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The AsO4−4 center in CsH2AsO4: A Halperin-Varma defect moving in a single well potential
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Solid S t a t e Communications, Vol. 46, No. 7, pp. 513-516, 1983 Printed in Great Britain.
0038-1098/83/190 513-04 $03.00/0 Pergamon P r e s s Ltd.
THE AsO~-CENTER IN CsH2As04: A HALPERIN-VARMA DEFECT MOVING IN A SINGLE WELL POTENTIAL P.S.S. G u i m a r a e s , R. G a z z i n e l l i , G.M. R i b e i r o and A.S. Chaves - D e p a r t m e n t o f P h y s i c s , ICEX, U n i v e r s l d a d e F e d e r a l de Minas G e r a i s , C . P . 7 0 2 , Belo Horizonte, Brazil (RECEIVED ON NOVEMBER 30th1982 by R.C.C.
LEITE)
4The ESR o f t h e AsO 4 c e n t e r in CsH_AsO. is i n v e s t i g a t e d ' from 4.2K t o 270K. The b e h a v i o r o f th~s p ~ r a m a g n e t i c c e n t e r is e s s e n t i a l l y different from i t s b e h a v i o r in t h e o t h e r members o f t h e KDP f a m i l y . Two p r o p e r t i e s o f the c e n t e r a r e r e m a r k a b l e : i t seems t o behave l l k e a H a l p e r i n - V a r m a kind of d e f e c t and t o move c l a s s i c a l l y in a s i n g l e - w e l l potential which can be r e p r e s e n t e d w i t h v e r y good a p p r o x i m a t i o n by square w e l l .
The m i c r o s c o p i c model f o r the f e r r o e l e c t r i c t r a n s i t i o n in hydrogen-bond c r y s t a l s o f the KH2PO4 (KDP) f a m i l y has been a m a t t e r of i n t e n s e i n v e s t i g a t i o n . In h i s c l a s s i c a l paper S l a t e r ( l ) propo~ ed a mechanism based in the o r d e r i n g of the hydrogens in a d o u b l e - w e l l p o t e n t i a l along the l i n e c o n n e c t i n g the o x i g e n s of n e i g h b o u r PO groups. The spontaneous p o l a r i z a t i o n 4 o f KDP occurs along the t e t r a g o n a l c - a x i s , whereas n e u t r o n d i f f r a c t i o n e x p e r i m e n t s by Bacon and Pease (2) show t h a t the hydrogen motion is almost e x a c t l y c o n t a i n e d in the abplane. B a c o n and Pease a t t r i b u t e d the p o l a r i z a t i o n o f the c r y s t a l t o the d i s placements of the potassium and phosphorus ions along the c - a x i s . The hidrogens, however, should p l a y a c e n t r a l r o l e in the t r a n s i t i o n mechanism in o r d e r to e x p l a i n the pronounced dependence o f the t r a n s i t i o n t e m p e r a t u r e T w i t h deuteration. The c o n n e c t i o n between Cthese f a c t s was c l a r i f i e d by Cochran ( 3 ) , who proposed a s o f t mode f o r KDP made up by a correlated motion o f the hydrogens and the heavy ions: as the two protons in the upper H-bonds o f a PO4 group move to s i t e s near t h a t group, the two p r o t o n s in the lower bonds move away, the P ions move down along the the c - a x i s and the K ions move up along t h i s same a x i s . The e f f e c t o f d e u t e r a t i o n upon the t r a n s i t i o n t e m p e r a t u r e was e x p l a i n e d by Pirenne (4) and Blinc (5) as due to purely q u a n t u m - m e c h a n i c a l effects, on rather distinct assumptions concerning the s i n g l e - p a r t i c l e potential for the motion of the protons (deuterons). Pirenne postulated a single-well potential for the bonds, whereas Blinc adopted the double-well potential proposed by Slater. The form of the potential for the bond is still a matter of dispute. Silva and Ro-
v e r s i (6) showed t h a t t h e a v a i l a b l e d a t a on the v a r i a t i o n o f the s t a t i c p r o p e r t i e s o f t h e c r y s t a l such as t h e i s o t o p i c depen dence o f t he t r a n s i t i o n t e m p e r a t u r e , Curie c o n s t a n t and s a t u r a t i o n p o l a r i z a t i o n , c a n n o t d i s c r i m i n a t e between the s q u a r e well potential initially e x p l o i t e d by P i r e n n e and the d o u b l e - w e l l t u n n e l l i n g bond proposed by B l i n c . E m p i r i c a l models f o r the h y d r o g e n - b o n d p o t e n t i a l were r e c e n t l y p r o p o s e d and i n v e s t i g a t e d by Lawrence and R o b e r t s o n (7) and by Inoue and S h i r a i s h i (8). Many i n v e s t i g a t i o n s have been done by ESR on the KDP f a m i l y u s i n g paramagnet i c c e n t e r s at the s i t e o f t h e P i o n . Such i n v e s t i g a t i o n s were s t r o n g l y m o t i v a t e d by t h e ESR s t uL d y by B l i n c , Cevc and Schara(9) on the AsO~- c e n t e r in KH_AsO. (KDA),whe re the spedtraU c a r a c t e r i s ~ i c ~f the f e r r o e l e c t r i c phase were found to remain in the p a r a e l e c t r l c phase up to a temper a t u r e T* c o n s i d e r a b l y h i g h e r than T . Reviews o f the s u b j e c t were made by c Adriaenssens (10) , Dalal ( I l l and others. The a u t h o r s o f those i n v e s t i g a t i o n s reached the unanimous c o n c l u s i o n t h a t the anomaly is due to the o c c u r r e n c e , in the p a r a e l e c t r i c phase, o f p o l a r i z e d c l u s t e r s which are l o n g - l i v e d in comparison w i t h the time scale of the soft-mode dyna mics. This l o w - f r e q u e n c y dynamics o f t h e o r d e r parameter was a l s o found to occur in many o t h e r s t r u c t u r a l phase t r a n s i t i o n s by i n v e s t i g a t i o n s using a g r e a t v a r i e t y of e x p e r i m e n t a l techniques and the phenomenon is denominated c e n t r a l peak (CP). Most Of the observed CP are now recognized t o be not i n t r i n s i c to p h a s e - t r a n s l t l o n dynamics, but caused by d e f e c t s o f the c r y s t a l . In p a r t i c u l a r , the accumulated e v i d e n c e support the c o n c l u s i o n t h a t a l l the CP observed by ESR e x p e r i m e n t s are a f f e c t e d by the
513
514
THE AsO ~ - ~ N T E R IN CsH2AsO 4
Vol. 46, No. 7
p a r a m a g n e t i c probe - a p o i n t d e f e c t on Th~ ESR s p i n H a m i l t o n i a n describing the system under s t u d y . Two a l t e r n a t i v e t h e AsO~- c e n t e r i s g i v e n by models a r e a v a i l a b l e f o r p o i n t - d e f e c t 4+ induced CP. H a l p e r i n and Varma ( 1 2 ) , in H = ~ . g...S. . . + ? . ~ . ~ + ~ i .~.~, (i) P P an i n d e p e n d e n t w o r k , d e v e l o p e d in d e t a i l p=l a model f i r s t proposed by Burns ( 1 3 ) . Such model, g e n e r a l l y known as H a l p e r i n where S = 1 / 2 , ] = 3 / 2 , 1 = I / 2 , a n d A and A p P Varma (HV) model, p o s t u l a t e s t h a t the are the hyperfine interaction tensors d e f e c t has an i n t r i n s i c dynamics which for the arsenic and t h e f o u r p r o t o n s breaks the l o c a l symmetry o f the system s u r r o u n d i n g t h e radlca]. The g r o s s f e a t u in the same way as the o r d e r p a r a m e t e r , r e s o f t h e ESR s p e c t r a are dominated byand c o n s e q u e n t l y i t s dynamics w i l l c o u p l e t h e l a r g e v a l u e o f A, w h i c h g i v e s o r i g i n l i n e a r l y w i t h t h e s o f t mode, i . e . , the to a large splitting of the I quartet. intrinsic dynamics o f t h e o r d e r p a r a m e t e r . Each l i n e o f t h i s quartet shows a p o o r l y That c o u p l i n g r e n d e r s a c r i t i c a l behavior r e s o l v e d s t r u c t u r e w h i c h h a v e b e e n shown t o t h e d e f e c t dynamics w i t h the s o f t mode (9,16,19) to result from the protons hyis t o o weak t o a f f e c t a p p r e c i a b l y t h a t perfine interactions and f r o m t h e d y n a m i c s . I n a v a r i a t i o n of the HV model the different orientations of the "gtensor, coupling of the defect dynamics with the soft corresponding to opposite ferroelectric mode is too weak to affect appreciably that dydomains, each one containing two cheminamics. Thus, the defect dynamics is not c r i t i cally-equi~alent but magnetically-unequ~ cal, i . e . , doesn o t follow the showing-down of valent As04- sites. This structure is the so'ft-mode near the c r i t i c a l temperature,but better resolved for the lowest-field i n s t e a d f o l l o w s the A r r h e n i u s law f o r (MI= 3/2) line of the quartet, and thus t h e r m a l l y a c t i v a t e d processes ( ] 4 ) . In we c o n c e n t r a t e d most of our a t t e n t i o n to the second model, proposed by H~Ick and the study of this line. Figure I shows T h o m a s (15) (HT), the defect does not the a n g u l a r v a r i a t i o n of the M.= 3/2 and b r e a k the local s y m m e t r y of the system, M = -3/2 lines, taken at 90K i~ the but c h a n g e s locally the p a r a m e t e r s of the f ~ r r o e l e c t r i c phase. The centers of the many-particle Hamiltonian which describes lines are isotropic in the a b - p l a n e . The the phase t r a n s i t i o n and, in p a r t i c u l a r , w h o l e s p e c t r u m shows no s i g n i f i c a n t the s o f t - m o d e behavior. Under certain fa changes from 4K to 270K, where the v o r a b l e c o n d i t i o n s the r e s u l t i n g effect p a r a m a g n e t i c center b e c o m e s unstable. is the increase in the t e m p e r a t u r e at The values of +9 and A o b t a i n e d from w h i c h one o b s e r v e s the local s y m m e t r y the m e a s u r e m e n t s in figure l are in b r e a k i n g a r o u n d the defect. Though all r e s o n a b l e a g r e e m e n t wit~ those p r e v i o u s three v a r i e t i e s of CP have been claimed to be ly o b t a i n e d by Dalai et. al (19). Howeobserved, it might be that all the CP observed by ESR in. the KDP family reported in the literature can ver, the s t r u c t u r e o b s e r v e d in the Ml= 3/2 t r a n s i t i o n is quite d i s t i n c t from be u n d e r s t o o d w i t h i n the f r a m e w o r k of that o b s e r v e d by Daia] et al. in CDA and the HT model (16,17). from the reported results in all the The crystal C s H _ A s O ~ ( C D A ) is other m e m b e r s of the KDP family. Our i s o m o r p h o u s with KDPZand 4 has a similar results are u n c o n s i ~ t e n t with the hypot r a n s i t i o n from a tetragonal (l~-2d) thesis that the AsO~- center p r e s e r v e s p a r a e l e c t r i c phase to an o r t h o r h o m b i c the s y m m e t r y of the AsO~- site. If this (Fdd2) f e r r o e l e c t r i c phase at T = I 4 0 K symmetry were p r e s e r v e d ; each member of (18). T h i s 4 P a p e r reports an ESR = study the As quartet should split, in the of the A s O ~ - c e n t e r in IDA which shows f e r r o e l e c t r i c phase, in two lines for s i g n i f i c a n t d i s t i n c t i o n s from the simi~ m a q n e t i c field in the d i r e c t i o n lar studies found in the l i t e r a t u r e for = a ÷ + +~ (17). However, as it can be other a r s e n i d e m e m b e r s of the KDP family, seen in figure 2, for that o r i e n t a t i o n and for CDA itself (19). The samples, of the field we have at least three o b t a i n e d from General Diode C o r p o r a t i o n , lines. In fact, by c o m p u t e r fitting the were i r r a d i a t e d at 77K with, X-ray for l i n e s h a p e we could see that there are the p r o d u c t i o n of the AsO~- center. The ~t four lines in figure 2, the line in the i r r a d i a t e d s a m p l e s were t r a n s f e r r e d to middle being an u n r e s o l v e d doublet. The an ESR s p e c t r o m e t e r at low t e m p e r a t u r e p r e c i s i o n of the sample o r i e n t a t i o n in in order, to p r e v e n t the d e s t r u c t i o n of the m a g n e t i c field (10) is high e n o u g h the A s O ~ - c e n t e r , w h i c h d e c a y s very to rule but m i s a l i q u e m e n t as a reason q u i c k l y - a t t e m p e r a t u r e s h i g h e r than about for the a p p r a r a n c e of more than two lines 270K. Two p a r a m a g n e t i c centers, A s O 4 - a n d in figure 2. The s p e c t r u m for H//C is AsO 2-, are c r e a t e d by i r r a d l a t i o n ( l ~ ) , a s also quite amazing. Instead of a triplet usual for the a r s e n i d e m e m b e r s of the which transforms into a quintet (9) at KDP family, but the A s O ~-T- c e n t e r has some t e m p e r a t u r e T* > Tc, t h e spectrum r e c e i v e d much more a t t e n t i o n in the lite shown in f i g u r e 3 was o b s e r v e d . That rature due to its a b i l i t y to m a n i f e s t CPspectrum shows no change when t h e tempep h e n o m e n a . This c e n t e r is formed by the r a t u r e is changed from 4K up t o 270K. The traI~ping of one extra e l e c t r o n by the l i n e s h a p e o b s e r v e d in f i g u r e 3 cannot be AsO~- radical and a c c o r d i n g to the f i t t e d by a q u i n t e t o r a t r i p l e t . In p r e ~ e n t e v i d e n c e s (17,19), the local f a c t , t h a t spectrum can be reproduced s y m m e t r y of this radical is p r e s e r v e d o n l y by the sum o f a v e r y l a r g e number o f after the c a p t u r e of the extra e l e c t r o n .
Vol. 46, No. 7
515
THE AsO~-CENTER IN CsH2AsO 4
4700
0/0
Gauss
j ~
T9 ,0K
/
4650
/
I
/
4600
Figure 2 - The s t r u c t u r e of the lowest field (M, = 3/2) line, at T = 90K and = 904~IMH~, fgr the m a g n e t i c field along X = a + b.
/
4550
T=90K 4500
Lo
I 450
3 - The s t r u c t u r e of the lowest field (M, = 3/2) line, at T = 197K and v = 9 0 0 5 1 M H z , for the m a g n e t i c field along c. The n o i s e l e s s line r e p r e s e n t s the best fit with formula 5 of the text.
I 400
I 35C
,5oo
and r e s o n a n c e m a g n e t i c field value of the c o o r d i n a t e s is 2 + h z + h2z HR ~ Ho l 0
,
30 °
60 =
:~;""'~
C
Figure I - Angular variation of the lowest-(M1=3/2) and highest field (M,=-3/2) lines a t T = 90K a n d v = 9 0 4 2 MH~. E a c h l i n e of the l = 3/2 quartet is a poorly resolved structure and the fields shown in the figure are taken at the center of the structure. The c e n t e r of the structure is isotropic in the ab-plane. The s p i n - H a m i l t o n i n a n parameter obtained from the data are gx = gy = gz = 2 . 0 0 0 + 0 . 0 0 5 , A = A =
(2757 +
10)
MHz,
Az
(3091
+- xlO)
MHz.Y
Iines and s u g g e s t s that the s y s t e m h== a c o n t i n u o u s d i s o r d e r . Trials for explaining thespectrum were made s u p p o s i n g that the AsO~-moves classically in a double well potential of the form V(z)
1450G
= -az 2 + bz 4,
a,b
> 0,
(2)
w h e r e z is p r o p o r t i o n a l to the local p o l a r i z a t i o n . The p r o b a b i l i t y of finding the c e n t e r at a c e r t a i n c o o r d i n a t e z is
p(z) = Ce- V ( z ) / k T ,
(3)
H R for
that (4)
The best c o m p u t e r f i t t i n g s of the l i n e s h a p e were o b t a i n e d with very s h a l l o w double-well p o t e n t i a l s and with hi>> h 2. An even better f i t t i n g was o b t a i n e d by a d o p t i n g the s q u a r e - w e l l potential and by making h 2 = 0. The s i n g l e - l i n e w h i c h gives the best fitting has a Gaussian lineshape, and thus the t h e o r e t i c a l l i n e s h a p e is
I(H)
d Hd
H + H fH ° - HI e x p l . 0 . 6 9 3 ( H _ H R ) 2 / y 2 1 d H R o I
(5) The comparison b e t w e e n t h e f u n c t i o n I (H) a n d e x p e r i m e n t is seen in figure 3. The fitting parameters were H = 1286 Gauss, H 1 = 55,6 Gauss and y ~ 15,5 Gauss. Some ramarks should be made about these results. From e q u a t i o n (4) and the fitting p a r a m e t e r s (h1>>h2), one sees that the resonance field can discriminate polarization up and p o l a r i z a t i o n down, i.e.,the paramagnetlc center breaks spontaneously the symmetry of the AsO~site and the resulting perturbation which i t c a u s e s on t h e s y s t e m c o n t a i n s
?
516
AsO~-CENTER~ IN CsH2AsO4
the i r r e d u c i b l e r e p r e s e n t a t i o n B2 o f the order parameter for the ferroelec~ric transition. O t h e r w i s e , H (z) s h o u l d c o n t a i n o n l y even powersRof z. T h i s is c o n s i s t e n t w i t h t h e a p p e a r a n c e o f more than two l l n e s in t h e X d i r e c t i o n , as d i s c u s s e d b e f o r e and shown in f i g u r e 2. The symmetry b r e a k i n g , e v i d e n t i a t e d by the a p p e a r a n c e o f a l i n e a r t e r m in the e x p a n s i o n o f H(z) and by th e e x i s t e n c e o f f o u r l i n e s f o r the magnetic f i e , l d along the X d i r e c t i o n , s u g g e s t s t h a t the AsO~probe behaves l i k e a H a l p e r i n Varma defect.
Vol. 46, No. 7
Furthermore, the As0~-defect does not move in a double w e l l p o t e n t i a l , but in a s h a l l o w s i n g l e w e l l p o t e n t i a l which can be described w i t h every good a p p r o x i m a t i o n by a square w e l l p o t e n t i a l . E v i d e n t l y , o n e should be aware of the f a c t t h a t the p o t e n t i a l f o r the motion of the d e f e c t i v e group can be q u i t e d i f f e r e n t from the p o t e n t i a l f o r the motion of the s u b s t i t u t e d AsO~- radical. We thank Dr. Ivone Mascarenhas f o r e s t a b l i s h i n g the c r y s t a l o r i e n t a t i o n by X-ray. This work was supported by FINEP, CNPq and CNEN.
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1. 2. 3. 4. 5. 6. 7. 8.
9. O. I. 2.
3. 4. 5. 6. 17. 18. 19.
J.C. S l a t e r , J. Chem. Phys. 9, 16 ( 1 9 4 1 ) . G.E. Bacon and R.S. Pease, P r o c . R. Soc. London 220, 397 ( 1 9 5 3 ) ; 239, 359 (1955) . W. Cochran, Advan. Phys. 10, 401 ( 1 9 6 1 ) . J P i r e n n e , P h y s i c a 15, 1"0-1-9 ( 1 9 4 9 ) . R B l i n c , J. Phys. C ~ m . Sol ids 13, 204 ( 1 9 6 0 ) . P R.P. S i l v a and J . A . R o v e r s i , P-Kys. Rev. B 21, 5237 ( 1 9 8 0 ) . M C. Lawrence and G.N. R o b e r t s o n , J. Phys. C: S o l i d St. Phys. I_33, L1053(1980) M Inoue and S. S h i r a i s h i , Ferroelectrics, 4_.55, 243 ( 1 9 8 2 ) . R B l l n c , P. Cevc and M. S c h a r a , Phys. Rev. 159, 411 ( 1 9 6 7 ) . G J. A d r i a e n s s e n s , J. Mag. Res. 2_._55, 511 (1977-')-7. N S. S a l a l , Adv. Hag. Resonance lO (198D). B I. f l a l p e r i n and C. M. Varrna, Pl~-ys. Rev. B 1/4, 4030 ( 1 9 7 6 ) . G Burns, Phys. Rev. B 1_33, 215 ( 1 9 7 6 ) . B L a m o t t e , J. G a i l l a r d and O. C o n s t a n t i n e s c u , J. Chem. Phys.- 57, 3319 (1972) K H. HEIck and H. Thomas, Z. Phys. B 27, 267 ( 1 9 7 7 ) ; 3_66, 151 ( 1 ~ 9 ) . G M. R i b e i r o , L.V. Gonzaga, A.S. Chaves, R. G a z z i n e l l i , R. B l i n c , P. Cevc, P P r e l o v s e k and N . I . S i l k i n , Phys. Rev. B 2_~5, 31l ( 1 9 8 2 ) ; and r e f e r e n c e s therein. N.S. D a l a i , J . A . Hebden, D.E. Kennedy and C.A. M c D o w e l l , Chem Phys. L e t t . 58, 554 ( 1 9 7 8 ) . W'~'.J. Hay and R.J. Nelmes, F e r r o e l e c t r i c s 14. 599 ( 1 9 7 6 ) . N.S. D a l a i , J.R. Dickinson and C.A. McDowe~l, J. Chem. Phys. 5_3_7, 4254 (1972).
Solid S t a t e Communications, Vol. 46, No. 7, pp. 513-516, 1983 Printed in Great Britain.
0038-1098/83/190 513-04 $03.00/0 Pergamon P r e s s Ltd.
THE AsO~-CENTER IN CsH2As04: A HALPERIN-VARMA DEFECT MOVING IN A SINGLE WELL POTENTIAL P.S.S. G u i m a r a e s , R. G a z z i n e l l i , G.M. R i b e i r o and A.S. Chaves - D e p a r t m e n t o f P h y s i c s , ICEX, U n i v e r s l d a d e F e d e r a l de Minas G e r a i s , C . P . 7 0 2 , Belo Horizonte, Brazil (RECEIVED ON NOVEMBER 30th1982 by R.C.C.
LEITE)
4The ESR o f t h e AsO 4 c e n t e r in CsH_AsO. is i n v e s t i g a t e d ' from 4.2K t o 270K. The b e h a v i o r o f th~s p ~ r a m a g n e t i c c e n t e r is e s s e n t i a l l y different from i t s b e h a v i o r in t h e o t h e r members o f t h e KDP f a m i l y . Two p r o p e r t i e s o f the c e n t e r a r e r e m a r k a b l e : i t seems t o behave l l k e a H a l p e r i n - V a r m a kind of d e f e c t and t o move c l a s s i c a l l y in a s i n g l e - w e l l potential which can be r e p r e s e n t e d w i t h v e r y good a p p r o x i m a t i o n by square w e l l .
The m i c r o s c o p i c model f o r the f e r r o e l e c t r i c t r a n s i t i o n in hydrogen-bond c r y s t a l s o f the KH2PO4 (KDP) f a m i l y has been a m a t t e r of i n t e n s e i n v e s t i g a t i o n . In h i s c l a s s i c a l paper S l a t e r ( l ) propo~ ed a mechanism based in the o r d e r i n g of the hydrogens in a d o u b l e - w e l l p o t e n t i a l along the l i n e c o n n e c t i n g the o x i g e n s of n e i g h b o u r PO groups. The spontaneous p o l a r i z a t i o n 4 o f KDP occurs along the t e t r a g o n a l c - a x i s , whereas n e u t r o n d i f f r a c t i o n e x p e r i m e n t s by Bacon and Pease (2) show t h a t the hydrogen motion is almost e x a c t l y c o n t a i n e d in the abplane. B a c o n and Pease a t t r i b u t e d the p o l a r i z a t i o n o f the c r y s t a l t o the d i s placements of the potassium and phosphorus ions along the c - a x i s . The hidrogens, however, should p l a y a c e n t r a l r o l e in the t r a n s i t i o n mechanism in o r d e r to e x p l a i n the pronounced dependence o f the t r a n s i t i o n t e m p e r a t u r e T w i t h deuteration. The c o n n e c t i o n between Cthese f a c t s was c l a r i f i e d by Cochran ( 3 ) , who proposed a s o f t mode f o r KDP made up by a correlated motion o f the hydrogens and the heavy ions: as the two protons in the upper H-bonds o f a PO4 group move to s i t e s near t h a t group, the two p r o t o n s in the lower bonds move away, the P ions move down along the the c - a x i s and the K ions move up along t h i s same a x i s . The e f f e c t o f d e u t e r a t i o n upon the t r a n s i t i o n t e m p e r a t u r e was e x p l a i n e d by Pirenne (4) and Blinc (5) as due to purely q u a n t u m - m e c h a n i c a l effects, on rather distinct assumptions concerning the s i n g l e - p a r t i c l e potential for the motion of the protons (deuterons). Pirenne postulated a single-well potential for the bonds, whereas Blinc adopted the double-well potential proposed by Slater. The form of the potential for the bond is still a matter of dispute. Silva and Ro-
v e r s i (6) showed t h a t t h e a v a i l a b l e d a t a on the v a r i a t i o n o f the s t a t i c p r o p e r t i e s o f t h e c r y s t a l such as t h e i s o t o p i c depen dence o f t he t r a n s i t i o n t e m p e r a t u r e , Curie c o n s t a n t and s a t u r a t i o n p o l a r i z a t i o n , c a n n o t d i s c r i m i n a t e between the s q u a r e well potential initially e x p l o i t e d by P i r e n n e and the d o u b l e - w e l l t u n n e l l i n g bond proposed by B l i n c . E m p i r i c a l models f o r the h y d r o g e n - b o n d p o t e n t i a l were r e c e n t l y p r o p o s e d and i n v e s t i g a t e d by Lawrence and R o b e r t s o n (7) and by Inoue and S h i r a i s h i (8). Many i n v e s t i g a t i o n s have been done by ESR on the KDP f a m i l y u s i n g paramagnet i c c e n t e r s at the s i t e o f t h e P i o n . Such i n v e s t i g a t i o n s were s t r o n g l y m o t i v a t e d by t h e ESR s t uL d y by B l i n c , Cevc and Schara(9) on the AsO~- c e n t e r in KH_AsO. (KDA),whe re the spedtraU c a r a c t e r i s ~ i c ~f the f e r r o e l e c t r i c phase were found to remain in the p a r a e l e c t r l c phase up to a temper a t u r e T* c o n s i d e r a b l y h i g h e r than T . Reviews o f the s u b j e c t were made by c Adriaenssens (10) , Dalal ( I l l and others. The a u t h o r s o f those i n v e s t i g a t i o n s reached the unanimous c o n c l u s i o n t h a t the anomaly is due to the o c c u r r e n c e , in the p a r a e l e c t r i c phase, o f p o l a r i z e d c l u s t e r s which are l o n g - l i v e d in comparison w i t h the time scale of the soft-mode dyna mics. This l o w - f r e q u e n c y dynamics o f t h e o r d e r parameter was a l s o found to occur in many o t h e r s t r u c t u r a l phase t r a n s i t i o n s by i n v e s t i g a t i o n s using a g r e a t v a r i e t y of e x p e r i m e n t a l techniques and the phenomenon is denominated c e n t r a l peak (CP). Most Of the observed CP are now recognized t o be not i n t r i n s i c to p h a s e - t r a n s l t l o n dynamics, but caused by d e f e c t s o f the c r y s t a l . In p a r t i c u l a r , the accumulated e v i d e n c e support the c o n c l u s i o n t h a t a l l the CP observed by ESR e x p e r i m e n t s are a f f e c t e d by the
513
514
THE AsO ~ - ~ N T E R IN CsH2AsO 4
Vol. 46, No. 7
p a r a m a g n e t i c probe - a p o i n t d e f e c t on Th~ ESR s p i n H a m i l t o n i a n describing the system under s t u d y . Two a l t e r n a t i v e t h e AsO~- c e n t e r i s g i v e n by models a r e a v a i l a b l e f o r p o i n t - d e f e c t 4+ induced CP. H a l p e r i n and Varma ( 1 2 ) , in H = ~ . g...S. . . + ? . ~ . ~ + ~ i .~.~, (i) P P an i n d e p e n d e n t w o r k , d e v e l o p e d in d e t a i l p=l a model f i r s t proposed by Burns ( 1 3 ) . Such model, g e n e r a l l y known as H a l p e r i n where S = 1 / 2 , ] = 3 / 2 , 1 = I / 2 , a n d A and A p P Varma (HV) model, p o s t u l a t e s t h a t the are the hyperfine interaction tensors d e f e c t has an i n t r i n s i c dynamics which for the arsenic and t h e f o u r p r o t o n s breaks the l o c a l symmetry o f the system s u r r o u n d i n g t h e radlca]. The g r o s s f e a t u in the same way as the o r d e r p a r a m e t e r , r e s o f t h e ESR s p e c t r a are dominated byand c o n s e q u e n t l y i t s dynamics w i l l c o u p l e t h e l a r g e v a l u e o f A, w h i c h g i v e s o r i g i n l i n e a r l y w i t h t h e s o f t mode, i . e . , the to a large splitting of the I quartet. intrinsic dynamics o f t h e o r d e r p a r a m e t e r . Each l i n e o f t h i s quartet shows a p o o r l y That c o u p l i n g r e n d e r s a c r i t i c a l behavior r e s o l v e d s t r u c t u r e w h i c h h a v e b e e n shown t o t h e d e f e c t dynamics w i t h the s o f t mode (9,16,19) to result from the protons hyis t o o weak t o a f f e c t a p p r e c i a b l y t h a t perfine interactions and f r o m t h e d y n a m i c s . I n a v a r i a t i o n of the HV model the different orientations of the "gtensor, coupling of the defect dynamics with the soft corresponding to opposite ferroelectric mode is too weak to affect appreciably that dydomains, each one containing two cheminamics. Thus, the defect dynamics is not c r i t i cally-equi~alent but magnetically-unequ~ cal, i . e . , doesn o t follow the showing-down of valent As04- sites. This structure is the so'ft-mode near the c r i t i c a l temperature,but better resolved for the lowest-field i n s t e a d f o l l o w s the A r r h e n i u s law f o r (MI= 3/2) line of the quartet, and thus t h e r m a l l y a c t i v a t e d processes ( ] 4 ) . In we c o n c e n t r a t e d most of our a t t e n t i o n to the second model, proposed by H~Ick and the study of this line. Figure I shows T h o m a s (15) (HT), the defect does not the a n g u l a r v a r i a t i o n of the M.= 3/2 and b r e a k the local s y m m e t r y of the system, M = -3/2 lines, taken at 90K i~ the but c h a n g e s locally the p a r a m e t e r s of the f ~ r r o e l e c t r i c phase. The centers of the many-particle Hamiltonian which describes lines are isotropic in the a b - p l a n e . The the phase t r a n s i t i o n and, in p a r t i c u l a r , w h o l e s p e c t r u m shows no s i g n i f i c a n t the s o f t - m o d e behavior. Under certain fa changes from 4K to 270K, where the v o r a b l e c o n d i t i o n s the r e s u l t i n g effect p a r a m a g n e t i c center b e c o m e s unstable. is the increase in the t e m p e r a t u r e at The values of +9 and A o b t a i n e d from w h i c h one o b s e r v e s the local s y m m e t r y the m e a s u r e m e n t s in figure l are in b r e a k i n g a r o u n d the defect. Though all r e s o n a b l e a g r e e m e n t wit~ those p r e v i o u s three v a r i e t i e s of CP have been claimed to be ly o b t a i n e d by Dalai et. al (19). Howeobserved, it might be that all the CP observed by ESR in. the KDP family reported in the literature can ver, the s t r u c t u r e o b s e r v e d in the Ml= 3/2 t r a n s i t i o n is quite d i s t i n c t from be u n d e r s t o o d w i t h i n the f r a m e w o r k of that o b s e r v e d by Daia] et al. in CDA and the HT model (16,17). from the reported results in all the The crystal C s H _ A s O ~ ( C D A ) is other m e m b e r s of the KDP family. Our i s o m o r p h o u s with KDPZand 4 has a similar results are u n c o n s i ~ t e n t with the hypot r a n s i t i o n from a tetragonal (l~-2d) thesis that the AsO~- center p r e s e r v e s p a r a e l e c t r i c phase to an o r t h o r h o m b i c the s y m m e t r y of the AsO~- site. If this (Fdd2) f e r r o e l e c t r i c phase at T = I 4 0 K symmetry were p r e s e r v e d ; each member of (18). T h i s 4 P a p e r reports an ESR = study the As quartet should split, in the of the A s O ~ - c e n t e r in IDA which shows f e r r o e l e c t r i c phase, in two lines for s i g n i f i c a n t d i s t i n c t i o n s from the simi~ m a q n e t i c field in the d i r e c t i o n lar studies found in the l i t e r a t u r e for = a ÷ + +~ (17). However, as it can be other a r s e n i d e m e m b e r s of the KDP family, seen in figure 2, for that o r i e n t a t i o n and for CDA itself (19). The samples, of the field we have at least three o b t a i n e d from General Diode C o r p o r a t i o n , lines. In fact, by c o m p u t e r fitting the were i r r a d i a t e d at 77K with, X-ray for l i n e s h a p e we could see that there are the p r o d u c t i o n of the AsO~- center. The ~t four lines in figure 2, the line in the i r r a d i a t e d s a m p l e s were t r a n s f e r r e d to middle being an u n r e s o l v e d doublet. The an ESR s p e c t r o m e t e r at low t e m p e r a t u r e p r e c i s i o n of the sample o r i e n t a t i o n in in order, to p r e v e n t the d e s t r u c t i o n of the m a g n e t i c field (10) is high e n o u g h the A s O ~ - c e n t e r , w h i c h d e c a y s very to rule but m i s a l i q u e m e n t as a reason q u i c k l y - a t t e m p e r a t u r e s h i g h e r than about for the a p p r a r a n c e of more than two lines 270K. Two p a r a m a g n e t i c centers, A s O 4 - a n d in figure 2. The s p e c t r u m for H//C is AsO 2-, are c r e a t e d by i r r a d l a t i o n ( l ~ ) , a s also quite amazing. Instead of a triplet usual for the a r s e n i d e m e m b e r s of the which transforms into a quintet (9) at KDP family, but the A s O ~-T- c e n t e r has some t e m p e r a t u r e T* > Tc, t h e spectrum r e c e i v e d much more a t t e n t i o n in the lite shown in f i g u r e 3 was o b s e r v e d . That rature due to its a b i l i t y to m a n i f e s t CPspectrum shows no change when t h e tempep h e n o m e n a . This c e n t e r is formed by the r a t u r e is changed from 4K up t o 270K. The traI~ping of one extra e l e c t r o n by the l i n e s h a p e o b s e r v e d in f i g u r e 3 cannot be AsO~- radical and a c c o r d i n g to the f i t t e d by a q u i n t e t o r a t r i p l e t . In p r e ~ e n t e v i d e n c e s (17,19), the local f a c t , t h a t spectrum can be reproduced s y m m e t r y of this radical is p r e s e r v e d o n l y by the sum o f a v e r y l a r g e number o f after the c a p t u r e of the extra e l e c t r o n .
Vol. 46, No. 7
515
THE AsO~-CENTER IN CsH2AsO 4
4700
0/0
Gauss
j ~
T9 ,0K
/
4650
/
I
/
4600
Figure 2 - The s t r u c t u r e of the lowest field (M, = 3/2) line, at T = 90K and = 904~IMH~, fgr the m a g n e t i c field along X = a + b.
/
4550
T=90K 4500
Lo
I 450
3 - The s t r u c t u r e of the lowest field (M, = 3/2) line, at T = 197K and v = 9 0 0 5 1 M H z , for the m a g n e t i c field along c. The n o i s e l e s s line r e p r e s e n t s the best fit with formula 5 of the text.
I 400
I 35C
,5oo
and r e s o n a n c e m a g n e t i c field value of the c o o r d i n a t e s is 2 + h z + h2z HR ~ Ho l 0
,
30 °
60 =
:~;""'~
C
Figure I - Angular variation of the lowest-(M1=3/2) and highest field (M,=-3/2) lines a t T = 90K a n d v = 9 0 4 2 MH~. E a c h l i n e of the l = 3/2 quartet is a poorly resolved structure and the fields shown in the figure are taken at the center of the structure. The c e n t e r of the structure is isotropic in the ab-plane. The s p i n - H a m i l t o n i n a n parameter obtained from the data are gx = gy = gz = 2 . 0 0 0 + 0 . 0 0 5 , A = A =
(2757 +
10)
MHz,
Az
(3091
+- xlO)
MHz.Y
Iines and s u g g e s t s that the s y s t e m h== a c o n t i n u o u s d i s o r d e r . Trials for explaining thespectrum were made s u p p o s i n g that the AsO~-moves classically in a double well potential of the form V(z)
1450G
= -az 2 + bz 4,
a,b
> 0,
(2)
w h e r e z is p r o p o r t i o n a l to the local p o l a r i z a t i o n . The p r o b a b i l i t y of finding the c e n t e r at a c e r t a i n c o o r d i n a t e z is
p(z) = Ce- V ( z ) / k T ,
(3)
H R for
that (4)
The best c o m p u t e r f i t t i n g s of the l i n e s h a p e were o b t a i n e d with very s h a l l o w double-well p o t e n t i a l s and with hi>> h 2. An even better f i t t i n g was o b t a i n e d by a d o p t i n g the s q u a r e - w e l l potential and by making h 2 = 0. The s i n g l e - l i n e w h i c h gives the best fitting has a Gaussian lineshape, and thus the t h e o r e t i c a l l i n e s h a p e is
I(H)
d Hd
H + H fH ° - HI e x p l . 0 . 6 9 3 ( H _ H R ) 2 / y 2 1 d H R o I
(5) The comparison b e t w e e n t h e f u n c t i o n I (H) a n d e x p e r i m e n t is seen in figure 3. The fitting parameters were H = 1286 Gauss, H 1 = 55,6 Gauss and y ~ 15,5 Gauss. Some ramarks should be made about these results. From e q u a t i o n (4) and the fitting p a r a m e t e r s (h1>>h2), one sees that the resonance field can discriminate polarization up and p o l a r i z a t i o n down, i.e.,the paramagnetlc center breaks spontaneously the symmetry of the AsO~site and the resulting perturbation which i t c a u s e s on t h e s y s t e m c o n t a i n s
?
516
AsO~-CENTER~ IN CsH2AsO4
the i r r e d u c i b l e r e p r e s e n t a t i o n B2 o f the order parameter for the ferroelec~ric transition. O t h e r w i s e , H (z) s h o u l d c o n t a i n o n l y even powersRof z. T h i s is c o n s i s t e n t w i t h t h e a p p e a r a n c e o f more than two l l n e s in t h e X d i r e c t i o n , as d i s c u s s e d b e f o r e and shown in f i g u r e 2. The symmetry b r e a k i n g , e v i d e n t i a t e d by the a p p e a r a n c e o f a l i n e a r t e r m in the e x p a n s i o n o f H(z) and by th e e x i s t e n c e o f f o u r l i n e s f o r the magnetic f i e , l d along the X d i r e c t i o n , s u g g e s t s t h a t the AsO~probe behaves l i k e a H a l p e r i n Varma defect.
Vol. 46, No. 7
Furthermore, the As0~-defect does not move in a double w e l l p o t e n t i a l , but in a s h a l l o w s i n g l e w e l l p o t e n t i a l which can be described w i t h every good a p p r o x i m a t i o n by a square w e l l p o t e n t i a l . E v i d e n t l y , o n e should be aware of the f a c t t h a t the p o t e n t i a l f o r the motion of the d e f e c t i v e group can be q u i t e d i f f e r e n t from the p o t e n t i a l f o r the motion of the s u b s t i t u t e d AsO~- radical. We thank Dr. Ivone Mascarenhas f o r e s t a b l i s h i n g the c r y s t a l o r i e n t a t i o n by X-ray. This work was supported by FINEP, CNPq and CNEN.
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