Temperature dependence of the hyperfine coupling constant of 151Eu2+ in SrF2 and BaF2

Volume 28B, n u m b e r 5

TEMPERATURE

PHYSICS

DEPENDENCE OF 151Eu

LETTERS

16 D e c e m b e r 1968

OF THE HYPERFINE COUPLING 2+ IN SrF 2 AND BaF 2 *

CONSTANT

S. L E E Department of Physics, St. Louis University D. P. A M E S a n d T , J. M E N N E Research Division, McDonnell Company, St. Louis, Missouri, USA Received 3 July 1968 The theory for the t e m p e r a t u r e dependence of the hyperfine constant of r a r e e a r t h S state ions in cubic c r y s t a l s is applied to m e a s u r e m e n t s taken on 151Eu2+ in S r F 2 and DaF 2. Satisfactory qualitative a g r e e ment is obtained. In a n e a r l i e r p a p e r [1] w e d e v e l o p e d t h e t h e o r y f o r t h e t e m p e r a t u r e d e p e n d e n c e of t h e h y p e r f i n e c o u p l i n g c o n s t a n t of r a r e e a r t h S - s t a t e i o n s (4f 7 configuration) in cubic environments, and measu r e m e n t s on C a F 2 : E u 2 + w e r e a l s o r e p o r t e d . In this paper we extend these studies to SrF2:Eu2+ and BaF2:Eu2+. S i n g l e c r y s t a l s of S r F 2 a n d B a F 2 w i t h a n o m i n a l 0 . 0 5 w e i g h t % E u 2+ w e r e p u r c h a s e d f r o m O p tovac, Inc. The X-band EPR spectra were obt a i n e d in t h e m a n n e r d e s c r i b e d p r e v i o u s l y [1]. F i g . 1 s h o w s t h e o b s e r v e d b e h a v i o r of t h e h y p e r fine coupling constant A over the temperature r a n g e f r o m 4° to 730°K f o r S r F 2 : E u 2 + a n d f r o m 4 ° to 4 5 4 ° K f o r B a F 2 : E u 2 + . U n f o r t u n a t e l y , s i g nal-to-noise-ratio problems impeded our measu r e m e n t s a t h i g h e r t e m p e r a t u r e s in t h e B a F 2 : E u 2+ c r y s t a l . T h e t o t a l c h a n g e in A i s a p p r o x i m a t e l y 3% i n S r F 2 : E u 2+ a s c o m p a r e d w i t h t h e 2% c h a n g e o b s e r v e d in C a F 2 : E u 2 + o v e r t h e same temperature range. T h e t e m p e r a t u r e d e p e n d e n c e of t h e h y p e r f i n e c o u p l i n g c o n s t a n t of t h e 4f i o n s i n c u b i c c r y s t a l s w a s t r e a t e d [1] by m e a n s of t h e o r b i t - l a t t i c e i n t e r a c t i o n VOL. W e a d m i x e d e x c i t e d 6 s o r b i t a l s i n t o t h e g r o u n d 4f o r b i t a l s of r a r e e a r t h i o n s v i a

t h e a n t i - s y m m e t r i c v i b r a t i o n s in VOL , a n d t h e n c a l c u l a t e d t h e c o n t r i b u t i o n of t h e e x c i t e d o r b i t a l s to the contact hyperfine field. By confining the calculation to long wavelength acoustic phonons with a Debye distribution, and by assuming a

3 4 . 0 ~ 33B Sr-F2 :Eu 2+ 33.6

-

I

0

I

200

400 T(°K)

600

800

Fig. 1. Hyperfine constant data on 151Eu2+ in SrF 2 and * This work was conducted in p a r t under the McDonnell BaF 2. Solid c u r v e s a r e obtained from eq. (1) using valDouglas Corporation Independent R e s e a r c h and Develues of Cex. opment P r o g r a m . Table 1 Values of the p a r a m e t e r s for Eu 24 in calcium, strontium, and b a r i u m fluoride. Host

Cex (OK)-6

(6°K-) C t h-

Cex/Cth

A(0) (10-4 cm -1 )

g

CaF 2

5.31 x 10 -18

SrF 2

2.81 × 10 -17

5.85 x 10 -19

9.1

- 3 4 . 2 5 ~ 0.05

1.9935 ~ 0.0005

7.92 x 10 -19

35.5

- 3 4 . 1 7 ~=0.06

BaF 2

2.03 x 10 -16

1.9925 ~ 0.0005

2.52 × 10 -18

80.5

- 3 3 . 7 5 ~ 0.05

1.9925 ~ 0.0052

369

PHYSICS LETTERS

Volume 28A, number 5

n e a r e s t - n e i g h b o r point c h a r g e m o d e l f o r the cubic XY 8 m o l e c u l a r c l u s t e r , we obtained

O / T xSdx A(T) =A(O) L1L CT6 j eX-1]]'

(1)

o w h e r e the constant C is given by

~ g ~ f l (Sz) ~ C = 3

Hc

n,n T

(R4f]r31Rns) (Rt~'~ [r31R4f) [E(4f)-E(ns)][E(4f)-E(n's)] ×

x(~PnslS(r)l~n,s } (32)(53)~

(ee'~ 2 (81)(343)p~2 \ R31 x 2

(2)

1

We have a s s u m e d that any l a t t i c e expansion eff e c t s on A a r e n e g l i g i b l e in t h e s e c r y s t a l s [1]. Our v a l u e s of A and g a r e in a g r e e m e n t with t h o s e r e p o r t e d by T i t l e [5]. Note that Cth is s m a l l e r than Cex in e v e r y c a s e . H o w e v e r , Cex i n c r e a s e s with i n c r e a s i n g a t o m i c weight of the host m a t e r i a l and Cth e x hibits this s a m e b e h a v i o r , although i t s r a t e of i n c r e a s e lags that of Cex. T h i s i n c r e a s e in the r a t i o Cex/Cth f r o m C a F 2 to B a F 2 might p r o v i d e s o m e indication of the i m p o r t a n c e of l o cal m o d e s , s i n c e only the odd v i b r a t i o n s of the m o l e c u l a r c l u s t e r c o n t r i b u t e to A(T) f o r Eu 2+, and the odd l o cal m o d e s a r e si g n i f i can t l y a f f e c t e d by a change in m a s s of the c e n t r a l ion. N e v e r t h e l e s s , the q u a l i t a t i v e fit to the data p r o v i d e d by eq. (1) and i l l u s t r a t e d in fig. 1 d e m o n s t r a t e s that the odd v i b r a t i o n s of the m o l e c u l a r c l u s t e r a r i s i n g f r o m the Debye s p e c t r u m of the l a t t i c e o s c i l l a t i o n s a l s o m a k e an i m p o r t a n t contribution to the t e m p e r a t u r e d e c r e a s e in the h y p e r f i n e coupling c o n stant of r a r e e a r t h ions.

All s y m b o l s , a s w e l l as the v a l u e s of quantities p e r t i n e n t to the Eu 2+ ion, a r e given in ref. 1. The s o l i d c u r v e s in fig. 1 a r e d e t e r m i n e d f r o m eq. (1) u s i n g C ex , the v a l u e of C which b e s t fits the data. E x p e r i m e n t a l and t h e o r e t i c a l v a l u e s of C a r e p r e s e n t e d in table 1. T h e l a t t e r w e r e d e t e r m i n e d b y using e' = - e , R = 2.511 A, p = 4 . 3 2 1 g / c m 3, O = 380°K, v l = 5.46 × 1 0 5 c m / s e c , vt= References = 2.92 × 1 0 5 c m / s e c , and H c = 342 kG f o r S r F 2 [2], and e' = - e , R = 2.685 A, p = 4.886 g / c m 3 1. T.J. Menne, D.P. 169 (1968) 333. O = 282°K, v l = 4.48 × 1 0 5 c m / s e c , v t = 2.30 x 105 2. D. Gerlich, Phys. c m / s e c , and H c = 338 kG f o r B a F 2 [3]. A l s o 3. D. Gerlieh, Phys. l i s t e d in t ab l e 1 fo r c o m p a r i s o n a r e the v a l u e s of 4. D.R. Huffman and C f o r C aF 2 : E u 2 + using O = 508OK [4] and the v a l (1960) 709. ues a p p e a r i n g in ref. 1 f o r the o t h e r p a r a m e t e r s . 5. R.S.Title, Phys. *****

370

16 December 1968

Ames and Sook Lee, Phys. Rev. Rev. 136 (1964) A1366. Rev. 135 (1964) A1331. M.H.Norwood, Phys. Rev. 117 Letters 6 (1963) 13.