Selected aspects of the lattice dynamics in high-Tc oxide superconductors

PhysicaC 162-164 (1989) 1705-1708 North-Holland

SELECTED ASPECTS OF THE LA'I'rlCE DYNAMICS IN HIGH-Tc OXIDE SUPERCONDUCTORS

H. RIETSCHEL,L. PINTSCHOVIUS,and W. REICHARDT Kernforschungszentrum Karlsruhe, Institut for Nukleare Festk6rperphysik, P.O.B. 3640, D-7500 Karlsruhe, Federal Republic of Germany We present selected results of inelastic neutron-scattering experiments on single-crystalline La2CuO4. For this compound we find very unusual features in the nuclear scattering law S(K,O) such as strong asymmetries in S(x,co) for x =~ + q and in particular an unexpected splitting of the breathing mode. For YBa2Cu307-8, very recent measurements seem to exhibit similar extra modes. A possible explanation tot these pronounced anharmonicities would be hybridization of lattice modes with electronic excitations thus indicating very strong electron-lattice coupling.

1. INTRODUCTION The theories so far proposed to explain high-To superconductivity in cuprates may roughly be classified into two groups: i) Theories where the condensation into the superconducting state requires only electronic degrees-of-freedom (e.g., excitonic or RVB-type theories) ii) Theories where the attractive interaction between the electrons (or holes) is mediated by the dynamic polarizability of the ionic lattice. There are numerous experimental findings which show undoubtedly that for the oxide superconductors, electronic degrees-of-freedom and lattice dynamics are strongly coupled in at least some portions of phase space. The clear-cut kink at Tc in the thermal conductivity of YBa2Cu307 1 or the sizeable isotop0 effect in (La,Sr)2CuO4 2 are examples for this. The coupling between the electrons and the lattice dynamics may even show up in the lattice excitations themselves producing renormalization. This was already observed in the phonon density-of-states (PDOS) of (La,Sr)2CuO4 and of YBa2Cu307-6 3 as measured by inelastic neutron-scattering on polycrystalline samples. But there are also arguments questioning the importance of electron-ion coupling for superconductivity in cuprates. Microscopic calculations of the electron-phonon coupling and subse0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

quent solutions of the Eliashberg equations can explain Tc's of only just 30 to 40 K 4 thus proving that electron-phonon coupling by itself cannot account for Tc = 92 K in YBa2Cu307. This theoretical result is supported by the virtually missing isotope effect in this compound. 2 This conclusion is only valid if the ionic displacements 8R caused by lattice polarization are small compared to lattice spacings R, 6R/Re 1. In that case, the harmonic approximation holds, and we are dealing with electrons, phonons, and their interaction, the adequate description being Eliashberg's theory. If, however, 8R/R~: 1 at least for some selected ionic movements, the harmonic approximation brakes down and phonons are no longer good quantum states. In this anharmonic regime, Eliashberg's theory is no longer the suitable frame and neither calculations like those of Ref. 4 nor harmonic evaluation of the isotope effect may be applied a priori. Indeed, it is wellknown that for the classical superconductor PdH, anharmonic H-vibrations lead to an even inverse isotope effect for H-, D substitution. Numerous theories have been proposed to explain high-To superconductivity on the base of anharmonic lattice dynamics. The various models for potaronic superconductivity (see, e.g., Ref. 5) belong to this group as well as the theories assuming anharmonic vibrations in double-well

1706

H. Rietschel et al. / Selected aspects of the lattice dynamics

potentials. 6 Although certainly intriguing, none of these theories has ever been quantified in a numerically controlled way, and we consider them more qualitative proposals needing further theoretical and experimental investigations. In this contribution, we present selected results of recent neutron-scattering experiments performed on single crystals of La2CuO4 indicating strong anharmonic effects for at least some lattice excitations. We will also briefly discuss very recent results for YBa2Cu307~. If in the following, the expression "phonon" is used, one should always bear in mind that this is just for the sake of brevity and that at least behind some "phonons", strong anharmonic lattice excitations may be hidden. Regarding experimental details and more extended discussion of the lattice dynamics, the reader is referred to Ref. 7 for La2CuO4 and to Ref. 8 (these Proceedings) for YBa2Cu307-6. 2. RESULTS La2CuO4- In many respects, the lattice dynamics of La2CuO4 are similar to those of the isostructural LazNiO4 which was investigated earlier. 9 A common feature is the fact that the modes polarized perpendicular to the basal planes are typical of an ionic insulator. In particular, there is a large LO-TO-splitting of the second highest A2u mode. On the other hand, modes polarized in the basal plane are typical of a metal. From this point of view, La2CuO4 behaves like a 2d-metal. In Fig. 1, we present the phonon dispersion curves for longitudinal polarization in main symmetry directions at room temperature. For simplicity, we use tetragonal notation. The orthorhombicity at RT leads to splittings of some branches (dotted lines). Some measurements were repeated at 525 K in the tetragonal phase. An attempt was made to describe these dispersion curves and the corresponding transverse modes (not shown) in a rigid-ion model with anisotropic screening and a breathing term to reproduce anomalies in the high optical branches.

22f 21

19

18 • A1 295K °A z xA1 525K v.A. 3

17

" E~

295K 525K

x rI

16

15 13q -It--

12

.

\%,...~

./,~"

11 I

q

+I/-...

g

,r'~

,I- ./.+/\ +L/./

'If

\4 \M ,

o

o.5

I

(~;,0,OJ

Longitudinal La2CuO4.

0

(0,0J;J

FIGURE 1 phonon dispersion

,

I

.

0.25

0.5

(~;,~;oj curves

for

For La2NiO4, this model had already given a fair although not perfect fit. 9 For La2CuO4, it worked much worse. We note that a much simpler model gave an excellent fit to the phonon dispersion curves in CuO4, a system of similar crystallographic complexity. We did not try to improve on the model since there is experimental evidence that no harmonic model can satisfactorily describe the lattice dynamics of La2CuO4. To begin with, we observed strong differences of inelastic structure factors which in harmonic

H. Rietschel et al. / Selected aspects of the lattice dynamics

approximation should be identical by symmetry. For instance for LA phonons with wave vector (q,0,0), the phonon intensity I should be symmetric around reciprocal lattice points • with (1,0,0) symmetry if corrected for trivial (~ + q)2 factors:

l(~+q,O,O). (ix-q)2 =I l(~-q,O,O). (~x+q)2

(I)

In Fig. 2, we show this ratio for LA phonons in (1,0,0) direction around the (2,0,0) and (4,0,0) reciprocal lattice points as determined in our neutron-scattering experiments. We find the relation (1) violated by up to 80%. Such asymmetries can be traced back to a coherent mixing of 1-phonon and 2-phonon terms caused by cubic anharmonicities in the scattering law and were first investigated long ago in context with anharmonicities in alcali halides.I0 The very pronounced asymmetries observed in our experiments are mostly probably related to the fact that the LA-(1,0,O) phonon branch is strongly interacting with the soft mode leading to the tetragonal-to-orthorhombic phase transformation. This is reflected in the considerable splitting of this branch in the orthorhombic phase (see Fig. 1).

I_

I . (T-q) z (T.q) 2

o o:(2+_~,0.0) o o

o:(4_+~,0,0)

1.5

LB2CuO~°j~,7 o.:O

1

0

I

I

0.1

0.2

FIGURE 2 Asymmetries in the intensity for LA phonons in La2CuO4.

1707

The strongest evidence, however, against a harmonic picture was observed in the high frequency branches involving Cu-O bond stretching vibrations. In these branches, pronounced renormalization effects in breathing-type modes at (0.5,0,0) and (0.5,0.5,0) were already found in La2NiO4 9 and expected to be even stronger in La2CuO4 since electronic band theory predicts the breathing mode at the X-point to be unstable. 4 The experimental result was very different: Instead of being very soft, this mode is split into two well defined excitations with v=22.4 and 14.9 THz, respectively. Going from the zone boundary to the zone center, the splitting does not decrease, but instead the intensity shifts completely to the high energy excitation (Fig. 3). A very similar behaviour was observed for modes with breathing character around (0.5,0,0). Very anomalous line shapes, which resemble somewhat the results for La2CuO4, had previously been observed in La2NiO4 in the (110)-direction, but not in the (100) direction. 9 As mentioned above, some splittings observed in low frequency branches are d u e to the orthorhombic distortion. To check if the splitting in the high frequency branches is also due to this, additional measurements were carried out above Ts: the splitting persisted unchanged. YBa2~u3OT~-Very recently, phonon-dispersion relations have also been measured for YBa2Cu307-6. First results are presented on this Conference. 8 Here, we summarize just those aspects which parallel those discussed above for La2CuO4. • YBa2Cu307 does not show LO-TO splitting for modes polarized along c-direction. Rather, it behaves like a true 3d metal. Whether the splitting reappears in YBa2Cu306 is not yet clear. • The intensities of the LA-(1,0,0) phonon branch do not show these pronounced asymmetries as found for La2CuO4. This is compatible with the fact that in YBa2Cu3OT, no soft-mode behaviour has been found.

1708

H. Rietschel et al. I Selected aspects o f the lattice dynamics

J

/

~

•

• ........~'J"-..._... u

-

u

~

i

: !

3. CONCLUSIONS

~:o

In oxide superconductors and related compounds, there is evidence that the lattice dynamics are not describable within a harmonic picture. In our mind, the most conspicuous feature is the appearance of extra modes in conjunction with breathing-type oxygen modes. It is also these modes which already showed strong anomalies in Ba(Pb,Bi)O3 and La2NiO4 and which are most strongly changed when going from YBa2Cu306 to YBa2Cu307. We interpret this extra mode as being due to hybridization of lattice modes with low* lying electronic excitations, probably a key observation for the understanding of high-To superconductivity in the cuprates.

=0.2

. -oil

-

,

=03 cu

~a .i-

I..

, o -

--~o

i

o--

.-..~C

~.

o

REFERENCES 1. U. Gottwick et al., Europhys. Lett. 4 (1987)

=0.~

1183

2.

' """~" , "~"

"::''~

.'

~-'o.s

i i

12

lZ,

16

18 v(THz)

20

22

2l+

I

FIGURE 3 Line shapes in La2CuO4at (3-~,3-~0). Extra modes as those found in La2CuO4 and La2NiO4 also exist in YBa2Cu307, again for breathing-type vibrations in (1,0,0) direction, but they disappear in YBa2Cu306. In this latter compound, we observe a pronounced hardening of Cu2-O2/3 bond-stretching vibrations.

KJ. Leafy et al., Phys. Rev. Lett. 59 (1987) 1236 and references therein 3. H. Rietschel et al., Physica C 153-155 (1988) 1067

4. W. Weber, Adv. in Sol. St. Phys. 28 (1988) 141 5. K.H. H6ck, H. Nickisch, and H. Thomas, Helv. Phys. Acta 56 (1983) 237 6. N.M. Plakida, V.L. Aksenov, and S.L. Drechsler, Europhys. Lett. 4 (1987) 1309 7. L. Pintschovius et al., Proc. of the Int. Sem. on High-To Superc., Dubna (1989), in print 8. W. Reichardt et al., these Proceedings 9. L. Pintschovius et al., Phys. Rev. 8 40 (1989) in print 10. R.A. Cowley and W.J.L. Buyers, J. Phys. C 2 (1969) 2262