-ings of the International Conference on Inelastic Scattering ofNeutrons, Grenoble, 1972 (IAEA, Vienna, 1972), p. 137.

7For detailed data reduction in the time-of-flight experiment,see N. Lustig, J. S. Lannin, J. M. Carpenter, and R.Hasegawa, Phys. Rev. B 32, 2778 (1985).

2 J. L. Peng, R. N. Shelton, and H. B. Radousky, Solid StateCommun. 71, 479 (1989).J. L. Peng and R. L. Greene, Physica C 172, 143 (1990).For the zone-center mode assignment, see E. T. Heyen, G.Kliche, W. Kress, W. Kdnig, M. Cardona, E. Rampf, J.Prade, U. Schroder, A. D. Kulkarni, F. W. de Wette, S. Pistol,D. Mck. Paul, E. Moran, and M. A. Alario-Franco, SolidState Commun. 74, 1299 (1990).M. Blume, A. J. Freeman, and R. E. Watson, J. Chem. Phys.37, 1245 (1962).M. K. Crawford, G. Burns, G. V. Chandrashekar, F. H.Dacol, W. E. Farneth, E. M. McCarron III, and R. J. Smal-ley, Solid State Commun. 73, 507 (1990).B. Renker, F. Gompf, E. Gering, N. Nucker, D. Ewert, W.Reichardt, and H. Rietschel, Z. Phys. B 67, 15 (1987).

34S. W. Lovesey, Theory of Thermal Neutron Scattering (OxfordUniversity Press, New York, 1984), Vol. 2, p. 35.Y. Y. Xue, P. H. Hor, R. L. Meng, Y. K. Tao, Y. Y. Sun, Z. J.Huang, L. Gao, and C. W. Chu, Physica C 165, 357 (1990)~