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SYMMETRY SELECTION RULES IN RAMAN
HETERODYNE DETECTION OF NUCLEAR
RESONANCE
P. Bloch, W. Brocklesby, R. Harley, D. Taylor
To cite this version:
SYMMETRY S E L E C T I O N RULES I N RAMAN HETERODYNE D E T E C T I O N OF NUCLEAR RESONANCE
++
P.D.
loch*,
W.S. ~rocklesby*, R.T. ~arley*' and D.R. Taylor * ~ ~ a r e n d o n Laboratory, Oxford, U. K.+GEC Research Limited, East lane, Wembley, Middlesex, U.K. ++Physics Dept., Queens University, Kingston, Canada
A b s t r a c t
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A general d i s c u s s i o n o f symmetry-based s e l e c t i o n r u l e s f o r t h e kaman heterodyne d e t e c t i o n o f n u c l e a r resonance i S g i ven. D e t a i l e dmeasurements f o r pr3+ i n a c u b i c h o s t YAG c o n f i r m s e l e c t i o n r u l e p r e d i c t i o n s i n z e r o magnetic f i e l d . S i g n i f i c a n t d e p a r t u r e s a r e observed i n t h e E a r t h ' s f i e l d which r e s u l t f r o m symmetry r e d u c t i o n and p a r t i a l removal o f s i t e cancel l a t i o n e f f e c t s .
I n t r o d u c t i o n
Raman heterodyne d e t e c t i o n [l] i s one o f s e v e r a l r e c e n t laser-based t e c h n i q u e s f o r s e l e c t i v e n u c l e a r resonance measurements o f o p t i c a l i m p u r i t i e s i n s o l i d s . These i n v o l v e r e s o n a n t e x c i t a t i o n e i t h e r u s i n g simultaneous l a s e r and r a d i o - f requency f i e l d s [2] o r l a s e r r a d i a t i o n a l o n e [3]. I n t h i s paper we g i v e a general d i s c u s s i o n o f s e l e c t i o n r u l e s f o r t h e Raman heterodyne e f f e c t based on symmetry arguments. Using an a d a p t a t i o n o f e a r l i e r t e c h n i q u e s C l ] , we have made d e t a i l e d e x p e r i m e n t a l t e s t s o f t h e p r e d i c t i o n s f o r t h e d i l u t e i m p u r i t y p r 3 + i n a c u b i c host, YAG. We f i n d s i g n i f i c a n t d e p a r t u r e s f r o m p r e d i c t e d z e r o - f i e l d s e l e c t i o n r u l e s i n t h e E a r t h ' s magnetic f i e l d ( 6 1 gauss) which a r e a s s o c i a t e d w i t h p a r t i a l removal, by t h e f i e l d , o f s i t e i n t e r f e r e n c e e f f e c t s [4,5].
Symmetry e f f e c t S
I n t h e Raman heterodyne method [l], n u c l e a r resonance induced by an a p p l i e d r a d i o frequency m a g n e t i c f i e l d , produces Raman s i d e bands a t t h e n u c l e a r frequency on a
C.W. l a s e r beam t r a n s m i t t e d t h r o u g h t h e sample (see F i g u r e 1). The l a s e r frequency must be r e s o n a n t w i t h a zero-phonon t r a n s i t i o n o f t h e i m p u r i t y under study, p r o v i d i n g o p t i c a l s e l e c t i o n . The t r a n s m i t t e d beam i s i n c i d e n t on a photodiode and t h e Raman s i d e bands a r e d e t e c t e d as a heterodyne beat s i g n a l i n i t s o u t p u t .
As f i r s t p o i n t e d o u t by T a y l o r [5], t h e Raman s i d e bands a r e generated by a n o n l i n e a r response d e s c r i b e d by
where U = f wrf and i,j and k denote c a r t e s i a p components. P i i s an o p t i c a l p o l a r i s a t i o n generated by i n c i d e n t l a s e r f i e l d E j a t frequency UI and r a d i o frequency
C7-524 JOURNAL
DE
PHYSIQUEmagnetic f i e l d Hk a t U,+-. The n o n l i n e a r s u s c e p t i b i l i t y ,
X,
i s a p r o p e r t y o f t h ec r y s t a l . I t i s a t h i r d rank a x i a l t e n s o r and must be i n v a r i a n t under t h e p o i n t symmetry o p e r a t i o n s of t h e c r y s t a l . Consequently c e r t a i n components x i j k may be z e r o and r e l a t i o n s e x i s t among t h e remainder. H f u l l t a b u l a t i o n o f ~ i j k f o r t h e 32 p o i n t groups i s g i v e n by B i r s s [6]. I n p a r t i c u l a r f o r s p h e r i c a l and c u b i c symmetry
X
has a s i n g l e non-zero component, a , and Eq ( 1 ) becomeswhich i s s i m i l a r i n f o r m t o an a.c. Faraday e f f e c t .
Heterodyne d e t e c t i o n o f t h e Raman s i d e bands r e q u i r e s a ' l o c a l o s c i l l a t o r 1 o p t i c a l f i e l d a t t h e p h o t o d e t e c t o r h a v i n g t h e same p o l a r i s a t i o n . I n many cases o f low symmetry t h e s i d e bands and i n c i d e n t l a s e r do have components o f t h e same p o l a r i s a t i o n ( i = j i n Eq ( 1 ) ) so t h a t t h e l a t t e r may be used as t h e l o c a l o s c i l l a t o r g i v i n g a h e t e r o d y n e s i g n a l p r o p o r t i o n a l t o
!
.
E
(1). However f o r h i g h e r symmetries, p a r t i c u l a r l y s p h e r i c a l and c u b i c (Eq ( 2 ) ) , t h e s i d e band and l a s e r p o l a r i s a t i o n s a r e o r t h o g o n a l ( i # j ) . I n t h e s e cases a s u i t a b l e l o c a l o s c i l l a t o r f i e l d may be o b t a i n e d f o r example u s i n g a l i n e a r p o l a r i s e r between t h e sample and t h e d e t e c t o r [5]. The heterodyne s i g n a l i s t h e n p r o p o r t i o n a l t o EdPd where d denotes t h e p o l a r i s e r a x i s .F i g u r e l : Experimental arrangement f o r Raman heterodyne d e t e c t i o n o f n u c l e a r resonance i n c u b i c c r y s t a l s . L a b e l s a r e e x p l a i n e d i n S e c t i o n 3.
3 Measurements
F i g u r e 1 i n d i c a t e s our e x p e r i m e n t a l arrangement f o r i n v e s t i g a t i o n o f Raman heterodyne n u c l e a r resonance s i g n a l s o f P ~ ~ + : Y A G a t 1.5K. The c r y s t a l symmetry i s Oh and t h e r e a r e s i x r a r e e a r t h s i t e s o f D2 symmetry p e r u n i t c e l l . The apparatus i s s i m i l a r t o t h a t used p r e v i o u s l y f o r s t u d i e s o f p r 3 + i n LaF3 [l] and YAlO3 [4] b u t has t h e i m p o r t a n t a d d i t i o n (as d i s c u s s e d above) o f t h e p o l a r i s e r (P) between sample (C) and d e t e c t o r (D) t o a l l o w o b s e r v a t i o n o f s i g n a l s f r o m c u b i c c r y s t a l s . About 20 mW of l i n e a r l y p o l a r i s e d l i g h t from a C.W. dye l a s e r o f bandwidth < 2 MHz (L) and t u n e d t o
t h e zero-phonon a b s o r p t i o n l i n e a t 6069 A was focussed a l o n g t h e (001) d i r e c t i o n t o a
d i a m e t e r o f -100 pm. A r a d i o frequency m g n e t i c f i e l d o f a m p l i t u d e -0.1 t o 1 gauss was a p p l i e d e i t h e r a l o n g (100) o r (001) u s i n g a broad band t r a v e l l i n g wave C O ~ 1
32
33
34
35
MHz
F i g u r e 2 : Energy l e v e l s o f pr3+ : YAG showing h y p e r f i n e s p l i t t i n g s o f lowest 3 ~ 4 and 102 c r y s t a l f i e l d components (3). The arrows i n d i c a t e one set o f p o s s i b l e o p t i c a l and r a d i o - f requency t r a n s i t i o n s f o r Raman heterodyne d e t e c t i o n o f t o 2312 t r a n s i t i o n s i n 3 ~ 4 a t 33.4 MHz. E,P and H r e f e r t o t h e f i e l d s i n Eq (1). F i g u r e 3 : Raman heterodyne resonance s i g n a l s f o r pr3' : YAG f o r various combinations o f p o l a r i s a t i o n s o f o p t i c a l and r a d i o - f requency f i e l d s . Traces a,c and e zero magnetic f i e l d ; b,d and f i n E a r t h ' s f i e l d . a and b, xyyz; c and d, xyyz + xxyz; e and f, Xxxx + Xyxx.
The t r a n s i t i o n a t 6069 P i s between t h e ground s t a t e component of 3 ~ ~ and t h e lowest component o f 1 ~ 2 . It has inhomogeneous width o f several cm- and homogeneous w i d t h -16 kHz [3]. The low r a r e - e a r t h s i t e symmetry (Dz), gives e l e c t r o n i c a l l y non-degenerate l e v e l s , each o f which i s s p l i t i n t o t h r e e components by second- magnetic h y p e r f i n e (pseudoquadrupole) i n t e r a c t i o n s w i t h t h e 1.~12 nucleus of
lqidpr
These s p l i t t i n g s , i n d i c a t e d i n Figure 2, are t y p i c a l l y 5-100 MHz131.
We have made measurements o f t h e ground s t a t e IZ = ? t o
*
3/2 and+
3/2 t o f 5/2 t r a n s i t i o n s i n c r y s t a l s c o n t a i n i n g 0.5% and 5% pr3+. F i g u r e 3 shows r e s u l t s o f measurements on a 0.5% sample f o r d i f f e r e n t combinations o f p o l a r i s a t i o n s i ,j and k i n Eq (1). Traces a,c and e were recorded under c o n d i t i o n s where care was taken t o screen t h e sample from t h e ambient magnetic f i e l d i n t h e l a b o r a t o r y u s i n g p-metal.
The measured magnitude o f t h i s f i e l d was < l gauss, e s s e n t i a l l y t h a t o f t h e Earth. Traces b,d and f show s i g n a l s observed when t h e sample was exposed t o t h i s f i e l d . For a and b t h e a x i s o f t h e p o l a r i s e r was o r i e n t e d p a r a l l e l t o t h e i n c i d e n t l a s e r p o l a r i s a t i o n whereas i n c t o f i t was set a t 45O t o it.4 Discussion
C7-526 JOURNAL
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PHYSIQUEThe s i g n a l s observed i n the E a r t h ' s f i e l d a r i s e from p a r t i a l removal o f s i t e i n t e r f e r e n c e e f f e c t s [4]. The n o n l i n e a r s u s c e p t i b i l i t y
X
i s given by a sum o f components from d i f f e r e n t r a r e e a r t h s i t e s (S) each o f which i s p r o p o r t i o n a l t o t h e product o f m a t r i x elements pSab f o r t h e i n d i v i d u a l resonant o p t i c a l and r a d i o frequency t r a n s i s t i o n swhere 1 and 2 denote t h e two nuclear l e v e l s and 3 t h e e x c i t e d o p t i c a l l e v e l . Since t h e s i t e symmetry (D ) i s lower than t h e o v e r a l l c r y s t a l symmetry (Oh), i t f o l l o w s t h a t many of t h e must be non zero although t h e i r sum
x i j t
i s zero. C a n c e l l a t i o n s a r i s e because t h e c o n t r i b u t i o n from one s i t e i s s e n s i t i v e t o t h e phase o f t h e m a t r i x elements as w e l l as t o t h e i r magnitude (see Eq (3)). It may t h e r e f o r e cancel w i t h t h e c o n t r i b u t i o n from another s i t e o f t h e same l o c a l symmetry but r e l a t e d by an o p e r a t i o n o f t h e c r y s t a l p o i n t group. The c a n c e l l a t i o n may be l i f t e d by a p p l i c a t i o n o f a magnetic f i e l d which reduces t h e o v e r a l l symmetry. Experimentally t h i s appears e i t h e r as separation o f Zeeman components from one s i t e , which produce s i g n a l s o f opposite signs (Zeeman i n t e r f e r e n c e ) o r as separation o f cancel l i n g s i g n a l s from d i f f e r e n t s i t e s by v i r t u e o f d i f f e r e n t g-factors ( s i t e i n t e r f e r e n c e ) . Thus t h e m a g n e t i c . f i e l d r e q u i r e d t o l i f t t h e s i t e o r Zeeman c a n c e l l a t i o n i s extremely small, being only o f order t h e quol-Lent o f Raman heterodyne l i n e w i d t h and g-factor. S u b s t a n t i a l s i g n a l s may a l s o be observed i n even smaller f i e l d s due t o p a r t i a l removal o f c a n c e l l a t i o n . For an a r b i t r a r y a p p l i e d f i e l d o r i e n t a t i o n t h e o v e r a l l symmetry becomes C i and a l l components o fX
are non zero. This i s c o n s i s t e n t w i t h observed s i g n a l s f o r YAG i n t h e E a r t h ' s magnetic f i e l d as i l l u s t r a t e d i n t r a c e s b,d and f o f Figure 3.Acknowledgement
We wish t o thank Dr N B Manson f o r supply o f t h e c r y s t a l s used i n our measurements. References
1 Mlynek, J., Wong, N.C., DeVoe, R.G., K i n t z e r , E.S. and Brewer, R.G., Phys. Rev, L e t t . 50(1983) 993 and Wong, N.C., K i n t z e r , E.S., Mlynek, J., DeVoe, R.G. and Brewer, R.G., Phys. Rev.
B28
(1983) 49932 Erickson, L.E., Opt. Commun. g ( 1 9 7 7 ) 147
3 Shelby, R.M., Tropper, A.C., Harley, R.T. and Macfarlane, R.M., Optics. L e t t . 8 (1983) 304
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4 Mitsunaga, M., K i n t z e r , E.S. and Brewer, R.G., Phys. Rev. L e t t .
