International Journal of Infrared and Millimeter Waves, Vol. 14, No. Z 1993

Far-Infrared and Mid-Infrared Absorption in (Bi,Pb)-Sr-(Ca,Y)-Cu-O

P. Calvani, 1 M. Capizzi, 1 P. Dore, 1 S. Lupi, t P. Maselli, 1 G. Paleologo, 1 G. Balestrino, z M. Marinelli, 2

E. Milani, 2 H. Berger, 3 P. Roy, 4 and Y.-L. Mathis 4

1Dipartimento di Fisica, Universit& di Roma La Sapienza

P.le A. Moro, 2-00185 Roma Italy

2Dipartimento di lngegneria Meccanica Universitd~ di Tor gergata

V. (9. Raimondo 8-00173 Roma, Italy

31nstitut de Physique Appliqude Ecole Politechnique Federale

PH Ecublens - CH-1015 Lausanne, Switzerland

4LURE- Universitd Paris-Sud, 91405 Orsay, France

Received November 24, 1992

Abstract

The reflectivities of seven films belonging to the Bi-Sr-Ca- Cu-O family, with T c ranging from 60 to 95 K, and of a single crystal of insulating Bi-Sr-Y-Cu-O, have been measured at room temperature in the normal phase. The optical conductivity has been analyzed in terms of Drude (D), mid-infrared (MIR), and charge-transfer (CT) contributions. As T c increases, the spectral weight within the charge-transfer gap (D+MIR) increases. Meanwhile, the peak frequency of the MIR band moves towards the far-infrared and the optical conductivity becomes more similar to that of a "normal" metal.

251

0195-927|/93/0200-0251507.00/0 9 1993 Plenum Publishing Corporation

252 Calvani, etaL

Introduction

In spite of a worldwide research effort begun in 1986, the mechanisms of superconductivity in high-Tc superconductors (HTCS), as well as many other physical properties of these materials, are still unexplained. When considering the normal state electronic properties of high-T c cuprates, for instance, one finds that none of them exhibits a simple metallic (Drude) behavior in the infrared. The complex optical conductivity 6-(o)) of metallic cuprates at temperature T>T c has then been described in the literature by two different phenomenological approaches. In a former approach, 6-(co) is modeled by a "pseudo-Drude" term where both the effective mass of the carriers and their scattering rate (1) depend on co. Holstein processes, (2) Holstein processes involving magnons, (3) a marginal Fermi liquid, (4) have been invoked to give such a pseudo-Drude behavior a physical basis. According to the latter point of view, the complex dielectric function ~ (co) can be decomposed (5) into an "ordinary Drude" term (where all parameters are independen t of frequency) plus one (or more) Lorentz oscillators centered in the mid-infrared (MIR band). This latter has been attributed to the broadening effect of doping on the charge-transfer bands, (6) or to polaronic effects. (7) Even if the physical origin of the MIR band is still uncertain, the existence of a contribution in the mid- infrared, which is independent of the Drude term, has received in the years experimental support. This can be summarized as follows: i) in the normal metallic phase of all HTCS, 6-(co) consists of a term centered at zero frequency, whose shape as expected depends on T (Drude term), and of a contribution at higher energy which seems not to depend on T; (8) ii) two uncorrelated contributions centered at co=0 and in the mid- infrared, respectively, are clearly identified when studying the behavior of 6-(co) with doping. Indeed, in La-Sr-Cu-O (9) and in Nd-Ce-Cu-O (10) the MIR band appears at very low dopant concentrations, i.e. in the semiconducting phase, where the zero- frequency (Drude) term is still negligible. By further doping, the intensity of the MIR band remains roughly constant while the

Far-Infrared Absorption 253

Drude term grows up and the Cu-O plane undergoes the insulating-to-metal transition.

The above experimental evidence justifies an analysis of reflectivity spectra of HTCS in terms of the following Drude- Lorentz dielectric function:

+

(co) + y s 2 0)2 + icoFD l " (0)2 O)2) _ icoFj

S21R + E (CO2CTi- CO2Z - icoFcTi (CO2IR - 0)2) - icoFMIR i

(1)

Here eoo accounts for all transitions at energies higher than 20000 cm -1 or 2.5 eV (the maximum frequency of this experiment), {0p is the plasma frequency and F D the width of the Drude (D) term. The third term on the right refers to phonons at frequencies coj with oscillator strenghts Sj and widths Fj; the fourth term refers to the MIR band. The oscillators at COCTi are introduced to fit the band which is generally attributed to charge-transfer transitions be tween O-2p and Cu-3d states. In the parent compounds of HTCS, this broad band extends from the near-infrared to the ultraviolet and can be modeled by two oscillators, CT1 and CT2, peaked at 2.0 and 3.0 eV in La2CuO 4 and at 1.5 and 2.8 eV in N d 2 C u O 4. U p o n dop ing CT1 increas ingly weakens by transferring spectral weight to the Drude term and to the mid- infrared band. The intensity of this latter reaches its maximum at low doping (-~ 5% in Nd-Ce-Cu-O, where it is peaked at - 0.5 eV) and then remains nearly constant even in the metallic phase. (10) In a recent work, (11) Falck et al. have shown that the CT1 l ineshape is well reproduced by a short-range electron-hole interaction, and that at low temperature CT1 is also associated to an excitonic contribution.

In the present experiment we study the infrared optical conductivity of films and single crystals belonging to the Bi-Sr- Ca-Cu-O family. We first investigate the insulating compound Bi2Sr2YCu20 8, which in this family may play the role which is

2 5 4 Calvani, et aL

played by the "parent" compounds La2CuO 4 and Nd2CuO 4 in relation with the 2-1-4 superconductors. In addition to the phonon spectrum, which to our knowledge is first determined here, we measure the charge-transfer energies O)CT 1 and c0CT2. Then, we discuss the reflecfivity of seven metallic Bi-Sr-Ca-Cu-O films, looking for a connection between the mid-infrared absorption and the superconducting properties of high-T c cuprates. The integrated intensity of the Drude+MIR oscillators (which approximately corresponds to the total absorption within the charge-transfer gap) will be shown to correlate with T c. A further correlation is found between the peak frequency of the extra-Drude, mid- infrared absorption, and the critical temperature. Such behavior is also confirmed by data of different authors, which will be discussed with particular regard to the case of YBa2Cu307-y (YBCO).

Experimental details

Eight samples belonging to the (Bi,Pb)-Sr-(Ca,Y)-Cu-O family have been investigated in the present study. Three Bil.8Pb0.2Sr2CaCu208+y highly oriented films with Tc= 65, 70, and 76 K were produced by epitaxial growth from the liquid phase (12) on LaGaO 3 substrates.Their thicknesses were of the order of 1 ~tm. Different critical temperatures were obtained by increasing their oxygen content (y>0) and lead was introduced into the composition in order to stabilize the oxygen non- stoichiometry. Three more films belonging to "phase one" with Tc=61, 83, and 85 K and one Bi2Sr2Ca2Cu3010 ("phase two") film with Tc=95 K, all of which were 0.2 ~tm thick, were instead deposited by sputtering on a MgO substrate. In addition to the above metallic samples, a Bi2Sr2YCu20 8 single crystal was measured, to identify the phonon spectrum and the charge transfer band in a "parent" insulating compound.

The room temperature reflectivity R(c~) of metallic samples was measured from 400 to 20000 cm -1 (0.05 - 2.5 eV), that of the insulating sample from 40 to 20000 cm -1 (0.005 - 2.5 eV). The measurements were performed at quasi-normal incidence by a rapid scanning interferometer, with the electric

Far-Infrared Absorption 2 5 5

field of radiation polarized in the a-b plane of the tetragonal crystal structure. A gold-plated sapphire window in the far- and mid-IR, a polished platinum sample in the near-IR and visible ranges, were employed as references.

The optical conductivity was obtained by fitting to the measured R(co) the model reflectivity which can be obtained from the complex dielectric function of Eq. (1). With respect to an analysis in terms of Kramers-Kr6nig transformations, this procedure to our opinion presents several advantages: i) no extrapolation of R(CO) to zero and to high frequency, which might be more or less arbitrary, is requested; ii) the separation of the different contr ibut ions to the optical conduct iv i ty is straightforward; iii) in the case of thin films, the contribution of the substrate to the observed reflectivity can be easily determined and subtracted, (13) while any direct application of K-K transformations would be incorrect.

Results and d i scuss ion

The far-infrared reflectivity of the Bi2Sr2YCu20 8 single crystal is reported in the inset of Fig. 1. By fitting to those data the Lorentz dielectric function, (1) for a vanishing plasma

frequency COp and a vanishing mid-infrared intensity S21R, we obtained the frequencies coj of the seven phonon peaks which correspond to the transverse optical modes. One can notice that seven infrar.ed active E u modes are indeed predicted for the D4h tetragonal cell of this compound. (14) The frequencies coj are reported in Table I and compared therein with the results obtained for Bi2Sr2NdCu208 by Shimada et al. (15).

The overall R(c0) of Bi2Sr2YCu20 8 is shown up to 20000 cm -1 in Fig. 1. It exhibits a broad charge-transfer band in the near-infrared, as also observed in a previous experiment of Terasaki et al.. (16) In Fig. 1, nevertheless, a second charge- transfer contribution is identified as a shoulder of the main peak at higher frequencies. A similar structure has been also observed in NCCO. (10) The frequencies of the charge-transfer oscillators

256

0.4

Calvani, et al.

E--*

C)

Fig. 1.

0.2

0.0

0 . 2

0.0 0

I I I I I I 200 400 600

i [ i 0 10000 ;80000

ENERGY (cm -t) The reflectivity R(r of a Bi2Sr2YCu208 single crystal.The far-infrared range is enlarged in the inset.

T a b l e I

Material Phonon frequencies 0~ c0CT 1 taCT 2 (cm -1) (cm -1)

Bi2Sr2YCu20 8 90 195 232 376 480 570 613 14300 19000 (this work)

Bi2Sr2NdCu20 8 65170195 240 370 480 580 (Ref. 15)

Table I. Peak frequencies of Lorentz oscillators for two insulating members of the BSCCO family.

Far-lnfrared Absorption

10

2 5 7

>~ 0.5 E-* I"--'4

E~ C) 0.0

5fl 0.5

T = 7 6 K C T C =65 K

Tlc=8a K I

10000 0

C I I !

! I

10000

L t I

=95 K

0.0 i 0 20000

ENERGY(cm -I) Fig. 2. The reflectivity R(c0) of four Bi-Sr-Ca-Cu-O films with

different critical temperatures.

CT1 and CT2, as extracted by fitting R(c0) to the model reflectivity obtained from Eq. (1), are also reported in Table I.

The reflectivities of the metallic films (Fig. 2) look quite different. The phonon contributions are shielded by the intense Drude absorption of free carriers (holes for Bi-Sr-Ca-Cu-O), which has a strong tail in the mid-infrared (MIR band). Moreover, the charge-transfer oscillators are weaker and broader than in the insulating compound of Fig. 1. The values of 0~CT 1 and o~CT 2 determined in Table I provide a useful check for those obtained from the fit in the metallic compounds.

The real part o(~) of the optical conductivity, as obtained from data in Fig. 2 by the fitting procedure described in the preceding section, are reported in Fig. 3. The Drude, MIR, and CT contributions to o(r are separately plotted. By integrating

2 5 8 Calvani, et al.

these curves one obtains (10) the effective number of carriers naeff corresponding to a particular contribution 0~ = (D, MIR, CT1, CT2) :

(co)= (2m*V/~e 2) ~ : o "~ (co) do) (2) naeff

Equation (2) allows to evaluate the so-called "spectral weight" in a certain energy range. For example, in view of Fig. 3,

nDeff +nMIRef f N neff(C0gap)

is the effective number of carriers within the charge-transfer gap, which from the present measurements on Bi2Sr2YCu208 is of the order of 1.5 eV. The ratio neff(C0gap)/neff(oo), where neff(o,,) is the

750

I

I

O

b

Fig. 3.

500

2 5 0 - -

0

I000

500

0

T =65 K C

-/.

---~\. , i / .

T = 8 3 K c

T = 7 6 K C

]1 T c =95 K Ii ~'~ ~',,

0 10000 0 10000 20000

ENERGY(cm -1) The optical conductivity cffc0) (dash-dotted), as obtained from the data of Fig. 2 The Drude (dashed), MIR (solid), and CT (dotted) contributions are also shown.

Far-Infrared Absorption 2 5 9

total number of effective electrons, is plotted in Fig. 4 for the highest reflectivity BSCCO samples here investigated and for the Nd-Ce-Cu-O compounds measured in Ref 19. In Fig. 4, neff(0~gap)/neff(~) is an increasing function of Tc, but it seems to saturate for high values of the critical temperature.

If one now goes back to Fig. 3, one can notice that the peak energy of the mid-infrared oscillator displaces towards the low frequencies as the sample critical temperature increases. This effect is confirmed in Fig. 5, where the peak energies of the MIR band, as determined here on BSCCO (dots) and by different authors in other HTCS families, are plotted vs. T c Data are referred to systems as different as BaPbl_xBixO3, (triangle, Ref. 17) La2xSrxCuO 4 (hexagon, Ref.18), Nd2_xCexC~ (reverse triangle, Ref. 19), YBa2Cu3OT_y, (square, Refs. 8, 20, 21)

0.5

8 0 . 4

0.3

t:~ 0.~ 3

(D 0 .1

Fig. 4.

El { : : I f ri

/

/ - /

-/

0

/ /

13

I 0 . 0 ~ ! I I t ~ I L

50 100

To(K) The ratio neff(C0gap)/neff(~), is plotted vs.T c for (Bi, Pb)- Sr-(Ca, Y)-Cu-O (squares, this work) and for Nd-Ce-Cu- O (stars, Ref. 19). The line is just a guide to the eye.

2 6 0 Calvani, et al.

0.8

::>

:>-. (D 12::

Z

0.4

A

9 9 MIR N O il N i t \

\ i l \ [ ]

\ o \

o

I . . . . I O . . . . I . . . . 12u

O

O 0 J , , , I . . . . ! . . . . 0 60

Fig.

To-(K) 5 T h e peak f r e q u e n c y coMIR of the e x t r a - D r u d e

contribution is plotted as a function of T c for the (Bi,Pb)- Sr-Ca-Cu-O samples here invest igated (dots) and for other HTCS compounds observed by different authors (see text). The line is just a guide to the eye.

Bi2Sr2CaCu20 8, (circles, Refs.6,22), T12Sr2CaCu20 8 (d iamond, Ref. 23) Pb2Sr2(Eu,Dy)Cu30 8 (star, Ref. 26).

All of values repor ted in Fig. 5 have been measured in single crystals or in highly oriented films with the electric field of radiat ion polarized in the a-b planes. Either they are explicitly reported by the authors, or they may be easily extracted from the plots of (;(co). It m u s t be e m p h a s i z e d tha t da ta on Pb2Sr2(Eu,Dy)Cu308 (stars) are part icularly meaningful , as the Drude term of these compounds is very small. Then they offer the opportuni ty of observing a well defined mid-infrared band in cuprates with critical temperatures as high as 65-80 K. The same holds for BSCCO samples which for tui tously present a low Drude reflectivity, as the one with T c = 76 K in Fig. 5. On the other hand, the inclusion of YBCO data in Fig. 5 requires a short

Far-Infrared Absorption 2 61

comment . As it is well known, YBCO singles out among HTCS in that both Cu-O planes and Cu-O chains contribute to the electrical as well as to the optical conduct ivi ty. Reflectivity measurements on un twinned YBCO microcrystals performed by linearly polarized radiation have revealed the existence of a mid- infrared band (as for the normal , tw inned crystals of Fig. 5). Nevertheless, they have given contradictory results as far as the e n e r g y and the a t t r ibut ion of the mid - in f r a red band are concerned. Indeed, whi le Rotter et al. (24) assign an oscillator peaked at 2000 cm -1 to the Cu-O cha ins , Koch et al. (25) do not find any extra-Drude contribution from the chains for photon frequencies lower than about 8000 crn -1. In turn, the Cu-O planes contribute a Lorentz oscillator at about 4600 cm -1. If one admits that the mid-infrared band comes out of the Cu-O planes, YBCO data can be meaningful ly compared with those of other HTCS and, as shown in Fig. 5, they substantially confirm the overall behavior of ~MIR vs . T c. In the opposite case, their exclusion will not inval idate the effect pointed out in Fig. 5, nor the following conclusion.

Indeed, Fig. 5 shows that O}MI R moves to the far-infrared as T c increases. Moreover, ~MIR appears to tend towards zero as T c approaches the m a x i m u m values present ly ob ta ined in cuprates (-~ 90 K for Y-Ba-Cu-O, = 110 K for Bi-Sr-Ca-Cu-O, and = 125 K for T1-Sr-Ca-Cu-O). Figs. 4 and 5 then point out that a relation exists between the infrared spectrum of HTCS and their critical temperature. As the effective number of carriers within the charge-transfer gap increases, and the mid-infrared band displaces its spectral weight towards zero energy, the critical temperature Tc of the sample increases.

Conclusion

The optical measurements presented in this paper have shown that in BSCCO and in other H T C S , both the spectral we igh t at low frequency and the peak frequency of the extra- Drude absorption are related to the critical temperature of the sample. The former quanti ty seems to reach a saturating value, the latter tends to zero, when T c = 100 K. The displacement of

262 Calvani, et aL

03MI R t ow a r ds the fa r - inf rared seems to be pa r t i cu la r ly meaningful . As r R tends towards zero, one sees from Eq. (1) that the MIR band tends to super impose to the D r u d e term. Nevertheless , as I"D<<I"MIR, the two contr ibut ions can still be dist inguished. Finally, it should be remarked that the behaviour of (0MIR, in Fig. 5 may imply the existence of an upper limit for the critical temperature of the cuprates, which should be not far f rom the highest T c values obta ined to date in this type of superconductors.

Acknowledgement

This work has been suppor ted in part by Proget to SATT of Consorzio INFM, and by Progetto Finalizzato Supercondutt ivit~ of Consiglio Nazionale delle Ricerche.

References

1)

2)

3) 4)

5)

6)

7)

8)

9)

10)

Z. Schlesinger, R. T. Collins, F. Holtzberg, C. Feild, G. Koren, and A. Gupta, Phys. Rev. B 41, 11237 (1990). S. L. Cooper, G. A. Thomas, J. Orenstein, D. H. Rapkine, M. Capizzi, T. Timusk, A. J. Millis, L. F. Schneemeyer, and J. V. Waszczak, Phys. Rev.B 40, 11358 (1989). C. X. Chen and H. B. Schuttler, Phys. Rev. B 43, 3771 (1991). C. M. Varma, P. B. Littlewood, S. Schmitt-Rink, E. Abrahams, and A. E. Rukenstein, Phys. Rev. Lett. 63, 1996 (1989), Physica C 165, 152 (1990). T. Timusk and D. B. Tanner, Infrared properties of High Tc Superconductors, in: Physical Properties of High Temperature Superconductors, ed. by D. M. Ginsberg, World Scientific, Singapore, 1989, 339. I. Terasaki, T. Nakahashi, S. Takebayashi, A. Maeda, and K. Uchinokura, Physica C 165, 152 (1990). D. Mihailovic, C. M. Foster, K. Voss, and A. J. Heeger, Phys. Rev. B 42, 7989 (1990). J. Orenstein, G. A. Thomas, A. J. Millis, S. L. Cooper, D. H. Rapkine, T. Timusk, L. F. Schneemeyer, and J. V. Waszczak, Phys. Rev. B 42, 6342 (1990). S. Uchida, T. Ido, H. Takagi, T. Arima, Y. Tokura, and S.Tajima, Phys. Rev. B 43, 7942 (1991). S. Lupi, P. Calvani, M. Capizzi, P. Maselli, W. Sadowski, and E. Walker, Phys. Rev. B 45, 12470 (1992).

Far-Infrared Absorption 2 6 3

11) J.P. Falck, A. Levy, M. A. Kastner, and R. J. Birgeneau, Phys. Rev. Lett. 69, 1109 (1992).

12) G. Balestrino, R. Di Leo, M. Marinelli, E. Milani, A. Paoletti, and P. Paroli, Physica C 162, 115 (1989).

13) P. Calvani, M. Capizzi, S. Lupi, and P. Maselli, Phisica C 180, 116 (1991).

14) A.D. Kulkarni and F. W. de Wette, private communication to the authors of Ref. 15.

15) M. Shimada, K. Mizuno,S. Miyamoto, M. Shimizu,and J. Tanaka, Physica C 193, 353 (1992).

16) I. Terasaki, T. Nakahashi, S. Takehayashi, A. Maeda and K. Uchinokura, Physica C 165, 152 (1990).

17) S. Tajima, S. Uchida, A. Masaki, H. Takagi, K. Kitazawa, S. Tanaka, and A. Katsui, Phys. Rev. B 32, 6302 (1985).

18) D. Mihailovic, C. M. Foster, K. Voss, and A. J. Heeger, Phys. Rev. B 42, 7989 (1990).

19) P. Calvani, M. Capizzi, F. Donato, S. Lupi, P. Maselli, W. Sadowski, and E. Walker, unpublished.

20) T. Timusk, D. A. Bonn, J. E. Greedan, C. V. Stager, J. D. Garrett, D. B. Tanner, Physica C 153-155, 1744 (1988).

21) Y. Watanabe, Z. Z. Wang, S. A. Lyon, N. P. Ong, D. C. Tsui, J. M. Tarascon, and E. Wang, Solid State Commun. 74, 757 (1990).

22) M. Reedik, D. A. Bonn, J. D. Garrett, J. E. Greedan, C. V. Stager, T. Timusk, K. Kamaras, and D. B. Tanner, Phys. Rev. B 38, 11981 (1988).

23) C.M. Foster, K. F. Voss, T. W. Hagler, D.Mihailovic, A. J. Heeger, M.M. Eddy, W. L. Olson, and E. J. Smith, Solid State Commun. 76, 651 (1990).

24) L.D. Rotter, Z. Schlesinger, R. T. Collins, F. Holtzberg, C. Field, U. W. Welp, G. W. Crabtree, J. Z. Liu, Y. Fang, K. G. Vandervoort, and S. Fleshier, Phys. Rev. Lett. 67, 2741 (1991).

25) B. Koch, H. P. Geserich, and T. H. Wolf, Solid State Commun. 71, 495 (1989).

26) M. Reedik, T. Timusk, J. S. Xue, and J. E. Greedan, Phys.Rev. B, in press.