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Evidence for polarization effects from optical and E.S.R. spectra of Yb3+ in the cubic crystal field of CaF2
Volume 26A, number 6
EVIDENCE
PHYSICS LETTERS
12 February 1968
FOR POLARIZATION EFFECTS FROM OPTICAL AND E.S.R. SPECTRA O F Y b 3+ IN THE CUBIC CRYSTAL FIELD OF CaF 2 W. LOW
Microwave Division, Department of Physics, The Hebrew University, Jerusalem, Israel Received 15 January 1968
The optical spectra of Yb 3+ in CaF2 permits the evaluation of the cubic crystalline field parameters as b 4 = 51.6 c m - l , and b 6 = 6.39 cm -1. Comparison with the data on Tm 2+ indicates that the crystal field for Yb3+ is considerably stronger, and is interpreted to arise from the polarization of the surroundings through the excess charge of the Yb3+.
W h e n e v e r a p a r a m a g n e t i c ion of e f f e c t i v e c h a r g e Z + n s u b s t i t u t e s f o r a d i a m a g n e t i c cation of c h a r g e Z, it is expected to p o l a r i z e the s u r roundings and to d r a w in the neighbouring n e g a tively c h a r g e d ions. It has been c o n j e c t u r e d that this may give r i s e to an i n c r e a s e in the e f f e c t i v e c r y s t a l f i el d and thus a f f e c t s the optical s p e c t r u m and the g f a c t o r in the s p i n - H a m i l t o n i a n [1,2]. We h a v e o b s e r v e d the optical a b s o r p t i o n and f l u o r e s c e n c e s p e c t r u m of Yb 3+ in C a F 2 in the cubic c r y s t a l f i e l d site. The s p e c t r u m can be r e p r e s e n t e d with two p a r a m e t e r s , b4 = 51.6 cm -1 and b 6 = 6.39 cm -1. T h i s should be c o m p a r e d with b 4 = 45.8 and b 6 = 5.05 cm -1 f o r the i s o e l e c t r o n i c ion T m 2+ in the s a m e c r y s t a l [3]. The c r y s t a l f i el d p a r a m e t e r s a r e p r o p r t i o n a l to ~r4)/a5 and ~r6)/a 7 r e s p e c t i v e l y . Bleaney e s t i m a t e s t h e i r magnitude f r o m s i m p l e point c h a r g e c a l c u l a t i o n s to be b a = +136 ( r 4) cm -1 and b 6 = = +6.42 ( r 6) cm -1. F r e e m a n and Watson [4] c a l culate the following v a l u e s : Tm2+: ( r 4) = 1.067 and ( r 6) = 3.640; yb3+: ( r 4) -- 0.960 and ( r 6 ) = = 3.104 in units of a.u. In the a b s e n c e of p o l a r i zation one would expect the c r y s t a l f i e l d of Yb 3+ to be s m a l l e r than that of T m z+, c o n t r a r y to the experimental results. The relatively large change in the c r y s t a l f i e l d can be accounted f o r by the e f f e c t i v e p o l a r i z a t i o n which d r a w s in the s u r r o u n d i n g F - ions. It is obvious that not too much r e l i a n c e can be p l a c e d on the n u m e r i c a l computation of ( r 4) by F r e e m a n and Watson, and on the point c h a r g e c a l c u l a t i o n s , s i n c e the e x p e r i m e n t a l r e s u l t s do not s e e m to fit f o r e i t h e r T m 2+ or Yb 3+. If we a s s u m e that ( r 4) f o r T m 2+ and Yb 3+ a r e a p p r o x i m a t e l y the s a m e , the r e sults could be a c c o u n t e d f o r by a d e c r e a s e in the 234
Yb 3+ - F - d i s t a n c e s of 3-4%. If we a s s u m e that the r a t i o of ~r4) for the two i s o e l e c t r o n i c ions is that found by F r e e m a n and Watson, a d e c r e a s e of 4-5% in the d i s t a n c e is found although no unique fit for both (r4) and (r6) would be obtained. Supporting e v i d e n c e is found f r o m the ENDOR m e a s u r e m e n t s of T m 2+ and Yb 3+ in C a F 2 [5,6]. F o r T m 2+ the e x p e r i m e n t a l r e s u l t s can be a p p r o x i m a t e d by m e a n s of a d i p o l e - d i p o l e o p e r a t o r and with a m a g n i t u d e of about 20% l a r g e r than a point dipole calculation. F o r Yb 3+, h o w e v e r , the e x p e r i m e n t a l m e a s u r e of the d i p o l e - d i p o l e c o n t r i b u t i o n i s about 40% l a r g e r than that f o r T m 2+. T h i s can be acco u n t ed for in p a r t by a d e c r e a s e in the e f f e c t i v e d i st an ce, and by an i n c r e a s e in c o v a l e n t bonding, through o v e r l a p i n t e g r a l s Pa, p~ and c r o s s p r o d u c t s ~/pop~. An i n c r e a s e in c o v a l e n t bonding for Yb 3+ is i n f e r r e d f r o m the i n t e r p r e t a t i o n of the E.S.R. s p e c t r a . One o b t ai n s an o r b i t a l r e d u c t i o n f a c t o r (1 - k ) = 0.02 for Yb 3+ c o m p a r e d with (1 - k) = 0.01 for T m 2+. D e t a i l s r e g a r d i n g the optical s p e c t r a will be published e l s e w h e r e .
References 1. 2. 3. 4.
W°Low, Phys. Rev. 105 (1957) 801. B. Bleaney, Proc. Roy. Soc. A277 (1963) 289. Z . J . K i s s , Phys. Rev. 127 (1962) 718. A . J . Freeman and R. E. Watson, Magnetism Vol. IIA eds. G.T.Rado and H. Suhl (Academic Press, N.Y., 1965). 5. R.G.Bessent and W. Hayes, Proc. Roy. Soc. A285 (1965) 430. 6. U.Ranon and J.S. Hyde, Phys. Rev. 141 (1966) 259.
EVIDENCE
PHYSICS LETTERS
12 February 1968
FOR POLARIZATION EFFECTS FROM OPTICAL AND E.S.R. SPECTRA O F Y b 3+ IN THE CUBIC CRYSTAL FIELD OF CaF 2 W. LOW
Microwave Division, Department of Physics, The Hebrew University, Jerusalem, Israel Received 15 January 1968
The optical spectra of Yb 3+ in CaF2 permits the evaluation of the cubic crystalline field parameters as b 4 = 51.6 c m - l , and b 6 = 6.39 cm -1. Comparison with the data on Tm 2+ indicates that the crystal field for Yb3+ is considerably stronger, and is interpreted to arise from the polarization of the surroundings through the excess charge of the Yb3+.
W h e n e v e r a p a r a m a g n e t i c ion of e f f e c t i v e c h a r g e Z + n s u b s t i t u t e s f o r a d i a m a g n e t i c cation of c h a r g e Z, it is expected to p o l a r i z e the s u r roundings and to d r a w in the neighbouring n e g a tively c h a r g e d ions. It has been c o n j e c t u r e d that this may give r i s e to an i n c r e a s e in the e f f e c t i v e c r y s t a l f i el d and thus a f f e c t s the optical s p e c t r u m and the g f a c t o r in the s p i n - H a m i l t o n i a n [1,2]. We h a v e o b s e r v e d the optical a b s o r p t i o n and f l u o r e s c e n c e s p e c t r u m of Yb 3+ in C a F 2 in the cubic c r y s t a l f i e l d site. The s p e c t r u m can be r e p r e s e n t e d with two p a r a m e t e r s , b4 = 51.6 cm -1 and b 6 = 6.39 cm -1. T h i s should be c o m p a r e d with b 4 = 45.8 and b 6 = 5.05 cm -1 f o r the i s o e l e c t r o n i c ion T m 2+ in the s a m e c r y s t a l [3]. The c r y s t a l f i el d p a r a m e t e r s a r e p r o p r t i o n a l to ~r4)/a5 and ~r6)/a 7 r e s p e c t i v e l y . Bleaney e s t i m a t e s t h e i r magnitude f r o m s i m p l e point c h a r g e c a l c u l a t i o n s to be b a = +136 ( r 4) cm -1 and b 6 = = +6.42 ( r 6) cm -1. F r e e m a n and Watson [4] c a l culate the following v a l u e s : Tm2+: ( r 4) = 1.067 and ( r 6) = 3.640; yb3+: ( r 4) -- 0.960 and ( r 6 ) = = 3.104 in units of a.u. In the a b s e n c e of p o l a r i zation one would expect the c r y s t a l f i e l d of Yb 3+ to be s m a l l e r than that of T m z+, c o n t r a r y to the experimental results. The relatively large change in the c r y s t a l f i e l d can be accounted f o r by the e f f e c t i v e p o l a r i z a t i o n which d r a w s in the s u r r o u n d i n g F - ions. It is obvious that not too much r e l i a n c e can be p l a c e d on the n u m e r i c a l computation of ( r 4) by F r e e m a n and Watson, and on the point c h a r g e c a l c u l a t i o n s , s i n c e the e x p e r i m e n t a l r e s u l t s do not s e e m to fit f o r e i t h e r T m 2+ or Yb 3+. If we a s s u m e that ( r 4) f o r T m 2+ and Yb 3+ a r e a p p r o x i m a t e l y the s a m e , the r e sults could be a c c o u n t e d f o r by a d e c r e a s e in the 234
Yb 3+ - F - d i s t a n c e s of 3-4%. If we a s s u m e that the r a t i o of ~r4) for the two i s o e l e c t r o n i c ions is that found by F r e e m a n and Watson, a d e c r e a s e of 4-5% in the d i s t a n c e is found although no unique fit for both (r4) and (r6) would be obtained. Supporting e v i d e n c e is found f r o m the ENDOR m e a s u r e m e n t s of T m 2+ and Yb 3+ in C a F 2 [5,6]. F o r T m 2+ the e x p e r i m e n t a l r e s u l t s can be a p p r o x i m a t e d by m e a n s of a d i p o l e - d i p o l e o p e r a t o r and with a m a g n i t u d e of about 20% l a r g e r than a point dipole calculation. F o r Yb 3+, h o w e v e r , the e x p e r i m e n t a l m e a s u r e of the d i p o l e - d i p o l e c o n t r i b u t i o n i s about 40% l a r g e r than that f o r T m 2+. T h i s can be acco u n t ed for in p a r t by a d e c r e a s e in the e f f e c t i v e d i st an ce, and by an i n c r e a s e in c o v a l e n t bonding, through o v e r l a p i n t e g r a l s Pa, p~ and c r o s s p r o d u c t s ~/pop~. An i n c r e a s e in c o v a l e n t bonding for Yb 3+ is i n f e r r e d f r o m the i n t e r p r e t a t i o n of the E.S.R. s p e c t r a . One o b t ai n s an o r b i t a l r e d u c t i o n f a c t o r (1 - k ) = 0.02 for Yb 3+ c o m p a r e d with (1 - k) = 0.01 for T m 2+. D e t a i l s r e g a r d i n g the optical s p e c t r a will be published e l s e w h e r e .
References 1. 2. 3. 4.
W°Low, Phys. Rev. 105 (1957) 801. B. Bleaney, Proc. Roy. Soc. A277 (1963) 289. Z . J . K i s s , Phys. Rev. 127 (1962) 718. A . J . Freeman and R. E. Watson, Magnetism Vol. IIA eds. G.T.Rado and H. Suhl (Academic Press, N.Y., 1965). 5. R.G.Bessent and W. Hayes, Proc. Roy. Soc. A285 (1965) 430. 6. U.Ranon and J.S. Hyde, Phys. Rev. 141 (1966) 259.