12 Optical Properties of Linear Chains S. L. H O L T University of Wyoming, Laramie, Wyo.
82070
Compounds o f t h e formulation RMX3, w h e r e R is a heavy alkali metal ion (Cs or Rb ) o r an organic cation s u c h as (CH3)4N+, M is a first row divalent transition m e t a l ion, and X is Cl¯, Br¯ o r I¯, display unusual magnetic behavior.(1,2) This b e h a v i o r i s predominately o n e - d i m e n s i o n a l and arises in large part because of the o n e - d i m e n s i o n a l m o l e c u l a r structure of these materials. F i g u r e 1 shows t h e chain-like con stitution exhibited by all compounds o f this type. These chains consist of face-sharing octahedra. The larger circles r e p r e s e n t the bridging halide ions while the smaller circles r e p r e s e n t the transition ions. As shown in Figure 2, t h e s e c h a i n s a r e physically separa ted by t h e cations, in this case, (CD ) N . These cations p r o v i d e the magnetic insulation between c h a i n s with the interchain distance and t h u s t h e strength of interchain interaction being d e p e n d e n t upon t h e size of cation, i.e., the larger the cation the smaller the interchain interaction. +
+
3
4
+
Figure 3 shows t h e p a t h w a y o f t h e e x c h a n g e . As d r a w n , it s u g g e s t s t h a t t h e e x c h a n g e involves primarily the o v e r l a p of the dz orbital o f C a t i o n 1 w i t h t h e ρσ orbital of the bridging anion followed,by the inter action of the ρσ electrons w i t h t h e dz o f C a t i o n 2. Indeed, other orbitals may be involved as is schemat ically shown in Figure 4. In this c a s e , we h a v e s u p e r e x c h a n g e illustrated for b o t h 9 0 ° b o n d e d c h r o m i u m ( I I I ) i o n s and 90° b o n d e d iron(II) ions. In the upper p a r t o f the figure, we h a v e t h e c h r o m i u m ( I I I ) c a s e and h e n c e , a r e dealing with 3 d-electrons. The d-electrons on C a t i o n 1 a r e f o u n d in t orbitals, as a r e t h o s e on C a t i o n 2. An electron from the ρσ orbital of the ligand is shown as b e i n g virtually exchanged into the e orbitals o f C a t i o n 1. The coupling process of lowest energy requires t h a t the 2
2
2g
g
164
12.
HOLT
Linear
165
Chains
(hOl)
ORIENTATION
podia* j
.1200)
I «(IOO) I (OOOÎ #
I
NUCLEAR RECIPROCAL RECIPI LATTICE POINTS
Figure
1.
:(OOI)
(002)
I
MAGIN 'OETIC INTENSITY PLANES
ZONE BOUNDARY
A portion of the linear chain of an RMX. compound (adopted from Ref. l)
{
(003)4^
++
Figure
2.
Crystal structure
of (CDJMnCk
(adopted
from Réf. I)
166
EXTENDED
INTERACTIONS
BETWEEN
METAL
IONS
Cation 2
Figure 3. The 90° exchange pathway between two interacting metal ions (adopted from Ref. 2)
Cotion I
Cation I Figure bonded
Anion
Anion
Cation 2
Cation 2
4. Superexchange pathway in (a) 90° C^-Cr *; (b) 90° bonded Fe +-Fe * (adopted from Ref. 2). 3
2
2
12.
HOLT
spin that
Linear
Chains
167
o f t h e v i r t u a l l y e x c h a n g e d e l e c t r o n be t h e same as i n the t2g s e t of C a t i o n 1. The P a u l i E x c l u s i o n P r i n c i p l e t h e n r e q u i r e s t h a t t h e o t h e r e l e c t r o n i n t h e ρσ o r b i t a l o f t h e l i g a n d h a v e a s p i n of o p p o s i t e s i g n ( i n t h i s c a s e down). Because t h e r e a r e no e l e c t r o n s i n t h e eg o r b i t a l s o f C a t i o n 2, o n l y one e x c h a n g e p r o c e s s i s p o s s i b l e , t h a t process t h a t g i v e s r i s e to a - J , i . e . , a n t i p a r a l l e l exchange c o u p l i n g b e t w e e n t h e ρσ e l e c t r o n o f t h e a n i o n and t2g e l e c t r o n s o f C a t i o n 2. The n e t e f f e c t i s t o a l l o w f e r r o m a g n e t i c coupling b e t w e e n C a t i o n 1 and C a t i o n 2 w i t h t h e o v e r a l l be h a v i o r shown by t h e compound b e i n g ferromagnetic. I n t h e l o w e r p a r t o f t h e f i g u r e , we h a v e t h e c a s e o f 9 0 ° e x c h a n g e b e t w e e n two Fe2+ i o n s . In t h i s case t h i n g s are not so c l e a r c u t . V i r t u a l exchange between t h e ρσ e l e c t r o n o f t h e a n i o n and t h e e l e c t r o n s i n t h e eg o r b i t a l s o f C a t i o n 1 i s a n t i f e r r o m a g n e t i c i n n a t u r e . T h i s does not d i c t a t e the o v e r a l l s p i n a r r a n g e m e n t however. As we c a n s e e t h e r e e x i s t s t h e p o s s i b i l i t y for ferromagnetic as w e l l as a n t i f e r r o m a g n e t i c exchange b e t w e e n t h e e l e c t r o n i n t h e ρσ o r b i t a l o f t h e anion and t h e e l e c t r o n s i n t h e d - o r b i t a l s o f C a t i o n 2. The r e s u l t a n t m a g n e t i c b e h a v i o r d e p e n d s o n l y upon w h i c h i s s t r o n g e r , t h e c o u p l i n g b e t w e e n t h e e l e c t r o n i n t h e ρσ o r b i t a l and t h e eg e l e c t r o n s o r t h e c o u p l i n g b e t w e e n t h e ρσ e l e c t r o n and t h e t 2 g e l e c t r o n s . I f t h i s cou p l i n g i s s u f f i c i e n t l y s t r o n g to produce p r e f e r e n t i a l a l i g n m e n t and i n v o l v e s s e v e r a l c a t i o n c e n t e r s t h e n c o n d i t i o n s have been f u l f i l l e d f o r the c r e a t i o n of spin-waves. The d r a w i n g i n F i g u r e 5 i s a s c h e m a t i c d e p i c t i o n o f a s p i n - w a v e i n a one d i m e n s i o n a l ferromagnetically coupled system. As one c a n s e e , a s p i n d e v i a t i o n a t one end o f t h e c h a i n c a u s e s s p i n d e v i a t i o n s down t h e l i n e producing the "spin-wave". As a q u a n t u m o f e n e r g y c a l l e d a phonon e x c i t e s a v i b r a t i o n , a quantum of e n e r g y c a l l e d a magnon c a u s e s a s p i n - w a v e . I f one has i s o l a t e d c h a i n s w i t h i n a m a t e r i a l , magnons w i l l i n d u c e spin-waves i n these chains independent of each o t h e r . The p r e s e n c e o f m a g n e t i c c o u p l i n g and t h e induce ment o f s p i n - w a v e s c a n be shown e x p e r i m e n t a l l y through i n e l a s t i c - n e u t r o n - s c a t t e r i n g techniques. Figure 6 shows t h e v a r i a t i o n w i t h t e m p e r a t u r e o f t h e e x c i t a t i o n which i s a s s o c i a t e d w i t h the p r e s e n c e of spin-waves i n t h e compound ( C D 3 ) 4 M n C l 3 . As c a n be s e e n t h e s p i n - w a v e i s w e l l d e f i n e d at 1.9°K. T h i s d e f i n i t i o n d e c r e a s e s as one i n c r e a s e s t h e t e m p e r a t u r e t o 4 0 ° K . T h i s marked d e c r e a s e i n i n t e n s i t y i s t o be e x p e c t e d as t h e threedimensional o r d e r i n g t e m p e r a t u r e h a s b e e n shown t o be
168
EXTENDED
,., y
y
Figure
5.
y
y
γ
ψ ψ
INTERACTIONS
ψ
γ y
of a spin wave, (a) View in the ac plane, (adopted from Ref. 3).
Schematic
BETWEEN
METAL
y
IONS
y
y
(b) View in the ab plane
TMMC λ · 64 A EXCITATION
* ··· _J
I
I
•
—1
_l
I
I
I
I
L_
V
I
I
l_
Figure 6. Variation with tempera ture of the excitation at (0.3, 0,1.10), q,.* = 0.10 reciprocal lattice units compound is (CD ) ~NMnCl (adopted from Réf. 1).
L
Α
_l
_J 0.0
I 1.0
I
I 1 20 30 ENERGY (meV)
L.
1 4.0
L_ 5.0
h
A
12.
HOLT
Linear
Chains
169
0.84°K. T h u s , as one i n c r e a s e s t h e t e m p e r a t u r e above t h i s , c o n t i n u a l l y g r e a t e r d i s o r d e r and d e c o u p l i n g a l o n g the c h a i n s w i l l o c c u r . One w o u l d e x p e c t , as a g e n e r a l p h e n o m e n o n , t h e p r e s e n c e o f s p i n - w a v e s s h o u l d be l e s s e v i d e n t t h e h i g h e r Τ i s a b o v e TJJ . Our p r i m a r y i n t e r e s t h e r e w i l l be w i t h t h e o p t i c a l m a n i f e s t a t i o n of these spin-waves. F i g u r e 7 shows t h e v a r i o u s t y p e s o f e l e c t r o n i c p r o c e s s e s one i s l i k e l y t o encounter i n a m a g n e t i c a l l y coupled t r a n s i t i o n metal containing material. We s h a l l f o c u s o u r a t t e n t i o n p r i m a r i l y upon t h o s e t r a n s i t i o n s w h i c h a r e s p i n f o r b i d d e n i n n a t u r e , i . e . , those w h i c h undergo a change i n s p i n - m u l t i p l i c i t y , s i n c e i t i s here t h a t the e f f e c t s o f t h e s p i n - w a v e phenomenon on t h e e l e c t r o n i c t r a n s i t i o n s w i l l be s e e n . The f i r s t p a r t o f F i g u r e 7 shows t h e p r o c e s s w h i c h o c c u r s when y o u h a v e a m a g n e t i c a l l y and o p t i c a l l y d i l u t e system i n which the s p i n - m u l t i p l i c i t y may change. T h i s i s a n o r m a l e x c i t a t i o n c a u s e d by a p h o t o n where the s u b l a t t i c e s a c t i n d e p e n d e n t l y o f each o t h e r . In t h e c a s e shown h e r e , we h a v e o n l y t h e e x c i t a t i o n o f an e l e c t r o n f r o m t h e g r o u n d s t a t e on s u b l a t t i c e A i n t o an e x c i t e d s t a t e w i t h t h e a c c o m p a n y i n g s p i n - f l i p . T h i s w i l l u s u a l l y be s e e n i n t h e s p e c t r u m o f a compound as a weak a b s o r p t i o n b a n d . The w e a k n e s s o f s u c h a t r a n s i t i o n a r i s e s b e c a u s e i t i s b o t h p a r i t y and s p i n f o r b i d d e n , AS^O. S u c h i s n o t t h e c a s e i n an o p t i c a l l y c o n c e n t r a t e d s y s t e m where c o o p e r a t i v e e x c i t a t i o n s such as we s e e i n t h e s e c o n d p a r t o f F i g u r e 7 may o c c u r . In t h i s c a s e , by e x c i t i n g an e l e c t r o n f r o m t h e g r o u n d s t a t e i n s u b l a t t i c e A and s i m u l t a n e o u s l y e x c i t i n g an e l e c t r o n w i t h t h e o p p o s i t e s p i n on s u b l a t t i c e B, we c a n c o n s e r v e t h e s p i n - a n g u l a r momentum, i . e . , AS=0. T h i s i s c a l l e d an e x c i t o n · e x c i t o n t r a n s i t i o n . The consequences of the c o n s e r v a t i o n of s p i n i s to p r o v i d e a band or t r a n s i t i o n which i s r e l a t i v e l y i n t e n s e i n comparison to a normal s p i n - f o r b i d d e n t r a n s i t i o n . (In t h e c a s e we h a v e c h o s e n b o t h t h e e x c i t a t i o n on s u b l a t t i c e A and t h e one on s u b l a t t i c e Β a r e by themselves spin-forbidden. T h i s i s n o t an e x c l u s i v e r e q u i r e m e n t f o r an e x c i t o n · e x c i t o n t r a n s i t i o n . ) Note a l s o t h a t i f t h i s e x c i t a t i o n o f A and Β a r e i n d i v i d u a l l y t h e same as t h e s i n g l e e x c i t o n e x c i t a t i o n shown i n t h e f i r s t p a r t of t h i s f i g u r e , then the c o o p e r a t i v e e x c i t o n * e x c i t o n t r a n s i t i o n w i l l o c c u r at a p p r o x i m a t e l y t w i c e the energy of the e x c i t o n - o n l y t r a n s i t i o n . In t h e t h i r d p a r t o f t h e f i g u r e , we h a v e an exciton+magnon t r a n s i t i o n . T h i s i s the f i r s t of these v a r i o u s phenomena w h i c h a r e s t r i c t l y c h a r a c t e r i s t i c o f a m a g n e t i c a l l y concentrated system. The f i r s t two
170
EXTENDED
—
* - t é A
INTERACTIONS
—
r
r
*
•
ι
-H-
- t é A
Β
BETWEEN
1
- i é
B
EXCITON
EXCITON • EXCITON
-4-
—μ
1
I
- t é Α
A
Β
EXCITON - MAGNON
B
EXCITON+MAGNON
Figure 7. Exciton and exciton · magnon processes A and B refer to opposite sublattices (adopted from Ref. 2)
FINE S T R U C T U R E O F \ TRANSITION
q
(*S) —
4
T ( G) | f
4
2.2*K
Figure 8. Exciton (El, E2) and exciton + magnon (VI, σΐ, σ2) transitions in MnF (adopted from Réf. 4) 2
METAL
IONS
12.
HOLT
Linear
Chains
171
p r o c e s s e s , t h e e x c i t o n and e x c i t o n · e x c i t o n t r a n s i t i o n s a r e c h a r a c t e r i s t i c o f m a g n e t i c a l l y d i l u t e s y s t e m s as w e l l as m a g n e t i c a l l y c o n c e n t r a t e d s y s t e m s . The c a s e o f the exciton+magnon e x c i t a t i o n r e q u i r e s a m a g n e t i c a l l y c o u p l e d system, however. The exciton+magnon t r a n s i t i o n is a combination of a normal s p i n - f o r b i d d e n t r a n s i t i o n s u c h as shown on s u b l a t t i c e A a n d a s p i n - d e v i a t i o n o f low e n e r g y , s u c h as shown on s u b l a t t i c e B. Here a g a i n , j u s t as i n t h e e x c i t o n · e x c i t o n t r a n s i t i o n we s e e t h a t t h e s e l e c t i o n r u l e AS=0 i s o b e y e d . I n o t h e r w o r d s , we h a v e an u p - s p i n on A g o i n g t o a d o w n - s p i n s i m u l t a n e o u s l y w i t h a d o w n - s p i n on Β g o i n g t o an u p - s p i n . The d i f f e r e n c e b e t w e e n t h i s and an e x c i t o n · e x c i t o n t r a n s i t i o n i s t h a t t h i s p r o c e s s a r i s e s o n l y i n the case o f magnetically c o u p l e d systems and t h e energy o f t h e a l l o w i n g e x c i t a t i o n on Β i s o f c o n s i d e r a b l y l e s s mag n i t u d e than t h a t f o r t h e normal exciton·exciton t r a n sition . The l a s t d i a g r a m i n F i g u r e 7 shows a s e c o n d pro c e s s by w h i c h t h e p r e s e n c e o f a c o o p e r a t i v e m a g n e t i c i n t e r a c t i o n i n t h e s y s t e m h e l p s t o a l l o w an e l e c t r o n i c excitation. This i s c a l l e d the exciton-magnon. In t h i s c a s e , we h a v e , as b e f o r e , a s p i n - f o r b i d d e n e x c i t a t i o n on s u b l a t t i c e A b u t as o p p o s e d t o t h e e x c i t o n + magnon, we h a v e a l r e a d y c r e a t e d an e x c i t a t i o n on s u b l a t t i c e Β w h i c h t h e n d e c a y s a t t h e same t i m e as t h e e x c i t a t i o n o c c u r s on s u b l a t t i c e A. As we c a n s e e , t h e s p i n i s c o n s e r v e d i n t h i s s y s t e m as w e l l as i n t h e p r e v i o u s two s y s t e m s . One o b s e r v a b l e d i f f e r e n c e b e t w e e n t h e e x c i t o n + magnon a n d e x c i t o n - m a g n o n i s t h e i r p o s i t i o n r e l a t i v e t o the pure e x c i t o n l i n e . I t s h o u l d be c l e a r from F i g u r e 7 t h a t t h e exciton+magnon w i l l occur at h i g h e r e n e r g i e s than the pure e x c i t o n l i n e , w h i l e the exciton-magnon w i l l occur at lower e n e r g i e s than the pure e x c i t o n line. T h e c a s e f o r t h e e x c i t o n + m a g n o n i s shown q u i t e g r a p h i c a l l y i n F i g u r e 8. T h e s e l a t t e r t h r e e e x c i t a t i o n s a l l h a v e one t h i n g i n common and t h a t i s t h e i r u n u s u a l i n t e n s i t y . The v a r i a t i o n o f t h e s e i n t e n s i t i e s , as a f u n c t i o n o f Τ w i l l d i f f e r , however. F i g u r e 9 shows t h e c a l c u l a t e d temp e r a t u r e dependence f o r both the exciton+magnon ( c o l d band) and e x c i t o n - m a g n o n ( h o t band) c a s e s . This sug g e s t s t h a t a major change i n o s c i l l a t o r s t r e n g t h s h o u l d occur below TJT. The m a g n i t u d e o f t h i s change w i l l d e p e n d u p o n t h e r e l a t i v e c o n t r i b u t i o n o f magnon h o t and c o l d b a n d s and p h o n o n modes. F i g u r e 10 shows t h e c a l c u l a t e d t e m p e r a t u r e depend e n c e ( s o l i d l i n e ) f o r a two e x c i t o n t r a n s i t i o n i n RbMnF3. As c a n be s e e n f r o m t h e e x p e r i m e n t a l result
EXTENDED
i.
INTERACTIONS
BETWEEN
Spin Wovt Theofy
=> 2 >» w
α
!
5«
ii ^
Hot Bond
100
200
Temperature
300
( K)
Figure 9. Calculated temperature dependence of magnon side bands in MnF> (adopted from Ref. 5)
Two Exciton Transition
Kid*
2[ A ( S)— T, ( G)] e
l e
e
4
4
e
7.0
60«έ
H50 ? H40
100
200
300 Κ
30
Temperature Figure 10. Temperature dependence of two-exciton absorption in RbMnF Ref. 6) {
of the intensity (adopted from
METAL
IONS
12.
Linear
HOLT
173
Chains
(dashed l i n e ) the agreement i s r e l a t i v e l y good. F i g u r e 11 p r o v i d e s us w i t h t h e e x p e r i m e n t a l l y d e t e r m i n e d i n t e n s i t y v a r i a t i o n of exciton-magnon t r a n s i t i o n s in RbMnF3 and MnF2. The c r i t e r i a t h e n f o r i d e n t i f y i n g magnon assisted transitions a r e : 1) t o l o o k t o e n e r g i e s s l i g h t l y h i g h e r and s l i g h t l y l o w e r t h a n t h e p a r e n t spin-forbidden t r a n s i t i o n f o r anomously i n t e n s e m a n i f o l d s and 2) ascertain i f an a n o m o l o u s i n t e n s i t y c h a n g e o c c u r s i n the r e g i o n of the Néel p o i n t . C r i t e r i o n 1) s h o u l d be q u a l i f i e d i n t h a t o n l y t h e magnon a s s i s t e d transitions may be v i s i b l e , t h e p a r e n t l i n e b e i n g t o o weak t o be observed. One o f t h e RMX3 s y s t e m s , i n w h i c h we h a v e h a d c o n s i d e r a b l e i n t e r e s t i s t h a t c o n t a i n i n g the transition metal ion n i c k e l . T a b l e I shows t h e v a r i o u s crystall o g r a p h i c p a r a m e t e r s f o r a number o f n i c k e l - c o n t a i n i n g compounds. A l s o i n c l u d e d a r e the room t e m p e r a t u r e m a g n e t i c moments, t h e i r W e i s s c o n s t a n t s a n d , w h e r e known, an i n d i c a t i o n o f t h e i r N é e l t e m p e r a t u r e s . As c a n be s e e n , t h e i n t e r c h a i n d i s t a n c e s v a r y f r o m 9.35 A i n t h e c a s e o f ( C H ^ ^ N i B ^ , down t o 6.85 A i n the case of ΤΙΝΙΟΙβ. T h i s t h e n s h o u l d g i v e us a l a r g e r a n g e i n which to look at the e f f e c t of i n t e r - versus intrachain coupling. To t h i s moment, t h e m e a s u r e m e n t s t h a t we h a v e made have been r e s t r i c t e d to ( C H 3 ) 4 N N i C l , C s N i C l 3 , CsNiBr3, RbNiCl3 * RbNiBr3. Indeed, even i n the case of the ( C H 3 ) 4 N i C l 3 we s e e f r o m T a b l e I t h a t i t h a s b e e n f o u n d t o be f e r r o m a g n e t i c , consequently s h o u l d n o t and, i n f a c t , d o e s n o t e x h i b i t any magnon a s s i s t e d transitions in i t s o p t i c a l spectrum. C o n s e q u e n t l y , our d i s c u s s i o n i s r e s t r i c t e d to the a l k a l i m e t a l s a l t s of the nickel halides. I n F i g u r e 12 we s e e t h e s p e c t r u m o f an ^ 2 % solid s o l u t i o n of C s N i C l 3 i n the c o l o r l e s s , non-magnetic diluent CsMgCl3. This i s b a s i c a l l y a normal spectrum f o r the Ni2+ i o n . The a b s o r p t i o n maximum o c c u r i n g a t approximately 7,000 cm" i s t h e ^A2g-*"^T2g(F) t r a n s i tion. T h i s i s f o l l o w e d by t h e s p i n - a l l o w e d ^A2g"** 3 T i g ( F ) t r a n s i t i o n a t 12,000 wave n u m b e r s . Superim p o s e d u p o n i t i s t h e s p i n - f o r b i d d e n A2g- * Eg t r a n s i tion. The 3 A 2 g + T 2 g t r a n s i t i o n t h e n l i e s a t ^ 1 8 0 0 0 cm" f o l l o w e d by t h e 3 A 2 - * l A i g t r a n s i t i o n a t 19000 cm" . The s p i n - a l l o w e d A2g^ Ti (P) transition is t h e n o b s e r v e d a t 22000 cm" . This i n turn i s followed by t h e s p i n - f o r b i d d e n A g - ^ T i g ( G) (^24,000 c m " ) , 3 A a - * E ( G ) (25 ,700 cm" ) and 3 A 2 g + T ( G ) (26 ,000 cm-ï) transitions. F i g u r e 13, t h e s p e c t r u m o f C s N i C l 3 a t 5 ° K , shows o
3
a n (
1
3
)
1
1
1
g
1
3
3
g
1
3
1
2
1
2
1
g
1
2 g
4
3
CsNiBr
R. W. A s m u s s e n
c.
Achiwa, J .
Ν.
b.
3
Phys
43,
-156
-100
-101 C
b
-69
0
b
a
(20°)'°
(20°)
(20°)
(20°)
Appl.
2 .84
3 .34
2 .94
3 .41
(80°)
θ,°κ
TN,°K
1932
11
(1972).
4.5
ferromagnetic
Z. a n o r g . u . a l l g e m . Chem., 2 8 3 , 1 ( 1 9 5 6 ) .
(1969).
eff
3 .16
Willett, J.
7.268(8)
6.955(1)
7.66
7.50
7.18
6.85
6.94
9.35(2)
7.268(8)
J a p a n , 2 7 , 561
a n d H. S o l i n g ,
Phys. Soc.
a n d R. D.
3.104(4)
2.953(1)
3.12
2.97
3.12
3.17(1)
3.577(1)
F . D. G e h r i n g
P6 /mmc
3
Ρ6 /mmc
3
P6 /mmc
3
Ρ6 /mmc
3
P6 /mmc
3
P6 /mmc
Cmcm
3
v
Compounds
,Β .Μ·
o f Some R N i X
Interchain
Parameters
Intrachain
and M a g n e t i c
Group
P6 /m
Space
B. C. G e r s t e i n ,
3
RbNiBr
a.
3
RbNiCl
3
3
CsNiCl
CsNiI
3
3
TlNiCl
3
CH NH NiCl
3
3
3
(CH ) NNiBr
4
3
3
(CH ) NNiCl
Compound
Structural
TABLE I
12.
Linear
HOLT
1 0
,
175
Chains
ι 100
,
ι 200
ι
ι 300
Κ
I
Temperature
Figure 11. Experimental temperature dependence of oscillator strengths for exciton-magnon transition A ( S) -> E,( G), A ( G) in MnF and RbMnF, (adopted from Ref. 7) 6
lff
6
4
4
4
lfl
4
t
Figure
12.
The 5°K
spectrum of CsMgCly.Ni, from Réf. S)
±Z
(adopted
EXTENDED
_2i
22
IS ENERGY
Figure
13.
14
INTERACTIONS
IQ
BETWEEN METAL
g_
cnrf'XIO"*
The 5 ° Κ spectrum of CsNiCh, from Ref. 8)
±Z
(adopted
ENERGY cn-fXIO"'
Figure 14. The 5°K CsNiBr,, i Z (adopted
spectrum of from Ref. 8)
IONS
12.
HOLT
Linear
Figure
111
Chains
15.
Temperature dependence CsNiBr , ±Z s
of the spectrum
of
3
3
CsNiCl
RbNiCl
Compound
u
1
w
1
Polarization
Oscillator
Α
3
A
A
3 2
3
8
g
^A
1
8
l
L
g
l g
(G)
(F)
( 0
( D )
(F)
2g
- T
3
T
3
^ Α
g
l g
2g
- T / E
2 g
(^)
3 A -*· Τ 2g 2g
A
3
3
2
2
2 g
T
3
g
l g
2.5
1.7
2.5
2.2 1.2 4.2
2.7
2.1
2.5
0.3
2.2
1.5
0.8 0.7 1.5
0.6
3.0
0.4
2.9
2.0
0.4
0.2
1.9
1.8
5.5
1.8
0.4
6.4
4.1
1.1
4.7
1.8
1.4
5
1.1
5
1.8
3
fxl0 (4°K)
i n RNiX
fxl05(77°K)
Transition
fxl0 (300°K)
f o r Selected
->\ (G)
3
3
- T
2g*
A
3
A
A
3
2 g
2 g
28-
3
A
A
3
3
A
2
A g^ T2g
3
3
Transition
Strengths
TABLE I I
2
Ο
25
I
II
CsNiBr
3
Compound
Table
\\
1
Polarization
Continued
/ E
3
g
- T
A
3
A
A
3
3
%
A
1
(G>
3
A
+ T
* S
2 g ^
2 g
e
A
G
)
(F)
l g
l g
g
(
(F)
l g
l g
v
( D )
l g
2g
- T
3
3 T
2 g ^
2 g
2g^
3
3 A
2
2 g
A „ -*-A, (G) 2g l g
A
3
3
A
3
Transition
·
6
9
7
11.7
·
8.1
'°
3
3
6.0
0.9
5
fxlQ (300°K)
5 5
2.6
3.3
3.6
5.2
2.4
5.4
4.8
0.7
4.8
2.8
8.5
1.4
5.4
1.8
1.9 4.4
1.0
0.9
0.5
fx xl lQ 0 ( (4 4° °K K) ) f
5 5
K) ) fxlQ ( (7 77 7° °K
I*
ο 5
180
EXTENDED
INTERACTIONS
BETWEEN
METAL
IONS
a marked d i f f e r e n c e i n the r e l a t i v e i n t e n s i t i e s o f s e v e r a l o f t h e b a n d s when c o m p a r e d t o F i g u r e 12. Of p r i n c i p l e i n t e r e s t are t h o s e bands w h i c h are above 18,000 wave n u m b e r s . That band at a p p r o x i m a t e l y 19,000 w h i c h h a s b e e n i d e n t i f i e d as t h e s p i n - f o r b i d d e n ^A2g"** ^ A i g t r a n s i t i o n i s seen to have gained i n t e n s i t y rela t i v e t o t h e s p i n - a l l o w e d t r a n s i t i o n s b o t h a b o v e and b e l o w i t . The same may be s a i d f o r t h e h i g h e r e n e r g y s p i n - f o r b i d d e n t r a n s i t i o n s w h i c h l i e above the allowed 3A -* Tig(F) transition. T u r n i n g now to the spectrum of C s N i B r 3 , F i g u r e 14, one c a n a g a i n s e e t h a t t h e same i n t e n s i t y p a t t e r n i s repeated. F i g u r e 15 shows t h e t e m p e r a t u r e d e p e n d e n c e i n the lower energy r e g i o n f o r b o t h the spin-allowed and s p i n - f o r b i d d e n b a n d s i n C s N i B r 3 . As c a n be s e e n , the p r i m a r y f e a t u r e of the t e m p e r a t u r e dependence i s a r a p i d i n c r e a s e i n the i n t e n s i t y of the f o r m a l l y s p i n f o r b i d d e n bands w i t h d e c r e a s i n g t e m p e r a t u r e . This i s i n c o n t r a s t to the d e c r e a s e i n i n t e n s i t y of the s p i n allowed t r a n s i t i o n s . This rapid increase i n i n t e n s i t y a t T>>T$j i s i n c o n t r a s t t o b o t h work r e p o r t e d by L o h r and M c C l u r e ( ^ ) on some m a n g a n e s e s a l t s and t o t h e w o r k o f F u j i w a r a et_ £ l (_7) c i t e d e a r l i e r , F i g u r e 11. That t h i s b e h a v i o r i s common t o a l l o f t h e antiferromagnetic RMX3 s t u d i e d i s g r a p h i c a l l y shown i n T a b l e I I w h e r e t h e o s c i l l a t o r s t r e n g t h s , both i n the JL C and 11C d i r e c t i o n s , a r e shown as a f u n c t i o n o f t h r e e t e m p e r a t u r e s ; room, 80° and 5 ° K . As may be s e e n , i n a l l c a s e s a r a p i d i n c r e a s e of the i n t e n s i t y of the magnon-assis t e d e x c i t o n l i n e s i n the a l k a l i h a l i d e s i s n o t e d . This s u g g e s t s t h a t the i n t e n s i t y p r o d u c i n g mechanism i s s i m i l a r i n a l l c a s e s and p e r h a p s o f a d i f f e r e n t nature t h a n t h a t s e e n f o r RbMnF3 and MnF2. This l a t t e r point i s one w h i c h d e s e r v e s more s t u d y . Unfortunately, the l i m i t e d amount o f d a t a a v a i l a b l e do n o t a l l o w us t o s o r t out i n t e r - v e r s u s i n t r a c h a i n effects. Close i n s p e c t i o n a l s o shows t h a t t h e p a r e n t e x c i t o n l i n e d o e s n o t a p p e a r t o be d i s c e r n a b l e i n t h e c a s e s shown. The exciton+magnon are c l e a r l y seen, however. 3
2 g
I w o u l d l i k e t o e x p r e s s my t h a n k s t o t h e N a t i o n a l S c i e n c e F o u n d a t i o n f o r s u p p o r t o f t h i s r e s e a r c h and t o J . A c k e r m a n , G. M. C o l e , and Ε . M. H o l t who collabor a t e d i n t h i s work. Work p a r t i a l l y supported by the N a t i o n a l Science Foundation grants GP-15432A1 and GP-41506.
12.
HOLT
Linear
Chains
181
Literature
Cited
1.
H u t c h i n g s , M. T., Shirane, G., Birgeneau, R. and S. L . Holt, P h y s . Rev., (1972), B5, 1999.
2.
A c k e r m a n , J. Inorg. Chim.
3.
Kittel, C., 4th edition,
4.
Sell, Phys.
5.
S h i n a g a w a , K. a n d T a n a b e , (1971), 30, 1280.
6.
Motizuki, K. a n d (1972), 11, 167.
7.
F u j i w a r a , T., G e b h a r d t , W., P e n t a n i d e s , K. a n d T a n a b e , Υ., J. P h y s . S c o . , J a p a n ( 1 9 7 2 ) , 33, 39.
8.
A c k e r m a n , J., Holt, Ε . M. a n d State Chem., (1974), 9, 279.
9.
L o h r , L . L . a n d M c C l u r e , D. S., J. Chem. ( 1 9 6 8 ) , 49, 3 5 1 6 .
F., Cole, G. M. a n d Acta, (1974),8, 3 2 3 . Introduction W i l e y , New
Holt,
Miyata,
S. L . ,
t o Solid S t a t e Y o r k , (1971) 539.
D. D., G r e e n e , R. L . a n d W h i t e , R e v . , ( 1 9 6 7 ) , 158, 489.
Sol.
Holt,
Physics,
R. Μ . ,
Y., J. P h y s .
S.,
J.
Soc. Japan,
State
Comm.,
S. L . , J. Sol.
Phys.,
