Temperature dependence of the linewidth of the 500 cm−1 Raman mode of YBa2Cu3O7−x

~

Solid State Communications, Printed in Great Britain.

Vol. 76, No. 3, pp. 391-395,

0038-i098/9053.00+.00 Pergamon Press plc

1990.

TEMPERATURE DEPENDENCE OF THE LINEWIDTH OF THE 500 cm-* RAMAN MODE OF YBa2Cu3OT_ x E. Altendorf, Physlcs Department,

J. Chrzanowskl

and J.C.

Slmon Fraser University,

Irwln

Burnaby, B.C.

VSA IS6

and J. Franck Physics Department,

Unlverslty of Alberta,

Edmonton,

Alberta

T6G 2Jl

(Received 13 July 1990 by R. Barrle} The temperature dependence of the 500 cm -I Raman actlve phonon has been carefully Investigated in Raman spectra obtalned from pressed and slntered pellets of YBa2Cu3OT_x wlth x = 0. The 500 cm I phonon arlses from vibrations of the O(4} brldglng oxygen atoms which are belleved to be situated in a strongly anharmonlc potential well. The llnewldth of the 500 cm -I mode has thus been studled as a function of temperature. In several samples the llnewldth was observed to decrease by about 3 cm near Tc and to Increase agaln at lower temperatures. A linear chaln model Is used to estimate the effect of charge transfer fluctuatlons on the 500 cm -I mode and the results suggest that coupling of such fluctuations to the 500 cm -I mode may Influence the observed behavlour near To.

I.

Introductlon

region about To, the separatlon decreases to about .10 A. Thus It appears that the 0(4) -1 atom and hence the 500 cm mode are coupled to electronic excltatlons Involved In the superconducting transition. These recent developments e have prompted us to carry out Raman scattering experiments on well characterized YBCO samples to investigate the temperature dependence in the l l n e w l d t h o f -1 the 500 cm mode. A typical Raman spectrum ls shown In Flgure 2. The llnewldth of the 500 -I cm mode has been found to have a deflnlte signature near To, In that the Full Width at Half Maxlmum (FWHM} first decreases and then increases as the temperature is lowered. This behavlour lmplles that the 500 cm -1 mode is coupled to the electronic excltatlons of YBCO in agreement w&th the prevlously mentloned EXAFS studies. In an attempt to gain some insight into the connection between the observed Raman behavlour and the EXAFS results, we have modelled the 500 cm -I mode using a llnear chain model (Flg. 1). Charge transfer fluctuatlons, associated with the 0(4} displacements seen in the EXAFS studies, are incorporated into the linear chain model by modlfylng the polarlzablllty derivatives associated with the 0(4) atoms. The results of these calculations are In reasonable agreement with the llnewldth charges observed near T¢ supporting the premise that charge transfer fluctuatlons are coupled to the 500 cm "I mode.

The Raman spectra obtalned % from pressed, slntered pellets of pure YBa2Cu 3 ~T-x (YBCO} I usually exhibit five peaks which correspond to phonons with nominal frequencies of 115, 150, 340, 435 and 500 cm -I when x is small. The symmetry p~opertles of these modes have been determined- from experiments carried out on oriented single crystals with selected polarizations of the incident and scattered light. A comparlson of the results of these 2-4 experiments to the predlctlons of lattlce dynamics calculations has also enabled the identification of the vibrational origin of the five modes. It is thus known that all flve modes have A~ symmetry with the atoms vibrating along the c-axis of the orthorhomblc unit cell of YBCO (Flg. 1}. The higher energy modes at 340 and 435 cm correspond to the out-of-phase and In-phase vibrations respectively of oxygen atoms on the 0(2} and 0(3) sites of the CuO 2 planes. The 500 cm -I phonon is due to vibrations of the oxygen atoms on the 0(4} sites with elgenvectors as indlcated by the arrows on the 0(4} atoms in Figure I. It has been suggested, that the vlbratlons of the axial oxygen atom are involved in the hlgh Tc superconductivity mechanism, s-7 In particular, EXAFS studles" have found that the 0(4} atoms are situated in a symmetric double well potentlal centered about the crystallographic 0{4} slte. Hence an 0(4) atom In the YBCO lattice can be situated in one of two possible positions correspondlng to the minima of the potential. Above and below To, these roughly equally populated posltlons are separated by .13 A, whlle In a transltlon

2.

EXperimental

The YBa~Cu3Ov_x samples studied were in the form of pressed slntered pellets, which 391

392

Vol. 76, No. 3

500 cm -I RAMAN MODE OF YBa, Cu 3 07_ x

Cu(1) ~'~Q_.

o(1)<~

,'

lk

0(4)

- -

Cu(1)

f 0(4)

,Cu(2)

o(a)- 1

~

o(2)~ Y Cu(2){ 0(3)

0(4)

100

400

w

Figure 2

w

YBa2Cu307

700

Frequency (era-I )

OBa 0(4)

Figure 1

I

Cu(2)

/

Chain

Prlmltlve unlt c e l l of Stolchlometrlc YBa2Cu307 with the basis atoms labelled. The stretching motion of -1 the 0(4) atoms resulting in 500 cm mode Is indicated by arrows. A segment of the linear chain used in the theoretical calculations is shown at right.

accuracy of a Stokes-antl-Stokes intensity measurement. Spectra were obtained from as grown pellets, freshly cut edges, and from pellets that were dry p o l l s ~ d or etched in a IZ Bromine-ethanol mixture. There was no detectable difference between the spectra obtained both before and after surface treatment. 3. 3.1

were used In oxygen Isotope studles, 9-11 and hence contain primarily "-0 or leO dependlng on the sample. All samples were calcined at 915 C, sintered and reslntered at 925 C. Raman measurements indicated softening by about 5 1 1 cm- of the 340 cm- phonon at about 90 K, as well as a frequency g r e ~ e r than 500 cm -t for the 0{4} phonon in the "-0 samples. These results imply complete oxygenation {x < .05), In agreement with critical temperatures greater than 87 K. Raman scattering experiments were carried out with the samples mounted in a vacuum to eliminate scattering from alr. The spectra were obtained at room temperature and excited using the 514.4 or 488.0 nm lines of an Argon Ion Laser. The scattered light was focussed onto the entrance silt of a triple spectrometer consisting of a double grating subtractlve dispersion input stage, followed by a single grating dispersive stage. The scattered llght was detected wlth an ITT-"mepslcron" imaging photomultlpller tube. Thls system provided a resolution of ± 1.0 to ± 3.0 cm -I dependent on the grating selected. The laser power of 25 raw was focussed o n the sample wlth a cylindrical lens. With thls arrangement the sample heating was confirmed to be negligible to within the

Raman spectrum of the R, sample described in the text at 80 K, containing flve A,g modes. Peaks t corresponding to 150 and 500 cm modes are indicated by arrows.

Results and Discussion

Linear Chain Model

The results mentioned In the introduction, suggest that the vibrations of the 0(4} atoms should be investigated In a more quantitative manner. To thls end, a linear chain model (Fig. i) has been used to investigate the frequency and llnewldth of the 500 cm -I mode. The equation of ~ptlon method described by Beeman and Alben ~ Is used to calculate t hle differential cross-sectlon of the 500 cm Raman mode in the linear chain. Following their approach the equations of motion for N atoms are: d2

m i -dt - z (ut=) = j ~

V1~,j~ uj~ ,

(1)

where m I is the mass of the Ith atom, ui~ is the ~-component of Its displacement from equlllbrlum and V Is the second derivative of the elastic energy wlth respect to the ~ and dlsplacements of atoms I and J respectively. Set all Initial velocities to zero, and let initial displacements at time t = 0 be specified

by

UoI ~ = U | ~

(t

= O) = ~

c~ L c~ m D~i ~ / m I

(2)

Vol. 76,

NO. 3 Is

where D ~

A|a

=

.

Lim .

{ ~: .

.

'~"

7

23

/

/

(3)

o m i ut~

the Stokes cross-sectlon

dZ~(~)

25

the change I n the #~ element of

the polarizability tensor due to the d i s p l a c e m e n t o f atom I a l o n g d l r e c t l o n a a n d ~ a n d e~ a r e u n i t p o l a r i z a t i o n v e c t o r s o f t h e s c a t t e r e d and i n c i d e n t l i g h t r e s p e c t i v e l y . If

\

19

is

h [n(~)+ I] G(~) }

-~ I

&

/

De .11

I

15 13

0

r

(5)

The exp(-¥t z) factor Islused to replicate the llnewldth of the 500 cm" mode and thus accounts for Itfetlme and apparatus broadening. The force constants used In the linear chain (Fig. I) are adjusted so that Initial antl-phase displacements of the 160(4) atoms alone the chal~ axis generate a single Raman mode at 500 cm-~ when equations (4) and (5) are solved numerically. Various disorder effects can now be implemented by randomly altering the initial displacements of the 0(4) atoms, or in the case of isotopic dlsorder, 11 the 0(4) masses themselves. It should be noted that in this study, the lifetime broadening is taken to be constant with respect to temperature. The usual monotonic decrease In llnewldth if included, would simply superimpose on the fluctuation induced effects observed near T c. The initial llnewldth of 19 cm-1, which determined the value of ~ used in the calculation is assumed to be due to a convolution of an instrumental llnewldth of about 3 cm -I and to contributions from lifetime and fluctuation effects. An estimate of the lifetime contribution can perhaps be obtained from the 150 cm -1 phonon (s~e Fig. 2) which has a llnewldth of about 12 cm Temperature Dependence of the 500 cm phonon llnewldth

-I

-I The measured llnewldth of the 500 cm mode as a function of temperature is shown in Figure 3 for two different samples (D2 and B~). D2 Is an ~-exchanged sample and RI is an 160 sample. RI had crltlcal temperature Tc = 91.64 K wlth a I0 to 90~ width of 1.0 K. The transltlon width for sample D2 was 1.2 K and T© was equal to 87.0 K. As is evident from Figure 3, the 500 cm -I llnewldth clearly decreases at a temperature near T~ and then increases again at lower temperatures. This decrease in llnewldth near the critical temperature (Figure 3) implies that the 500 cm mode Is coupled to the electronic excltatlons of YBCO in some manner. As mentioned in the introduction, evidence for

' 1"00

'

'

Temperature

Figure 3 AI~ ul (t) cos(~t) exp(-~t2)dt

0

3.2

1

(4)

where n ( ~ ) i s t h e t e m p e r a t u r e d e p e n d e n t Bose f u n c t i o n and

[ ~

////R

Io

0" \

"~ 17

then given by:

~-~o

2

393

500 cm- I RAMAN MODE OF ¥Ba 2 Cu 3 07_ x

' 2 0 0'

'

'

' 300

(K)

Temperature dependence of the FWI~4 of the 500 cm"1 mode from samples D2 ( t r i a n g l e s ) and RI ( c i r c l e s ) described in the text.

s u c h c o u p l i n g h a s a l s o b e e n o b t a i n e d ~y M u s t r e de Leon e t a l f r o m EXAFS e x p e r l m e n t s . S o f t e n i n g I n t h e 500 cm-I phonon n e a r Tc i s o b s e r v e d I n some o f t h e s a m p l e s , b u t t h e e f f e c t i s s m a l l (~ I~) i n d i c a t i n g t h a t t h e e f f e c t i v e harmonic force constants remain essentially unaltered. B a t l s t l c and c o w o r k e r s 14 c o n s i d e r e d t h e effects of charge transfer fluctuations between t h e Cu02 p l a n e s and CuOz c l u s t e r s c o n t a i n i n g C u ( 1 ) , 0 ( 4 ) and 0 ( 1 ) a t o m s . T h e i r r e s u l t s indicate that such fluctuations will result in a s t a t i c d e f o r m a t i o n o f t h e 500 cm-1 mode, t h a t Is, a change in the Cu(1)-O(4) dls~ances. The r e s u l t s o f EXAFS s t u d i e s , namely the e x i s t e n c e o f two Cu(1) - 0 ( 4 ) d i s t a n c e s s e p a r a t e d by .13 A, may t h e r e f o r e i n d i c a t e t h e presence of such charge transfer fluctuations. These studies also Indicate that the separation b e t w e e n t h e two 0 ( 4 ) p o s i t i o n s d e c r e a s e s by a b o u t .03 A I n a t r a n s i t i o n r e g i o n n e a r Tc. In t h i s p a p e r we a s s u m e t h a t t h e bond o r d e r (number o f b o n d i n g e l e c t r o n s ) , o f t h e Cu(1) - 0(4) bond, fluctuates between 1,2 and ~ 0 electrons outside the transltlon region. Near ~c modifications in the charge transfer occur-and the bond order is ad hoc assumed to fluctuate between I, 1.5 and .5 (fractional bond orders correspond to averages). Guided by the bohavlour of simpler molecular systems we further assume that the polarizability derivative associated wlth the Cu(1) - 0(4) bond is proportional to the bond order. Is Charge fluctuations in the bond order therefore induce fluctuations in the polarizability derivative D associated with the 0(4) atom. Work on T~ based superconductors 16 indicates that such fluctuations possess no long range order, hence In modelling this effect using the llnear chain (Fig. I), we randomly assign polarizability derivatives D ± AD to the 0(4) atoms in the chain. The results of our calculatlons are shown in Figure 4, and indicate a reduction in the llnewldth of the 500 cm -I mode by about I cm-I near T c which Is In reasonable agreement with our experimental observations (Fig. 3). This suggests that the

394

500 cm -I RAMAN MODE OF YBa 2 Cu 3 07_ x

Vol. 76, No. 3

llnewldth changes observed near T c are perhaps indirectly related to charge transfer excitations. 4.

Conclusions

A careful examlnatiop of the temperature d e p e n d e n c e o f t h e 500 cm- phonon i n s e v e r a l p r e s s e d p e l l e t s o f YBCO h a s r e v e a l e d t h a t i t s llnewldth undergoes a noticeable decrease near the critical temperature. We h a v e r e p r o d u c e d t h i s c h a n g e by a s s u m i n g a random p o l a r i z a b i l i t y d e r i v a t i v e a s s o c i a t e d w i t h t h e 0{4) a t o m s a l o n g t h e c - a x i s and i n t r o d u c i n g t h i s i n t o a l i n e a r c h a i n model. T h i s r e s u l t i s b e l i e v e d t o be qualitatively consistent with the results of EXAFS e x p e r i m e n t s which i n d i c a t e t h a t v i b r a t i o n s of the 0(4) atoms are s t r o n g l y coupled to charge t r a n s f e r e x c i t a t i o n s in the YBCO compounds.

475

500

525

F r e q u e n c y (cm -1 ) Figure 4. Calculated Raman spectra of the 500 -I cm mode indicating the influence of charge transfer fluctuations. Curve a} represents the results of Cu(1) - 0(4) bond order fluctuations between ~ O, I and 2. Curve b) represents the results of bond order fluctuations between .5, I and 1 . 5 . Curve c) r e p r e s e n t s t h e 500 cm"1 p e a k w i t h no f l u c t u a t i o n s p r e s e n t .

Finally, it should be noted that a llnewldth variation similar to that shown in Figure 3 has been observed In about slx different samples. In two other samples that were investigated, however, the llnewldth variation was much smaller and was within the experimental uncertainty. The reason for thls lack of reproducibility is not yet known but we plan to carry out similar experiments on single crystals In order to Investlgate this aspect further. We are attempting to obtain single crystals with a c-axls dlmenslon large enough to permit the acquisition of Haman spectra that wlll correspond to the {zz) element of the Haman tensor. Acknowledgement Two of the authors (EA and JCI) have benefitted from many helpful discussions with Drs. M. Pllschke and G. Klrczenow of the SFU Physics Department. The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.

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500 cm -I RAMAN MODE OF YBa 2 Cu 3 07_ x

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