396 J. Opt. Soc. Am. B/Vol. 6, No. 3/March 1989

Optical reflectivity studies of magnetically orientedYBa2 Cu307-6

F. Lu, C. H. Perry, K. Chen, and R. S. Markiewicz

Northeastern University, Boston, Massachusetts 02115

Received August 9, 1988; accepted November 16, 1988

The optical reflectivity spectra of magnetically oriented YBa 2Cu3 07-6 are reported over a wide energy range from 50to 24 000 cm-' (6 meV to 3 eV). A strong optical anisotropy is observed, with most phonon modes associated withthe E 1 c spectrum. An anisotropic effective-medium theory is used to permit direct comparison of these data withspectra from unoriented grains. The excitonic feature is found to be considerably more intense in the unorientedsample.

1. INTRODUCTION

The optical properties of the YBa2Cu307-6 system have re-ceived considerable attention by many researchers becauseof the observed superconducting transition near 93 K inboth mixed- and single-phase materials." Because of thelarge optical anisotropy associated with the structural prop-erties of these high-T, materials, it has been difficult tointerpret the measured IR spectra unambiguously. Mostprevious work was performed on randomly oriented ceramicsamples.5-10 Some research has been reported on epitaxialfilms,"1 single crystals,'2 and anneal-oriented surfaces,'3 butthese materials are restricted for use in investigations withthe electric vector in the conducting a-b plane. In this workwe report a new method for obtaining polarized reflectivitydata from 50 to 24 000 cm-' (6 meV to 3 eV) for both E I and E | . By orienting the synthesized polycrystallinepowdered material in a strong magnetic field, we were able toprepare large (1 cm X 1 cm X 2 mm) pellets, which are morethan 95-98% aligned (all grains having a common c axis).We discussed our initial optical'4 and magnetic'5 investiga-tions on slightly less well-oriented samples in earlier publi-cations.

The data were subjected to both Kramers-Kronig (KK)and classical dispersion analyses. The real part of the di-electric constant and the conductivities obtained from theseparate analyses are compared. The derived parameters(plasma modes, excitation energies, linewidths, oscillatorstrengths, etc.) for both polarizations are discussed in termsof the optical anistropy. The reflectivity spectra of unor-iented YBa2Cu307-6 are almost identical to those publishedpreviously.5-9 We used an anisotropic effective-mediummodel to simulate the reflectivity of the unoriented samplewhen the parameters derived from the oriented material areused. The reflectivity could be reproduced reasonably wellexcept in the region of the so-called excitonic feature, whichwas considerably less pronounced in the oriented materialfor both E I and E || c. This difference is not due to afinite grain size effect per se because the grains in bothsamples (oriented and unoriented) are approximately thesame size.

2. EXPERIMENTAL

A. Sample PreparationSince the initial observation that grains of YBa2Cu307-5could be aligned in a strong magnetic field with the grain caxis pointing along the field direction, a number of experi-ments have utilized this technique. In the initial experi-ments of Farrell et al.,16 the oriented grains were sealed in anepoxy for subsequent analysis. Arendt et al.17 were able toproduce considerably denser samples by suspending thepowder in a fluid, evaporating the fluid in a strong field, andsubsequently sintering the settled powder (the sintering tak-ing place after the field has been removed). We have repro-duced these oriented, sintered pellets by using acetone orchloroform as the suspending fluid and a 15 T superconduct-ing magnet to align the grains. Moreover, by letting thegrains settle into a Be-Cu die, we are able to press thesamples into pellets before sintering them, thereby produc-ing samples of density comparable with that of the usualpolycrystalline pellets.

The degree of orientation is determined by x-ray reflec-tion spectra. Figures 1, 2, and 3 show typical results for asample in epoxy, a sintered sample, and a pressed, sinteredsample, respectively, compared with the x-ray spectrum ofan unoriented sample. The reflectivity is from the broadface of the sample, perpendicular to the c axis in an orientedsample, so that in a perfectly aligned sample only (001) re-flections would occur. The degree of orientation I, is em-pirically specified as follows: In each sample the intensityof the (001) reflection 7, is measured and normalized to the(301) reflection, which is the most intense reflection in theunoriented sample. Then, the orientation is defined by

( Io )PI= 1--'1 X 100%,1/

where I10 is the normalized intensity in the unoriented sam-ple. Finally, an average P is taken over reflections. Theorientation is found to be best for samples prepared in ep-oxy, with values of P > 95% not uncommon. The orienta-tion of the pressed and of the sintered samples is somewhat

0740-3224/89/030396-07$02.00 © 1989 Optical Society of America

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Vol. 6, No. 3/March 1989/J. Opt. Soc. Am. B 397

(a) ( U) t |o0 0 0o 0

50 40 30 20

(b)

0

o 0 s0~~~

50 40 30 20

29Fig. 1. X-ray reflection spectrum of YBa2 Cu307-6. (a) Field-ori-ented grains in epoxy matrix, orientation P = 96%; (b) unorientedpellet. Note that the peak labeled 110 also includes contributionsfrom 103 and 013.

(a)

LO 0 tOo - oo - o

50 40 30 20

(b)

I I I

50 40 30 20

29Fig. 2. X-ray reflection spectrum of field-oriented sinteredYBa2 Cu3 07-6 pellet. There is some variation of orientation acrossthe thickness (1 mm) of the pellet. (a) Top surface, P = 90%; (b)bottom surface, P = 95%.

lower, but with care an average P > 90% can be attained. Nosignificant difference in P is found in pressed versus sinteredsamples. Annealing of the samples actually enhances P,presumably by promoting grain growth; however, if the sam-ples are heated to too high a temperature, the orientation islost.

The oriented YBa2Cu307-6 pellets were cut across thediameter to expose a face containing the axis; the face wasapproximately 10 mm X 4 mm in area. This surface and theone containing the a-b plane were dry polished with variousgrinding compounds of decreasing size, down to 0.3-ym alu-minum grit, until a mirrorlike finish was obtained. The

surface finish depended on the sample preparation (press-ing, sintering, etc.). Samples used for optical studies had auniform dense appearance, comparable with that of unor-iented pressed ceramic materials, and contained only a smallnumber of occlusions. As these imperfections were less than5 Am in size, they had little effect on the mid- and far-IRreflectance studies but caused some scattering losses in thenear-IR and visible regions.

B. SpectroscopyNear-normal incidence reflection measurements were per-formed over 50-4500 cm-' by using a Michelson interferom-eter. Detectors, beam splitters, filters, and polarizers wereoptimized for each spectral range. A grating spectrometerequipped with Si and PbS detectors was utilized in the 4000-24 000-cm-1 region. The absolute reflectivity was obtainedby comparing the sample spectrum with that of a freshlyaluminized/silvered mirror. The complete spectrum from50 to 24 000 cm-' (6 meV to 3 eV) for both E I and E 11 was normalized in the overlap regions to give a smooth,continuous curve; deviations were less than +2% from onespectral region to the next.

The room-temperature spectra for the magnetically ori-ented YBa 2Cu 307-6 sample are shown in Fig. 4. The crossesand open squares indicate data points (not all are shown) forE I and E || , respectively. The solid lines are fits to themeasured values; the model and fitting will be discussed inSection 3. The unpolarized spectrum taken from the a-bface showed the same, almost featureless, reflectivity behav-ior as that measured with E I . Deviations were less than+2% in the absolute reflectivity. The measured reflectancefor a polycrystalline ceramic sample, prepared in an identi-cal manner but not subjected to a magnetic field orientation,is shown in Fig. 5 (dashed curve). The solid curve in Fig. 5 isderived from an effective-medium theory by utilizing thefitting parameters obtained from the polarized reflectancedata and will be referred to below.

(a) |

K)00

0

I I I l

50 40 30 20

b)

50 40 30 20

29Fig. 3. X-ray reflection spectrum of field-oriented, pressed, andsintered YBa2 Cu3 07-6 pellet. (a) Top surface, P = 98.5%; (b) bot-tom surface, P = 98.1%.

Lu et al.

(

398 J. Opt. Soc. Am. B/Vol. 6, No. 3/March 1989

01.0

0.8

X 0.6

0N 0.4

0.2

0.0 0

E(eV)0.1 0.2 0.3 0.4 0.5

1000 2000 3000 4000v(cm 1)

Fig. 4. The IR reflectivity from the magnetically orientedYBa2Cu307-6 sample for (+) E ± e and (a) E || a. Note the sharppeaks at-180 and -320 cm-l in the E || e data. The solid curves arefits to the reflectance data when the parameters listed in Table 1 areused.

E(eV)

1.0

0.8

X 0.6C

N 0.4

0.2

0.00 5000 10000 15000

v(cm- 1 )20000 25000

Fig. 5. The dashed curve shows the reflectivity from an unoriented(P = 0) YBa 2Cu30 7.6 sample. The solid curve is a reflectance curvegenerated by using the parameters (set A) in Table 1 in an aniso-tropic effective-medium model and a grain size of 10 gim. Alsoshown are the E c data of Refs. 11 (dashed curve) and 12 (dotted-dashed curve).

C. Data AnalysisThe reflectance data were subjected to a KK analysis inorder to derive the frequency-dependent dielectric constante(v) = ' + ie" and the conductivity a(l) = (1/2)e"v, where v isthe frequency of the incident radiation. The transformedreal part e'(v) and the a(v) for E I e and E || a are shown inFigs. 6 and 7, respectively. The corresponding a(v) for theunoriented sample is shown in Fig. 8. The KK methodassumes no model to fit the data. Our present studies didnot extend below 50 cm-1 ; extrapolations can lead to arti-facts in the transformation at low frequencies, and the calcu-lated conductivities are slightly lower than the dc values. In

the unoriented sample (Fig. 8) the low-frequency conductiv-ity is closer to the dc value.

The polarized reflectivity data were also analyzed with astandard dielectric function model for both perpendicular(l) and parallel (11) polarizations:

eg -~i [ An (,)j2(i) - v2 - iVy(i) 2 + ivy(i) )

where i = 1, 1. Here eXi is the high-frequency backgrounddielectric constant and wj, yj, and Sj = f

2/Wj

2 refer to thefrequency, damping constant (or inverse relaxation time),and relative oscillator strength of the jth excitation, respec-tively. No distinction is made as to whether the excitation is

E(eV)0 0.025 0.05 0.075

W

0

D.

04

-10 _

0.1

0 200 400 600 800 1000v(cm- 1 )

Fig. 6. Real part of the dielectric constant e' from 50-4000 cm-l for(solid curve) E and (dashed curve) E 1 e derived from a KKanalysis of the data shown in Fig. 4. Zero crossings occur at 200 and185 cm-l and can be associated with LO phonons.

0

200

1 1500

C)

b100

9n 50Z0o

U

0 1000 2000 3000 4000v(cm-')

Fig. 7. The conductivity from 50 to 4000 cm-' for E and E || c,

as derived from a KK analysis of the data shown in Fig. 4. Peakscorrespond to TO phonons. Note the broad maximum between2600 and 3000 cm-' (0.35-0.4 eV) that occurs in both polarizations.The conductivity scale is the same for E and E || I

Lu et al.

Vol. 6, No. 3/March 1989/J. Opt. Soc. Am. B 399

0

500

cb

0~DC)

z00)

400

300

200

100

0

E(eV)2

0 5000 10000 15000v(cm1 ')

Fig. 8. The dashed curve shows the conductivitycm-1, as derived from a KK analysis of the refleciunoriented sample shown in Fig. 5. Note the laroccurs between 5000 and 10 000 cm-' (0.6-1.2tropic effective-medium model (solid curve), whEin Table 1 (set A) are used, does not completely emental data.

Table 1. Parameters Derived fromOscillator and Drude Term Fit [Eq.

Reflectance Shown in Fig.

Set AParameter Ell El E

lop 647 592 54''Yp 512 183 64ECo1 - - 98S, - - 8.5'71 - - 20'C02 149 138 15(S2 1.01 2.43 0.8,'(2 24 67 20(S)3 310 284 31(S 3 0.5 0.88 0.5'73 88 179 96C04 544 529 53!S 4 0.36 2.02 0.4!74 310 611 33(W5 837 820 83(S5 0.031 0.022 0.0275 130 22 12'C°6 1391 1391 139S6 0.005 0.009 0.0C'(6 50 101 41We 5737 4072 442Se 1.43 1.93 1.3'Ye 30 000 15 700 17 8C. 3.9 5 4Pdc 19 6 32

3 a phonon, exciton, etc. wp is a Drude-type plasma frequen-cy, and 1/yp is the transport relaxation time. The reflectiv-ity amplitude, r, is given by ri = (1 - jE)/(1 + /), wherethe reflectance Ri = IJ'1 2. The parameters obtained fromthe analysis for E ± e and E || c are listed in Table 1 and

- -_ __ _correspond to the solid curves in Fig. 4. The two parametersets given in Table 1 give comparable fits to the reflectance

600 800 1000 data shown in Fig. 4. The optical conductivity, as derived- - - - _ from the two parameter sets, is shown in Fig. 9. The differ-

ences will be discussed now.

3. DISCUSSION OF SPECTRA

In analyzing the spectra we must not forget that these sam-ples are still not perfectly aligned, so some features from theE 11 c spectrum may show up weakly in the E I c data and

20000 25000 vice versa. For instance, a Drude term is found for E 11 c,even though the dc resistivity has a large anisotropy. Also,

from 50 to 25 000 the phonons should be extremely weak in the E c datatance data for the because of the large Drude term. Thus although the pho-ge maximum that nons in the E ± c spectrum appear at slightly lower frequen-

en the parameters cies than in the E | c spectrum, the possibility remains thatxplain the experi- they are produced by misoriented grains. Indirect evidence

for misorientation would show up as anomalously large oscil-lator strengths for the E c phonon modes in Table 1. Thisis because the model calculation adjusts Sj to produce the

a Classical observed phonon intensities in the presence of screening.(1)] to the Because the lattice parameters satisfy c/3a _ 1.01, we could[a naively expect that wj11 w and SjI _ 2Sj11. The observa-

Set Bb tions that wjI > j11 for all modes, when SjI/Sji 1 >> 2 forj = 1El El and j = 4, suggests that misorientation is still a problem.

The finite plasma frequency for E || c, which leads to a dc253 resistivity anisotropy that is much smaller than is typically535 observed, also points to the same conclusion. Future ex-63 periments should involve the use of better aligned samples78 or comparison with E c data on single crystals or epitaxial

141 films to be able to resolve these problems.§2 1.42

52289

7 0.57161532

L2 1.75611

,6 821:8 0.019

300 139214 0.007

940 32573 1.63)0 10 000

5.5590

a The units are inverse centimeters except for S(j), the relative oscillatorstrength, and e., which are dimensionless, and the dc resistivity Pde = 2ay/EWp2, which is in milliohm centimeters. we is the excitonic feature in thenear-IR region.

b Parameter set B includes a low-frequency phonon w1, which has a largeoscillator strength, especially for E I . This set gave a slightly better fit(lower x2) in the low-frequency region. Also the high-frequency conductiv-ities (solid curves) shown in Fig. 9 agree more closely with those obtained froma KK analysis (Fig. 7).

_

C)

cb

0:D

z0

150

100

50

0 5000 10000 15000 20000 25000v(cm- 1 )

Fig. 9. The calculated conductivity a for E and E II- c whenusing the fitting parameter set A (dashed curves) or set B (solidcurves). Set B simulates more closely the conductivity obtainedfrom the KK analysis (Fig. 7).

Lu et al.

400 J. Opt. Soc. Am. B/Vol. 6, No. 3/March 1989

A. PhononsThe conductivity peaks below 600 cm-' are in reasonableagreement with those found in far-IR reflectivity studies ofa-b-plane-oriented YBa2Cu307-6 by Bonn et al.' 3 The realpart of the dielectric constant (Fig. 6) is more phononlikewith an overdamped Drude contribution. The zero cross-ings at 200 and 185 cm-' for E 1 and E 11 , respectively,probably correspond to the LO phonons located at -150 (11)and -140 cm-' (I). The peaks in at -800 (5) and 1200cm' ( 6) occur in both polarizations and in the polycrystal-line material. The frequencies are too high for them to befundamental modes of the YBa2Cu30 7-6 lattice, and they areprobably due to impurities or imperfections.

Generally the phonon spectra observed in the two polar-izations are relatively simple. If we exclude W5 , W6, and we,three phonons remain (four if we include set B) polarizedalong c and perpendicular to c in each case. This is quitedifferent from the 21 IR-active modes predicted from grouptheory for the orthorhombic phase.'8 It is closer to what wemight expect for the tetragonal (D4h) structure, and theresults look more like LaNiO 4.' 9 No doubt this is due to thenear degeneracy of the Bl,(r2-) and B2,(r 3 ) phonons, asthese cannot be distinguished in the IR reflectivity of the a-b plane. It is tempting to interpret the -540- and 530-cm-'lines as the Cu-O in-plane stretching, the 310- and 285-cm'1lines to Cu-O out-of-plane bending, and the 150- and 140-cm'1 lines to lattice modes involving the cation and the Cu-O octahedra for modes polarized parallel and perpendicularto the c axis. This interpretation may be too simpleminded,but as far as the IR modes are concerned it probably is themost reasonable explanation until improved oriented pelletsor large single crystals become available.

B. Drude Term, Low-Frequency PhononParameter set B in Table 1 differs from set A by including anoverdamped low-frequency mode wl, which has a high oscil-lator strength for E 1 . Its strength is comparable withthat of the soft phonons found in perovskite ferroelectrics,such as potassium tantalate 20 or tetragonal lead titanate. 2 'The addition of this phonon w, gives a better fit to thereflectivity minimum in the low-frequency regions for bothE 1 and E || , and it causes a more faithful reproduction ofthe conductivity arrived at from the KK analysis (compareFigs. 7 and 9). The conductivity drops off more rapidly inthe high-frequency region for parameter set B than for set A.Discrepancies in the low-frequency minima have also beenobserved in Lal.85Sro.15CuO4 by Schlesinger et al.22 Theynoted that their far-IR measured reflectance spectrum doesnot follow the Drude curve and that at low frequencies ( <250 cm-') the reflectivity is significantly lower than theDrude value, suggesting the existence of a strong low-fre-quency IR-active mode. This interpretation would agreewith set B in Table 1. However, set A gives almost the samefit and a Drude term for E I that is underdamped. Thetotal relative oscillator strengths for versus 11 is 2.2 for setA and 7.1 for set B, which means that the ratios of theeffective charges ZI/Z I are approximately 1.5 and 2.7, re-spectively. The results are quite different from those foundfor oriented single crystals of LaNiO 4 by Bassat et al.' 9 andby Tajima et al.23 for BaPbj.-.Bi.03. The plasma frequen-cies for either parameter set are much lower than were re-ported previously. 5 -'3 When we consider set A, wp for both 11

and 1 are quite similar (647 and 592 cm-'); the correspond-ing relaxation rates are 512 and 183 cm-', respectively.

C. ExcitonsThe peaks in the conductivity at -2800 cm-' (0.32 eV) for EI and -3000 cm-' (0.38 eV) for E || c are quite weak. Ifthey correspond to the exciton peak reported by others inthe polycrystalline material, they have comparable widthsbut are shifted to lower frequency and make a considerablysmaller contribution to the conductivity. Figure 8 (dashedcurve) shows this behavior for the unoriented sample, whichdisplays a broad peak at approximately 7000 cm-' (0.9 eV).In thick film samples" and in single crystals of the relatedLa 2-,SrxCuO 4 compound, 2 4 this feature is even weaker inthe conductivity. It is possible that the intense peak seen inunoriented ceramics may be enhanced artifically by thegranular nature of the material. However, the reflectivityin this spectral range is actually considerably stronger inepitaxial films" and single crystals'2 (Fig. 5).

4. EFFECTIVE-MEDIUM THEORY FORNONORIENTED SAMPLE

There is a significant difference between the field-orientedand the unoriented samples in the excitonic region, as wasalready discussed. This can best be appreciated by compar-ing the data on the unoriented sample with an effective-medium theory (EMT) average of the oriented sample data.This is done in Figs. 6 and 8. In this section we describe theanisotropic EMT that generated these averages. This dif-fers from earlier EMT's,2 5 26 mainly in the treatment of theintermediate-frequency regime. In the calculations we usethe parameters obtained from the oriented material to cre-ate the reflectivity and the conductivity of the randomlyoriented polycrystalline ceramics.

In formulating an anisotropic EMT model, a separateaveraging scheme is required for the polycrystalline grains inthe high- and low-frequency regimes, and a simple interpola-tion scheme is used to connect them. In the low-frequencyregime, when the wavelength is large compared with theaverage grain size, the same EMT is used as for the dcconductivity o-,27 only it is applied to the complex dielectricconstant e rather than to a. In the present case the polycrys-talline superconductor is modeled as an array of sphericalgrains with anisotropic properties. Specifically, the grainsare considered to be nearly two-dimensional conductors,with low conductivity in the c direction. The parameters forthe different phonon modes parallel and perpendicular tothe c axis are taken from the analysis of the field-orientedsamples (Table 1). For simplicity, properties within theconducting plane are assumed to be isotropic. Such ananisotropic dielectric constant tensor was recently observedfor the closely related compound La2NiO 4, for which largesingle crystals can be prepared.' 9 Although anisotropicEMT's generally require extensive numerical calculations, itis known that an anisotropic EMT of a one-component sys-tem with uniaxial anisotropy is equivalent to an EMT for atwo-component system with isotropic grains,27 wherein twothirds of the grains have dielectric e and one third have e1.

In the hilgh-frequency regime the wavelength of the light lsmuch smaller than the average grain size, and the light isreflected incoherently from individual grains having all pos-

Lu et al.

Vol. 6, No. 3/March 1989/J. Opt. Soc. Am. B 401

sible orientations. In this limit the reflectivity must beaveraged over directions, yielding R = 2 /RI + /R 11. Thedifference between the two types of average can readily beappreciated in the extreme two-dimensional limit. Assumethat the high-frequency dielectric constant is 1 and that theconductivity along the c axis is strictly zero. Then, averag-ing the reflectivities would lead to R - 2/3 as w - 0, whereasthe correct result is that R - 1 in this limit.

An exact treatment of the crossover regime is beyond thescope of this paper. In principle, Mie scattering resonancescan occur when the wavelength just matches the grain diam-eter. However, in practice grain coupling is strong enoughand the grain size distribution is sufficiently broad that anysuch structure will be washed out completely. Hence asimple interpolation scheme should qualitatively reproducethe data. Our technique is to average the reflectivitiesthroughout the entire frequency range,

Reff = 2/iR(EIeff) + /iR(Elleff), (2)

but to define effective dielectric constants that extrapolateto the two limiting cases:

ei as w -> ofeffi f as I

where av is the value obtained with the EMT and i = ±, 1.The form of the interpolating function is of secondary im-portance, but it is essential to recognize that the crossoverwill occur when kd _ 1, where d is a typical grain radius and kis the wave number inside the grain (for simplicity, theEMT value of hi is used). We find that the result is nothighly sensitive to the exact value of d, and a typical value of10 m was used in Fig. 6. The particular interpolationfunction is

i i + (1 - )av. (3)

where

= 1/[1 + (d) 2],

The calculated curves shown in Figs. 6 and 8 use theparameters in Table 1 (sets A and B are practically equiva-lent).

5. CONCLUSIONS

We have found that field-oriented pellets of YBa2Cu307 -6show strong optical anisotropy and, in general, behave simi-larly to single crystals. By developing an anisotropic EMT,we have been able to compare these results with data for apellet of randomly oriented grains and have found that theexcitonic effect is considerably weakened in the orientedsample. The reason for this difference is not clear becauseboth samples were composed of similar-sized grains. Onepossible explanation is that the peak is enhanced by a Mie-type resonance because it occurs approximately in the cross-over regime where grain size and effective wavelength arecomparable. However, the full explanation may be morecomplex: Although the conductivity peak is not present incrystals'2 and epitaxial films," the reflectivity is considera-bly stronger in this frequency range (Fig. 5).

Unfortunately, we have not had much success in invertingthe anisotropic EMT in order to recover the anisotropic

optical properties from the polycrystalline average data. Ingeneral we find that the data can be fit comparably byascribing any particular feature either to the E || c or E cbranch.

ACKNOWLEDGMENTS

The research of F. Lu and C. H. Perry is supported by theNational Science Foundation (grant DMR-8604706), andthat of K. Chen and R. S. Markiewicz is supported in part bya grant from E.I. du Pont de Nemours & Company. Thefield alignment work was carried out at the F. Bitter Nation-al Magnet Laboratory, which is supported at the Massachu-setts Institute of Technology by the National Science Foun-dation.

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