Recent results in Raman spectroscopy of high-Tc superconductors

I Php Printed

Chem B/ids Vol. in Great Britain.

RECENT HIGH-T,

54. No.

IO. pp. 1287-12%.

0022.3697/93 16.00 + 0.00 0 1993 Pergmon Press Ltd

1993

RESULTS IN RAMAN SUPERCONDUCTORS MANUEL Max-Plan&-Institut Heisenbergstr.

SPECTROSCOPY

OF

CARDONA fiir Festk6rperforechung

1, D-7000 Stuttgart

80, F.R.G.

ABSTRACT. We discuss some outstanding problems in the field of Raman scattering by high-T, SUperconductors and review recent results with emphasis on photons, electron-phonon interaction and f-electron crystal field transitions. Xeyworrls:

High-T, Superconductors,

Raman Scattering,

Electron-Phonon

Interaction

INTRODUCTION Raman spectroscopy is a powerful technique for investigating and characterizing high-?“, superconductors (Thomsen 1991a, Feile 1989) It has revealed low-frequency elementary excitations such as phonons, magnons, intraband electronic excitations in the normal state, excitations in the superconducting state, and crystal field excitations in materials containing rare-earth ions. Here we discuss some unsolved problems related to the Raman spectra of high-T, superconductors and present selected recent results. Raman spectra can be obtained either The visible laser lines usually employed has to reckon with a typical sampling representative of the bulk within this UPS samples a depth of -5 A, XPS diffraction a few pm, while neutron spectroscopies discrepancies reflecting be found.

from bulk single crystals, thin films or ceramic samples. are strongly absorbed by the high-T, material so that one depth of 500 to 1000 A. The surface should be clean and depth, a condition not difficult to fulfill. By comparison, 50 A, ir spectroscopy 4000 A and x-ray emission or scattering samples macroscopic lengths. With different differences between surface and bulk properties may thus

Another feature of Raman spectroscopy is the possibility of altering the scattering efficiency (i.e. the cross section) by changing the laser frequency. At certain frequencies, often coinciding with structure in the dielectric response, maxima in the Raman efficiencies are observed (Reyen eb al. 1990). These maxima, which exemplify resonant Raman scattering, can be used to optimize Raman signals (Wake ef al. 1991) and also to obtain information on the interaction of the scattering excitations with interband electronic transitions (Wake et al. 1991). In some cases Raman forbidden transitions (such as ir-active phonons, see Heyen eZ al. 1992) become allowed under resonant conditions. Another advantageous feature of Raman scattering arises from the second rank Raman tensor. This tensor has a number of irreducible components (four in the L&n point group of many high T, superconductors) which can be separated by varying the polarization of the incident beam, and that of an analyzer placed in front of the monochromator, with respect to the crystal axes. In this manner, the symmetry of the excitations involved can be unambiguously determined.

PHONONS Because of the simplicity of the technique and the modest requirements on sample size and quality, the first information on phonons of high T, superconductor was obtained by Raman spectroscopy (for reviews see Thomsen 1991a, Feile 1989). Although the 123 materials have become canonical for these studies, the Raman phonons of other families of high Te superconductors have also been investigated. Nearly all have inversion symmetry and hence the optically active phonons (k ~0) can be classified into ir (odd) and Raman active (even). In the Raman spectra of 123 materials only five fully symmetric (A,) phonons appear strongly. They correspond to vibrations of Ba, CUII, Olv, Orr and 011, along c. For tetragonal (&,) or nearly-tetragonal PCSYll~

1287

M.

1288

CARDONA

(Dzh) symmetry the 011-Orrr vibrations yield two such modes, namely A, (440 cm-‘) and 81, (340 cm-‘, odd upon a C, rotation). The B1, mode plays a pivotal role in the investigation of phonons in 123 materials, it can be easily and unambiguously identified because of its d-wavelike scattering pattern. Also its frequency is close to that of the superconducting gap 2A, a fact which results in renorm~izations close to T’ (Fried1 et ai. 1990). A survey of ir and Raman phonons of YBazGu307 is given in Fig. 1. Two points remain unsolved:

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Only the upper half

1. The frequency of the so-called “silent mode” which is odd and ir-allowed in &h symmetry

but becomes silent in the D.+h tetragonal (&,) symmetry. It appears in the calculation of Fig. 1 at 300 cm-’ but has not been observed optically because of its weak ir-activity. Neutron scattering suggests ml90 cm-’ for its frequency (Pyka et al. 1991). 2. The Raman modes shown involve (contrary to the ir modes) mainly vibrations of only

one kind of atom. The A, modes at 112 (Ba) and 154 (Gu) cm-‘, however, are rather close and, in principle they can mix. Nearly (50 - 50) mixing is found in first principles calculations of these phonons (Cohen et al. 1990, Rodriguez et al. 1990). This result is contradicted, however, by isotopic substitution of copper (Mascarenhas et al. 1989) and by resonant Raman measurements (Heyen et al. 1990) which favor unmixed Cu and Ba modes. A modification of the 123’s leads to the 124 compounds (YBa2Cu40a) with two chains per primitive cell instead of one. Hence the Gu and 0 atoms of the chains are not at inversion

Raman spectroscopyof high-T, superconductors

1289

centers. Their vibrations lead to Raman and ir active modes which in 123 are only ir active (Heyen et al. 1990a). The Raman and ir phonons of the so-called T’ materials (e.g. Ndz-=Ce,CuOh) have also been investigated (Beyen et al. 1991a). Copper, at a center of inversion, is only involved in ir-active modes. Raman (and ir) modes result from the Nd atoms (Arr modes at -220 em-*) and from two of the oxygens (Bls-like Raman modes at -330 cm” and Eg modes at -480 cm-r). An unsolved problem is the appearance of a strong line at 580 cm” in the C&doped material which cannot be assigned to any symmetry-allowed Raman mode. Isotopic substitution has shown that this line is related to oxygen vibrations (Wegerer et al. 1993) but its exact nature remains unknown. Raman spectroscopy can be used for materials characterization. We discuss first the study of the epitaxial quality of films of the 123 compounds based on the Raman Br, modes. Films grown on [loo] SrTiOs have the c-axis perpendicular to the substrate but the a-b axes may be either at random or epitaxial (except for twinning). For the t(zz)E configuration the latter lead to a constant scattering intensity when the film is rotated around c. For epitaxial films, intensity minima (near zero) are obtained when the incident and scattered polarizations are parallel to z + y (or to x - y) (Thomsen et al. 1992). The -500 cm’ 1 Raman vibrations of the apical oxygens have been recently used (Hadjiev et al. 1993) for the investigation of room te~~erat~~ annealing observed for quenched samples of YBasCus0s.s (Veal et ul. 1990). At room temperature the chain oxygens are initially disordered. After a few hours, however, they order into the so-called 011 structure with chains alternatively filled and empty of oxygen. This phenomenon is also manifested in the visible (Kircher e2 al. 1992) and ir (K’lrc her et al. 1993) optical spectra. We show in Fig. 2 the evolution with time of the A, mode of the apical oxygen after quenching and keeping the sample at room temperature. The observed spectra have been fitted with lorentzians: three main components appear, the one centered at 489, corresponding to 011, grows with time while the others (011 at -500 cm-’ and T at -475 cm-‘) decrease. It has also been shown by Raman scattering that YBasCusOr_a (especially for S different from 0, 0.5 and 1) usually contains a mixture of the three phases 01 (6 = 0), 011 (6 = 0.5) and T (6 = 1) (Iliev et al. 1993) These three spectral components have different resonant behavior. Hence the line shape changes drastically with laser frequency. Even the position of its maximum may change from one laser line to another. Consequently, great care must be exercised when trying to determine b from the position of this peak.

SUPERCONDUCTING GAPS The high-T, superconductors exhibit in their normal state a low-frequency continuum of electronic transitions which has been much investigated but is not wholly understood (see e.g. Reznik et al. 1992). Below T, a gap (or pseudogap, see below) opens in this continuum with a cusp at a frequency believed to be representative of 2A (Lyons et al. 1987, Staufer et al. 1992, Boekholdt et al. 1991, Krantz et al. 1989, Heyen et al. 1991b). Typical values of 2A/~T~ II 5 are found. Sometimes, however, two different gaps appear in the free carrier scattering continuum, depending on polarization configuration. For Bi#rzCaCuzOs, for instance, the gap in zt polarizations seems to be about half that found in tz or pg polarizations (Boekholdt 1991) In the case of YBa$&Os similar results are found for zz polarization (2A/kT, N 6) while for gg 2A/kT, N 3 is obtained. A model which can account for this for gap anisotropy has been proposed by Abrikosov (1991). Usually but unex~ctedly the energy 24 does not decrease when, in a given family of materials, Tc is lowered by doping (e.g. in YBa&!usOr by removing oxygen or replacing Y by Pr). Likewise, 2A does not decrease when T approaches T, in the manner described by the BCS theory (Staufer

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t=10

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Tc=-JL7K

CARDONA Fig. 2: Room temperature evolution of YBa2CusOs.s after quenching.The lower part of each vignette dieplays spectra sharpened through fast Fourier transform techniques (from Hadjiev et al. 1993).

c

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(4

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f

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520

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et al. 1992). Instead, it remains nearly constant and drops, if at all, only very close to Tc. This behavior is one of the many puzzling facts which remain to be explained by the elusive theory of high-T, superconductors,

Another ununderstood fact is that the gap which opens in Raman spectra below Tc is not a sharp gap but a so-called pseudogap, where the intensity decreases monotonically from w = 2A down to w = 0. This decrease is usually linear (Cooper ef al. 1988) but for BizSrsCaCusOs a nearly quadratic dependence on w is observed below 2A (Boekholdt ed ai. 1991, Yamanaka ef al. 1988). ELECTRON-PHONON LNTERACTXON The phonon frequency and changes in width observed when crossing Tc are related to interaction of the particular phonon with the electronic continuum (Wittlin et of. 1987, Macfarlane eZ al. 1987). Of special interest are the BIP-like phonons which have nearly the same frequency (-340 cm-‘) as the 26 given above. The transition at Tc is expected to downshift phonon

Ramanspectroscopyof high-T,superconductors

1291

frequencies which lie slightly below 2A (this is observed for the 340 cm-’ phonons) and upshift those above 2A (e.g., the A, phonons at 440 cm” which corresponds to 011-0111 vibrations) (Thomsen et al. 1990). Likewise, phonons with frequencies above 2A should broaden below T, while those below 2A should sharpen as decay channels are removed in the gap. A study of these effects, based on the theory of Zeyher and Zwicknagl (1990) has been performed for of REBa&u30r compounds (Fried1 ef al. 1990, Thomsen ef al. 1990). By varying the rare-earth metal (RE) and the oxygen isotope, the phonon frequencies can be varied over a 20% range while the gap remains nearly the same. Fits of the observed shifts and broadening6 to the theory enable one to determine the gap 2A N 5.OT, and the electron-phonon coupling constant (A II 0.8 if all phonons would couple like B1, phonons). This coupling constant suffices to explain a T, of up to 30 K but not the 90 K under consideration. While the softening of the Bi, phonons is generally accepted, a broadening below T, is not always found. This has generated considerable controversy (McCarty et al. 1992, Altendorf ef al. 1992). The Bi, phonon of YBa&usOr can either broaden strongly or sharpen weakly below Te depending on sample preparation. In my opinion broadening occurs in samples of high stoichiometry and purity. Oxygen deficiency (Altendorf 1992) and also substitutional doping with either Au, Fe, or Pr (Thomsen et al. 1991a) lead to a sharpening below Tc which corresponds in the theory to an increase in the average gap with respect to purer samples. The origin of these effects is not well understood (Thomsen et al. 1991a). We show in Figs. 3 and 4 the changes in linewidth and frequency with temperature measured for the B1, phonon for several values of 6. Figure 5 displays linewidth data (Thomsen et al. 1991a) for an Au-doped sample and for a II I 21

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CAROONA

nominally pure sample grown in a zirconia crucible (McCarty et al. 1992). Note the similarity with the 6 = 0.05 data of Fig. 3. Note in Fig. 4 that the samples which exhibit a sharpening Fig. 5: Linewidth of the El0 phonon of YBazCusOr vs. temperature for two samples, one with 7.5% of the Cu replaced by Au. The other nominally pure but grown in a Zr crucible. See text. From C. Thomsen and M. Cardona, Physica C 206 (1993) 137.

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of the B1, mode below T, display a smaller softening than those which broaden below T,, a fact which also suggests a decrease in the gap from the former to the latter. These effects have been investigated for twinned and twin-free single crystals with micro-F&man techniques in order to examine their topography in the different grains and at grain boundaries (Hadjiev et al. 1991). The behavior of Fig. 6 can be understood if one postulates that untwinned regions are slightly oxygen deficient because of the poor diffusion coefficient along c. Highly twinned regions and grain boundaries provide paths for the diffusion aiong a, b of oxygen, which should lead to low 6’s. In this manner the results of Fig. 6 become consistent with those of Fig. 3. The anomaly in the frequency of the BQ phonon at Te has been recently observed by neutron scattering (Pyka ei al. 1993). Anomalies at TE are also found for the ir-active phonons (Genzel ef al. 1989), in particular those at 280 cm-’ and 309 cm ml (Fig. 1). In substituted 123 materials the softening of these phonons can start a few tens of degrees above T,, thus suggesting some phase transition different from that which leads to superconductivity (Litvinchuk el al 1993a). Similar effects have been observed for the frequency shifts of the 124 materials (Litvinchuk ei al. 1993a). In all these cases, and despite the anomalies in the shift, the change in linewidth starts at T,. This effect still looks for an explanation. Recent work on the change in phonon widths with temperature in Yi_,Pr,Ba&.&Os indicates that the gaps of these materials (which are superconducting for z < 0.7) scale like T, as expected for conventional superconductors (Litvinchuk et al. 1993b). This is in contrast to results for the 123 materials.

CRYSTAL FIELD EXCITATIONS Many high Tc superconductors contain rare-earth ions (usually trivalent RE3+) which, with the exception of La3+ and Ce4+ have 4f electrons. These electrons must be treated as many-body atomic states leading to eigenstates of the total J which can be handled, to a first approximation, by assuming L . S coupling. We use here for one of these L - S multiples the notation “+~LJ, whereL=S,P,D,F ,.... The degeneracy of the muitiplet (2s + 1) is partly lifted by the crystal

Raman spectroscopyof high-T, superconductors

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Temperature (K) field (cf). The transitions between the ground state of the cf multiplet (or a thermally excited state) and a higher excited state are called cf excitations. They have been observed for many RE in 123 (Soderholm et al. 1991; Allenspach et al. 1989) and 214 (Bothroyd et al. 1992) compounds by neutron scattering. Raman results have, so far, only been reported for Nd3+ in 123 (Heyen ef al. 1991), 214 (Jandl et al. 1993), and in PbzSrzNdCusOs (Wegerer et al. 1993a). In 123 and in PbzfrzNdCusOs the RE occupies a center of inversion. As a result, transitions between cf levels are optically forbidden, a fact which leads to negligible Raman cross sections unless the cf excitations are mixed with phonons. This explains the difficulty of detecting cf excitations in Raman scattering: their frequency must be very close to a phonon of the same symmetry. That phonon and the cf excitation must also couple through electron-phonon interaction. Such is the case for the B1, phonons and the cf excitations within the 4I9,2 multiplet at -300 cm-’ (Fig. 7). We show in Fig. 8 the Raman spectra of the ~~~-phonon-cf-excitation coupled modes in Pb~Sr~NdCusOs. Note that the weak cf peak decreases with increasing temperature. This is due to the thermal population of the higher cf levels and the depopulation of the ground state

M.

1294

CARLIONA

P b2Sr,NdCu30~ z(xy)f

80

K

40

K

0

Fig. 7: Splittings of the ‘ls,s ground Nd3+ in a cubic (Oh), tetragonal (D*h) thorhombic (&h) crystal field. The latter to be that of NdBa&uaOr (Heyen et al.

state of and oris taken 1991c).

Fig. 8: Raman spectra of the coupled .&, phonon (~275 cm-‘) - cf excitation (335 cm-‘) in Pb&+NdCuaOa (Wegerer et a1.1993). Note that in this material the BQ mode is obtained for zy polarization (with respect to orthorhombic axes} since the orthorhombic axes are rotated by 45’ with respect to the tetragonal ones.

I.‘...‘...‘...‘...‘..

280 320 Raman

360 shift

400 440 (cm-‘)

(Fig. 7). The lines of Fig. 8 are theoretical fits based of electron-phonon coupling treated to all orders (within the one-phonon plus one cf-excitationsystem). From these fits an electron-phonon coupling constant is found which compares favorably with that obtained through cf calculations (Ruf ef al. 1993). Recently cf excitations Raman active on their own merits have been observed in Nd&uO* (Jandl et al. 1993). The difference with respect to the 123’s and Pb2Sr~NdGusOs is probably due to the fact that the RE’s in the Nd-214 are not at a center of inversion. Hence cf transitions become dipole allowed and can function as intermediate states in Raman scattering. In the Nd-214 not only cf within the *&,2 multiplet are seen but also between 4I9,2 and the next multiplet (41rr/r).

ACKNOWLEDGEMENT I would like to thank G. Thomsen for a critical reading of the manuscript, W. Kress for help in the comp~ition of Fig. 1, and all colleagues who have contributed to the work reported here.

Raman spectroscopy of high-T, superconductors

t295

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12%

ibf.

P. Allenspach,

A. Furrer, P. Briesch

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and P. Unterniihrer,

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to be

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to be published.