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Acoustic paramagnetic resonance in KMgF3:Mn++
Volume 31A. number 5
PHYSICS LETTERS
A r a d i a l mixing of p a r t i c l e s i s a l s o produced. Of c o u r s e if the e l e c t r i c a l field is not s y m m e t r i cally applied, the p a r t i c l e motion is no l o n g e r s t r i c t l y r a d i a l and the r e s u l t a n t mixing o c c u r s both in the r a d i a l and the a z i m u t h a l d i r e c t i o n s .
9 March 1970
R~fe~'~ces 1. R. A. Ellis, private communication. 2. S. Puri, Phys. Fluids 9 (1966) 2043; Plasma heating and diffusion in stochastic fields, SUIPR Report no. 161. (Stanford University, California, 1967,p.14
T h i s work has been p e r f o r m e d as p a r t of the joint r e s e a r c h p r o g r a m m e of the Institut fiir P l a s m a p h y s i k and E u r a t o m .
ACOUSTIC
PARAMAGNETIC
RESONANCE
IN
KMgF3:Mn++
D. K. G A R R O D The Clarendon Laboratory., Oxford, UK Received 29 January 1970
Both A M s ~ i and A M o = 2 transitions have been observed in KMgF3:Mn++. The spin-phonon interaction is of the quadrt~polar type S . d . S and the magneto-elastlc constants Gll and G44 and their relative sign have been determined.
Using conventional p u l s e echo t e c h n i q u e s [ 1] the a c o u s t i c p a r a m a g n e t i c r e s o n a n c e of the 6S ion Mn ++ in the cubic e n v i r o n m e n t of KMgF 3 has been o b s e r v e d f o r phonon p r o p a g a t io n d i r e c t i o n s (100) and (110). Working at f r e q u e n c i e s in the r a n g e 8.5 - 9 . 8 GHz and at a t e m p e r a t u r e of 1.7°K, the a c o u s t i c attenuation was m e a s u r e d a s a function of the magnitude and o r i e n t a t i o n of the e x t e r nal m a g n e t i c field. D e s p i t e the e x t r e m e l y weak s p i n - l a t t i c e coupling, both AM s -- 1 and AM s = 2 t r a n s i t i o n s w e r e o b s e r v a b l e and typical r e s o n a n c e t r a c e s a r e shown in fig. 1. As may be s e e n f r o m that f i g u r e the r e s o n a n c e s , in which g = 2.00 ± 0.01, a r e r a t h e r broad and no h y p e r f i n e or t r a n s f e r r e d h y p e r f in e s t r u c t u r e is d i s t i n g u i s h a b l e . T h i s in c o n t r a s t to E P R r e s u l t s [2]. T h e o b s e r v a t i o n of the AM s = 2 t r a n s i t i o n is s i g n i fi can t b e c a u s e , as pointed out by R o s e n b e r g and W i g m o r e [3] with r e f e r e n c e to KMgF 3 :Ni ++, it is i m p o s s i b l e in a cubic m a t e r i a l to d i s t i n g u i s h between the d ip o l a r and q u a d r u p o l a r m e c h a n i s m s f r o m the a n g u l a r dependence of the AM s -- 1 a b s o r p t i o n . The p r e s e n c e of the AM s = 2 t r a n s i t i o n e s t a b l i s h e s that t h e r e must be at l e a s t two spin o p e r a t o r s in the dominant i n t e r a c t i o n t e r m and the a n g u l a r d e p e n d e n c e s of the AM s = 1 and AM s = 2 t r a n s i t i o n s , a s i l l u s t r a t e d in fig. 2, show that it i s a q u a d r u p o l a r m e c h a n i s m of the type S. d . S. F r o m the m e a s u r e m e n t s , the two independent 232
constants, Gll and G 4 4 , [1] of the magnetoelastic tensor were found to be: G l l = 0.30; G 4 4 = 0.09 cm'I/unit strain, with an error due to noise of + 0.02 in each case. There is also a
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FIELD
Fig. 1. Absorption traces of the AM~= 1 and AM~ = 2 transitions for KMgF3:0.048 Mn++. -T= 1.7OK, v ~= 9058 MHz, acoustic propagation(100).
PHYSICS
Volume 31A, n u m b e r 5
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LETTERS
9 M a r c h 1970
p o s s i b l e s y s t e m a t i c e r r o r of 10% w h i c h w o u l d a f fect both quantities similarly, arising mainly f r o m t h e Mn ++ c o n c e n t r a t i o n d e t e r m i n a t i o n a n d also from instrument calibration. These results may be compared and contrasted w i t h t h e v a l u e s G l l = 1.4 a n d G44 : 0.28 c m -1 u n i t s t r a i n f o r M g O : M n +÷. m e a s u r e d by a c o u s t i c s a t u r a t i o n of E P R [4] a n d by u n i a x i a l s t r e s s on E P R [5]. T h e r e a r e to t h e a u t h o r ' s k n o w l e d g e no p u b l i s h e d r e s u l t s f o r K M g F 3 :Mn ++. A n u m b e r of c a l c u l a t i o n s u s i n g v a r i o u s m e c h a n i s m s h a v e b e e n m a d e to e s t i m a t e t h e m a g n i t u d e of t h e s p i n - l a t t i c e c o u p l i n g in M g ' O : M n ~ ~- [ 6 - 8 ] a n d a s u m m a r y of t h e p o s s i b l e m e c h a n i s m s i n v o l v e d a n d f u r t h e r r e f e r e n c e s a r e g i v e n by S h a r m a [9]. T h e r e a r e to d a t e no p u b l i s h e d c a l culations for the coupling in KMgF3, however, in v i e w of t h e p r o g r e s s b e i n g m a d e i n t h e c r y s t a l f i e l d c a l c u l a t i o n s of f l u o r i n e ~ c o o r d i n a t e d c o m p o u n d s , e s p e c i a l l y K N i F 3 a n d K M n F 3 , it i s to b e hoped that an accurate spin-lattice coupling calc u l a t i o n t a k i n g f u l l a c c o u n t of c o v a l e n c y a n d o v e r lap effects will soon be possible. T h e a u t h o r i s i n d e b t e d to D r . H. M R o s e n b e r g for supervision and helpful discussions, The work w a s c a r r i e d o u t d u r i n g t h e t e n u r e of a n S.R.C. research studentship.
References Fig. 2. The angular variation of the peak absorption of the AMs = 1 and AMs = 2 t r a n s i t i o n s . T = 1.74OK, v = = 9274 MHz, acoustic propagation (100~, 0 = angle of rotation of magnet. Also plotted are the expected quad r u p o l a r angular v a r i a t i o n s which have been n o r m a l ized to 0.36 d B / c m at 0 = 225 ° and 0.19 d B / c m at 0 = 180 ° for the AM s = 1 and A M s = 2 t r a n s i t i o n s r e s p e c tively.
1. w. I. Dobrov, Phys. Rev. 134 (1964) A 734. 2. T. P. P. Hall. W. Hayes, R.W.H. Stevenson and J. Wiikens, J. Chem. Phys. 38 (1963) 1977. 3. H. M R o s e n b e r g and J. K. Wigmore, Proc. Roy. Soc. A302 (1967) 69. 4. N. 8. Shiren, Bull. Am. Phys. Soe. 7 (1962) 29. 5. E. R, F e h e r , Phys. Rev. 136 (1964) A 145. 6. M. Blume and R. Orbach, Phys. Rev. 127 (1962) 1587, 7. A. M. Leushin, Soy. Phys. Sol. State 5 (1963) 440. 8. J. Kondo, Prog, Theor. Phys. 28 (1962) 1026. 9. R.R. Sharma, Phys. Rev. 176 (1968) 467.
233
PHYSICS LETTERS
A r a d i a l mixing of p a r t i c l e s i s a l s o produced. Of c o u r s e if the e l e c t r i c a l field is not s y m m e t r i cally applied, the p a r t i c l e motion is no l o n g e r s t r i c t l y r a d i a l and the r e s u l t a n t mixing o c c u r s both in the r a d i a l and the a z i m u t h a l d i r e c t i o n s .
9 March 1970
R~fe~'~ces 1. R. A. Ellis, private communication. 2. S. Puri, Phys. Fluids 9 (1966) 2043; Plasma heating and diffusion in stochastic fields, SUIPR Report no. 161. (Stanford University, California, 1967,p.14
T h i s work has been p e r f o r m e d as p a r t of the joint r e s e a r c h p r o g r a m m e of the Institut fiir P l a s m a p h y s i k and E u r a t o m .
ACOUSTIC
PARAMAGNETIC
RESONANCE
IN
KMgF3:Mn++
D. K. G A R R O D The Clarendon Laboratory., Oxford, UK Received 29 January 1970
Both A M s ~ i and A M o = 2 transitions have been observed in KMgF3:Mn++. The spin-phonon interaction is of the quadrt~polar type S . d . S and the magneto-elastlc constants Gll and G44 and their relative sign have been determined.
Using conventional p u l s e echo t e c h n i q u e s [ 1] the a c o u s t i c p a r a m a g n e t i c r e s o n a n c e of the 6S ion Mn ++ in the cubic e n v i r o n m e n t of KMgF 3 has been o b s e r v e d f o r phonon p r o p a g a t io n d i r e c t i o n s (100) and (110). Working at f r e q u e n c i e s in the r a n g e 8.5 - 9 . 8 GHz and at a t e m p e r a t u r e of 1.7°K, the a c o u s t i c attenuation was m e a s u r e d a s a function of the magnitude and o r i e n t a t i o n of the e x t e r nal m a g n e t i c field. D e s p i t e the e x t r e m e l y weak s p i n - l a t t i c e coupling, both AM s -- 1 and AM s = 2 t r a n s i t i o n s w e r e o b s e r v a b l e and typical r e s o n a n c e t r a c e s a r e shown in fig. 1. As may be s e e n f r o m that f i g u r e the r e s o n a n c e s , in which g = 2.00 ± 0.01, a r e r a t h e r broad and no h y p e r f i n e or t r a n s f e r r e d h y p e r f in e s t r u c t u r e is d i s t i n g u i s h a b l e . T h i s in c o n t r a s t to E P R r e s u l t s [2]. T h e o b s e r v a t i o n of the AM s = 2 t r a n s i t i o n is s i g n i fi can t b e c a u s e , as pointed out by R o s e n b e r g and W i g m o r e [3] with r e f e r e n c e to KMgF 3 :Ni ++, it is i m p o s s i b l e in a cubic m a t e r i a l to d i s t i n g u i s h between the d ip o l a r and q u a d r u p o l a r m e c h a n i s m s f r o m the a n g u l a r dependence of the AM s -- 1 a b s o r p t i o n . The p r e s e n c e of the AM s = 2 t r a n s i t i o n e s t a b l i s h e s that t h e r e must be at l e a s t two spin o p e r a t o r s in the dominant i n t e r a c t i o n t e r m and the a n g u l a r d e p e n d e n c e s of the AM s = 1 and AM s = 2 t r a n s i t i o n s , a s i l l u s t r a t e d in fig. 2, show that it i s a q u a d r u p o l a r m e c h a n i s m of the type S. d . S. F r o m the m e a s u r e m e n t s , the two independent 232
constants, Gll and G 4 4 , [1] of the magnetoelastic tensor were found to be: G l l = 0.30; G 4 4 = 0.09 cm'I/unit strain, with an error due to noise of + 0.02 in each case. There is also a
m
o '7" -p --I
I;o MA
,
NE
IC
.
2;o
ko,
FIELD
Fig. 1. Absorption traces of the AM~= 1 and AM~ = 2 transitions for KMgF3:0.048 Mn++. -T= 1.7OK, v ~= 9058 MHz, acoustic propagation(100).
PHYSICS
Volume 31A, n u m b e r 5
0 °
~
0.3'
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0'2 •
>
o
o
o
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180" A Q.
1.4o"
220
16o
6
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260
2o0
3oo
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0
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005
LETTERS
9 M a r c h 1970
p o s s i b l e s y s t e m a t i c e r r o r of 10% w h i c h w o u l d a f fect both quantities similarly, arising mainly f r o m t h e Mn ++ c o n c e n t r a t i o n d e t e r m i n a t i o n a n d also from instrument calibration. These results may be compared and contrasted w i t h t h e v a l u e s G l l = 1.4 a n d G44 : 0.28 c m -1 u n i t s t r a i n f o r M g O : M n +÷. m e a s u r e d by a c o u s t i c s a t u r a t i o n of E P R [4] a n d by u n i a x i a l s t r e s s on E P R [5]. T h e r e a r e to t h e a u t h o r ' s k n o w l e d g e no p u b l i s h e d r e s u l t s f o r K M g F 3 :Mn ++. A n u m b e r of c a l c u l a t i o n s u s i n g v a r i o u s m e c h a n i s m s h a v e b e e n m a d e to e s t i m a t e t h e m a g n i t u d e of t h e s p i n - l a t t i c e c o u p l i n g in M g ' O : M n ~ ~- [ 6 - 8 ] a n d a s u m m a r y of t h e p o s s i b l e m e c h a n i s m s i n v o l v e d a n d f u r t h e r r e f e r e n c e s a r e g i v e n by S h a r m a [9]. T h e r e a r e to d a t e no p u b l i s h e d c a l culations for the coupling in KMgF3, however, in v i e w of t h e p r o g r e s s b e i n g m a d e i n t h e c r y s t a l f i e l d c a l c u l a t i o n s of f l u o r i n e ~ c o o r d i n a t e d c o m p o u n d s , e s p e c i a l l y K N i F 3 a n d K M n F 3 , it i s to b e hoped that an accurate spin-lattice coupling calc u l a t i o n t a k i n g f u l l a c c o u n t of c o v a l e n c y a n d o v e r lap effects will soon be possible. T h e a u t h o r i s i n d e b t e d to D r . H. M R o s e n b e r g for supervision and helpful discussions, The work w a s c a r r i e d o u t d u r i n g t h e t e n u r e of a n S.R.C. research studentship.
References Fig. 2. The angular variation of the peak absorption of the AMs = 1 and AMs = 2 t r a n s i t i o n s . T = 1.74OK, v = = 9274 MHz, acoustic propagation (100~, 0 = angle of rotation of magnet. Also plotted are the expected quad r u p o l a r angular v a r i a t i o n s which have been n o r m a l ized to 0.36 d B / c m at 0 = 225 ° and 0.19 d B / c m at 0 = 180 ° for the AM s = 1 and A M s = 2 t r a n s i t i o n s r e s p e c tively.
1. w. I. Dobrov, Phys. Rev. 134 (1964) A 734. 2. T. P. P. Hall. W. Hayes, R.W.H. Stevenson and J. Wiikens, J. Chem. Phys. 38 (1963) 1977. 3. H. M R o s e n b e r g and J. K. Wigmore, Proc. Roy. Soc. A302 (1967) 69. 4. N. 8. Shiren, Bull. Am. Phys. Soe. 7 (1962) 29. 5. E. R, F e h e r , Phys. Rev. 136 (1964) A 145. 6. M. Blume and R. Orbach, Phys. Rev. 127 (1962) 1587, 7. A. M. Leushin, Soy. Phys. Sol. State 5 (1963) 440. 8. J. Kondo, Prog, Theor. Phys. 28 (1962) 1026. 9. R.R. Sharma, Phys. Rev. 176 (1968) 467.
233