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New results on the acoustic paramagnetic resonance of V3+ in MgO
Volume
37A,
NEW
number
i
RESULTS
PHYSICS
ON
THE
ACOUSTIC V 3+
LETTERS
PARAMAGNETIC IN
25 October
RESONANCE
1971
OF
MgO*
R. BUISSON a n d A. N A H M A N I Laboraloire de SpectrornOtrie Physique **, Cedex 53, 38-Grenoble, France Received 6 September 1971 New e x p e r i m e n t a l r e s u l t s of acoustic p a r a m a g n e t i c r e s o n a n c e of V 3+ in MgO a r e p r e s e n t e d , which differ from previously r e p o r t e d work. A suggestion is given for t h e i r interpretation.
T h e 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 V 3+ : M g O h a s b e e n o b s e r v e d by R a m p t o n et al. ~1]. T h e i r r e s u l t s w e r e i n t e r p r e t e d a s d u e to V °+ i o n s in t e t r a g o n a l s y m m e t r y , t h e o r i g i n of t h i s s y m m e t r y b e i n g n o t u n d e r s t o o d [2]. We r e p o r t h e r e e x p e r i m e n t a l r e s u l t s d i f f e r e n t f r o m t h o s e of r e f . [1] in m a n y a s p e c t s . T h e e x periments, made with an apparatus described e l s e w h e r e [3], w e r e c a r r i e d out in t h e t e m p e r a t u r e r a n g e 14 - 2 0 ° K b e c a u s e r e s o n a n c e i s o b served between excited states. Acoustic attenuat i o n of l o n g i t u d i n a l a c o u s t i c w a v e s of f r e q u e n c y 9300 M H z i s m e a s u r e d v e r s u s m a g n e t i c f i e l d /'/, the propagation vector k being directed along a ~100) d i r e c t i o n . T h e f i g u r e s h o w s t h e v a r i a t i o n of t h i s a t t e n u a t i o n (in a r b i t r a r y u n i t s ) f o r v a r i o u s f i e l d o r i e n t a t i o n s . T h e r e l a t i v e o r i e n t a t i o n s of / ' / a n d k w i t h r e s p e c t to t e t r a g o n a l c u b i c a x i s a r e i n d i c a t e d . T h e h y p e r f i n e s t r u c t u r e of v a n a d i u m i s c l e a r l y v i s i b l e . T h e two l i n e s at low f i e l d a r e t h e w e l l k n o w n A m = 2 a n d A m = 1 t r a n s i t i o n s of F e 2+ in c u b i c s i t e s . If we d e c i d e to c a l l " l i n e " a m a x i m u m in t h e a c o u s t i c a t t e n u a t i o n , we c a n a l s o t r y to i n t e r p r e t t h e r e s u l t s w i t h a n a x i a l s p i n H a m i l t o n i a n of t e t r a g o n a l s y m m e t r y . T h e p e r s i s t e n c e of a " l i n e " at g ~ 1.4 w h e n / t l i e s in a n y { 1 0 0 } p l a n e l e a d s , w i t h S = ~,1 togll ~ 0, g ± ~ 1 . 4 a n d n o t g l s ~ 0 . 7 , g± ~ 0 a s g i v e n in r e f . [1] w h e r e t h e c h o i c e S = 1 was made. However, axial symmetry can be discounted because, with /'///(1117 only one line should be seen while the experimental observed s p e c t r u m (not g i v e n h e r e ) i s n e a r l y t h e s a m e a s t h a t o b t a i n e d w i t h 0 = 40 °. In a d d i t i o n , t h e v a l u e of g~ ~ 0 c a n n o t b e e x p l a i n e d b y a c h a r g e c o m pensation which would destroy the cubic symme* Supported in p a r t by the D.G.R.S.T. ** L a b o r a t o i r e associ4 au C.N.R.S.
try. Neither can a static Jahn-Teller effect exp l a i n t h e r e s u l t s , b e c a u s e t h e g v a l u e s a r e too far from the free spin gvalue. W e s u g g e s t t h a t V ~+ i o n s a r e in c u b i c s i t e s distorted by random strains and that the resonance occurs inside an excited triplet, the ground state being a doublet. This configuration is obt a i n e d w h e n o n e g o e s to s e c o n d o r d e r f o r t h e s p i n orbit coupling. As the spin lattice coupling is strong and the Zeeman effect small, the lines a r e v e r y b r o a d , a n d t h e m i x i n g of t h e s t a t e s c a n e v e n b e so i m p o r t a n t t h a t a m a x i m u m in t h e acoustic attenuation need not necessarily reflect t h e p r e s e n c e of a l i n e . T h e r e f o r e , we t h i n k t h a t t h e a b s o r p t i o n at g ~ 1.4 i s d u e to a A m = 2 t r a n s i t i o n w h i l e t h e o t h e r p a r t of t h e s p e c t r u m i s d u e to A m = 1 t r a n s i t i o n s f o r i o n s in m o r e o r l e s s d i s t o r t e d s i t e s . U s i n g t h i s h y p o t h e s i s and t h e l i n e i n t e n s i t i e s (the w i d t h s a r e n e a r l y t h e s a m e ) at 14 a n d 20°K~ we get a d o u b l e t - t r i p l e t s p l i t t i n g of ( 7 + 1 ) c m -~. T h i s v a l u e i s c o m p a t i b l e w i t h t h e r e s u l t s of r e f . [1]: if we c h o o s e t h e s a m e l e v e l c o n f i g u r a t i o n a s t h e y do, o u r r e s u l t s g i v e a v a l u e f o r t h e i r D p a r a m e t e r of 9.9 c m -1 a s c o m p a r e d to (10.2±1) c m - 1 . T h i s s u g g e s t i o n i s b a s e d on t h e g r e a t s i m i l a r ity of t h e F e 2+ a n d V 3+ s p e c t r a : (i) A m = 2 l i n e s h a v e t h e s a m e a n g u l a r v a r i a t i o n in i n t e n s i t y , (ii) t h e s m a l l a t t e n u a t i o n w h i c h a p p e a r s on t h e h i g h f i e l d s i d e of t h e F e 2 + ( A m = 2 ) l i n e f o r 5 = 40 ° c o u l d b e t h e a n a l o g u e of t h e ( s t r o n g e r ) a t t e n u a t i o n w h i c h e x i s t s on t h e h i g h f i e l d s i d e of t h e V3+(Am=2) l i n e , (iii) t h e v a r i a t i o n s of t h e i n t e n s i t i e s of t h e F e 2+ ( A m =1) l i n e a n d of t h e a t t e n u a t i o n n e a r t h e t h e o r e t i c a l p o s i t i o n of t h e V 3 + ( A m = I ) l i n e a r e s i m ilar for the lower figure. There remain however s o m e u n e x p l a i n e d f e a t u r e s in t h i s m o d e l , b u t we t h i n k t h a t a m o r e d e t a i l e d a n a l y s i s of t h e m i x i n g of t h e s t a t e s b y t h e r a n d o m s t r a i n s will c l a r i f y it.
Volume
37A,
number
1
PHYSICS
]/~y
~I\~\
"~.
/
~
T -20°K 2
.
4
6
8KGs
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Z 0
..~,
l-~I i ]\•
F-
"./~~- -....,
/
m I-
Z iii
LETTERS
~
U-so ........................ ....,
¢
//
/,"i1",..." ,#
I."
i
.........
.-
...........
"-- .... ---
.tI
25 October
1971
published elsewhere together with the experiment a l r e s u l t s o b t a i n e d w i t h V 3+ in CaO w h i c h a r e s i m i l a r to t h o s e r e p o r t e d h e r e . We m u s t n o t e t h a t o u r s u g g e s t i o n i s c o m p l e t e ly d i f f e r e n t f r o m t h a t of Ray [4] b a s e d on t h e r e s u l t s of r e f . [1], who a l s o p r o p o s e s a n a v e r a g e c u b i c s y m m e t r y f o r t h e i o n s b u t e x p l a i n s all t h e s p e c t r u m a s due to Am = 2 l i n e s of s t r o n g l y distorted sites. F i n a l y , if o u r s u g g e s t i o n i s c o r r e c t , t h e o b served g value implies a Ham reduction factor K ( T 1) ~ 0.4 [5]. T h e c o u p l i n g w i t h t h e T 2 m o d e s . which is smaller than the coupling with the E modes even without Ham reduction, is further r e d u c e d b e c a u s e K ( T 2 ) = K(T1). O n e c a n t h e n u n d e r s t a n d why t h e s p e c t r u m a p p e a r s to h a v e t e t r a g o n a l s y m m e t r y w h i l e t h e i o n s a r e in c u b i c s i t e s "in a v e r a g e " . W i t h s u c h a r e d u c t i o n , t h e d o u b l e t - t r i p l e t s p l i t t i n g c a n n o t b e e x p l a i n e d by a s e c o n d o r d e r e f f e c t of s p i n - o r b i t c o u p l i n g on t h e electronic s t a t e s b u t it c a n b e , a s s u g g e s t e d by R a y [4], by a s e c o n d o r d e r e f f e c t on t h e vibronic states.
........
~:J'"
0
T=14°K
~
2
4
0=0' 6
Fig.
References
8 KGs
1.
A l s o , t h e s h a p e of t h e d i s t r i b u t i o n of t h e s e s t r a i n s i s of g r e a t i m p o r t a n c e . S o m e c a l c u l a t i o n s to f i n d t h e l i n e s h a p e a r e in p r o g r e s s a n d w i l l b e
*****
10
[1] R. G. B r a b i n - S m i t h and V. W. Rampton, 3. Phys. C2 (1969) 1759. [2] C. A. Bates, L. C. Goodfellow and K. W, H. Stevens, O. Phys. C3 (1970) 1831. [3] R. Buisson and C. Jaeolin, J. de Phys. 30 (1969) 103. [4] T. Ray, Solid. St. Coin. 9 (1971) 911. [5J F, S. Ham. Phys. Rev. 138A (1965) 1727.
37A,
NEW
number
i
RESULTS
PHYSICS
ON
THE
ACOUSTIC V 3+
LETTERS
PARAMAGNETIC IN
25 October
RESONANCE
1971
OF
MgO*
R. BUISSON a n d A. N A H M A N I Laboraloire de SpectrornOtrie Physique **, Cedex 53, 38-Grenoble, France Received 6 September 1971 New e x p e r i m e n t a l r e s u l t s of acoustic p a r a m a g n e t i c r e s o n a n c e of V 3+ in MgO a r e p r e s e n t e d , which differ from previously r e p o r t e d work. A suggestion is given for t h e i r interpretation.
T h e 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 V 3+ : M g O h a s b e e n o b s e r v e d by R a m p t o n et al. ~1]. T h e i r r e s u l t s w e r e i n t e r p r e t e d a s d u e to V °+ i o n s in t e t r a g o n a l s y m m e t r y , t h e o r i g i n of t h i s s y m m e t r y b e i n g n o t u n d e r s t o o d [2]. We r e p o r t h e r e e x p e r i m e n t a l r e s u l t s d i f f e r e n t f r o m t h o s e of r e f . [1] in m a n y a s p e c t s . T h e e x periments, made with an apparatus described e l s e w h e r e [3], w e r e c a r r i e d out in t h e t e m p e r a t u r e r a n g e 14 - 2 0 ° K b e c a u s e r e s o n a n c e i s o b served between excited states. Acoustic attenuat i o n of l o n g i t u d i n a l a c o u s t i c w a v e s of f r e q u e n c y 9300 M H z i s m e a s u r e d v e r s u s m a g n e t i c f i e l d /'/, the propagation vector k being directed along a ~100) d i r e c t i o n . T h e f i g u r e s h o w s t h e v a r i a t i o n of t h i s a t t e n u a t i o n (in a r b i t r a r y u n i t s ) f o r v a r i o u s f i e l d o r i e n t a t i o n s . T h e r e l a t i v e o r i e n t a t i o n s of / ' / a n d k w i t h r e s p e c t to t e t r a g o n a l c u b i c a x i s a r e i n d i c a t e d . T h e h y p e r f i n e s t r u c t u r e of v a n a d i u m i s c l e a r l y v i s i b l e . T h e two l i n e s at low f i e l d a r e t h e w e l l k n o w n A m = 2 a n d A m = 1 t r a n s i t i o n s of F e 2+ in c u b i c s i t e s . If we d e c i d e to c a l l " l i n e " a m a x i m u m in t h e a c o u s t i c a t t e n u a t i o n , we c a n a l s o t r y to i n t e r p r e t t h e r e s u l t s w i t h a n a x i a l s p i n H a m i l t o n i a n of t e t r a g o n a l s y m m e t r y . T h e p e r s i s t e n c e of a " l i n e " at g ~ 1.4 w h e n / t l i e s in a n y { 1 0 0 } p l a n e l e a d s , w i t h S = ~,1 togll ~ 0, g ± ~ 1 . 4 a n d n o t g l s ~ 0 . 7 , g± ~ 0 a s g i v e n in r e f . [1] w h e r e t h e c h o i c e S = 1 was made. However, axial symmetry can be discounted because, with /'///(1117 only one line should be seen while the experimental observed s p e c t r u m (not g i v e n h e r e ) i s n e a r l y t h e s a m e a s t h a t o b t a i n e d w i t h 0 = 40 °. In a d d i t i o n , t h e v a l u e of g~ ~ 0 c a n n o t b e e x p l a i n e d b y a c h a r g e c o m pensation which would destroy the cubic symme* Supported in p a r t by the D.G.R.S.T. ** L a b o r a t o i r e associ4 au C.N.R.S.
try. Neither can a static Jahn-Teller effect exp l a i n t h e r e s u l t s , b e c a u s e t h e g v a l u e s a r e too far from the free spin gvalue. W e s u g g e s t t h a t V ~+ i o n s a r e in c u b i c s i t e s distorted by random strains and that the resonance occurs inside an excited triplet, the ground state being a doublet. This configuration is obt a i n e d w h e n o n e g o e s to s e c o n d o r d e r f o r t h e s p i n orbit coupling. As the spin lattice coupling is strong and the Zeeman effect small, the lines a r e v e r y b r o a d , a n d t h e m i x i n g of t h e s t a t e s c a n e v e n b e so i m p o r t a n t t h a t a m a x i m u m in t h e acoustic attenuation need not necessarily reflect t h e p r e s e n c e of a l i n e . T h e r e f o r e , we t h i n k t h a t t h e a b s o r p t i o n at g ~ 1.4 i s d u e to a A m = 2 t r a n s i t i o n w h i l e t h e o t h e r p a r t of t h e s p e c t r u m i s d u e to A m = 1 t r a n s i t i o n s f o r i o n s in m o r e o r l e s s d i s t o r t e d s i t e s . U s i n g t h i s h y p o t h e s i s and t h e l i n e i n t e n s i t i e s (the w i d t h s a r e n e a r l y t h e s a m e ) at 14 a n d 20°K~ we get a d o u b l e t - t r i p l e t s p l i t t i n g of ( 7 + 1 ) c m -~. T h i s v a l u e i s c o m p a t i b l e w i t h t h e r e s u l t s of r e f . [1]: if we c h o o s e t h e s a m e l e v e l c o n f i g u r a t i o n a s t h e y do, o u r r e s u l t s g i v e a v a l u e f o r t h e i r D p a r a m e t e r of 9.9 c m -1 a s c o m p a r e d to (10.2±1) c m - 1 . T h i s s u g g e s t i o n i s b a s e d on t h e g r e a t s i m i l a r ity of t h e F e 2+ a n d V 3+ s p e c t r a : (i) A m = 2 l i n e s h a v e t h e s a m e a n g u l a r v a r i a t i o n in i n t e n s i t y , (ii) t h e s m a l l a t t e n u a t i o n w h i c h a p p e a r s on t h e h i g h f i e l d s i d e of t h e F e 2 + ( A m = 2 ) l i n e f o r 5 = 40 ° c o u l d b e t h e a n a l o g u e of t h e ( s t r o n g e r ) a t t e n u a t i o n w h i c h e x i s t s on t h e h i g h f i e l d s i d e of t h e V3+(Am=2) l i n e , (iii) t h e v a r i a t i o n s of t h e i n t e n s i t i e s of t h e F e 2+ ( A m =1) l i n e a n d of t h e a t t e n u a t i o n n e a r t h e t h e o r e t i c a l p o s i t i o n of t h e V 3 + ( A m = I ) l i n e a r e s i m ilar for the lower figure. There remain however s o m e u n e x p l a i n e d f e a t u r e s in t h i s m o d e l , b u t we t h i n k t h a t a m o r e d e t a i l e d a n a l y s i s of t h e m i x i n g of t h e s t a t e s b y t h e r a n d o m s t r a i n s will c l a r i f y it.
Volume
37A,
number
1
PHYSICS
]/~y
~I\~\
"~.
/
~
T -20°K 2
.
4
6
8KGs
-[-------''~
Z 0
..~,
l-~I i ]\•
F-
"./~~- -....,
/
m I-
Z iii
LETTERS
~
U-so ........................ ....,
¢
//
/,"i1",..." ,#
I."
i
.........
.-
...........
"-- .... ---
.tI
25 October
1971
published elsewhere together with the experiment a l r e s u l t s o b t a i n e d w i t h V 3+ in CaO w h i c h a r e s i m i l a r to t h o s e r e p o r t e d h e r e . We m u s t n o t e t h a t o u r s u g g e s t i o n i s c o m p l e t e ly d i f f e r e n t f r o m t h a t of Ray [4] b a s e d on t h e r e s u l t s of r e f . [1], who a l s o p r o p o s e s a n a v e r a g e c u b i c s y m m e t r y f o r t h e i o n s b u t e x p l a i n s all t h e s p e c t r u m a s due to Am = 2 l i n e s of s t r o n g l y distorted sites. F i n a l y , if o u r s u g g e s t i o n i s c o r r e c t , t h e o b served g value implies a Ham reduction factor K ( T 1) ~ 0.4 [5]. T h e c o u p l i n g w i t h t h e T 2 m o d e s . which is smaller than the coupling with the E modes even without Ham reduction, is further r e d u c e d b e c a u s e K ( T 2 ) = K(T1). O n e c a n t h e n u n d e r s t a n d why t h e s p e c t r u m a p p e a r s to h a v e t e t r a g o n a l s y m m e t r y w h i l e t h e i o n s a r e in c u b i c s i t e s "in a v e r a g e " . W i t h s u c h a r e d u c t i o n , t h e d o u b l e t - t r i p l e t s p l i t t i n g c a n n o t b e e x p l a i n e d by a s e c o n d o r d e r e f f e c t of s p i n - o r b i t c o u p l i n g on t h e electronic s t a t e s b u t it c a n b e , a s s u g g e s t e d by R a y [4], by a s e c o n d o r d e r e f f e c t on t h e vibronic states.
........
~:J'"
0
T=14°K
~
2
4
0=0' 6
Fig.
References
8 KGs
1.
A l s o , t h e s h a p e of t h e d i s t r i b u t i o n of t h e s e s t r a i n s i s of g r e a t i m p o r t a n c e . S o m e c a l c u l a t i o n s to f i n d t h e l i n e s h a p e a r e in p r o g r e s s a n d w i l l b e
*****
10
[1] R. G. B r a b i n - S m i t h and V. W. Rampton, 3. Phys. C2 (1969) 1759. [2] C. A. Bates, L. C. Goodfellow and K. W, H. Stevens, O. Phys. C3 (1970) 1831. [3] R. Buisson and C. Jaeolin, J. de Phys. 30 (1969) 103. [4] T. Ray, Solid. St. Coin. 9 (1971) 911. [5J F, S. Ham. Phys. Rev. 138A (1965) 1727.