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Cross relaxations in ruby detected by optical method
Volume 34A, number 3
CROSS
PHYSICS LETTERS
RELAXATIONS
IN RUBY
22 February 1971
DETECTED
BY
OPTICAL
METHOD
T. MURAMOTO
Faculty of Education, Shiga University, Otsu, Japan and Y. FUKUDA and T. HASHI
Department of Physics, Kyoto University, Kyoto, Japan Received 4 January 1971
Various cross relaxation signals in ruby are observed by monitoring the fluorescent light intensity versus magnetic field. Those between ~. (2E) and 4A 2 are investigated in some detail. Signals due to level crossing and exchange coupled ion pairs are also observed. The v a r i o u s types of s i g n a l s due to c r o s s r e l a x a t i o n and l e v e l c r o s s i n g w e r e o b s e r v e d in ruby (0.02 ~ 0.3% C r 2 0 3 ) at low t e m p e r a t u r e . The intensity of the total f l u o r e s c e n t light R 1 f r o m a ruby i r r a d i a t e d by a m e r c u r y lamp w a s m e a s u r e d as a function of applied s t a t i c m a g n e t i c fie ld H o modulated at an audio f r e q u e n c y with an a mpl i t u d e of about 20 Oe. The p h o t o m u l t i p l i e r output was d i s p l ay ed on a r e c o r d e r using a conve nt i o n al l o c k - i n a m p l i f i e r . Fig. 1 shows a r e c o r d e r t r a c e obtained f o r a ruby (0.15%) at 2°K t o g e t h e r with the e n e r g y l e v e l d i a g r a m of Z e e m a n s u b l e v e l s of optically e x c i t e d s t a t e ~.(2E) and ground s t a t e 4A 2 at 0 = 0, w h e r e 0 is the angle b e t w e e n H o and optic axis c 3. The typical s i g n a l s a r e l a b e l e d by the l e t t e r s . The s h a r p i n c r e a s e s A 1, A 2, B 1 and B 2 of the f l u o r e s c e n t light R 1 can be a s s i g n e d as the s i g nals due to c r o s s r e l a x a t i o n between E(2E) and 4A 2. The Z e e m a n s p li tt in g of E(2E) is equal to one of the l e v e l s p l i t t i n g s in 4A 2 at A 1 and A2, and equal to the sum of two l e v e l splittings in 4A 2 at B 1 and B 2. The i n c r e a s e at A 2 is about one p a r t in 500 of the total intensity. The s a m e kind of s i g n a l s w e r e o b s e r v e d at 0 ~ 0 and t h e i r p o s i t i o n s a r e well in a g r e e m e n t with the p r e d i c tion f r o m the spin H a m i l t o n i a n s f o r E(2E)
= I gel~HzSz +
li[:l;~!!;i~
4:-,L i
] JE!
! ! !
!'!
I '!: i ! , : 1 ! ~
!!
~2
Igel~(HxSx+HySy)
and fo r 4A 2
i
0
~
14.
1000 I
i
2000 I
i
3000 I
Oe
c~ = g,,~HzS z + g±fl(HxSx+ HySy ) + D[S2 -~S(S +1)] where 1.982, cross tained
}get = 2.445 [1], Ig e] = 0.0515 [2], g , = g . = 1.979 and D = - 5 . 7 3 6 GHz [3]. The r e l a x a t i o n t i m e of 20 g s e c or l e s s was obat A 2 by pulsed field method.
Fig. 1. Cross relaxation and level crossing signals in 0.15% ruby (disk, 13 mm@ x 1.5 ram) at 2°K a n d e = 0, and the energy level diagram of E(2E) and 4A 2. 40 Hz field modulation with amplitude of 20 Oe is used.
175
Volume 34A, number 3
PHYSICS LETTERS
The m e c h a n i s m s of optical detection of these s i g n a l s a r e as follows. In our e x p e r i m e n t a l conditions the s~0in t e m p e r a t u r e of E(2E) is lower than that of ~A2, b e c a u s e of the spin m e m o r y effect in the pumping p r o c e s s [4]. When the c r o s s r e l a x a t i o n takes place between E(2E) and 4A2, the spin t e m p e r a t u r e of E(2E) is r a i s e d and the population of the upper Z e e m a n sublevel of E(2E) is i n c r e a s e d . It c a u s e s the i n c r e a s e of the total f l u o r e s c e n t light R 1 on account of the selective r e a b s o r p t i o n in 4A 2 at low t e m p e r a t u r e [5]. The r o l e of the radio frequency field in the excited state ESR e x p e r i m e n t [1,2] is now r e p l a c e d by the c r o s s relaxation. Because of the s m a l l population in E(2E), the population change in "~A2 is negligible. The intensity of these s i g n a l s were not changed up to about 2.6OK and d e c r e a s e d v e r y rapidly as i n c r e a s i n g t e m p e r a t u r e , which is c o n s i s t e n t with the fact that the spin m e m o r y effect b e c o m e s ineffective above 2.6°K [4]. The two c r o s s r e l a x a t i o n p r o c e s s e s , optical and s p i n - s p i n , may be r e s p o n s i b l e for the phenom e n a d e s c r i b e d above. According to the s e l e c t i o n r u l e s , the f o r m e r p r o c e s s is forbidden for the s i g n a l s c o n s i d e r e d , and r e c e n t l y it was o b s e r v e d by Szabo that the s p e c t r a l diffusion in R 1 is absent [6]. T h e r e f o r e optical p r o c e s s is c o n s i d e r e d to be of l e s s i m p o r t a n c e , and the following facts also suggest that s p i n - s p i n p r o c e s s is dominant. 1) The intensity of the signal A 1 is s m a l l e r than that of A2 in fig. 1, which is c o n s i s t e n t with the fact that the spin t r a n s i t i o n in 4A 2 at A 1 is ~ s z = +2, while at A2, A S z = + 1. These become c o m p a r a b l e at 0 ~ 10 o. 2) The energy level d i a g r a m b e c o m e s quite s i m i l a r to that at A 1 and the optical c r o s s r e l a xation is t h e o r e t i c a l l y allowed at Ho = 5380 Oe. However, no significant difference between two c r o s s r e l a x a t i o n s i g n a l s was observed.
176
22 February 1971
3) The line width of the s i g n a l s is about 200 MHz and c o m p a r a b l e with the ESR line width in 4A 2 which is wider than that in F](2E). The signal C in fig. 1 is observed just at the level c r o s s i n g point in '~A2. (The same kind of signal is also o b s e r v e d at 4140 Oe.) The line widths a r e about 0.02 cm -1 which is c o m p a r a b l e with the optical line width of R 1 free from r a n dom s t r a i n s . The s i g n a l s D 1 and D2 ( d e c r e a s e s in R1) are observed where two level splittings in 4A 2 a r e equal. The s i g n a l s C and D r e m a i n at 4.2OK in c o n t r a s t to the s i g n a l s A and B. The m e c h a n i s m s for these s i g n a l s to be observed a r e not fully understood. Although not labeled in fig. 1, there a r e many s i g n a l s due to exchange coupled ion p a i r s which b e c o m e s t r o n g e r in m o r e c o n c e n t r a t e d s a m p l e s . These s i g n a l s were identified by m o n i t o r i n g the f l u o r e s c e n t light N 1 or N 2 instead of R 1. Some of them were i n c r e a s e d in i n t e n s i t y as i n c r e a s i n g t e m p e r a t u r e up to 4.2°K. Many other s i g n a l s a r e left unexplained. The p r e s e n t technique is v e r y useful to study c r o s s r e l a x a t i o n s and e n e r g y t r a n s f e r p r o c e s s e s in solids with s h a r p f l u o r e s c e n t l i n e s , and p r o vides a method of d e t e r m i n i n g Z e e m a n splittings of both excited and ground s t a t e s without any use of radio frequency s o u r c e s . References
[1] s. Geschwind, R.J. Collins and A. L. Sehawlow, Phys. Rev. Letters 3 (1959) 545. [2] T. Muramoto, Y. Fukuda and T. Hashi, J. Phys. Soe. Japan 26 (1969) 1551. [3] G. M. Zverev and A. M. Prokhorov, Zh. Eksp. i Teor. Fiz. 34 (1958) 513. [4] G. F. Imbusch and S. Geschwind, Phys. Rev. Letters 17 (1966) 238. [5] F. Varsanyi, D. L. Wood and A. L. Schawlow, Phys. Rev. Letters 3 (1959) 544. [6] S. Szabo, Phys. Rev. Letters 25 (1970) 924.
CROSS
PHYSICS LETTERS
RELAXATIONS
IN RUBY
22 February 1971
DETECTED
BY
OPTICAL
METHOD
T. MURAMOTO
Faculty of Education, Shiga University, Otsu, Japan and Y. FUKUDA and T. HASHI
Department of Physics, Kyoto University, Kyoto, Japan Received 4 January 1971
Various cross relaxation signals in ruby are observed by monitoring the fluorescent light intensity versus magnetic field. Those between ~. (2E) and 4A 2 are investigated in some detail. Signals due to level crossing and exchange coupled ion pairs are also observed. The v a r i o u s types of s i g n a l s due to c r o s s r e l a x a t i o n and l e v e l c r o s s i n g w e r e o b s e r v e d in ruby (0.02 ~ 0.3% C r 2 0 3 ) at low t e m p e r a t u r e . The intensity of the total f l u o r e s c e n t light R 1 f r o m a ruby i r r a d i a t e d by a m e r c u r y lamp w a s m e a s u r e d as a function of applied s t a t i c m a g n e t i c fie ld H o modulated at an audio f r e q u e n c y with an a mpl i t u d e of about 20 Oe. The p h o t o m u l t i p l i e r output was d i s p l ay ed on a r e c o r d e r using a conve nt i o n al l o c k - i n a m p l i f i e r . Fig. 1 shows a r e c o r d e r t r a c e obtained f o r a ruby (0.15%) at 2°K t o g e t h e r with the e n e r g y l e v e l d i a g r a m of Z e e m a n s u b l e v e l s of optically e x c i t e d s t a t e ~.(2E) and ground s t a t e 4A 2 at 0 = 0, w h e r e 0 is the angle b e t w e e n H o and optic axis c 3. The typical s i g n a l s a r e l a b e l e d by the l e t t e r s . The s h a r p i n c r e a s e s A 1, A 2, B 1 and B 2 of the f l u o r e s c e n t light R 1 can be a s s i g n e d as the s i g nals due to c r o s s r e l a x a t i o n between E(2E) and 4A 2. The Z e e m a n s p li tt in g of E(2E) is equal to one of the l e v e l s p l i t t i n g s in 4A 2 at A 1 and A2, and equal to the sum of two l e v e l splittings in 4A 2 at B 1 and B 2. The i n c r e a s e at A 2 is about one p a r t in 500 of the total intensity. The s a m e kind of s i g n a l s w e r e o b s e r v e d at 0 ~ 0 and t h e i r p o s i t i o n s a r e well in a g r e e m e n t with the p r e d i c tion f r o m the spin H a m i l t o n i a n s f o r E(2E)
= I gel~HzSz +
li[:l;~!!;i~
4:-,L i
] JE!
! ! !
!'!
I '!: i ! , : 1 ! ~
!!
~2
Igel~(HxSx+HySy)
and fo r 4A 2
i
0
~
14.
1000 I
i
2000 I
i
3000 I
Oe
c~ = g,,~HzS z + g±fl(HxSx+ HySy ) + D[S2 -~S(S +1)] where 1.982, cross tained
}get = 2.445 [1], Ig e] = 0.0515 [2], g , = g . = 1.979 and D = - 5 . 7 3 6 GHz [3]. The r e l a x a t i o n t i m e of 20 g s e c or l e s s was obat A 2 by pulsed field method.
Fig. 1. Cross relaxation and level crossing signals in 0.15% ruby (disk, 13 mm@ x 1.5 ram) at 2°K a n d e = 0, and the energy level diagram of E(2E) and 4A 2. 40 Hz field modulation with amplitude of 20 Oe is used.
175
Volume 34A, number 3
PHYSICS LETTERS
The m e c h a n i s m s of optical detection of these s i g n a l s a r e as follows. In our e x p e r i m e n t a l conditions the s~0in t e m p e r a t u r e of E(2E) is lower than that of ~A2, b e c a u s e of the spin m e m o r y effect in the pumping p r o c e s s [4]. When the c r o s s r e l a x a t i o n takes place between E(2E) and 4A2, the spin t e m p e r a t u r e of E(2E) is r a i s e d and the population of the upper Z e e m a n sublevel of E(2E) is i n c r e a s e d . It c a u s e s the i n c r e a s e of the total f l u o r e s c e n t light R 1 on account of the selective r e a b s o r p t i o n in 4A 2 at low t e m p e r a t u r e [5]. The r o l e of the radio frequency field in the excited state ESR e x p e r i m e n t [1,2] is now r e p l a c e d by the c r o s s relaxation. Because of the s m a l l population in E(2E), the population change in "~A2 is negligible. The intensity of these s i g n a l s were not changed up to about 2.6OK and d e c r e a s e d v e r y rapidly as i n c r e a s i n g t e m p e r a t u r e , which is c o n s i s t e n t with the fact that the spin m e m o r y effect b e c o m e s ineffective above 2.6°K [4]. The two c r o s s r e l a x a t i o n p r o c e s s e s , optical and s p i n - s p i n , may be r e s p o n s i b l e for the phenom e n a d e s c r i b e d above. According to the s e l e c t i o n r u l e s , the f o r m e r p r o c e s s is forbidden for the s i g n a l s c o n s i d e r e d , and r e c e n t l y it was o b s e r v e d by Szabo that the s p e c t r a l diffusion in R 1 is absent [6]. T h e r e f o r e optical p r o c e s s is c o n s i d e r e d to be of l e s s i m p o r t a n c e , and the following facts also suggest that s p i n - s p i n p r o c e s s is dominant. 1) The intensity of the signal A 1 is s m a l l e r than that of A2 in fig. 1, which is c o n s i s t e n t with the fact that the spin t r a n s i t i o n in 4A 2 at A 1 is ~ s z = +2, while at A2, A S z = + 1. These become c o m p a r a b l e at 0 ~ 10 o. 2) The energy level d i a g r a m b e c o m e s quite s i m i l a r to that at A 1 and the optical c r o s s r e l a xation is t h e o r e t i c a l l y allowed at Ho = 5380 Oe. However, no significant difference between two c r o s s r e l a x a t i o n s i g n a l s was observed.
176
22 February 1971
3) The line width of the s i g n a l s is about 200 MHz and c o m p a r a b l e with the ESR line width in 4A 2 which is wider than that in F](2E). The signal C in fig. 1 is observed just at the level c r o s s i n g point in '~A2. (The same kind of signal is also o b s e r v e d at 4140 Oe.) The line widths a r e about 0.02 cm -1 which is c o m p a r a b l e with the optical line width of R 1 free from r a n dom s t r a i n s . The s i g n a l s D 1 and D2 ( d e c r e a s e s in R1) are observed where two level splittings in 4A 2 a r e equal. The s i g n a l s C and D r e m a i n at 4.2OK in c o n t r a s t to the s i g n a l s A and B. The m e c h a n i s m s for these s i g n a l s to be observed a r e not fully understood. Although not labeled in fig. 1, there a r e many s i g n a l s due to exchange coupled ion p a i r s which b e c o m e s t r o n g e r in m o r e c o n c e n t r a t e d s a m p l e s . These s i g n a l s were identified by m o n i t o r i n g the f l u o r e s c e n t light N 1 or N 2 instead of R 1. Some of them were i n c r e a s e d in i n t e n s i t y as i n c r e a s i n g t e m p e r a t u r e up to 4.2°K. Many other s i g n a l s a r e left unexplained. The p r e s e n t technique is v e r y useful to study c r o s s r e l a x a t i o n s and e n e r g y t r a n s f e r p r o c e s s e s in solids with s h a r p f l u o r e s c e n t l i n e s , and p r o vides a method of d e t e r m i n i n g Z e e m a n splittings of both excited and ground s t a t e s without any use of radio frequency s o u r c e s . References
[1] s. Geschwind, R.J. Collins and A. L. Sehawlow, Phys. Rev. Letters 3 (1959) 545. [2] T. Muramoto, Y. Fukuda and T. Hashi, J. Phys. Soe. Japan 26 (1969) 1551. [3] G. M. Zverev and A. M. Prokhorov, Zh. Eksp. i Teor. Fiz. 34 (1958) 513. [4] G. F. Imbusch and S. Geschwind, Phys. Rev. Letters 17 (1966) 238. [5] F. Varsanyi, D. L. Wood and A. L. Schawlow, Phys. Rev. Letters 3 (1959) 544. [6] S. Szabo, Phys. Rev. Letters 25 (1970) 924.