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On the nonlinear dependence of photomagnetic effects on the light intensity
Volume 30A, number 5
PHYSICS LETTERS
m o d e l calculation is p r o v i d e d by a c o m p a r i s o n with the changes of F e r m i s u r f a c e a r e a s o b s e r v e d f r o m dHvA m e a s u r e m e n t s in a l u m i n u m unde r h y d r o s t a t i c p r e s s u r e [6]. T h e m o d e l p r e dic ts that 1/A (dA/dP) f o r the/3 and 7 c r o s s s e c t i o n s a r e 1.35 and - 0 . 4 3 % / k b a r r e s p e c t i v e l y , c o m p a r e d with the v a l u e s 1.2 + 0.15 and -0.47 + 0.06%/kbar o b s e r v e d e x p e r i m e n t a l l y .
3November 1969
References 1. K.C. Kepler and J. A. Rayne, Phys. Letters 28A (1968) 163. 2. A.B. Pippard, Phil. Mag. 46 (1955) 1104. 3. A.B. Pippard, Proc. Roy. Soc. A257 (1960) 165. 4. W.A. Harrison, Pseudopotentials in the theory of metals (W. A. Benjamin, Inc., New York, 1966}. 5. N.W. Ashcroft, Phil. Mag. 96 (1963) 2055. 6. P.J. Melz, Phys. Rev. 152 (1966) 540.
T h i s work was supported by a g r a n t f r o m the National S c i e n c e Foundation.
ON T H E
NONLINEAR
DEPENDENCE ON T H E L I G H T
OF PHOTOMAGNETIC INTENSITY
EFFECTS
I. K. KIKOIN, S.D. LAZAREV, G . A . SHEPELSKY and G. D. YEFREMOVA
lturchatov Institute. Moscow, USSR Received 19 August 1969
The light intensity dependence of the photomagnetic effects in the quantum region is studied experimentally (in degenerated InSb and InAs samples in magnetic fields up to 2? kOe at 1.8-4.2OK). It is shown that this dependence in the magnetic field region where the photomagnetic effect has the anomalous sign, is nonlinear, and at some light intensity the photomagnetic electromotive force changes its sign.
E x p e r i m e n t a l data on quantum o s c i l l a t i o n s of the p h o t o m ag n et i c E M F in a m a g n e t i c field f o r n - t y p e InSb and InAs s a m p l e s a r e p r e s e n t e d in r e f s . 1-3. Below we p r e s e n t s o m e r e s u l t s of studying the light intensity dependence of the p h o t o m a g n e t i c E M F on s a m p l e s with e l e c t r o n c o n c e n t r a t i o n s 5 × 1015 - 1017 c m - 3 . The m e a s u r e m e n t s w e r e c a r r i e d out in the t e m p e r a t u r e ra ng e 1.8 -4.2OK in m a g n e t i c f i e l d s up to 2? kOe. I n v e s t i g a t i o n s led to unexpected r e s u l t s . It a p p e a r e d that in the m a g n e t i c f i e l d s w h e r e the p h o t o m a g n e t i c effect has the i n v e r s e sign, t h e r e is an unusual d e p e n d e n c e of the p h o to m a g n e ti c E M F on the light intensity. R e s u l t s of e x p e r i m e n t s a r e p r e s e n t e d in fig. 1. The c u r v e 1 is obtained at a m a g n e t i c field at which the sign of p h o t o m a g n e t i c effect is n o r m a l . In this c a s e the dependence of the p h o to m a g n e ti c E M F on the i l l u m i n a t i o n intensity is n o r m a l . The c u r v e s 2, 3 and 4 a r e obtained f o r m a g n e t i c f i e l d s at which the sign of the p h o t o m a g n e t i c effect is r e v e r s e d . In this c a s e the p h o t o m a g n e t i c E M F i n c r e a s e s in absolute v al u e with light in te n s i ty f o r v e r y s m a l l i n t e n s i t i e s only. With an i n c r e a s e in the light in 282
t en si t y the p h o t o m ag n et i c E M F r e a c h e s a m a x i m u m , p a s s e s through z e r o and changes sign. C o m p a r i s o n of the c u r v e s 2, 3, 4 showed that the light intensity at which the p h o t o m a g n e t i c e f V~n~
t.-"4
m~
3O
0 -80
Fig. 1. Photomagnetic EMF dependence on the lighl intensity I for an n-InSb sample. The curves show different magnetic fields the value of which can be obtained from the figure of the right-hand angle.
Volume 30A, number 5
PHYSICS L E T T E R S
fect changes its sign (and thus goes into the n o r m a l region) e s s e n t i a l l y depends upon the value of the magnetic field. The c u r v e s c o r r e s p o n d to different m a g n e t i c fields (the points 2, 3 and 4 on the c u r v e of the photomagnetic effect dependence on the magnetic field H). Thus at higher light i n t e n s i t i e s one may obtain a field dependence of the photomagnetic EMF which s t i l l r e m a i n s o s c i l l a t i n g but the photomagnetic EMF is completely in the n o r m a l region (with magnetic fields which a r e e x p e r i m e n t a l l y available). Additional e x p e r i m e n t s showed that the p h e n o m e n a o b s e r v e d a r e not due to the heating of the sample. P a r t i c u l a r l y , the e x p e r i m e n t s have shown that t h e r e is no change in the sign of the photomagnetic EMF with light i n t e n s i t y on p o l ished s a m p l e s in the s a m e magnetic fields. By polishing, of c o u r s e , the t e m p e r a t u r e conditions of the e x p e r i m e n t do not change, but the diffusion c u r r e n t of c a r r i e r s f r o m i l l u m i n a t e d to n o n - i l l u m i n a t e d s u r f a c e of the s a m p l e c o n s i d e r ably d e c r e a s e s . The change of sign of the photomagnetic effect u n d e r these conditions will o c c u r p r o b a b l y at
3 November 1969
higher i n t e n s i t i e s of the incident light. It is not easy to give an unambiguous i n t e r p r e t a t i o n of the above r e s u l t s b e c a u s e the n a t u r e of the pel'iodic change in sign of the photomagnetic effect at l a r g e magnetic field (i.e., the exi s t e n c e of the ' a n o m a l o u s ' region in the photom a g n e t i c effect) is not yet c l e a r . In this connection it should be noted that the r e s u l t s of s p e c t r a l i n v e s t i g a t i o n s [4] w h e r e the change of the sign of the photomagnetic effect was o b s e r v e d , can get quite a different e x p l a n a tion.
Reference s 1. I. K. Kikoin and S. D. Lazarev, JETP Letters 3 (1966) 434. 2. I.K. Kikoin and S. D. Lazarev, JETP Letters 5 (1967) 393. 3. R. V. Parfenyev, I.I. Farbstein and S. S. Shalyt, Zh, Eksp. i Teor. Fig. 53 (1967) 1571. 4. Yu. A. Bykovsky, V. F. Yelesin, V.I. Kadushkin, S. D. Lazarev, E.A. Protasov and G. A. Shepelsky, JETP Letters 7 (1968) 202.
SPONTANEOUS COHERENCE EMITTED BY D I C K E ' S
OF RADIATION SYSTEM
Z. AWIE RIANOW Institute of Physics, The Warsaw Technical University, Warsaw. Poland
Received 27 September 1969
In this paper coherence properties of the spontaneous radiation emitted by a two-level energetic system in a super-radiant state are studied.
The e l e c t r o m a g n e t i c field emitted spontaneously by the s y s t e m can be calculated by applying the s a m e f o r m a l i s m [1]. The l i n e a r d i m e n s i o n s of the s y s t e m of m o l e c u l e s c o n s i d e r e d here a r e a s s u m e d s m a l l e r than the emitted wavelength. Omitting the static i n t e r a c t i o n s between the m o l e c u l e s , and t h e i r c o l l i s i o n s , and a s s u m i n g that e v e r y molecule p o s s e s s e s only two n o n - d e g e n e r a t e e n e r g e t i c l e v e l s , one can put the total H a m i l t o n i a n for N m o l e c u l e s i n t e r a c t i n g with the radiation field in the f o r m
: ~k3 + ½~(~2~ ~2~2) -A(ot)(el ~I+ e2~}2) p v P
(I)
w h e r e e l , e 2 a r e constant r e a l v e c t o r s , the s a m e for all the m o l e c u l e s ; /}1, /}2, R3 a r e components of the total e n e r g e t i c spin of the s y s t e m ; and ~ v , /~v a r e t h e canonical v a r i a b l e s of the vth mode of e l e c t r o m a g n e t i c field. The o p e r a t o r s R1, R2, R3 and Qv, P v satisfy the well-known c o m m u t a t i o n r e l a t i o n s [1,2]. * Present address: Department of Physics. The Szezecin Technical University, Szczecin, Poland. 283
PHYSICS LETTERS
m o d e l calculation is p r o v i d e d by a c o m p a r i s o n with the changes of F e r m i s u r f a c e a r e a s o b s e r v e d f r o m dHvA m e a s u r e m e n t s in a l u m i n u m unde r h y d r o s t a t i c p r e s s u r e [6]. T h e m o d e l p r e dic ts that 1/A (dA/dP) f o r the/3 and 7 c r o s s s e c t i o n s a r e 1.35 and - 0 . 4 3 % / k b a r r e s p e c t i v e l y , c o m p a r e d with the v a l u e s 1.2 + 0.15 and -0.47 + 0.06%/kbar o b s e r v e d e x p e r i m e n t a l l y .
3November 1969
References 1. K.C. Kepler and J. A. Rayne, Phys. Letters 28A (1968) 163. 2. A.B. Pippard, Phil. Mag. 46 (1955) 1104. 3. A.B. Pippard, Proc. Roy. Soc. A257 (1960) 165. 4. W.A. Harrison, Pseudopotentials in the theory of metals (W. A. Benjamin, Inc., New York, 1966}. 5. N.W. Ashcroft, Phil. Mag. 96 (1963) 2055. 6. P.J. Melz, Phys. Rev. 152 (1966) 540.
T h i s work was supported by a g r a n t f r o m the National S c i e n c e Foundation.
ON T H E
NONLINEAR
DEPENDENCE ON T H E L I G H T
OF PHOTOMAGNETIC INTENSITY
EFFECTS
I. K. KIKOIN, S.D. LAZAREV, G . A . SHEPELSKY and G. D. YEFREMOVA
lturchatov Institute. Moscow, USSR Received 19 August 1969
The light intensity dependence of the photomagnetic effects in the quantum region is studied experimentally (in degenerated InSb and InAs samples in magnetic fields up to 2? kOe at 1.8-4.2OK). It is shown that this dependence in the magnetic field region where the photomagnetic effect has the anomalous sign, is nonlinear, and at some light intensity the photomagnetic electromotive force changes its sign.
E x p e r i m e n t a l data on quantum o s c i l l a t i o n s of the p h o t o m ag n et i c E M F in a m a g n e t i c field f o r n - t y p e InSb and InAs s a m p l e s a r e p r e s e n t e d in r e f s . 1-3. Below we p r e s e n t s o m e r e s u l t s of studying the light intensity dependence of the p h o t o m a g n e t i c E M F on s a m p l e s with e l e c t r o n c o n c e n t r a t i o n s 5 × 1015 - 1017 c m - 3 . The m e a s u r e m e n t s w e r e c a r r i e d out in the t e m p e r a t u r e ra ng e 1.8 -4.2OK in m a g n e t i c f i e l d s up to 2? kOe. I n v e s t i g a t i o n s led to unexpected r e s u l t s . It a p p e a r e d that in the m a g n e t i c f i e l d s w h e r e the p h o t o m a g n e t i c effect has the i n v e r s e sign, t h e r e is an unusual d e p e n d e n c e of the p h o to m a g n e ti c E M F on the light intensity. R e s u l t s of e x p e r i m e n t s a r e p r e s e n t e d in fig. 1. The c u r v e 1 is obtained at a m a g n e t i c field at which the sign of p h o t o m a g n e t i c effect is n o r m a l . In this c a s e the dependence of the p h o to m a g n e ti c E M F on the i l l u m i n a t i o n intensity is n o r m a l . The c u r v e s 2, 3 and 4 a r e obtained f o r m a g n e t i c f i e l d s at which the sign of the p h o t o m a g n e t i c effect is r e v e r s e d . In this c a s e the p h o t o m a g n e t i c E M F i n c r e a s e s in absolute v al u e with light in te n s i ty f o r v e r y s m a l l i n t e n s i t i e s only. With an i n c r e a s e in the light in 282
t en si t y the p h o t o m ag n et i c E M F r e a c h e s a m a x i m u m , p a s s e s through z e r o and changes sign. C o m p a r i s o n of the c u r v e s 2, 3, 4 showed that the light intensity at which the p h o t o m a g n e t i c e f V~n~
t.-"4
m~
3O
0 -80
Fig. 1. Photomagnetic EMF dependence on the lighl intensity I for an n-InSb sample. The curves show different magnetic fields the value of which can be obtained from the figure of the right-hand angle.
Volume 30A, number 5
PHYSICS L E T T E R S
fect changes its sign (and thus goes into the n o r m a l region) e s s e n t i a l l y depends upon the value of the magnetic field. The c u r v e s c o r r e s p o n d to different m a g n e t i c fields (the points 2, 3 and 4 on the c u r v e of the photomagnetic effect dependence on the magnetic field H). Thus at higher light i n t e n s i t i e s one may obtain a field dependence of the photomagnetic EMF which s t i l l r e m a i n s o s c i l l a t i n g but the photomagnetic EMF is completely in the n o r m a l region (with magnetic fields which a r e e x p e r i m e n t a l l y available). Additional e x p e r i m e n t s showed that the p h e n o m e n a o b s e r v e d a r e not due to the heating of the sample. P a r t i c u l a r l y , the e x p e r i m e n t s have shown that t h e r e is no change in the sign of the photomagnetic EMF with light i n t e n s i t y on p o l ished s a m p l e s in the s a m e magnetic fields. By polishing, of c o u r s e , the t e m p e r a t u r e conditions of the e x p e r i m e n t do not change, but the diffusion c u r r e n t of c a r r i e r s f r o m i l l u m i n a t e d to n o n - i l l u m i n a t e d s u r f a c e of the s a m p l e c o n s i d e r ably d e c r e a s e s . The change of sign of the photomagnetic effect u n d e r these conditions will o c c u r p r o b a b l y at
3 November 1969
higher i n t e n s i t i e s of the incident light. It is not easy to give an unambiguous i n t e r p r e t a t i o n of the above r e s u l t s b e c a u s e the n a t u r e of the pel'iodic change in sign of the photomagnetic effect at l a r g e magnetic field (i.e., the exi s t e n c e of the ' a n o m a l o u s ' region in the photom a g n e t i c effect) is not yet c l e a r . In this connection it should be noted that the r e s u l t s of s p e c t r a l i n v e s t i g a t i o n s [4] w h e r e the change of the sign of the photomagnetic effect was o b s e r v e d , can get quite a different e x p l a n a tion.
Reference s 1. I. K. Kikoin and S. D. Lazarev, JETP Letters 3 (1966) 434. 2. I.K. Kikoin and S. D. Lazarev, JETP Letters 5 (1967) 393. 3. R. V. Parfenyev, I.I. Farbstein and S. S. Shalyt, Zh, Eksp. i Teor. Fig. 53 (1967) 1571. 4. Yu. A. Bykovsky, V. F. Yelesin, V.I. Kadushkin, S. D. Lazarev, E.A. Protasov and G. A. Shepelsky, JETP Letters 7 (1968) 202.
SPONTANEOUS COHERENCE EMITTED BY D I C K E ' S
OF RADIATION SYSTEM
Z. AWIE RIANOW Institute of Physics, The Warsaw Technical University, Warsaw. Poland
Received 27 September 1969
In this paper coherence properties of the spontaneous radiation emitted by a two-level energetic system in a super-radiant state are studied.
The e l e c t r o m a g n e t i c field emitted spontaneously by the s y s t e m can be calculated by applying the s a m e f o r m a l i s m [1]. The l i n e a r d i m e n s i o n s of the s y s t e m of m o l e c u l e s c o n s i d e r e d here a r e a s s u m e d s m a l l e r than the emitted wavelength. Omitting the static i n t e r a c t i o n s between the m o l e c u l e s , and t h e i r c o l l i s i o n s , and a s s u m i n g that e v e r y molecule p o s s e s s e s only two n o n - d e g e n e r a t e e n e r g e t i c l e v e l s , one can put the total H a m i l t o n i a n for N m o l e c u l e s i n t e r a c t i n g with the radiation field in the f o r m
: ~k3 + ½~(~2~ ~2~2) -A(ot)(el ~I+ e2~}2) p v P
(I)
w h e r e e l , e 2 a r e constant r e a l v e c t o r s , the s a m e for all the m o l e c u l e s ; /}1, /}2, R3 a r e components of the total e n e r g e t i c spin of the s y s t e m ; and ~ v , /~v a r e t h e canonical v a r i a b l e s of the vth mode of e l e c t r o m a g n e t i c field. The o p e r a t o r s R1, R2, R3 and Qv, P v satisfy the well-known c o m m u t a t i o n r e l a t i o n s [1,2]. * Present address: Department of Physics. The Szezecin Technical University, Szczecin, Poland. 283