Physica C 235-240 (1994) ! 163-1164 North-H011and PHYSICA $

Dynamic atomic displacements in YBa2Cu306+x a s a function of temperature

J .J . Castro a, E. Y~pez b*, A. Calles c, J .R. Soto c and A. Cabrera c a D e p a r t a m e n t o de Ffsica, C INVESTAV, IPN, Apdo. Post . 14-740, 07000 M6xico D.F..

bEscuela Super io r de Ffsica y MatemKticas , IPN, 07738 M6xico D.F..

~Facultad de Ciencias, U N A M , Apdo . Post. 70-646, 04510 M6xico D.F. .

Mean-square d isplacements in t he supe rconduc to r Y Ba2Cu30~+:c are calculated using the par t ia l phonon densi ty of s ta tes t h r o u g h the solut ion of the dynamica l matr ix . We make a comparison of the results found and s tudy the consistency of the m e t h o d for analys ing displacement proper t ies . In pa r t i cu l a r we discuss the movements of chain O(l) and apical 0(4) oxygens. F r o m a compar i son of the results wi th da ta coming f rom diffraction experi- ments we look for possible anomalous behaviour of the oxygens as a func t ion of t empe ra tu r e .

1. I N T R O D U C T I O N

One of the mos t i m p o r t a n t supercon- duct ing cupra tes is the YBa:Cu306+.r, due to some of its in te res t ing special features. One of t h e m is the anomalous behav iou r of the R a m a n a n d inf rared peaks associated to the 0(4) m o v e m e n t s as a func t ion of x [1- 2], the a m o u n t of oxygen O(l) in the chains. The par t icular i ty , we are refer ing to, is the shift to the r igh t of the high ene rgy mode unt i l the sys tem becomes superconduc t ing , where the m o d e s ta r t s to shift to lower en- ergies. This f requency behav iou r has in- pired e x p e r i m e n t a l work in order to s tudy the d isp lacements of the apical oxygen in the Y B a C u O sys tem [3]. The a im of the present work is to s tudy the behav iou r of the 0(4) v ib ra t ions paying special a ten t ion to the m e a n - s q u a r e d isp lacements (MSD)

tures. We s tudy the system f rom x = 0 to 1. for a t e m p e r a t u r e range be tween 0 and 300K.

2. M E T H O D

The t h e r m a l pa rame te r s are calcqlated

*Partially supported by COFFA, IPN, M6xico

v

q)

E

i n t eg ra t ing the corresponding opera to rs us ing the par t ia l p h o n o n density of s ta tes ( P P D O S ) for each species in the system. The P P D O S comes f rom all in tegrat ion in the first Bril louin zone of the phonon states weighted for each a tom. The energy and eigenvectors of no rma l modes of v ibra t ion were obtained f rom the diagonalizat ion of the dynamical ma t r i x cons t ruc ted using a Born-Mayer pot~ntial . The t r ea tmen t for x ~ 0 was done wi th the supercell technique in order to have the p rope r p ropor t ion of chain oxygens in the crystal . Once the x is defined the O(l) are placed randomly, for each k point , in the different possible chain- oxygen sites. We belive the influence of the O(!) in the MSD of 0(4) could be ano the r

!

0 . 0 1 2 ~ ~ ............. i 0 1 00 200 300

Temperature (K)

Figure !. 0(4) mean-square ampl i tudes as a funct ion of t e m p e r a t u r e and s' -

O, 0.2, 0.4,0.6, 0.8, 1.

0921-4534/94/S07.00 © 1994 - Elsevier Science B.V. All rights reserved.

SSDI 0921-4534(94)01145- !

! ! 6 4 JJ. Castro et al./Physic:t C 235-240 (1994) !163-1164

mani fes ta t ion of an anomalous b ehav iou r of the 0(4) v ib ra t ions , which can be corre- la ted wi th the f r equency anomaly. In order to t:lucidate w h e t h e r this behav io r i~ dr iven or not by the suI)erconduct iv i ty , the model we choose for t h e s t r u c t u r e is a r ig id one. T h a t means: t he force cons tan ts : a tomic distances and la t t i ce p a r a m e t e r s [4] are the same for all x. In this way, the resul ts as a f imct ion of x cannot be a t t r i b u t e d to the s u p e r c o n d u c t i v i t y t rans i t ion , because we art: not forc ing any s t r u c t u r a l t r ans i t ion in the mt)del due to supe rconduc t iv i ty .

A

v

~3 03

E

0 . 0 1 6 1- ................................................. !

, 1

0 . 0 1 2 ' ........................................................ ' 0 0 . 2 0 . 4 0 . 6 0 . 8 1

x

Figure 2. 0 ( 4 ) disl)lacenlt~nts as a f imct ion ()f.r fin' 7 ' = O.

O3 if)

E

0 . 0 4 + . . . . . . , , . . . , , . . , . , . . : : ; : : . . ,.. . . : , : , . ' 'T I , J 8

, . . . . . " . . . . . . " " . .~,**~,~. 0. 6 :t .Il I i [ I 1 i 11 1 t l 1 l l 1 i I l l ! 1 I t 1 t i t_J?tj.4

0 ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

0 1 0 0 2 0 0 3 0 0

T e m p e r a t u r e (K)

Figure 3. 0(1) d i sp lacenmnts as a funct ion of t t :mi)era ture an d .r = 0.2.0.4, 0.6, 0.8.1.

3. R E S U L T S

!'.: Figure: I w(; show the MSD fi~r O(,i) as a fmlction of the t e m p e r a t u r e up to 300K for tho st'vt;ral .r values. It can ch-arly b(; ()bservt:d tL(, inf luence of 0(1) ill the 0(I) ~lisl)lac(:m(;nts. In Figure 2 we show th(: (,)(-1) (li~I)lac(:mt;nts as a fim(:tion of .r fin. zero t ( :ml)erature. As can be ,s(,(it,,- f rom Fig-

ure 3, the MSD for t he O(1) is increas ing as x a n d it is not very sens i t ive to the t e m p e r - a tu re . The a m p l i t u d e for 0(4) essent ia l ly decreases wi th x a n d it is more s t rong ly t e m p e r a t u r e d e p e n d e n t . However , t he re is a c lear anomalous b e h a v i o r a r o u n d x = 0.4, just w h e n the t r a n s i t i o n to the supe rcon- d u c t i n g s ta te s t a r t s in the sys tem.

4 . C O N C L U S I O N S

The anomaly we f o u n d due to the O(1) inf luence in the 0(4) d i sp lacemen t is a re- sul t due only to t h e s t ruc tu re , consider- ing only ha rmon ic effects. The t e m p e r a - t u r e dependence for t h e d i sp lacements is a s m o o t h funct ion in t he 0(4) a m p l i t u d e s . T h e anomalous b e h a v i o u r of the 0(4) is s imi la r to the one in t he f requency r e p o r t e d in R a m a n and in f ra red exper imen t s . T h e s u p e r c o n d u c t i v i t y does no t drive the pe- cul ia r changes in the 0(4) amp l i t udes be- cause our model does no t have any infi)r- m a t i o n abou t the s u p e r c o n d u c t i n g mecha- n ism. The oppos i te ques t ion still r emains : doe, s this s t r uc tu r a l ano lna lous effect, as a func t ion of x, helps to the supe rconduc t i v - i ty t r ans i t ion? .

R E F E R E N C E S

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