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Temperature dependence of the Raman and infrared phonons of MBa2Cu3O7-δ-type superconductors
~Solid State Communications, Vol.64,No.4, pp.477-481, Printed in Great Britain.
1987.
0038-1098/87 $3.00 + .00 Pergamon Journals Ltd.
T e m p e r a t u r e dependence o f the Raman and i n f r a r e d MBa2Cu307_~-type s u p e r c o n d u c t o r s A.
phonons o f
Wittlin*, R. L i u , M. Cardona, L. G e n z e l , W. K 6 n i g , W. B a u h o f e r , H j . M a t t a u s c h , and A. Simon Max-Planck-lnstitut fur Festk6rperforschung, H e i s e n b e r g s t r a 6 e I , 7000 S t u t t g a r t 80, F e d e r a l R e p u b l i c o f Germany F. #
Garc{a-Alvarado
.
J
.
Departamento de Qulm~ca I n o r g a n l c a , F a c u l t a d de C i e n c i a s O u l m l c a s , U n i v e r s i d a d Complutense, 28040 M a d r i d , Spain J
.
(Received J u l y
15,
1 9 8 7 by M. Cardona)
An anomalous t e m p e r a t u r e dependence o f the ~340 cm-1 Raman phonons o f YBa2Cu307_6 has been r e c e n t l y r e p o r t e d by M a c f a r l a n e et a l . Here we s h o w t h a t t h i s phenomenon, a phonon s o f t e n i n g w i t h d e c r e a s i n g T f o r T < Tc, i s common t o many m a t e r i a l s o f the f a m i l y (M = Y, Sm, Eu, Ho, Gd). We a l s o show t h a t the i t - a c t i v e Davidov c o u n t e r p a r t o f t h i s phonon, and a n o t h e r J r - a c t i v e phonon a t s l l g h t l y lower f r e q u e n c y , a l s o e x h l b i t s i m i l a r e f f e c t s . These phonons are a t t r i b u t e d t o bending v l b r a t i o n s o f the Cu2-02 and Cu3-03 bonds. A l l o t h e r i r and Raman phonons o b s e r v e d e x h i b i t a normal t e m p e r a t u r e dependence ( i . e . , h a [ d e n i n g w i t h d e c r e a s i n g T even f o r T < T c ) . l h e 310 cm phonon o f the t e t r a g o n a l n o n - s u p e r c o n d u c t i n g YBa2Cu306 a l s o shows a normal b e h a v i o r v s . T.
Raman 1-8 ana i r - s p e c t r o s c o p y 9-13 have r e c e n t l y become p o p u l a r t o o l s f o r the i n v e s t i g a t i o n o f the new h i g h Tc s u p e r c o n d u c t o r s . The l a t t e r y i e l d s i n f o r m a t i o n about i r - p h o n o n s and the s u p e r c o n d u c t i n g gaps w h i l e in the f o r m e r Raman phonons are seen. Raman and i n f r a r e d a c t i v i t i e s are m u t u a l l y e x c l u s i v e in m a t e r i a l s w i t h i n v e r s i o n symmetry such as t h o s e o f the two classical families o f h~gh T c s u p e r conductors (Lal_×Srx)2Cu04 1 and
~ .
HoBa2Cu30?-~
LU
MBagCu~Ov ~ a~ , - o (M ~ y~ ~'TheNd'symmetrySm' Eu, Gd,ana_ Ho, Er, Lu, . . . . ' lysis o f t h e i r and Raman modes o f t h e former is given in Ref. 3 while that of the latter is given in Ref. 7.
O Z
0 Iii ._1 Ii m rr
The MBa2Cu307_6 a r e , in t h e i r s u p e r c o n d u c t i n g phase, o r t h o r h o m b i c , b e l o n g i n g t o the Pmmm space group (mmm p o l n t ) w i t h one f o r m u l a u n l t per p r i m l t i v e c e l l (see F i g . 1 o f R e f . 7 ) . The M-atoms g e n e r a t e t h r e e J r - a c t i v e modes o f x , y, z symmetry w h i l e t h e p a i r o f e q u i v a l e n t Ba atoms g e n e r a t e I r and R a m a n - a c t i v e D a v l d o v d o u b l e t s ( x z , y z , and zz s y m m e t r i e s ) . The t h r e e Cu-atoms g i v e r l s e t o one s e t o f Davldov d o u b l e t s (3×2 modes) and t h r e e J r - a c t i v e modes w h l l e the seven O-atoms
200
240
280
320
360
400
(.o [ cm -1]
I.
* On leave of absence from Institute of Physics, Polish Academy of Science, 02 668 Warsaw, Poland. 477
R e f l e c t a n c e s p e c t r a o f HoBa2~u307_ ~ between 200 cm and 400 cm . Vertical l i n e h e l p s t o v i s u a l i z e t h e phonon f r e q u e n c y changes w i t h t e m p e r a t u r e .
478
RAMAN AND INFR~NED PHONONS OF MBa2Cu307_~-TYPE SUPERCONDUCTORS
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peaks f o u n d in t h e s a m e r e g i o n . M o r e o v e r , we show t h a t in t h e t e t r a g o n a l , oxygen deficient compound YBa2Cu306, w h i c h i s not s u p e r c o n d u c t i n g ( s e m i c o n d u c t o r or insulator) t h e peaks o b s e r v e d in t h e same r e g i o n show t h e s t a n d a r d b e h a v i o r w i t h d e c r e a s i n g t e m p e r a t u r e . Thus t h e weak s o f t e n i n g o b s e r v e d f o r t h e s e phonons in t h e s u p e r c o n d u c t i n g phase has t o be r e l a t e d , in some u n u n d e r s t o o d manner, t o t h e phenomenon o f s u p e r c o n d u c t i v i t y in these materials.
o') c
.d 0
The measurement t e c h n i q u e s have been d e s c r i b e d e l s e w h e r e . The o x y g e n d e f i c i e n t M = Y sample was p r e p a r e d by h e a t i n g in an Ar a t m o s p h e r e a t 950°C f o r one h o u r . I t was f o u n d t o be n o n s u p e r c o n d u c t i n g by r e s i s t a n c e measurements down t o 4 K. A l s o , t h e Raman s p e c t r a show i t i s n o t metallic. Guinier diffractograms show t h a t t h e s e samples a r e s i n g l e phase and tetragonal. Their structure is c o n s i s t e n t w i t h t h a t g i v e n in R e f . 16. The i n f r a r e d s p e c t r a cm_~ o f • h ese samples al so peak a t 276 and 315 ( a t 300 K ) .
.J
z 0 or) or) IJJ Y
if)
200
2.
300 400 STOKES SHIFT [cm-1]
Analogous to Fig. HoBa2Cu307_ 6 •
1.
Raman s p e c t r a
of
g e n e r a t e 3 sets o f D a v i d o v - d o u b l e t s (3x3 modes) and t h r e e i t - a c t i v e modes. Among t h e O- and C u - g e n e r a t e d modes a r e t h e stretching vibrations o f t h e Cu-O bonds which o c u r b e t w e e n 400 and 650 cm-~. 1 , 2 , 4 ' 7 ' 8 The p r e s e n t p a p e r r e f e r s t o t h e p h o non s t r u c t u r e s which a r e seen b e t w e e n 250 and 350 cm-1 f o r M = Y, Eu, Sm, Ho, Gd. Two peaks a r e o b s e r v e d in t h i s r e g i o n in t h e i r s p e c t r a ( F i g . 1 f o r Ho) e i t h e r one o r two in t h e Raman s p e c t r a ( F i g . 2 f o r M = H o ) . The two peaks a r e w e l l r e s o l v e d f o r M = Ho, as shown in F i g . 2. In t h e c a s e s in w h i c h o n l y one Raman peak i s seen (M = Y, Sm) t h e r e i s s o m e i n d i c a t i o n t h a t t h e l o w e r f r e q u e n c y component e x i s t s but is u n r e s o l v e d . A very interesting f e a t u r e has been r e p o r t e d r e c e n t l y f o ~ t h e Raman peak o b s e r v e d a t ~340 cm f o r M=Y (4). T h i s peak f i r s t shifts slightly upwards in frequency (i.e., hardens) with decreasing t e m p e r a t u r e down t o ~100 K ( a p p r o x i m a t e l y equal, within error, t o T c ) . But b e l o w t h i s t e m p e r a t u r e , i t a n o m a l o u s l y dec r e a s e s ; t h e d e c r e a s e amounts t o a b o u t 6 cm ~ a t 10 K. In t h i s p a p e r we p r e s e n t d a t a s h o w i n g t h a t t h i s phenomenon i s g e n e r a l t o many s u p e r c o n d u c t o r s o f t h e MB2Cu307_ a f a m i l y (M = Y, Sm, Eu, Ho, Gd). I t i s a l s o seen n o t o n l y in t h e Raman s p e c t r a ( F i g . 2) b u t a l s o in t h e i r
The i r and Raman s p e c t r a o f a sample w i t h M = Ho a r e shown in F i g s . I and 2, respectively, at several temperatures. Two peaks a r e c l e a r l y o b s e r v e d in b o t h s e t s o f s p e c t r a . These d o u b l e t s have similar spl~tings, t h e Raman one l y i n g a b o u t 20 cm ~ h i g h e r t h a n t h e i r c o u n t e r part. I t i s t h u s r e a s o n a b l e t o assume t h a t we a r e d e a l l n g w i t h D a v i d o v d o u b lets. The a n o m a l y j u s t m e n t i o n e d can be observed directly by r e f e r r i n g t h e peak p o s i t i o n s to the t h i n v e r t i c a l lines of F i g s . i and 2: between 300 and i 0 0 K t h e peak f r e q u e n c i e s a r e n~ r l y c o n s t a n t w h i l e a d r o p o f ~6 cm -~a i s o b s e r v e d b e t ween 100 and 10 K. The t e m p e r a t u r e dependence o f t h e wavenumbers o f maxima o f t h e two i r p e a k s , and o f t h e u p p e r component o b s e r v e d in t h e Raman s p e c t r a , a r e shown in F i g . 3 f o r a l l samples m e a s u r e d . We have a l s o i n c l u d e d in t h i s f i g u r e t h e c o r r e sponding data for the non-superconducting M = Y t t r i u m sample w h i c h snows a smooth wavenumber i n c r e a s e w i t h d e c r e a s i n g temp e r a t u r e , w i t h o u t any a n o m a l y . The d a t a f o r a l l s u p e r c o n d u c t i n g samples e x h i b i t t h e anomalous b e h a v i o r m e n t i o n e d a b o v e , the t e m p e r a t u r e s h i f t s being quantitatlvely very similar in a l l c a s e s . We have a l s o i n v e s t i g a t e d the t e m p e r a t u r e dependence o f a l l o t h e r phonons o b s e r v e d p r o m i n e n t l y in t h e s e s p e c t r a : i t a p p e a r s t o be n o r m a l . We show, as an e x a m p l e in F i g . 3, t h e t e m p e r a t u r e v a r i a t } o n of the Cu-O band s t r e t c h i n g peak seen in Raman a t a r o u n d 500 cm-1: normal b e h a v i o r (hardening with decreasing temperature) i s o b s e r v e d . A l s o t h e low f r e q u e n c y peaks seen in t h e i r (~15~ c m - l ) l l , 1 2 and Raman s p e c t r a (~150 cm - 1 ) w h i c h ~re r e l a t e d t o vibrations o f t h e Ba atoms I do n o t show anomalous b e h a v i o r . In o r d e r t o e x c l u d e the p o s s i b i l i t y t h a t t h e o b s e r v e d anoma-
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~ [cm_1]
RAMAN AND INFRARED PHONONS OF MBa2Cu307_~-TYPE SUPERCONDUCTORS
................ 0 Y ( A r ) ....... XHo ----[3 Gd
a)
320
...... ........
OSm • Eu
b)
479
........ •
Eu
................ × H o 510 -
-
-
-
O
Y
. . . . . . . O Y (Ar
(,j [ c r n -1 ]
505 .
.
.
.
.
.
.
.
315
500 310
495, 305~.
280
,
0
,
100
200
300
T[K]
270
0
100
200
300
T [ K ]
3.
Temperature dependence of phonon f r e quencies of MBa2Cu$07_~ (M = Ho, Gd, Sm, Eu) and of s e m l c o n d u c t i n g YBa2Cu306 • a) R e f l e c t a n c e measurement r e s u l t s . b) Raman measurements r e s u l t s . Note anomalous s o f t e n i n g of phonons below 100 K in s u p e r c o n d u c t i n g compounds and normal t e m p e r a t u r e dependence of phonon f r e q u e n c i e s f o r YBa2Cu306 •
lous s h i f t s be due t o l i n e s h a p e e f f e c t s ( a l t h o u g h i t i s u n l i k e l y t h a t t h e y would be the same in i r as in Raman) we have extended our L o r e n t z i a n o s c i l ] ~ t o r f i t s of the i r r e f l e c t a n c e s p e c t r a l Z t o a t e m p e r a t u r e dependent one. I t i s found t h a t the r e f l e c t i o n peaks s h i f t upwards by about 8 cm ~ below Tc even f o r cons t a n t phonon f r e q u e n c i e s , an e f f e c t which i s p u r e l y of d i e l e c t r i c o r i g i n . Thus the observed s o f t e n i n g s must be r e a l .
with
Because of t h e i r anomalous b e h a v i o r v a r y i n g temperature, i t is i m p o r t a n t
t o t r y t o a s s i g n the d o u b l e t s of F i g s . 1 and 2 t o symmetry t y p e s and t o c o n j e c t u r e what t h e i r e i g e n v e c t o r s may be. They are w e l l below the Cu-O s t r e t c h r e g i o n and w e l l above the f r e q u e n c i e s e s t i m a t e d f o r v i b r a t i o n s i n v o l v i n g s t r o D g l y the motions of M or Ba (below 200 cm I ) . 17 We thus assign them t o bending modes of the Cu-O bonds. In t h i s c o n t e x t s e v e r a l p o s s i b i lities a r i s e : bond bending of the 02-Cu2 and 03-Cu3 bonds f o r m i n g the two warped squares in each u n i t c e l l ( F i g . 1 of Ref. 7 ) , wagging of the 04-Cu4 d u m b b e l l s , and a l s o bending of the 01-Cul bonds.
480
RAMAN AND INPTLARED PHONONS OF MBa2Cu307_6-TYPE SUPERCONDUCTORS
From t h e f a c t t h a t t h e d o u b l e t s appear a t n e a r l y t h e same p o s i t i o n in t h e nons u p e r c o n d u c t i n g sample ( i . e . , after d r i v i n g o u t t h e 01) we c o n c l u d e t h a t t h e y have n o t h i n g t o do w i t h t h e 0 1 - C u l bonds. By t h e same t o k e n we e x c l u d e t h e 04-Cu4 d u m b b e l l s : because o f t h e l r p r o x i m i t y o f 01 t h e i r bending f r e q u e n c y would be e x p e c t e d t o s o f t e n c o n s i d e r a b l y upon d r i v i n g out the 0 1 ' s . We a r e t h u s l e f t w i t h t h e bending modes o f Cu2-02 and Cu3-03 ( d e f o r m a t i o n o f t h e warped s q u a r e s ) . They s h o u l d gen e r a t e f o u r Davidov p a i r s c o r r e s p o n d i n g to: (A) (B) (C) (D)
Cu2-02 Cu2-02 Cu3-03 Cu3-03
vibrating ' ' "
along y ' z ' x ' z
(1)
In o r d e r t o p r o c e e d f u r t h e r in our a s s i g n m e n t we s h o u l d , i d e a l l y , perform measurements w i t h p o l a r i z e d l i g h t on o r i e n t e d s i n g l e c r y s t a l samples. S i n g l e c r y s t a l s a v a i l a b l e so f a r are r a t h e r s m a l l , u n s u i t a b l e f o r i r measurements, a l t h o u g h r e c e n t l y p r e p a r e d t h i n f i l m s may be s u i t a b l e ( 1 8 ~ Raman measurements on them c a n , in p r i n c i p l e , be p e r f o r m e d , w i t h a Raman m i c r o p r o b e . Such w o r k , p e r f o r m e d on polycrystalline specimens w i t h r e l a t i v e l y large c~ystallites has r e c e n t l y app e a r e d . ~ The c r y s t a l l i t e s were, however, o r i e n t e d w i t h o p t i c a l t e c h n i q u e s using a polarizatlon m i c r o s c o p e , lhe assumption was made t h a t t h e samples were o p t i c a l l y u n i a x i a l w i t h the o p t i c a l a x i s along the c (z)-direction, an a s s u m p t i o n based on the n e a r l y t e t r a g o n a l n a t u r e of the translation lattice. We b e l i e v e t h a t such a s s u m p t i o n may be i n c o r r e c t s i n c e ~t leads t o the assignment of the s t r o n g Raman p~ak seen f o r M = Y t t r i u m a t 338 cm-Z t o x y - s y m m e t r y Raman mo~es which are f o r b i d d e n f o r our s t r u c t u r e . A p o s s i b l e way o u t o f t h l s dilemma may l i e in t h e f a c t t h a t , even f o r l a t t i c e c o n s t a n t s a = b, t h e u n l t c e l l is v e r y f a r from t e t r a g o n a l because o f t h e a s y m m e t r i c p l a c e m e n t o f atoms 01 a l o n g b b u t n o t a l o n g a. I f we assume t h a t t h e optical susceptibility is due e x c l u s i v e l y t o the l o n g i t u d i n a l polarizability of the Cu-O bonds we c o n c l u d e t h a t t h e o p t i c a l
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axis lies actually along y: there are three such bonds along y, only two along x and z . H e n c e , t h e x y s y m m e t r y f o u n d f o r t h e 338 cm - I line i n R e f . 2 may t u r n out t o be x z , in agreement with the selection rules for vibrations (A) in Eq. i . Since t h e yz component o f t h e Raman t e n s o r is not g i v e n in R e f . 2, we may assume, in agreement w l t h t h e s t r u c t u r e o f t h e u n i t cell, that vibrations (C) a l s o c o n t r l b u t e t o t h i s l i n e ( t h e y s h o u l d be n e a r l y deg e n e r a t e in f r e q u e n c y ) . Thus we a t t r i b u t e t h e upper component o f t h e d o u b l e t s o f F i g . I t o v i b r a t i o n s o f Cu3-03 a l o n g x and Cu2-02 a l o n g y. The l o w e r component can then be s a f e l y a s s l g n e d t o t h e v i b r a t i o n s o f t h e s e bonds a l o n g z. The d o u b l e t s o f F i g . 2 is then a t t r i b u t e d t o the Davidov c o n j u g a t e : upper component xz and yz s y m m e t r y , l o w e r one z z . The n a t u r e of the observed anomaiou~ temperature shift below [c is not known. We p o i n t out, however, that ]t cannot be understood on t h e b a s e s o f s e l f - e n e r g y c h a n g e s due t o c h a n g e s i n t h e e l e c t r o n phonon-interaction with t h e opening_z the gap. For a gap a t ~ 2 0 0 cm below t h e phonon f r e q u e n c y in q u e s t l o n , one would e x p e c t a phonon h a r d e n l n g below Tc. Our r e s u l t s l e a d t o t h e s p e c u l a t l o n t h a t a second gap may be o p e n l n g above the phonon f r e q u e n c y . The e x l s t e n c e uf such gaps has been r e c e n t l y s u g g e s t e d by t h e p r e s e n t a u t h o r s . 12
12,1~f
In conclusion, we h a v e a s s i g n e d the i r and Raman d o u b l e t s observed between 250 and 350 cm - I in a few superconductors o f t h e M B a6 g C u~~ 0 7 _ family to Davidov palrs involving the deformation of the w a r p e d Cu-O s q u a r e frames which exlst ~n these materials. We h a v e sh o w n t h a t the frequencies o f t h e s e modes a l l soften a n o m a l o u s l y below Tc, a f a c t which must be r e l a t e d t o the mechanism o f s u p e r c o n ductlvity: no s o f t e n i n g o c c u r s f o r t h e e q u i v a l e n t l i n e s o f the s e m i c o n d u c t l n g materiai YBa2Cu306.
We w o u l d l i k e to thank Prof. M. Alarlo for a number of useful discussions. T h a n k s a r e a l s o due t o H. H i r t , Siemers, and P. W u r s t e r for sklllful technical helps.
References i.
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B. B a t t l o g , R.J. C a v a , A. J a y a r a m a n , R.B. van Dover, G.A. Kourouklis, S. Sunshine, D.W. M u r p h y , L.W. R u p p , H . S . C h e n , A. W h i t e , K.T. Short, A.M. Mujsce, and E . A . R i e t m a n n , Phys. Rev. Lett. 5 8 , 2333 ( 1 9 8 7 ) . R . O . H e m l e y and H . K . MaD, P h y s . R e v . Lett. 5 8 , 2340 ( 1 9 8 7 l . S. 8 ] u m e n r o e d e r , E. Z i r n g i e b l , d . D. T h o m p s o n , P. K i l l o u g h , ,].1 . S m i t h ,
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8. 9.
10. 11. 12. 13.
RAMAN AND INFRARED PHONONS OF MBa2Cu307_ 6-TYPE SUPERCONDUCTORS
Mattausch, W. Bauhofer, A. Simon, F. G a r c i a - A l v a r a d o , E. Moran, M. V a l l e t , J . M . G o n z a l e z - C a l b e t , M.A. A l a r i o , S o l i d S t a t e Commun. 63, 839 (1987). Z. l q b a l , S.W. S t e i n h a u s e r , A. Bose, N. C i p o l l i n i , and H. E c k a r d t , Phys. Rev. B, in press. P.E. S u l e w s k i , A.J. S i e v e r s , S.E. Russek, H.D. H a l l e n , D.K. L a t h r o p , and R.A. Buhrman, Phys. Rev. B 35, 5330 (1987). U. W a l t e r , M.S. Sherwin, A. Stacy, P.L. R i c h a r d s , and A. Z e t t l , Phys. Rev. B 35, 5327 (1987). D.A. Bonn, J . E . Greedan, C.V. S t a g e r , and T. Timusk, Phys. Rev. L e t t . 58, 2249 (1987). L. Genzel, A. W i t t l l n , J. Kuhl, Hj. Mattausch, W. Bauhofer, and A. Simon, S o l i d S t a t e Commun. 63, 843 (1987). S. Sugai , S. Uchida, H. T a k a g i , K. K i t a z a n a , and S. Tanaka, Jap. J. Appl. Phys. 26, L879 (1987).
481
14. J.D. Jorgensen, H.-B. S c h u t t l e r , D.G. Hinks, D.W. Capone I I , K. Zhang, M.B. Brodsky, and D.J. S c a l a p i n o , Phys. Rev. L e t t . 58, 1024 (1987). 15. D.W. Murphy, S. Sunshine, R.B. von Dover, R.J. Cava, B. B a t l o g g , S.M. Zahnrak, and L.F. Schneemeyer, Phys. Rev. L e t t . 58, 1888 (1987). 16. P. Bo r d e r , C. C h a i l l o n d , J . J . Capponi, J. Chenovas, and M. Marezio~ to be p u b l i s h e d ; M. Onoda, S. Shamoto, M. Sato, and S. Hosoya, Jap. J. Appl. Phys. 26, L876 (1987}. 17. M. Cardona, L. Genzel, and A. W i t t l i n , t o be p u b l i s h e d . 18. P. Chaudhari, RoH. Koch, R.B. L a i b o w i t z , T.R. McGuire, R.J. Gambino, Phys. Rev. L e t t . 58, 2684 (1987).
1987.
0038-1098/87 $3.00 + .00 Pergamon Journals Ltd.
T e m p e r a t u r e dependence o f the Raman and i n f r a r e d MBa2Cu307_~-type s u p e r c o n d u c t o r s A.
phonons o f
Wittlin*, R. L i u , M. Cardona, L. G e n z e l , W. K 6 n i g , W. B a u h o f e r , H j . M a t t a u s c h , and A. Simon Max-Planck-lnstitut fur Festk6rperforschung, H e i s e n b e r g s t r a 6 e I , 7000 S t u t t g a r t 80, F e d e r a l R e p u b l i c o f Germany F. #
Garc{a-Alvarado
.
J
.
Departamento de Qulm~ca I n o r g a n l c a , F a c u l t a d de C i e n c i a s O u l m l c a s , U n i v e r s i d a d Complutense, 28040 M a d r i d , Spain J
.
(Received J u l y
15,
1 9 8 7 by M. Cardona)
An anomalous t e m p e r a t u r e dependence o f the ~340 cm-1 Raman phonons o f YBa2Cu307_6 has been r e c e n t l y r e p o r t e d by M a c f a r l a n e et a l . Here we s h o w t h a t t h i s phenomenon, a phonon s o f t e n i n g w i t h d e c r e a s i n g T f o r T < Tc, i s common t o many m a t e r i a l s o f the f a m i l y (M = Y, Sm, Eu, Ho, Gd). We a l s o show t h a t the i t - a c t i v e Davidov c o u n t e r p a r t o f t h i s phonon, and a n o t h e r J r - a c t i v e phonon a t s l l g h t l y lower f r e q u e n c y , a l s o e x h l b i t s i m i l a r e f f e c t s . These phonons are a t t r i b u t e d t o bending v l b r a t i o n s o f the Cu2-02 and Cu3-03 bonds. A l l o t h e r i r and Raman phonons o b s e r v e d e x h i b i t a normal t e m p e r a t u r e dependence ( i . e . , h a [ d e n i n g w i t h d e c r e a s i n g T even f o r T < T c ) . l h e 310 cm phonon o f the t e t r a g o n a l n o n - s u p e r c o n d u c t i n g YBa2Cu306 a l s o shows a normal b e h a v i o r v s . T.
Raman 1-8 ana i r - s p e c t r o s c o p y 9-13 have r e c e n t l y become p o p u l a r t o o l s f o r the i n v e s t i g a t i o n o f the new h i g h Tc s u p e r c o n d u c t o r s . The l a t t e r y i e l d s i n f o r m a t i o n about i r - p h o n o n s and the s u p e r c o n d u c t i n g gaps w h i l e in the f o r m e r Raman phonons are seen. Raman and i n f r a r e d a c t i v i t i e s are m u t u a l l y e x c l u s i v e in m a t e r i a l s w i t h i n v e r s i o n symmetry such as t h o s e o f the two classical families o f h~gh T c s u p e r conductors (Lal_×Srx)2Cu04 1 and
~ .
HoBa2Cu30?-~
LU
MBagCu~Ov ~ a~ , - o (M ~ y~ ~'TheNd'symmetrySm' Eu, Gd,ana_ Ho, Er, Lu, . . . . ' lysis o f t h e i r and Raman modes o f t h e former is given in Ref. 3 while that of the latter is given in Ref. 7.
O Z
0 Iii ._1 Ii m rr
The MBa2Cu307_6 a r e , in t h e i r s u p e r c o n d u c t i n g phase, o r t h o r h o m b i c , b e l o n g i n g t o the Pmmm space group (mmm p o l n t ) w i t h one f o r m u l a u n l t per p r i m l t i v e c e l l (see F i g . 1 o f R e f . 7 ) . The M-atoms g e n e r a t e t h r e e J r - a c t i v e modes o f x , y, z symmetry w h i l e t h e p a i r o f e q u i v a l e n t Ba atoms g e n e r a t e I r and R a m a n - a c t i v e D a v l d o v d o u b l e t s ( x z , y z , and zz s y m m e t r i e s ) . The t h r e e Cu-atoms g i v e r l s e t o one s e t o f Davldov d o u b l e t s (3×2 modes) and t h r e e J r - a c t i v e modes w h l l e the seven O-atoms
200
240
280
320
360
400
(.o [ cm -1]
I.
* On leave of absence from Institute of Physics, Polish Academy of Science, 02 668 Warsaw, Poland. 477
R e f l e c t a n c e s p e c t r a o f HoBa2~u307_ ~ between 200 cm and 400 cm . Vertical l i n e h e l p s t o v i s u a l i z e t h e phonon f r e q u e n c y changes w i t h t e m p e r a t u r e .
478
RAMAN AND INFR~NED PHONONS OF MBa2Cu307_~-TYPE SUPERCONDUCTORS
Vol. 64, No. 4
peaks f o u n d in t h e s a m e r e g i o n . M o r e o v e r , we show t h a t in t h e t e t r a g o n a l , oxygen deficient compound YBa2Cu306, w h i c h i s not s u p e r c o n d u c t i n g ( s e m i c o n d u c t o r or insulator) t h e peaks o b s e r v e d in t h e same r e g i o n show t h e s t a n d a r d b e h a v i o r w i t h d e c r e a s i n g t e m p e r a t u r e . Thus t h e weak s o f t e n i n g o b s e r v e d f o r t h e s e phonons in t h e s u p e r c o n d u c t i n g phase has t o be r e l a t e d , in some u n u n d e r s t o o d manner, t o t h e phenomenon o f s u p e r c o n d u c t i v i t y in these materials.
o') c
.d 0
The measurement t e c h n i q u e s have been d e s c r i b e d e l s e w h e r e . The o x y g e n d e f i c i e n t M = Y sample was p r e p a r e d by h e a t i n g in an Ar a t m o s p h e r e a t 950°C f o r one h o u r . I t was f o u n d t o be n o n s u p e r c o n d u c t i n g by r e s i s t a n c e measurements down t o 4 K. A l s o , t h e Raman s p e c t r a show i t i s n o t metallic. Guinier diffractograms show t h a t t h e s e samples a r e s i n g l e phase and tetragonal. Their structure is c o n s i s t e n t w i t h t h a t g i v e n in R e f . 16. The i n f r a r e d s p e c t r a cm_~ o f • h ese samples al so peak a t 276 and 315 ( a t 300 K ) .
.J
z 0 or) or) IJJ Y
if)
200
2.
300 400 STOKES SHIFT [cm-1]
Analogous to Fig. HoBa2Cu307_ 6 •
1.
Raman s p e c t r a
of
g e n e r a t e 3 sets o f D a v i d o v - d o u b l e t s (3x3 modes) and t h r e e i t - a c t i v e modes. Among t h e O- and C u - g e n e r a t e d modes a r e t h e stretching vibrations o f t h e Cu-O bonds which o c u r b e t w e e n 400 and 650 cm-~. 1 , 2 , 4 ' 7 ' 8 The p r e s e n t p a p e r r e f e r s t o t h e p h o non s t r u c t u r e s which a r e seen b e t w e e n 250 and 350 cm-1 f o r M = Y, Eu, Sm, Ho, Gd. Two peaks a r e o b s e r v e d in t h i s r e g i o n in t h e i r s p e c t r a ( F i g . 1 f o r Ho) e i t h e r one o r two in t h e Raman s p e c t r a ( F i g . 2 f o r M = H o ) . The two peaks a r e w e l l r e s o l v e d f o r M = Ho, as shown in F i g . 2. In t h e c a s e s in w h i c h o n l y one Raman peak i s seen (M = Y, Sm) t h e r e i s s o m e i n d i c a t i o n t h a t t h e l o w e r f r e q u e n c y component e x i s t s but is u n r e s o l v e d . A very interesting f e a t u r e has been r e p o r t e d r e c e n t l y f o ~ t h e Raman peak o b s e r v e d a t ~340 cm f o r M=Y (4). T h i s peak f i r s t shifts slightly upwards in frequency (i.e., hardens) with decreasing t e m p e r a t u r e down t o ~100 K ( a p p r o x i m a t e l y equal, within error, t o T c ) . But b e l o w t h i s t e m p e r a t u r e , i t a n o m a l o u s l y dec r e a s e s ; t h e d e c r e a s e amounts t o a b o u t 6 cm ~ a t 10 K. In t h i s p a p e r we p r e s e n t d a t a s h o w i n g t h a t t h i s phenomenon i s g e n e r a l t o many s u p e r c o n d u c t o r s o f t h e MB2Cu307_ a f a m i l y (M = Y, Sm, Eu, Ho, Gd). I t i s a l s o seen n o t o n l y in t h e Raman s p e c t r a ( F i g . 2) b u t a l s o in t h e i r
The i r and Raman s p e c t r a o f a sample w i t h M = Ho a r e shown in F i g s . I and 2, respectively, at several temperatures. Two peaks a r e c l e a r l y o b s e r v e d in b o t h s e t s o f s p e c t r a . These d o u b l e t s have similar spl~tings, t h e Raman one l y i n g a b o u t 20 cm ~ h i g h e r t h a n t h e i r c o u n t e r part. I t i s t h u s r e a s o n a b l e t o assume t h a t we a r e d e a l l n g w i t h D a v i d o v d o u b lets. The a n o m a l y j u s t m e n t i o n e d can be observed directly by r e f e r r i n g t h e peak p o s i t i o n s to the t h i n v e r t i c a l lines of F i g s . i and 2: between 300 and i 0 0 K t h e peak f r e q u e n c i e s a r e n~ r l y c o n s t a n t w h i l e a d r o p o f ~6 cm -~a i s o b s e r v e d b e t ween 100 and 10 K. The t e m p e r a t u r e dependence o f t h e wavenumbers o f maxima o f t h e two i r p e a k s , and o f t h e u p p e r component o b s e r v e d in t h e Raman s p e c t r a , a r e shown in F i g . 3 f o r a l l samples m e a s u r e d . We have a l s o i n c l u d e d in t h i s f i g u r e t h e c o r r e sponding data for the non-superconducting M = Y t t r i u m sample w h i c h snows a smooth wavenumber i n c r e a s e w i t h d e c r e a s i n g temp e r a t u r e , w i t h o u t any a n o m a l y . The d a t a f o r a l l s u p e r c o n d u c t i n g samples e x h i b i t t h e anomalous b e h a v i o r m e n t i o n e d a b o v e , the t e m p e r a t u r e s h i f t s being quantitatlvely very similar in a l l c a s e s . We have a l s o i n v e s t i g a t e d the t e m p e r a t u r e dependence o f a l l o t h e r phonons o b s e r v e d p r o m i n e n t l y in t h e s e s p e c t r a : i t a p p e a r s t o be n o r m a l . We show, as an e x a m p l e in F i g . 3, t h e t e m p e r a t u r e v a r i a t } o n of the Cu-O band s t r e t c h i n g peak seen in Raman a t a r o u n d 500 cm-1: normal b e h a v i o r (hardening with decreasing temperature) i s o b s e r v e d . A l s o t h e low f r e q u e n c y peaks seen in t h e i r (~15~ c m - l ) l l , 1 2 and Raman s p e c t r a (~150 cm - 1 ) w h i c h ~re r e l a t e d t o vibrations o f t h e Ba atoms I do n o t show anomalous b e h a v i o r . In o r d e r t o e x c l u d e the p o s s i b i l i t y t h a t t h e o b s e r v e d anoma-
Vol. 64, No. 4
~ [cm_1]
RAMAN AND INFRARED PHONONS OF MBa2Cu307_~-TYPE SUPERCONDUCTORS
................ 0 Y ( A r ) ....... XHo ----[3 Gd
a)
320
...... ........
OSm • Eu
b)
479
........ •
Eu
................ × H o 510 -
-
-
-
O
Y
. . . . . . . O Y (Ar
(,j [ c r n -1 ]
505 .
.
.
.
.
.
.
.
315
500 310
495, 305~.
280
,
0
,
100
200
300
T[K]
270
0
100
200
300
T [ K ]
3.
Temperature dependence of phonon f r e quencies of MBa2Cu$07_~ (M = Ho, Gd, Sm, Eu) and of s e m l c o n d u c t i n g YBa2Cu306 • a) R e f l e c t a n c e measurement r e s u l t s . b) Raman measurements r e s u l t s . Note anomalous s o f t e n i n g of phonons below 100 K in s u p e r c o n d u c t i n g compounds and normal t e m p e r a t u r e dependence of phonon f r e q u e n c i e s f o r YBa2Cu306 •
lous s h i f t s be due t o l i n e s h a p e e f f e c t s ( a l t h o u g h i t i s u n l i k e l y t h a t t h e y would be the same in i r as in Raman) we have extended our L o r e n t z i a n o s c i l ] ~ t o r f i t s of the i r r e f l e c t a n c e s p e c t r a l Z t o a t e m p e r a t u r e dependent one. I t i s found t h a t the r e f l e c t i o n peaks s h i f t upwards by about 8 cm ~ below Tc even f o r cons t a n t phonon f r e q u e n c i e s , an e f f e c t which i s p u r e l y of d i e l e c t r i c o r i g i n . Thus the observed s o f t e n i n g s must be r e a l .
with
Because of t h e i r anomalous b e h a v i o r v a r y i n g temperature, i t is i m p o r t a n t
t o t r y t o a s s i g n the d o u b l e t s of F i g s . 1 and 2 t o symmetry t y p e s and t o c o n j e c t u r e what t h e i r e i g e n v e c t o r s may be. They are w e l l below the Cu-O s t r e t c h r e g i o n and w e l l above the f r e q u e n c i e s e s t i m a t e d f o r v i b r a t i o n s i n v o l v i n g s t r o D g l y the motions of M or Ba (below 200 cm I ) . 17 We thus assign them t o bending modes of the Cu-O bonds. In t h i s c o n t e x t s e v e r a l p o s s i b i lities a r i s e : bond bending of the 02-Cu2 and 03-Cu3 bonds f o r m i n g the two warped squares in each u n i t c e l l ( F i g . 1 of Ref. 7 ) , wagging of the 04-Cu4 d u m b b e l l s , and a l s o bending of the 01-Cul bonds.
480
RAMAN AND INPTLARED PHONONS OF MBa2Cu307_6-TYPE SUPERCONDUCTORS
From t h e f a c t t h a t t h e d o u b l e t s appear a t n e a r l y t h e same p o s i t i o n in t h e nons u p e r c o n d u c t i n g sample ( i . e . , after d r i v i n g o u t t h e 01) we c o n c l u d e t h a t t h e y have n o t h i n g t o do w i t h t h e 0 1 - C u l bonds. By t h e same t o k e n we e x c l u d e t h e 04-Cu4 d u m b b e l l s : because o f t h e l r p r o x i m i t y o f 01 t h e i r bending f r e q u e n c y would be e x p e c t e d t o s o f t e n c o n s i d e r a b l y upon d r i v i n g out the 0 1 ' s . We a r e t h u s l e f t w i t h t h e bending modes o f Cu2-02 and Cu3-03 ( d e f o r m a t i o n o f t h e warped s q u a r e s ) . They s h o u l d gen e r a t e f o u r Davidov p a i r s c o r r e s p o n d i n g to: (A) (B) (C) (D)
Cu2-02 Cu2-02 Cu3-03 Cu3-03
vibrating ' ' "
along y ' z ' x ' z
(1)
In o r d e r t o p r o c e e d f u r t h e r in our a s s i g n m e n t we s h o u l d , i d e a l l y , perform measurements w i t h p o l a r i z e d l i g h t on o r i e n t e d s i n g l e c r y s t a l samples. S i n g l e c r y s t a l s a v a i l a b l e so f a r are r a t h e r s m a l l , u n s u i t a b l e f o r i r measurements, a l t h o u g h r e c e n t l y p r e p a r e d t h i n f i l m s may be s u i t a b l e ( 1 8 ~ Raman measurements on them c a n , in p r i n c i p l e , be p e r f o r m e d , w i t h a Raman m i c r o p r o b e . Such w o r k , p e r f o r m e d on polycrystalline specimens w i t h r e l a t i v e l y large c~ystallites has r e c e n t l y app e a r e d . ~ The c r y s t a l l i t e s were, however, o r i e n t e d w i t h o p t i c a l t e c h n i q u e s using a polarizatlon m i c r o s c o p e , lhe assumption was made t h a t t h e samples were o p t i c a l l y u n i a x i a l w i t h the o p t i c a l a x i s along the c (z)-direction, an a s s u m p t i o n based on the n e a r l y t e t r a g o n a l n a t u r e of the translation lattice. We b e l i e v e t h a t such a s s u m p t i o n may be i n c o r r e c t s i n c e ~t leads t o the assignment of the s t r o n g Raman p~ak seen f o r M = Y t t r i u m a t 338 cm-Z t o x y - s y m m e t r y Raman mo~es which are f o r b i d d e n f o r our s t r u c t u r e . A p o s s i b l e way o u t o f t h l s dilemma may l i e in t h e f a c t t h a t , even f o r l a t t i c e c o n s t a n t s a = b, t h e u n l t c e l l is v e r y f a r from t e t r a g o n a l because o f t h e a s y m m e t r i c p l a c e m e n t o f atoms 01 a l o n g b b u t n o t a l o n g a. I f we assume t h a t t h e optical susceptibility is due e x c l u s i v e l y t o the l o n g i t u d i n a l polarizability of the Cu-O bonds we c o n c l u d e t h a t t h e o p t i c a l
Vol. 64, No. 4
axis lies actually along y: there are three such bonds along y, only two along x and z . H e n c e , t h e x y s y m m e t r y f o u n d f o r t h e 338 cm - I line i n R e f . 2 may t u r n out t o be x z , in agreement with the selection rules for vibrations (A) in Eq. i . Since t h e yz component o f t h e Raman t e n s o r is not g i v e n in R e f . 2, we may assume, in agreement w l t h t h e s t r u c t u r e o f t h e u n i t cell, that vibrations (C) a l s o c o n t r l b u t e t o t h i s l i n e ( t h e y s h o u l d be n e a r l y deg e n e r a t e in f r e q u e n c y ) . Thus we a t t r i b u t e t h e upper component o f t h e d o u b l e t s o f F i g . I t o v i b r a t i o n s o f Cu3-03 a l o n g x and Cu2-02 a l o n g y. The l o w e r component can then be s a f e l y a s s l g n e d t o t h e v i b r a t i o n s o f t h e s e bonds a l o n g z. The d o u b l e t s o f F i g . 2 is then a t t r i b u t e d t o the Davidov c o n j u g a t e : upper component xz and yz s y m m e t r y , l o w e r one z z . The n a t u r e of the observed anomaiou~ temperature shift below [c is not known. We p o i n t out, however, that ]t cannot be understood on t h e b a s e s o f s e l f - e n e r g y c h a n g e s due t o c h a n g e s i n t h e e l e c t r o n phonon-interaction with t h e opening_z the gap. For a gap a t ~ 2 0 0 cm below t h e phonon f r e q u e n c y in q u e s t l o n , one would e x p e c t a phonon h a r d e n l n g below Tc. Our r e s u l t s l e a d t o t h e s p e c u l a t l o n t h a t a second gap may be o p e n l n g above the phonon f r e q u e n c y . The e x l s t e n c e uf such gaps has been r e c e n t l y s u g g e s t e d by t h e p r e s e n t a u t h o r s . 12
12,1~f
In conclusion, we h a v e a s s i g n e d the i r and Raman d o u b l e t s observed between 250 and 350 cm - I in a few superconductors o f t h e M B a6 g C u~~ 0 7 _ family to Davidov palrs involving the deformation of the w a r p e d Cu-O s q u a r e frames which exlst ~n these materials. We h a v e sh o w n t h a t the frequencies o f t h e s e modes a l l soften a n o m a l o u s l y below Tc, a f a c t which must be r e l a t e d t o the mechanism o f s u p e r c o n ductlvity: no s o f t e n i n g o c c u r s f o r t h e e q u i v a l e n t l i n e s o f the s e m i c o n d u c t l n g materiai YBa2Cu306.
We w o u l d l i k e to thank Prof. M. Alarlo for a number of useful discussions. T h a n k s a r e a l s o due t o H. H i r t , Siemers, and P. W u r s t e r for sklllful technical helps.
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