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Transverse magnetoreflection of CuCl in the near UV
Volume 29A, number 5
PHYSICS
c o u n t e r ) was u s e d and m e r c u r y of p u r i t y 99.99% w a s m a i n t a i n e d in n i t r o g e n gas. Fig. 1 shows the m a i n peak of X - r a y d i f f r a c tion p a t t e r n s f o r two kinds of s a m p l e at - 35 ° , - 15 o, 15 ° , 50 ° and 8 0 o c r e s p e c t i v e l y . A d i f f e r e n c e on the high an g le side of the main peak w a s o b s e r v e d at - 35 °, - 15 ° and 15°C. But such a d i f f e r e n c e was not o b s e r v e d at 50 ° and 80°C. Fig. 2 shows the t e m p e r a t u r e dependence of v i s c o s i t y c o e f f i c i e n t f o r liquid m e r c u r y u s i n g the c a p i U a r l y method [6] p r o v i d e d by one of the a u t h o r s (T.I.). In the v i s c o s i t y c o e f f i c i e n t , such a d i f f e r e n c e was a l s o o b s e r v e d with the r a n g e f r o m - 35°C to 60°C. At 50°C the v i s c o s i t y c o e f f i c i e n t d i f f e r s f r o m the r e s u l t of X - r a y d i f f r a c tion a n a l y s i s , b e c a u s e d i f f e r e n c e w a s s t il l o b s e r v e d . But a f t e r holding at s a m e t e m p e r a t u r e f o r 24 h o u r s such a d i f f e r e n c e d i s a p p e a r e d (see fig. 2). At 25°C t h i s b e h a v i o u r was not o b s e r v e d f o r 90 hours. F r o m t h e s e r e s u l t s in the m e a s u r e m e n t of X - r a y s c a t t e r i n g i n t e n s i t y and v i s c o s i t y c o e f f i c ie nt f o r the two kinds of s a m p l e s of liquid m e r c ur y, it is concluded that s o m e d i f f e r e n c e in the
TRANSVERSE
19 May 1969
LETTERS
a t o m i c d i s t r i b u t i o n e x i s t between the s a m p l e m e l t e d a f t e r once s o l i d i f i e d and the s a m p l e c o n d e n s e d into the liquid st at e a f t e r once e v a p o r a t e d and t h i s d i f f e r e n c e does not e x i s t at t e m p e r a t u r e s above 70°C, and the d i s c r e p a n c y b et w een the e a r l y e x p e r i m e n t s f o r liquid m e r c u r y m ay have been cau se by the d i f f e r e n c e in the t h e r m a l t r e a t ment.
References 1. R. E. Kruh, G. T. Clyton, C. Head and G. Sandalin, Phys. Rev. 129 (1963) 1479. 2. V. G. Rivlin, R. M. Waghorne and G. I. Williams, Phil. Mag. 13 (1966) 1169. 3. C.N.J. Wagner, H. Oeken and M. L. Joshi, Z. Naturforsch. A20 (1965) 325. 4. R. Kaplow, S. L. Strong and B. L. Averbach, Phys. Rev. 138 (1965) A1336. 5. P . J . Black and J. A. Cundall, Acta. Cryst. 18 (1965) 807. 6. H.R. Thresh, Trans. A. S. M. 55 (1962) 790.
MAGNETOREFLECTION
OF
CuC1
IN T H E
NEAR
UV
W. STAUDE
Physikalisches Institut der Universitiit, Frankfurt arn Main, Germany Received 7 April 1969
Transverse magnetoreflection measurements give evidence for a longitudinal and a triplet state near the first exciton band in CuC1.
The r e f l e c t i v i t y of CuCl single c r y s t a l s and i t s change induced by a m a g n e t i c f i e l d B have b e e n m e a s u r e d in the s p e c t r a l r e g i o n of the e x c i t o n s b et ween 3.17 and 3.55 eV. In t h i s l e t t e r we r e p o r t on the t r a n s v e r s e m a g n e t o r e f l e c t i o n n e a r the f i r s t exciton band Z 3 [1]. F r o m the r e f l e c t i o n data the c o m p l e x d i e l e c t r i c constant ~(w, B ) is c a l c u l a t e d v i a K r a m e r s - K r o n i g t r a n s f o r m a t i o n . F o r t h i s c a l c u l a t i o n o u r data have b e e n c o m p l e t e d f o r the v i s i b l e r e g i o n by the r e f r a c t i v e index m e a s u r e m e n t s by Kaifu and K o m a t s u [2] and f o r the f a r u. v. up to 9.9 eV by the r e f l e e t i v i t y data m e a s u r e d in t h i s institute. The f i g u r e shows the r e f l e c t i o n s p e c t r u m and 228
the i m a g i n a r y p a r t of the d i e l e c t r i c constant in the r e g i o n of the band Z 3 in a m a g n e t i c f i e l d of 45 kG f o r two d i f f e r e n t p o l a r i s a t i o n s , E / / B and E - B . In the m a g n e t i c f i e l d two additional bands a r i s e , the f i r s t one (T) on the low e n e r g y side f o r p o l a r i s a t i o n E l / B , the o t h e r one (L) on the high e n e r g y side f o r p o l a r i s a t i o n E ± R The band T has a width of aobut 0.4 MeV; the line width of the band L ( ~ 0.15 MeV) is d e t e r m i n e d by the r e solving p o w er of the s p e c t r o m e t e r (~25 000), the a c t u a l line width m ay be s m a l l e r . We a t t r i b u t e the band L to a t r a n s i t i o n into the longitudinal ex ci t o n st at e f o r two r e a s o n s : (1) The band shows the e x p e c t e d p o l a r i s a t i o n
Volume 29A, number 5
P H Y S I C S LE T T E RS
Wovelength 3865 387..0 '
.
~
L /
3~.5 nm
"~ 3o
2O I0
42 K ;~'SkG
I k
'°0 ~ A # /-",A
a p p e a r s in the longitudinal m a g n e t o r e f l e c t i o n m e a s u r e m e n t s n e a r the second exciton band Z1,2, which is v e r y likely due to the state r 4 ( 3 P 2 ) .
4
3(
19 May 1969
\
%
T h i s explanation of the band T leads to the r e s u l t , that the s p i n - o r b i t splitting of the hole s t a t e s m u s t be negative. This i s in a g r e e m e n t with Song's c a l c u l a t i o n s [6] and the m e a s u r e m e n t s by Mohler [7]. F r o m the e n e r g e t i c p o s i t i o n s of the b a n d s Z1,2, Z 3 and T it i s p o s s i b l e to deduce the s p i n - o r b i t splitting and exchange i n t e r a c t i o n p a r a m e t e r s k and A, r e s p e c t i v e l y , u s i n g the t h e o r y of Onodera and Toyozawa [8]. They a r e
60
0 :~.
ffm~
1 2O
3210
3205 320 eV 3195 PhotonEnergy Fig. 1. N o r m a l incidence magnetoreflectivity (curves 1) and i m a g i n a r y p a r t of the dielectric constant (curves 2) for the f i r s t exciton band of CuCI.
b e h a v i o u r [3]: If the m a g n e t i c field i s p a r a l l e l to the y - a x i s , the c o m p o n e n t s P x and Pz of the e x c i t e d P - s t a t e a r e mixed. Light t r a v e l l i n g along the x - a x i s can t h e r e f o r e excite the longitudinal s t a t e P x only ff it is p o l a r i z e d in the z - d i r e c t i o n . (2) The longitudinal state should a p p e a r where the condition ~(oJ, 0) = 0 holds [4]. In o u r case t h i s condition is not fulfilled f o r any r e a l co. The band L a p p e a r s , however, at a f r e q u e n c y , where Re (¢) = 0. The i m a g i n a r y p a r t of ~ at this f r e quency is v e r y s m a l l , such that the above m e n tioned condition i s n e a r l y fulfilled. The band T on the low e n e r g y side was f i r s t r e p o r t e d by C e r t i e r et al. [5], and was i n t e r p r e t e d a s due to a t r a n s i t i o n into a t r i p l e t exciton state. Our m e a s u r e m e n t s of the p o l a r i s a t i o n b e h a v i o u r of t h i s band c o n f i r m that the c o r r e s p o n d i n g state i s r2(3Po). The o t h e r p o s s i b l e state r 4 ( 3 P 2) is r u l e d out by the o b s e r v e d dependence on the pol a r i s a t i o n : f i r s t l y , it should exhibit a finite o s c i l l a t o r s t r e n g t h f o r /~±B, and secondly, a band
A=8.7
MeV
~ =-63MeV.
A m o r e detailed r e p o r t on the work on t r a n s v e r s e a s well a s on longitudinal m a g n e t o r e f l e c t i o n of CuC1 will be p r e s e n t e d shortly. I a m indebted to Prof. W. M a r t i e n s s e n for his c o n s t a n t e n c o u r a g e m e n t and to Dr. E. Kr~tzig for h i s helpful a s s i s t a n c e . I would like to thank E. Mohler for valuable d i s c u s s i o n s and the development of the c o m p u t e r p r o g r a m , the Deutsche F o r s c h u n g s g e m e i n s c h a f t for f i n a n c i a l support, and the F r a n k f u r t C r y s t a l Growing Unit for supplying the CuC1 c r y s t a l s . The n u m e r i c a l c a l c u l a t i o n s were c a r r i e d out at the Deutsches R e c h e n zentrum Darmstadt.
References 1. M. Cardona, Phys. Rev. 129 (1963) 69. 2. Y. Kaifu and T. Komatsu, J. Phys. Soc. Jap. 25 (1968) 644. 3. S.A. Moskalenko and M. I. Shmiglyuk, Soy. Phys. Semiconductors 1 (1967) p. 353. 4. R.S. Knox, Theory of excitons, Solid State Physics, Supplement 5 (Academic Press, New York and London 1963). 5. M. Certier, C. Wecker and S. Nikitine, Phys. Letters 28A (1968) 307. 6. K.S. Song, J. de Physique 28 (1967) 195. 7. E. Mohler, Phys. Stat. Sol. 29 (1968) K55. 8. Y. Onodera and Y. Toyozawa, J. Phys. Soc. Jap. 22 (1967) 833.
229
PHYSICS
c o u n t e r ) was u s e d and m e r c u r y of p u r i t y 99.99% w a s m a i n t a i n e d in n i t r o g e n gas. Fig. 1 shows the m a i n peak of X - r a y d i f f r a c tion p a t t e r n s f o r two kinds of s a m p l e at - 35 ° , - 15 o, 15 ° , 50 ° and 8 0 o c r e s p e c t i v e l y . A d i f f e r e n c e on the high an g le side of the main peak w a s o b s e r v e d at - 35 °, - 15 ° and 15°C. But such a d i f f e r e n c e was not o b s e r v e d at 50 ° and 80°C. Fig. 2 shows the t e m p e r a t u r e dependence of v i s c o s i t y c o e f f i c i e n t f o r liquid m e r c u r y u s i n g the c a p i U a r l y method [6] p r o v i d e d by one of the a u t h o r s (T.I.). In the v i s c o s i t y c o e f f i c i e n t , such a d i f f e r e n c e was a l s o o b s e r v e d with the r a n g e f r o m - 35°C to 60°C. At 50°C the v i s c o s i t y c o e f f i c i e n t d i f f e r s f r o m the r e s u l t of X - r a y d i f f r a c tion a n a l y s i s , b e c a u s e d i f f e r e n c e w a s s t il l o b s e r v e d . But a f t e r holding at s a m e t e m p e r a t u r e f o r 24 h o u r s such a d i f f e r e n c e d i s a p p e a r e d (see fig. 2). At 25°C t h i s b e h a v i o u r was not o b s e r v e d f o r 90 hours. F r o m t h e s e r e s u l t s in the m e a s u r e m e n t of X - r a y s c a t t e r i n g i n t e n s i t y and v i s c o s i t y c o e f f i c ie nt f o r the two kinds of s a m p l e s of liquid m e r c ur y, it is concluded that s o m e d i f f e r e n c e in the
TRANSVERSE
19 May 1969
LETTERS
a t o m i c d i s t r i b u t i o n e x i s t between the s a m p l e m e l t e d a f t e r once s o l i d i f i e d and the s a m p l e c o n d e n s e d into the liquid st at e a f t e r once e v a p o r a t e d and t h i s d i f f e r e n c e does not e x i s t at t e m p e r a t u r e s above 70°C, and the d i s c r e p a n c y b et w een the e a r l y e x p e r i m e n t s f o r liquid m e r c u r y m ay have been cau se by the d i f f e r e n c e in the t h e r m a l t r e a t ment.
References 1. R. E. Kruh, G. T. Clyton, C. Head and G. Sandalin, Phys. Rev. 129 (1963) 1479. 2. V. G. Rivlin, R. M. Waghorne and G. I. Williams, Phil. Mag. 13 (1966) 1169. 3. C.N.J. Wagner, H. Oeken and M. L. Joshi, Z. Naturforsch. A20 (1965) 325. 4. R. Kaplow, S. L. Strong and B. L. Averbach, Phys. Rev. 138 (1965) A1336. 5. P . J . Black and J. A. Cundall, Acta. Cryst. 18 (1965) 807. 6. H.R. Thresh, Trans. A. S. M. 55 (1962) 790.
MAGNETOREFLECTION
OF
CuC1
IN T H E
NEAR
UV
W. STAUDE
Physikalisches Institut der Universitiit, Frankfurt arn Main, Germany Received 7 April 1969
Transverse magnetoreflection measurements give evidence for a longitudinal and a triplet state near the first exciton band in CuC1.
The r e f l e c t i v i t y of CuCl single c r y s t a l s and i t s change induced by a m a g n e t i c f i e l d B have b e e n m e a s u r e d in the s p e c t r a l r e g i o n of the e x c i t o n s b et ween 3.17 and 3.55 eV. In t h i s l e t t e r we r e p o r t on the t r a n s v e r s e m a g n e t o r e f l e c t i o n n e a r the f i r s t exciton band Z 3 [1]. F r o m the r e f l e c t i o n data the c o m p l e x d i e l e c t r i c constant ~(w, B ) is c a l c u l a t e d v i a K r a m e r s - K r o n i g t r a n s f o r m a t i o n . F o r t h i s c a l c u l a t i o n o u r data have b e e n c o m p l e t e d f o r the v i s i b l e r e g i o n by the r e f r a c t i v e index m e a s u r e m e n t s by Kaifu and K o m a t s u [2] and f o r the f a r u. v. up to 9.9 eV by the r e f l e e t i v i t y data m e a s u r e d in t h i s institute. The f i g u r e shows the r e f l e c t i o n s p e c t r u m and 228
the i m a g i n a r y p a r t of the d i e l e c t r i c constant in the r e g i o n of the band Z 3 in a m a g n e t i c f i e l d of 45 kG f o r two d i f f e r e n t p o l a r i s a t i o n s , E / / B and E - B . In the m a g n e t i c f i e l d two additional bands a r i s e , the f i r s t one (T) on the low e n e r g y side f o r p o l a r i s a t i o n E l / B , the o t h e r one (L) on the high e n e r g y side f o r p o l a r i s a t i o n E ± R The band T has a width of aobut 0.4 MeV; the line width of the band L ( ~ 0.15 MeV) is d e t e r m i n e d by the r e solving p o w er of the s p e c t r o m e t e r (~25 000), the a c t u a l line width m ay be s m a l l e r . We a t t r i b u t e the band L to a t r a n s i t i o n into the longitudinal ex ci t o n st at e f o r two r e a s o n s : (1) The band shows the e x p e c t e d p o l a r i s a t i o n
Volume 29A, number 5
P H Y S I C S LE T T E RS
Wovelength 3865 387..0 '
.
~
L /
3~.5 nm
"~ 3o
2O I0
42 K ;~'SkG
I k
'°0 ~ A # /-",A
a p p e a r s in the longitudinal m a g n e t o r e f l e c t i o n m e a s u r e m e n t s n e a r the second exciton band Z1,2, which is v e r y likely due to the state r 4 ( 3 P 2 ) .
4
3(
19 May 1969
\
%
T h i s explanation of the band T leads to the r e s u l t , that the s p i n - o r b i t splitting of the hole s t a t e s m u s t be negative. This i s in a g r e e m e n t with Song's c a l c u l a t i o n s [6] and the m e a s u r e m e n t s by Mohler [7]. F r o m the e n e r g e t i c p o s i t i o n s of the b a n d s Z1,2, Z 3 and T it i s p o s s i b l e to deduce the s p i n - o r b i t splitting and exchange i n t e r a c t i o n p a r a m e t e r s k and A, r e s p e c t i v e l y , u s i n g the t h e o r y of Onodera and Toyozawa [8]. They a r e
60
0 :~.
ffm~
1 2O
3210
3205 320 eV 3195 PhotonEnergy Fig. 1. N o r m a l incidence magnetoreflectivity (curves 1) and i m a g i n a r y p a r t of the dielectric constant (curves 2) for the f i r s t exciton band of CuCI.
b e h a v i o u r [3]: If the m a g n e t i c field i s p a r a l l e l to the y - a x i s , the c o m p o n e n t s P x and Pz of the e x c i t e d P - s t a t e a r e mixed. Light t r a v e l l i n g along the x - a x i s can t h e r e f o r e excite the longitudinal s t a t e P x only ff it is p o l a r i z e d in the z - d i r e c t i o n . (2) The longitudinal state should a p p e a r where the condition ~(oJ, 0) = 0 holds [4]. In o u r case t h i s condition is not fulfilled f o r any r e a l co. The band L a p p e a r s , however, at a f r e q u e n c y , where Re (¢) = 0. The i m a g i n a r y p a r t of ~ at this f r e quency is v e r y s m a l l , such that the above m e n tioned condition i s n e a r l y fulfilled. The band T on the low e n e r g y side was f i r s t r e p o r t e d by C e r t i e r et al. [5], and was i n t e r p r e t e d a s due to a t r a n s i t i o n into a t r i p l e t exciton state. Our m e a s u r e m e n t s of the p o l a r i s a t i o n b e h a v i o u r of t h i s band c o n f i r m that the c o r r e s p o n d i n g state i s r2(3Po). The o t h e r p o s s i b l e state r 4 ( 3 P 2) is r u l e d out by the o b s e r v e d dependence on the pol a r i s a t i o n : f i r s t l y , it should exhibit a finite o s c i l l a t o r s t r e n g t h f o r /~±B, and secondly, a band
A=8.7
MeV
~ =-63MeV.
A m o r e detailed r e p o r t on the work on t r a n s v e r s e a s well a s on longitudinal m a g n e t o r e f l e c t i o n of CuC1 will be p r e s e n t e d shortly. I a m indebted to Prof. W. M a r t i e n s s e n for his c o n s t a n t e n c o u r a g e m e n t and to Dr. E. Kr~tzig for h i s helpful a s s i s t a n c e . I would like to thank E. Mohler for valuable d i s c u s s i o n s and the development of the c o m p u t e r p r o g r a m , the Deutsche F o r s c h u n g s g e m e i n s c h a f t for f i n a n c i a l support, and the F r a n k f u r t C r y s t a l Growing Unit for supplying the CuC1 c r y s t a l s . The n u m e r i c a l c a l c u l a t i o n s were c a r r i e d out at the Deutsches R e c h e n zentrum Darmstadt.
References 1. M. Cardona, Phys. Rev. 129 (1963) 69. 2. Y. Kaifu and T. Komatsu, J. Phys. Soc. Jap. 25 (1968) 644. 3. S.A. Moskalenko and M. I. Shmiglyuk, Soy. Phys. Semiconductors 1 (1967) p. 353. 4. R.S. Knox, Theory of excitons, Solid State Physics, Supplement 5 (Academic Press, New York and London 1963). 5. M. Certier, C. Wecker and S. Nikitine, Phys. Letters 28A (1968) 307. 6. K.S. Song, J. de Physique 28 (1967) 195. 7. E. Mohler, Phys. Stat. Sol. 29 (1968) K55. 8. Y. Onodera and Y. Toyozawa, J. Phys. Soc. Jap. 22 (1967) 833.
229