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Electron cross relaxation and nuclear polarization in ruby
Volume. 27A, number 1
PHYSICS LETTERS
n e a r the a s y m p t o t e of the d i s p e r s i o n r e l a t i o n . The fact that the r a t i o of p h a s e v e l o c i t y and t h e r m a l v e l o c i t y a p p e a r s to be a n o r m a l i z i n g p a r a m e t e r [1] also finds s o m e j u s t i f i c a t i o n in cold p l a s m a t h eo r y . A s s u m i n g v e r y thick g l a s s w a l l s , we can p r o v e f r o m eq. (2) that the a t t e n u a tion c o e f f i c i e n t n e a r the a s y m p t o t e is p r o p o r t i o n a l to the s q u a r e of the p h a s e constant aa
~
-g (fin)2 "
(3)
The c o l l i s i o n f r e q u e n c y is given by v = P P c V T ( w h e r e p is the gas p r e s s u r e , P c the c o l l i s i o n p r o b a b i l i t y and VT the e l e c t r o n t h e r m a l v e l o c i t y ) a n d Vp = w / f l ; which, c o m b i n e d with eq. (1), gives: e' Q ~ i+E'
ELECTRON
1
Vp
(4)
2apP c vT
CROSS
In co n cl u si o n , cold p l a s m a t h e o r y s e e m s to be capable of explaining the i n c r e a s e d attenuation of s u r f a c e w a v e s in the r e g i o n of low p h ase v e l ocity.
References
I+E' v E'
20 May 1968
RELAXATION
AND
1. Y. Akao, Y.Ida and T.Oike, Proc. VIII Int. Conf. on Phen. in ionized gases, Vienna 1967. (Springer Verlag) p. 344. 2. J. Surutka, Elektromagnetika, (Gradjevinska Knjiga, Belgrade, 1965} p.510. 3. A.W. Trivelpiece and R. W. Gould, Journ. Appl. Phys. 30 (1959} 1784. 4. F.W. Crawford and S. A. Self, Int. J. of Electronics 18 (1965} 569. 5. Th. Moreno, Microwave transmission design date, (McGraw Hill, New York, 1948) p. 202.
NUCLEAR
POLARIZATION
IN R U B Y
V. A. ATSARKIN, A. E. M E F E O D and M . I . RODAK
Received 18 April 1968
Dynamic nuclear polarization of 27A1 is obtained under cross-relaxation conditions of Cr 3+ ions in ruby. This effect is shown to be due to the thermal contact between the nuclei Zeeman system of 27A1 and the electron spin-spin reservoir. In a r e c e n t p a p e r [1] we r e p o r t e d e x p e r i m e n t s , which d e m o n s t r a t e d a r e l a t i o n s h i p b e t w e e n e l e c t r o n spin c r o s s r e l a x a t i o n of C r 3+ ions and dynam i c n u c l e a r p o l a r i z a t i o n of 27A1 in ruby. T h e p r e s e n t c o m m u n i c a t i o n i s c o n c e r n e d with f u r t h e r i n v e s t i g a t i o n s of t h i s r e l a t i o n s h i p . The e x p e r i m e n t was c a r r i e d out on a A120 3 c r y s t a l containing 0.03% Cr3+, at 1.7OK. We o b s e r v e d s i m u l t a n e o u s l y ESR of Cr3+ at 3 c m and NMR of 27A1 at 2-7 MHz. Unlike the w e l l known d y n a m i c n u c l e a r p o l a r i z a t i o n method [2,3] w h e r e the " f o rb i d d en " e l e c t r o n - n u c l e a r t r a n s i t i o n s at ve + v r a r e s a t u r a t e d , we s a t u r a t e d an ESR line at the c e n t r e , i.e. at v e. Fig. 1. shows the e x p e r i m e n t a l r e s u l t s f o r v a r i o u s O n e a r 66 ° (8 is an angle b et ween dc m a g n e t i c field and t h e c r y s t a l axis). The (2-3) t r a n s i t i o n was s a t u r a t e d and e l e c t r o n spin c r o s s r e l a x a t i o n p r o c e s s b e t w e e n (2-3) and (1-2) o c c u r r e d . It can be s e e n that the
magnitude of n u c l e a r p o l a r i z a t i o n E ( c i r c l e s at the fig. I) e n h a n c e s c o n s i d e r a b l y when e l e c t r o n spin c r o s s r e l a x a t i o n is slightly detuned: E > O a t v 2 3 v12 (0 > 660). F o r exact e l e c t r o n spin c r o s s r e l a x a t i o n conditions (v23 = v12) we get E = 0. S i m i l a r r e s u l t w e r e obtained f o r h a r m o n i c e l e c t r o n spin c r o s s r el ax at i o n . To i n t e r p r e t the r e s u l t s , the concept of e l e c t r o n s p i n - s p i n t e m p e r a t u r e Tss was u s e d [4-7]. A c c o r d i n g to this t h e o r y [4,6,7] the tendency of c r o s s r e l a x a t i o n b et w een two t r a n s i t i o n s , f o r i n s t a n c e (2-3) and (1-2), is not the e q u a l i z i n g of t h e i r Z e e m a n n t e m p e r a t u r e s T2_ 3 and T l _ 2 , but t h e v an i sh i n g of ( v 1 2 / T l _ 2 - v 2 3 / T 2 - 3 + A / Tss) , w h e r e t, = v23 - v12. If one of the t r a n s i t i o n s is s a t u r a t e d ( v 2 3 / T 2 _ 3 ~ 0), Tss c h a n g e s as well a s TI_ 2 and we get: 1 / T s s = V l 2 / A - 1 / T I _ 2. To d e t e r m i n e 1 / T s s , m e a s u r e m e n t s of the i n 57
Volume 27A, n u m b e r 1
PHYSICS
LETTERS
v e r s e Z e e m a n t e m p e r a t u r e l/T1-2 w e r e m a d e a t various A while the (2-3) transition was saturated. The ESR signal magnitude (which is proportional t o To/TI_2) i s s h o w n in fig. 1 ( c r o s s e s , s o l i d curve). This solid curve was multiplied by the f a c t o r - V l 2 / A a n d s o t h e v a l u e of To/Tss w a s o b t a i n e d (fig. 1, d o t t e d c u r v e ) . O n e c a n s e e t h a t the agreement is excellent between the calculat e d c u r v e To/Tss a n d t h e e x p e r i m e n t a l v a l u e s of t h e n u c l e a r p o l a r i z a t i o n E f o r IAI ~< 6 0 0 - 7 0 0 MHz. This indicated that the Zeeman nuclear temperat u r e T n of 27A1 p r a c t i c a l l y c o i n c i d e s w i t h T s s in t h i s r a n g e of A . T h e e q u a l i z i n g of T n a n d T s s i n o u r c a s e c a n be caused by the "forbidden" electron-nuclear t r a n s i t i o n s s a t u r a t i o n [3] o r b y t h e d i r e c t t h e r m a l contact between the electron spin-spin reservoir a n d t h e n u c l e i [8,9]. S i n c e i n t h e l a t t e r c a s e t h e t e m p e r a t u r e e q u a l i z i n g w o u l d o c c u r in t h e a b s e n c e of m i c r o w a v e f i e l d a s w e l l , t h e n u c l e a r spin-lattice relaxation could proceed via the e l e c t r o n s p i n - s p i n r e s e r v o i r [9], a n d u n d e r e l e c tron spin cross relaxation conditions a decrease i n n u c l e a r s p i n - l a t t i c e r e l a x a t i o n t i m e T~ w o u l d b e e x p e c t e d [10]. W e d i d d e t e c t s u c h a d ~ c r e a s e i n T ~ (up to 5 0 % ) u n d e r d e t u n e d e l e c t r o n s p i n c r o s s r e l a x a t i o n c o n d i t i o n s . U n l i k e Y o s h i o k a ' s d a t a [11] w e o b s e r v e d two r e g i o n s of a d e c r e a s e i n v , : a t < 0 a n d A > 0, w h i l e a t A = 0 t h e r e i s no d e crease in agreement with the theoretical predict i o n s [10]. The relation between Tss and TI_ 2 (hence b e t w e e n T n a n d T l _ 2 ) e n a b l e s u s to c a r r y o u t a n i n t e r e s t i n g e x p e r i m e n t . W h i l e m e a s u r i n g T 1_2 (and (2-3) transition being saturated) an additional r.f. p o w e r a t t h e 27A1 N M R f r e q u e n c y w a s a p p l i e d . T h e p a r t i a l s a t u r a t i o n of N M R r e s u l t e d , a s o n e w o u l d e x p e c t , i n a d e c r e a s e of T':I^, i.e. in i n 1-2: c r e a s e of t h e ( 1 - 2 ) t r a n s i t i o n s a t u r a t i o n . H e n c e one can change the saturation transfer between e l e c t r o n i c t r a n s i t i o n s i n v o l v e d in e l e c t r o n s p i n c r o s s r e l a x a t i o n , b y a p p l y i n g r.f. p o w e r t o t h e nuclei at NMR frequency. We a r e g r a t e f u l t o M. E. Z h a b o t i n s k y a n d A. V. Frantsesson for useful discussions. * * * * *
58
20 May 1968
l
,90
u
g
3
E...~ "r,-,o I ~...~2 "JO
201
~
4
0. I
-20
. •
,o
. -t~, 0
i
•
•
MHz
i-JO
Fig. 1. The right scale: n u c l e a r polarization enhancement E under e l e c t r o n spin c r o s s relaxation conditions (circles) and calculated values of To/Tss (dotted curve). The left scale: m e a s u r e d values of To/TI_2, (2-3) t r a n s i t i o n being s a t u r a t e d ( c r o s s e s and solid curve). A = U23 - u12. At the top: Cr3+ electronic Zeeman levels and e l e c t r o n spin c r o s s relaxation t r a n sitions at 0 = 66 o. 1. V.A. Atsarkin, A. E. Mefeod, M.I. Rodak, P i s ' m a Zh. Eksp. i Teor. Fiz. 6 (1967) 942. 2. A. Abragam, W. G. P r o c t o r , Compt. Rend. 246 (1958) 2253. 3. A. Abragam, M. Borghini, P r o g r e s s in Low T e m p e r a t u r e P h y s i c s , ed. C. J. Gorter, 4 (North-Holland, A m s t e r d a m 1964) 384. 4. B.N. P r o v o t o r o v , Zh. Eksp. i Teor. Fiz. 41 (1961) 1582; 42 (1962) 882. 5. A . C . A n d e r s o n , S.R. Hartmann, Phys. Rev. 128 (1962) 2023. 6. M.I. Rodak, Zh. Eksp. i Teor. Fiz. 45 (1963) 730; Fiz. Tverd. Tela 6 (1964) 521. 7. J. Jeener, H.Eisendrath, R. Van Steenwinkel, Phys. Rev. 133 (1964) A478. 8. M.A.Kozhushner, B.N. Provotorov, Radiospektroskopiya Tverdogo Tela, Atomizdat, 5 (Moscow, 1967). 9. L. L. Buishvili, Zh. Eksp. i Teor. Fiz. 49 (1965) 1868. 10. R.L.Kyhl, B.D. Nageswara-Rao, Phys. Rev. 158 (1967) 284. 11. H. Yosbioka, J. Phys. Soc. Japan 20 (1965) 623.
PHYSICS LETTERS
n e a r the a s y m p t o t e of the d i s p e r s i o n r e l a t i o n . The fact that the r a t i o of p h a s e v e l o c i t y and t h e r m a l v e l o c i t y a p p e a r s to be a n o r m a l i z i n g p a r a m e t e r [1] also finds s o m e j u s t i f i c a t i o n in cold p l a s m a t h eo r y . A s s u m i n g v e r y thick g l a s s w a l l s , we can p r o v e f r o m eq. (2) that the a t t e n u a tion c o e f f i c i e n t n e a r the a s y m p t o t e is p r o p o r t i o n a l to the s q u a r e of the p h a s e constant aa
~
-g (fin)2 "
(3)
The c o l l i s i o n f r e q u e n c y is given by v = P P c V T ( w h e r e p is the gas p r e s s u r e , P c the c o l l i s i o n p r o b a b i l i t y and VT the e l e c t r o n t h e r m a l v e l o c i t y ) a n d Vp = w / f l ; which, c o m b i n e d with eq. (1), gives: e' Q ~ i+E'
ELECTRON
1
Vp
(4)
2apP c vT
CROSS
In co n cl u si o n , cold p l a s m a t h e o r y s e e m s to be capable of explaining the i n c r e a s e d attenuation of s u r f a c e w a v e s in the r e g i o n of low p h ase v e l ocity.
References
I+E' v E'
20 May 1968
RELAXATION
AND
1. Y. Akao, Y.Ida and T.Oike, Proc. VIII Int. Conf. on Phen. in ionized gases, Vienna 1967. (Springer Verlag) p. 344. 2. J. Surutka, Elektromagnetika, (Gradjevinska Knjiga, Belgrade, 1965} p.510. 3. A.W. Trivelpiece and R. W. Gould, Journ. Appl. Phys. 30 (1959} 1784. 4. F.W. Crawford and S. A. Self, Int. J. of Electronics 18 (1965} 569. 5. Th. Moreno, Microwave transmission design date, (McGraw Hill, New York, 1948) p. 202.
NUCLEAR
POLARIZATION
IN R U B Y
V. A. ATSARKIN, A. E. M E F E O D and M . I . RODAK
Received 18 April 1968
Dynamic nuclear polarization of 27A1 is obtained under cross-relaxation conditions of Cr 3+ ions in ruby. This effect is shown to be due to the thermal contact between the nuclei Zeeman system of 27A1 and the electron spin-spin reservoir. In a r e c e n t p a p e r [1] we r e p o r t e d e x p e r i m e n t s , which d e m o n s t r a t e d a r e l a t i o n s h i p b e t w e e n e l e c t r o n spin c r o s s r e l a x a t i o n of C r 3+ ions and dynam i c n u c l e a r p o l a r i z a t i o n of 27A1 in ruby. T h e p r e s e n t c o m m u n i c a t i o n i s c o n c e r n e d with f u r t h e r i n v e s t i g a t i o n s of t h i s r e l a t i o n s h i p . The e x p e r i m e n t was c a r r i e d out on a A120 3 c r y s t a l containing 0.03% Cr3+, at 1.7OK. We o b s e r v e d s i m u l t a n e o u s l y ESR of Cr3+ at 3 c m and NMR of 27A1 at 2-7 MHz. Unlike the w e l l known d y n a m i c n u c l e a r p o l a r i z a t i o n method [2,3] w h e r e the " f o rb i d d en " e l e c t r o n - n u c l e a r t r a n s i t i o n s at ve + v r a r e s a t u r a t e d , we s a t u r a t e d an ESR line at the c e n t r e , i.e. at v e. Fig. 1. shows the e x p e r i m e n t a l r e s u l t s f o r v a r i o u s O n e a r 66 ° (8 is an angle b et ween dc m a g n e t i c field and t h e c r y s t a l axis). The (2-3) t r a n s i t i o n was s a t u r a t e d and e l e c t r o n spin c r o s s r e l a x a t i o n p r o c e s s b e t w e e n (2-3) and (1-2) o c c u r r e d . It can be s e e n that the
magnitude of n u c l e a r p o l a r i z a t i o n E ( c i r c l e s at the fig. I) e n h a n c e s c o n s i d e r a b l y when e l e c t r o n spin c r o s s r e l a x a t i o n is slightly detuned: E > O a t v 2 3
Volume 27A, n u m b e r 1
PHYSICS
LETTERS
v e r s e Z e e m a n t e m p e r a t u r e l/T1-2 w e r e m a d e a t various A while the (2-3) transition was saturated. The ESR signal magnitude (which is proportional t o To/TI_2) i s s h o w n in fig. 1 ( c r o s s e s , s o l i d curve). This solid curve was multiplied by the f a c t o r - V l 2 / A a n d s o t h e v a l u e of To/Tss w a s o b t a i n e d (fig. 1, d o t t e d c u r v e ) . O n e c a n s e e t h a t the agreement is excellent between the calculat e d c u r v e To/Tss a n d t h e e x p e r i m e n t a l v a l u e s of t h e n u c l e a r p o l a r i z a t i o n E f o r IAI ~< 6 0 0 - 7 0 0 MHz. This indicated that the Zeeman nuclear temperat u r e T n of 27A1 p r a c t i c a l l y c o i n c i d e s w i t h T s s in t h i s r a n g e of A . T h e e q u a l i z i n g of T n a n d T s s i n o u r c a s e c a n be caused by the "forbidden" electron-nuclear t r a n s i t i o n s s a t u r a t i o n [3] o r b y t h e d i r e c t t h e r m a l contact between the electron spin-spin reservoir a n d t h e n u c l e i [8,9]. S i n c e i n t h e l a t t e r c a s e t h e t e m p e r a t u r e e q u a l i z i n g w o u l d o c c u r in t h e a b s e n c e of m i c r o w a v e f i e l d a s w e l l , t h e n u c l e a r spin-lattice relaxation could proceed via the e l e c t r o n s p i n - s p i n r e s e r v o i r [9], a n d u n d e r e l e c tron spin cross relaxation conditions a decrease i n n u c l e a r s p i n - l a t t i c e r e l a x a t i o n t i m e T~ w o u l d b e e x p e c t e d [10]. W e d i d d e t e c t s u c h a d ~ c r e a s e i n T ~ (up to 5 0 % ) u n d e r d e t u n e d e l e c t r o n s p i n c r o s s r e l a x a t i o n c o n d i t i o n s . U n l i k e Y o s h i o k a ' s d a t a [11] w e o b s e r v e d two r e g i o n s of a d e c r e a s e i n v , : a t < 0 a n d A > 0, w h i l e a t A = 0 t h e r e i s no d e crease in agreement with the theoretical predict i o n s [10]. The relation between Tss and TI_ 2 (hence b e t w e e n T n a n d T l _ 2 ) e n a b l e s u s to c a r r y o u t a n i n t e r e s t i n g e x p e r i m e n t . W h i l e m e a s u r i n g T 1_2 (and (2-3) transition being saturated) an additional r.f. p o w e r a t t h e 27A1 N M R f r e q u e n c y w a s a p p l i e d . T h e p a r t i a l s a t u r a t i o n of N M R r e s u l t e d , a s o n e w o u l d e x p e c t , i n a d e c r e a s e of T':I^, i.e. in i n 1-2: c r e a s e of t h e ( 1 - 2 ) t r a n s i t i o n s a t u r a t i o n . H e n c e one can change the saturation transfer between e l e c t r o n i c t r a n s i t i o n s i n v o l v e d in e l e c t r o n s p i n c r o s s r e l a x a t i o n , b y a p p l y i n g r.f. p o w e r t o t h e nuclei at NMR frequency. We a r e g r a t e f u l t o M. E. Z h a b o t i n s k y a n d A. V. Frantsesson for useful discussions. * * * * *
58
20 May 1968
l
,90
u
g
3
E...~ "r,-,o I ~...~2 "JO
201
~
4
0. I
-20
. •
,o
. -t~, 0
i
•
•
MHz
i-JO
Fig. 1. The right scale: n u c l e a r polarization enhancement E under e l e c t r o n spin c r o s s relaxation conditions (circles) and calculated values of To/Tss (dotted curve). The left scale: m e a s u r e d values of To/TI_2, (2-3) t r a n s i t i o n being s a t u r a t e d ( c r o s s e s and solid curve). A = U23 - u12. At the top: Cr3+ electronic Zeeman levels and e l e c t r o n spin c r o s s relaxation t r a n sitions at 0 = 66 o. 1. V.A. Atsarkin, A. E. Mefeod, M.I. Rodak, P i s ' m a Zh. Eksp. i Teor. Fiz. 6 (1967) 942. 2. A. Abragam, W. G. P r o c t o r , Compt. Rend. 246 (1958) 2253. 3. A. Abragam, M. Borghini, P r o g r e s s in Low T e m p e r a t u r e P h y s i c s , ed. C. J. Gorter, 4 (North-Holland, A m s t e r d a m 1964) 384. 4. B.N. P r o v o t o r o v , Zh. Eksp. i Teor. Fiz. 41 (1961) 1582; 42 (1962) 882. 5. A . C . A n d e r s o n , S.R. Hartmann, Phys. Rev. 128 (1962) 2023. 6. M.I. Rodak, Zh. Eksp. i Teor. Fiz. 45 (1963) 730; Fiz. Tverd. Tela 6 (1964) 521. 7. J. Jeener, H.Eisendrath, R. Van Steenwinkel, Phys. Rev. 133 (1964) A478. 8. M.A.Kozhushner, B.N. Provotorov, Radiospektroskopiya Tverdogo Tela, Atomizdat, 5 (Moscow, 1967). 9. L. L. Buishvili, Zh. Eksp. i Teor. Fiz. 49 (1965) 1868. 10. R.L.Kyhl, B.D. Nageswara-Rao, Phys. Rev. 158 (1967) 284. 11. H. Yosbioka, J. Phys. Soc. Japan 20 (1965) 623.