Vol. 6, No. 3/March 1989/J. Opt. Soc. Am. B 403

Infrared studies of single-crystal La2_,SrxCuO4-b andYBa2Cu307-6

A. C. Nichol, F. L. Pratt, W. Hayes, C. Chen, B. E. Watts, and B. M. Wanklyn

Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK

Received September 27, 1988; accepted November 29, 1988

Polarized infrared reflectance measurements are reported for crystals of La2s-SrxCuO4-6 and YBa2Cu30 7 -6. Free-carrier reflectance is observed in the copper oxide planes, and strong phonons are observed in the perpendiculardirection. The interpretation of the infrared optical properties is discussed.

INTRODUCTION

The high-T, superconductors La2 _Sr.CuO4-b (LSCO) (x0.15) and YBa 2Cu30 7 -6 (YBCO) have been studied inten-sively by using a wide range of techniques. Studies by infra-red reflection spectroscopy have sought first to verify theexistence of a superconducting energy gap and second toinvestigate general electronic excitations of these materials.The lack of large crystals suitable for infrared studies hasbeen a problem, and the majority of measurements havebeen made on polycrystalline samples. However, correctanalysis of polycrystalline measurements must take into ac-count the anisotropy of the crystallites, and the necessaryinformation can be obtained only from single-crystal mea-surements. In this paper we present infrared reflectancemeasurements on single crystals and discuss the informationthat can be obtained regarding the electronic structure fromsuch measurements.

This investigation is primarily concerned with the elec-tronic properties of the normal state, although some mea-surements of the temperature dependence of the reflectanceof superconducting YBCO are briefly discussed. The start-ing point for discussion of the optical properties is a dielec-tric function of the simple Drude form for free carriers:

E(X) = e - W 2/O(W + iy), (1)

where cp is the unscreened plasma frequency, which is relat-ed to the carrier density n and effective mass m* by cop2 =ne2/(f0M*); y is the scattering rate; and E is the backgrounddielectric constant due to high-energy electronic excitations.There may be departures from Eq. (1) because of many-bodyeffects, but it may still be used to describe the dielectricfunction if up and y are permitted to be frequency depen-dent. Additional contributions to E(w) from a possible inter-band transition, eib(co), and from phonons, Eph(W), may beadded to the right-hand side of Eq. (1) in the form of Lorentz-ian oscillators:

Eib(CO) = [b 2/(Wib2 - 2 - iC07b)], (2a)

Eph(W) = E [n'/(wn 2- W2 - iY)], (2b)

n

where Qib represents the oscillator strength of the interband

transition; Wib is the center frequency; Yib is the width; andfor the phonons, , 0, and y, represent the TO frequency,the oscillator strength, and the width, respectively.

EXPERIMENT

The single crystals were obtained by flux growth, CuO fluxfor LSCO' and CuO/BaO flux for YBCO.2 The largestLSCO crystals had dimensions as great as several millime-ters in each direction, whereas the YBCO crystals were al-ways smaller, the largest being in the form of ab-orientedplates -1.5 mm square and -50 Atm thick. For the far-infrared measurements (20-500 cm-') an RIIC BeckmanFS720 Fourier-transform interferometer was used in con-junction with a helium-cooled composite bolometer. In themiddle-infrared region (400-4300 cm-') a Perkin-Elmer1710 Fourier-transform spectrometer was used, and for therange 4000-30 000 cm-1 a Perkin-Elmer Lambda 9 gratingspectrometer was used. For low-temperature measure-ments, samples were held in an Oxford Instruments continu-ous-flow cryostat, and the reflectivity was obtained by nor-malizing to an Al or brass reference mirror held in the cryo-stat along with the sample. A Specac beam condenser wasused in conjunction with suitable polarizers to measure thepolarized reflectance. The angle of incidence was in theregion 15° to -300, depending on the measuring system.Absolute values for the reflectance were difficult to obtain;this is due primarily to the small size and variable surfacequality of the crystals. This uncertainty in the absolutevalue was taken into account in the fitting procedures byusing a normalizing factor to optimize the fit. For the largeLSCO crystals, the normalizing correction was only a fewpercent, whereas for the smaller YBCO crystals it could beseveral tens of percent. The measured anisotropy and fre-quency dependence of the reflectance would not, however,be affected by uncertainty in the absolute-reflectance mag-nitude.

The La-Sr ratio was determined by electron-probe micro-analysis; 0 contents were not determined. Orientation ofcrystals and confirmation of the structure were determinedby x-ray diffraction. Superconducting transition tempera-tures for the single crystals were determined by the Meissnereffect; the main flux exclusion occurred at -8 K for the

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

LSCO crystals and at -65 K for the YBCO crystals. Theserelatively low transition temperatures indicate a low 0 con-tent in the bulk of the crystals.

Measurements were made both on original as-grown crys-tal faces and on cut and polished faces for the LSCO crystals;the YBCO crystals were too small and fragile for such sur-face treatment. Two effects on the reflectance were ob-served as a result of polishing:

(1) Where a large plasma reflectance was seen on theoriginal surface, a lower plasma frequency was observed onpolishing down into the bulk of the crystal; this indicatesthat 0 only penetrated a thin surface layer in the annealingprocess.

(2) Polishing was also found to reduce frequency-depen-dent scattering due to a rough surface; such scattering typi-cally reduced the observed reflectance by -50% at 4000cm'.

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La 2 _.SrCuO4-5 REFLECTANCE

The lattice structure of the high-T, superconductors sug-gests that the electronic properties will be highly aniso-tropic, and hence an anisotropic reflectance is expected.Such reflectance anisotropy has been reported in single crys-tals of both the related compound La2NiO4 (Ref. 3) and alsoin La2CuO4 ,4 and anisotropy has been assumed in the reflec-tance analysis of polycrystalline LSCO.5 -7

A direct measurement at room temperature of the reflec-tance anisotropy of the ac face of a single crystal of LSCO,which had been aligned, cut, and polished, is shown in Figs.1(a) and 1(b). For radiation polarized perpendicularly to c,the reflectance is dominated by free carriers; weak phononfeatures observed here appear to be due to incomplete rejec-tion of the strong c-polarized phonons. The reflectance canbe fitted in the region above 1000 cm-' by a highly dampedDrude term. No 0 annealing had been carried out on the

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Fig. 1. The infrared reflectance of an aligned, cut, and polished crystal of LSCO at 300 K for an ac face with E Ic and E | a (a) in the region be-low 1000 cm', (b) in the region 400-4300 cm-1. (c) A Drude model fit to the ac-face reflectance with E a, fitted in the region 1000-4300 cml,and (d) reflectance of an ab face with E II a.

0D0

a:

(b)

Elc

ElkcI,-

(d)

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Vol. 6, No. 3/March 1989/J. Opt. Soc. Am. B 405

Table 1. Electron and Phonon Parameters Consistent with the Observed Reflectance of Single-Crystal LSCO

Drude Parameters Phonon Parameters Interband ParametersWP CWn 'Yn n COib 'Yib Qib

Face (Polarization) (cm-l) (cm-') E (cm') (cm-') (cm-') (cm-,) (cm'1) (cm-')

ac (E||c) - - 3 232 60 750(polished) 505 45 250 - - -

ac (E ll a) 7.6X103 1.5X104 3 - - -

(polished)ab (E |l a), 7.6X 103 1.1X10 4 4 - - - 3.5X103 7.0X103 4.5X 103

(polished)ab (E |l a) 2.0X10 4 1.0X10 4 4 - - -

(unpolished)ab (E ll a) 4.6X 103 8 X 102 4 - - - 3.5X103 1.0 X 103 5.5 X 103

(unpolished,heat treated)

crystal after polishing, and the plasma frequency and carrierconcentration are consequently quite low (see Table 1). Atfrequencies below 1000 cm-' the reflectance is higher thanexpected from the Drude fit to the reflectance at higherfrequencies [Fig. 1(c)].

For radiation polarized in the c direction, the reflectanceis typical of an insulator and is dominated by phonons.There are two strong c-polarized phonons, and their fre-quencies and widths as obtained from Kramers-Kroniganalysis of the reflectance are listed in Table 1. Thesephonons correspond to the c-axis phonons reported at 240and 501 cm-' in single-crystal La2 CuO4 ,4 which result fromin-phase and out-of-phase motion of successive 0 layers.The reflectance up to 4300 cm-' is shown both for an ac face[Fig. 1(b)] and an ab face [Fig. 1(d)]. The ab-face reflec-tance has vibrational structure visible, which is not presentfor E I c on the ac face [Fig. 1(b)]; we suggest that thesephonons are due to the presence of insulating regions on theab face.

For c polarization there is no indication of any absorptionnear 0.5 eV (-4000 cm-'); previous measurements on poly-crystalline material have indicated a broad electronic ab-sorption at this energy, which appeared to be correlated withthe carrier concentration.8 The only evidence for this ab-sorption band is in the ab reflectance [Fig. 1(d)], where itcould explain the relatively high reflectance near 4000 cm-';however, the mode has to be broad to give the featurelessreflectance seen in this region (see Table 1). The reflec-tance for the ac face with polarization E I c shows no sign ofthis mode.

Further information on the properties of the 0.5-eV modeis obtained from a study of the effect on the ab-face reflec-tance of annealing at 900'C in air for 180 h (Fig. 2). Thefree-carrier plasma frequency is observed to shift to lowerfrequency while a strong-reflectance feature appears near0.5 eV. At the same time, phonon structure in the form ofdips in the reflectance appears in the spectrum near 500 and1000 cm-'; these dips are the result of absorption in a semi-transparent insulating layer that has formed on the surfaceof the crystal. These results suggest that the 0.5-eV modemay not be related directly to free carriers but rather may beassociated with an insulating region in the sample, probablyhighly 0 deficient, which forms on exposed ab-oriented crys-tal surfaces (a similar heat treatment in flowing 02 gave noindication of any reflectance feature at 0.5 eV).

A broad absorption peak near 0.5 eV has also been ob-served as a result of photoexcitation of La 2CuO 4-6 at 2.6 eV,9

and so this mode has been observed in several differentexperiments. However, there is no conclusive evidence atpresent that it is an intrinsic excitation of the carriers re-sponsible for the superconductivity, and we suspect that it isin fact a transition associated with an extrinsic state in theenergy gap of insulating regions in the sample. The pres-ence of unscreened phonon structure in the ab reflectance[Fig. 1(d)] offers clear evidence that such regions exist. Fur-ther studies are required to settle this question.

YBa2Cu 3O7- REFLECTANCE

The reflectance of the ab face of a YBCO crystal at roomtemperature is shown in Fig. 3, both before and after anneal-ing in 0. Before annealing [Fig. 3, curve (a)] phonons arevisible in the reflectance as well as interference fringes,which indicates the relatively low absorption in the insulat-

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Fig. 2. Reflectance of an unpolished ab face of LSCO crystal at 300K; dotted curve, as grown; solid curve, after 180 h at 900°C in air.

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Fig. 3. Infrared reflectance of a single crystal of YBCO at 300 K foran ab face: curve (a), before annealing; curve (b), after annealingfor 4 days at 600'C in 02. [The spectrum of curve (b) is considera-bly more noisy than that of curve (a)].

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Table 2. Electron and Phonon Parameters Consistentwith the Observed Reflectance of Single-Crystal

YBCO

Drude Parameters Phonon ParametersFace Cp C Wn 'Yn On

(Polarization) (cm-') (cm-') (cm-') (cm-') (cm-')

ab (E 11 alE 1l b) 1.7 X 104 4.8 X 10' 3.5 - - -

ab (Ela/El 1b) - - - 594 25 330(unannealed)

ing state. After annealing [Fig. 3 curve (b)], the phonons arescreened by free carriers, and there is a pronounced free-carrier reflectance. The reflectance in the annealed crystalover the range 400-16 000 cm-' is shown in Fig. 4 togetherwith a Drude fit (see Table 2); the Drude parameters arecomparable with those reported by Schlesinger et al.10 forsuperconducting single-crystal YBCO. Departures fromDrude reflectance are seen near 10 000 cm-', possibly be-cause of interband transitions. Although we have used aDrude model to fit the ab reflectance, we note that it is alsopossible to fit the YBCO reflectance with a combination ofinterband and lower-frequency intraband terms in the di-electric function, as suggested by Tanner et al." The pro-posed interband term would have to be broad compared withits center frequency, and such a term would essentially beindistinguishable from a second Drude contribution to thedielectric function. Because of the broad nature of the re-flectance features it is difficult to distinguish between theabove interpretations.

TEMPERATURE DEPENDENCE OFREFLECTANCE

A number of workers have looked for the presence of anenergy gap in the infrared by looking at the ratio of reflec-tance above and below the superconducting transition bothin LSCO12-18 and in YBCO.6"l", 9-24 An increase in low-frequency reflectance is generally observed in the supercon-ducting state, but the reflectance does not increase to unityas would be expected below an energy gap, according toMattis-Bardeen electrodynamics. 25 This could be the re-sult of a reduced overall reflectance due to surface rough-ness, but such effects tend not to be important at frequenciesbelow approximately 500 cm-'. One approach to explainingthis behavior is to assume that only part of the surface of thesample becomes superconducting because of inhomogeneity.A reduced reflectance change also follows from consider-ation of the effective dielectric function of the polycrystal-line surface modeled by using the effective-medium approxi-mation26 27; the small reflectance change occurs because thereflectance of ab-oriented crystallites is already high, andany increased reflectance due to the onset of superconduc-tivity can only bring about a small fractional change in theoverall reflectance. At the same time, the frequencies andwidths of the phonon modes may also be temperature depen-dent, giving rise to substantial changes in the observed re-flectivity. Another source of reflectance change on goinginto the superconducting state, proposed by Bonn et a.,17results from a zero crossing of the real part of the dielectricfunction because of the superconducting plasma responseand is not directly related to excitation across the supercon-ducting energy gap.

The temperature dependence of the reflectance of the abface of a superconducting YBCO crystal (T - 70 K) wasstudied down to 14 K in the region 400-4300 cm-'. Nosignificant changes could be observed in the reflectance inthis region; the stability of the experiment was such thatreflectance changes of >1% in the region of 500 cm-' wouldbe observable. This result is in contrast to a previouslyreported reflectance increase of -4% near 500 cm-', fromjust above to well below T, in crystals with T - 92 K.'0"'

r_

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Vol. 6, No. 3/March 1989/J. Opt. Soc. Am. B 407

DISCUSSION

Departures from Drude fits to the middle-infrared region(>1000 cm-') are seen on going to lower frequencies (<1000cm'1), particularly for LSCO [Fig. 1(c)], which indicate thatmore than a single Drude term is required in the dielectricfunction. The term dominating the region above 1000 cm-'may take the form of either a Drude term with a largescattering rate or a broad interband transition. The plasmafrequencies we observe after 0 annealing give carrier con-centrations of 3.4 X 1021 cm-3 for YBCO and 4.5 X 1021 cm3

for LSCO if the effective mass is taken as m* me. Thecarrier density for YBCO is comparable with that obtainedwhen a hole concentration of 1-26 (6 0.1) per cell (4.6 X1021 cm'3) is assumed, whereas for LSCO one hole per Sratom would give a carrier density of 1.6 X 1021 cm- 3 in theabsence of 0 vacancies. The greater than expected plasmafrequency observed in LSCO may result from a low effectivemass for the carriers, or alternatively there may be a largecontribution from carriers excited from lower-lying bands.

Band-structure calculations on YBCO 283

2 have suggestedthe existence of interband transitions that depend on thedistribution of the bridging 0, and Chui et al.32 have sug-gested that the optical conductivity between 0.1 and 1 eV isentirely due to these transitions. This would explain thedependence on 0 content and the lack of temperature de-pendence of the optical properties in this region. The infra-red optical properties of LSCO are similar to those of YBCO,but band-structure calculations for LSCO in its fully oxy-genated form333 do not give any indication of suitablebands, which could explain the optical properties in terms ofinterband transitions. However,' O vacancies in LSCOmight be expected to have electronic transitions similar tothose discussed for YBCO. Theoretical and experimentalstudies of the effect of 0 vacancies on the optical propertieswould be a useful area for further investigation.

An alternative viewpoint is to consider that the regionabove -1000 cm-' is associated with free carriers rather thaninterband excitations. The difference between the tem-perature-dependent properties of the carriers at zero fre-quency and their temperature-independent properties atoptical frequencies can be explained by a scattering rate thatis temperature dependent at low frequencies but that in-creases with frequency until saturation is reached. Thissaturation occurs somewhere in the infrared where the meanfree path becomes comparable with the lattice spacing.This type of scattering would be expected in a two-dimen-sional square lattice near half-band filling,34 and it has beenused to describe the far-infrared properties of polycrystal-line LSCO27 and YBCO16 as well as the mixed valence com-pound CePd3.35 The frequency-dependent scattering im-plies an effective mass enhancement at low frequencies.

CONCLUSION

We have presented measurements of the polarized reflec-tance spectra for crystals of both LSCO and YBCO materi-als. These measurements give direct confirmation of thelarge degree of anisotropy in the dielectric function of thesematerials. Evidence has been presented indicating that the0.5-eV mode in LSCO may be associated with 0-deficientsample regions. Broad electronic absorption is observed inthe infrared in both LSCO and YBCO. This absorption

either may be the result of 0-related interband excitation ormay be due to free-carrier intraband excitation for which thecarriers have a frequency-dependent scattering rate. It isdifficult to distinguish between these explanations in theYBCO case because the carrier density is directly correlatedwith the 0 content in that material. In LSCO, however, it ispossible to change the carrier concentration through the Srcontent and to vary the 0 content independently to a certainextent. Thus LSCO would appear to be the more suitablesystem for further studies aimed at separating free-carrierand 0-related contributions to the optical properties. Fur-ther measurements on single crystals will be needed to es-tablish in detail the transition from dc to infrared frequen-cies and to separate the various contributions to the infraredproperties.

ACKNOWLEDGMENTS

We wish to thank P. Haycock and P. Thomas for x-rayorientation of the crystals, A. J. de Groot and G. P. Rapsonfor Meissner measurements, and the United Kingdom Sci-ence and Engineering Research Council for support of thisresearch.

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