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Magnetic-field-induced narrowing of far-infrared magneto-optical absorption of neutral donors in GaAs
~ ) Pergamon
Solid State Communications, Vol. 93, No. 5, pp. 363-366, 1995 Elsevier Science Ltd Printed in Great Britain 0038-1098/95 $.9.50+.00 0038-1098(94)00799-3
MAGNETIC-FIELD-INDUCED NARROWING OF FAR-INFRARED MAGNETO-OPTICAL ABSORPTION OF NEUTRAL DONORS IN GaAs Hiromi Kobori, Masutaka Inoue and Tyuzi Ohyama Department of Physics, Faculty of Science, Osaka University Machikaneyama 1-16, Toyonaka, Osaka 560, Japan
We have studied the magnetic-field-induced narrowing of far-infrared (FIR) magneto optical absorption line for ls-2p. 1 transition of hydrogenic shallow donors in n-GaAs, of which line-width is dominated by the concentration broadening. The concentration range of donor is 1.5 × 10~cm 3 to 6.0 × 1016cm3, which extends over the concentration for occurrence of metal-insulator transition (Mott transition), i.e., 1.6 × 1016cm3. The linewidth narrowing due to magnetic field is considered to arise from the strong shrinkage of 2p. 1 state. Keywords: SEMICONDUCTORS, EPITAXY, IMPURITIES IN SEMICONDUCTORS
method based on the assumption that the donors are arranged in a regular close-packed lattice. Newman [4] (1956) has studied the concentration effects on the line-spectra of holes bound to acceptors in Si. He found that above 1016cm3 the spectral lines begin to broaden and the line structure has been completely destroyed at 101Bern3. Romero et al. [5] (1990) has made the magnetotransport and far-infrared spectroscopy experiments in GaAs in the vicinity of MetalInsulator Transition (MIT). They observed ls-2p transitions even above the critical concentration of MIT. In this paper, we have studied the magnetic field effect on the concentration broadening for ls-2p +1transition in n-GaAs with various doping levels. The concentration range of donors is from 1.5 × 10~5cm3 to 6.0 × 1016cm"3, which covers the critical concentration for MIT.
1. INTRODUCTION There has been a principal interest in both the experimental and theoretical studies of shallow impurities in semiconductors. The line-broadening of the photoabsorption spectra, due to Stark effect, phonons and/or overlap of wavefunctions between shallow impurities, have been also paid attention. In addition, the energy levels of shallow impurities have been intensively investigated in the absence or the finite of the magnetic field. The Stark broadening, which originates in a inhomogeneous electric field by surrounding ionized impurities, is a primary factor of the line-broadening for highly compensated semiconductors at low temperatures (Ohyama [1] (1980)). The phonon broadening comes to dominate the line-width for weakly doped semiconductors at moderately high temperatures (Navarro et al. [2] (1987)). The broadening caused by the overlap of wavefunction between the neighboring impurities is called the concentration broadening. Baltensperger [3] (1953) has calculated Is, 2s and 2p level broadening of hydrogenic shallow donor as a function of the distance between the interacting donors in the absence of the magnetic field, using the Wigner-Sei~
2. EXPERIMENTAL
PROCEDURES
Five n-type GaAs samples are employed with different doping levels. The concentrations of donors and acceptors and the growth methods for these samples are shown in Table I. The thickness of the epitaxially grown layer on
Table I Sample
Type
Nd (1015cm3)
Na (1015cm3)
Compensation Ratio
Growth Method
A B
n n
1.5 2.3
1.0 0.3
C
n
4.8
0.8
D E
n n
14 60
Nd>>N a Nd>>N a
0.67 0.13 0.17 ~0 -0
LPE MBE MBE MBE MBE
363
364
MAGNETIC-FIELD-INDUCED NARROWING
semi-insulating substrates is about 5 ttm. As the far-infrared light source, we employed a discharge type ( H20 and D20 ) FIR pulse laser, which generates the lights with the wavelengths of 220 and 119/.t m for I42O, and 172 and 84It m for D20. The repetition rate of the FIR laser is 30Hz. The xenon flash lamp was used for a intrinsic photoexcitation and was synchronized with the FIR laser at 15Hz. The pulse width of the xenon flash lamp is about 1 It s and a temperature rise of sample is less than 0.5K at 4.2K. The signal was detected by Sb doped Ge and Putley type n-InSb detectors. The magnetic field was applied up to 10T in Faraday configuration. The absorption spectra were obtained by use of a two channel boxcar integrator with 0.5 Its aperture. The change in the absorption coefficient, A ~t, between resonant and non-resonant conditions is obtained by
101
•
•
"''''1
•
"
"''''1
n-GaAs
[] O
1s-2p+l
<>
A
.-.
[] <>
10o
r" O 220~m o zx
$
1721tm zx 9 119~rn [] <> 84p.m
•._! --- 1 0 -1
4.2K Illuminated
10-2
d.A a=ln (IJI,) where d is the sample thickness, and I, and I= are the intensities of the transmitted FIR laser beams under the resonant and non-resonant conditions.
"
Vol. 93, No. 5
....... '
1015
Donor
........ '
1016
........
Concentration
' 1017
(cm-3)
Fig. 2 The dependence on the donor concentration of the line-width for ls-2p,~ transition in GaAs at 4.2K.
3. EXPERIMENTAL RESULTS Figure 1 shows the absorption spectra for ls-2p,~ transition for hydrogenic shallow donors in n-GaAs with various doping levels. The absorption spectra with the wavelength of 119itm were obtained for the delay-time of -50/z s after the intrinsic photoexcitation of a xenon flash lamp at 4.2K. We confirmed that the donor-acceptor recombination lifetime is more than 1ms for all employed GaAs samples after the photoexcitation. The shallow donors were almost completely neutralized by illuminating the samples by a xenon flash lamp to eliminate the Stark broadening. In addition, we confirmed from the experimental results on the temperature dependence that the phonon effect did not influence the line-widths at 4.2K cO i-
T=4.2K
GaAs
" ~
~.=119~.m Nd=
for all employed samples. We neglect the effect of acceptors because all employed samples are n-types and the effective Bohr radius of acceptor is -5 times less than that of donor in GaAs. Accordingly, the line-broadening is dominated by increasing of the donor concentration. The peak shift to higher magnetic field is also observed with the increment of the donor concentration. Figure 2 shows the dependence on the donor concentration of the linewidth of ls-2p+~ transition. The line-widths are seen to be proportional to NDx(X : 1.2-1.3, ND: donor concentration) except that of sample GaAs-E. The magnetic field dependence of the absorption spectra is shown in Fig. 3 for sample GaAs-B at 4.2K for
09 t-
GaAs-B T=4.2K
. m
J5
Nd= 2.3xl 01~cm3
g
Illuminated
L
v
016
?:
c
xl ~ / k.~_
C
4.8xl 0
.
TM
4~m
c 0 O_ 0 o9 ..0
~2.3xl
0 TM }..
<
1.5x10 is
O o9
< (
I
0
I
I
I
I
6.0 8.0 2.0 4.0 Magnetic Field ( T )
Fig. 1 The absorption spectra for ls-2p, 1 transition in various n-GaAs samples at 4.2K for the wavelength of 119 Itm.
0
I
I
2.0
I
I
4.0
Magnetic
I
1
I
6.0 Field
I
8.0 (T)
Fig. 3 The absorption spectra for ls-2p, 1 transition in sample GaAs-B at 4.2K for the wavelengths of 220, 172, 119 and 84 It m.
101
365
MAGNETIC-FIELD-INDUCED NARROWING
Vol. 93, No. 5 ,
......
•
•
•
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••=|
,5
"
"
'
1
'
'
'
1
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'
=
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n-GaAs
-----
[]
t-
,, o
$ _J
E
C,
D
1
"
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'
"
v
2.0 "o n"
[]
.m
•-
v O
10o
'
ls_2p+ 1
O
I--
'
Kohn-LuRinger ~ p e
n't
v
O
'
[]
z~ o
1.5
[]
C
o
z~
B
o >
o
A
z~
1 0 -1 0
1.0
4.2K Illuminated •
=
•
•1||
1 0 -2
•
1
.
.
•
.
. . , l
10
0.0
Magnetic Field (T) Fig. 4 The dependence on the magnetic field of the line-width for ls-2p,l transition in GaAs at 4.2K.
various FIR wavelengths. The narrowing of the linewidth is observed with increasing magnetic field. We show in Fig. 4 the dependence on the magnetic field of the line-width for ls-2p, 1 transition. The line-widths are seen to vary as BY(Y : -0.64--0.73, B : magnetic field) except that of sample GaAs-E.
=
0.5
.
=
I
=
=
=
0.2
I
=
,
0.4
,
I
=
.
.
0.6
I
,
=
=
0.8
1.0
Fig. 5 The dependence on the magnetic field strength 7 of the effective Bohr radii of ls and 2p, 1states in the unit of that of l s state in the absence of magnetic field.
~bls~ (p, z) = C is exp [- ( p 2/av12s + z 2 / ap 12s) 1 / 2 ] and KL ~b2p+1 (p, Z) = C2p+1 e iq~p x exp [ - ( p 2/av ~+1 + z 2 / ap ~p+l ) 1 / 2 ],
4. DISCUSSIONS In this section, we will qualitatively discuss the dependence of the line-width of the absorption spectrum for ls-2p,1 transition on the concentration and the magnetic field. Baltensperger [3] (1953) has calculated the extent of the ls, 2s and 2p bands of hydrogenie shallow donor in the absence of the magnetic field, using the Wigner-Seitz method for donors arranged in a regular close-packed lattice. The calculation shows that the hydrogenic Is and 2p states begin to broaden at r~=(3/4 zcNn)V3/%" = -6, and -12, respectively, where N D is the donor concentration and a s' the effective Bohr radius for donors. If as" for GaAs is taken as 99A, the concentration broadening for l s and 2p states starts from the concentration of 1.1x10 ~5 and 1.4x10 14c r n 3, respectively. Accordingly, the broadening for ls-2p, 1 optical transition is considered to be dominated by that of 2p,1 state. Since the concentrations of GaAs samples employed in this experiment are Nn=l.5xl0 15-..6.0x10 16an",3 and the Stark as well as phonon broadening is ineffectual in our experimental situations, the line-widths are thought to be dominated by the concentration broadening for 2P,1 state. Next we consider the magnetic field effect on the hydrogenic donor. When ~"=$icod'2Ry" (o~¢: cyclotron frequency, Ry': effective Rydberg energy of a hydrogenic impurity) is less than 1, the Kohn-Luttinger type (hydrogen type ) [6] wavefunctions give the approximately good variational functions for l s and 2p,1 states. When the magnetic field is applied along z-axis, the wavefunctions for ls and 2p, 1 states are given as
where /92 = x2 + y2, C1* and C~1 are the normalization factors, av and ap are the Bohr radii for the directions vertical and parallel to the magnetic field, respectively. Using the Kohn-Luttinger type wavefunctions, we carried out the variational calculations and obtained the 7 dependence of the effective Bohr radii for l s and 2p.1 states and show in Fig,5. As for our experiments, T ranges from 0.14 to 0.92. As seen in Fig.5, the effective Bohr radii of 2p,1 state are strongly affected by the magnetic field. At 9"=0.92, the effective Bohr radii of 2p,1 state shrink about up to the half of that in the absent of magnetic field. On the other hand, those of ls state have weak dependence on the magnetic field compared with 2p. 1state. Consequently, the narrowing of the line-width induced by the magnetic field is considered mainly to arise from the strong shrinkage of 2p.~ state for our experiments.
5. CONCLUSIONS Both the donor concentration and the magnetic field dependence for the absorption spectrum of 1s-2p.l transition of hydrogenic shallow donors have been studied for the concentration broadening through the FIR magnetoabsorption measurements. The magnetic-field-induced narrowing of the line-width was observed and explained qualitatively. The narrowing due to the magnetic field is considered to come from the strong shrinkage of 2p, 1state.
366
MAGNETIC-FIELD-INDUCED NARROWING
Vol. 93, No. 5
6. REFERENCES
1. T. Ohyama, Phys. Star. Solidi A98,373 (1980), 2. H. Navarro, E. E. Hailer and F. K¢ilmann Phys. Rev. B37, 10822 (1987) 3. W. Baltensperger, Pldl. Mag. 44, 1355 (1953),
4. R. Newman, Phys. Rev. 103 103 (1956), 5. D. Romero, S. Liu, H. D. Drew and K. Ploog, Phys. Rev. B42 3179 (1990) 6. W. Kohn and J. M. Luttinger, Phys. Rev. 98 915 (1955)
Solid State Communications, Vol. 93, No. 5, pp. 363-366, 1995 Elsevier Science Ltd Printed in Great Britain 0038-1098/95 $.9.50+.00 0038-1098(94)00799-3
MAGNETIC-FIELD-INDUCED NARROWING OF FAR-INFRARED MAGNETO-OPTICAL ABSORPTION OF NEUTRAL DONORS IN GaAs Hiromi Kobori, Masutaka Inoue and Tyuzi Ohyama Department of Physics, Faculty of Science, Osaka University Machikaneyama 1-16, Toyonaka, Osaka 560, Japan
We have studied the magnetic-field-induced narrowing of far-infrared (FIR) magneto optical absorption line for ls-2p. 1 transition of hydrogenic shallow donors in n-GaAs, of which line-width is dominated by the concentration broadening. The concentration range of donor is 1.5 × 10~cm 3 to 6.0 × 1016cm3, which extends over the concentration for occurrence of metal-insulator transition (Mott transition), i.e., 1.6 × 1016cm3. The linewidth narrowing due to magnetic field is considered to arise from the strong shrinkage of 2p. 1 state. Keywords: SEMICONDUCTORS, EPITAXY, IMPURITIES IN SEMICONDUCTORS
method based on the assumption that the donors are arranged in a regular close-packed lattice. Newman [4] (1956) has studied the concentration effects on the line-spectra of holes bound to acceptors in Si. He found that above 1016cm3 the spectral lines begin to broaden and the line structure has been completely destroyed at 101Bern3. Romero et al. [5] (1990) has made the magnetotransport and far-infrared spectroscopy experiments in GaAs in the vicinity of MetalInsulator Transition (MIT). They observed ls-2p transitions even above the critical concentration of MIT. In this paper, we have studied the magnetic field effect on the concentration broadening for ls-2p +1transition in n-GaAs with various doping levels. The concentration range of donors is from 1.5 × 10~5cm3 to 6.0 × 1016cm"3, which covers the critical concentration for MIT.
1. INTRODUCTION There has been a principal interest in both the experimental and theoretical studies of shallow impurities in semiconductors. The line-broadening of the photoabsorption spectra, due to Stark effect, phonons and/or overlap of wavefunctions between shallow impurities, have been also paid attention. In addition, the energy levels of shallow impurities have been intensively investigated in the absence or the finite of the magnetic field. The Stark broadening, which originates in a inhomogeneous electric field by surrounding ionized impurities, is a primary factor of the line-broadening for highly compensated semiconductors at low temperatures (Ohyama [1] (1980)). The phonon broadening comes to dominate the line-width for weakly doped semiconductors at moderately high temperatures (Navarro et al. [2] (1987)). The broadening caused by the overlap of wavefunction between the neighboring impurities is called the concentration broadening. Baltensperger [3] (1953) has calculated Is, 2s and 2p level broadening of hydrogenic shallow donor as a function of the distance between the interacting donors in the absence of the magnetic field, using the Wigner-Sei~
2. EXPERIMENTAL
PROCEDURES
Five n-type GaAs samples are employed with different doping levels. The concentrations of donors and acceptors and the growth methods for these samples are shown in Table I. The thickness of the epitaxially grown layer on
Table I Sample
Type
Nd (1015cm3)
Na (1015cm3)
Compensation Ratio
Growth Method
A B
n n
1.5 2.3
1.0 0.3
C
n
4.8
0.8
D E
n n
14 60
Nd>>N a Nd>>N a
0.67 0.13 0.17 ~0 -0
LPE MBE MBE MBE MBE
363
364
MAGNETIC-FIELD-INDUCED NARROWING
semi-insulating substrates is about 5 ttm. As the far-infrared light source, we employed a discharge type ( H20 and D20 ) FIR pulse laser, which generates the lights with the wavelengths of 220 and 119/.t m for I42O, and 172 and 84It m for D20. The repetition rate of the FIR laser is 30Hz. The xenon flash lamp was used for a intrinsic photoexcitation and was synchronized with the FIR laser at 15Hz. The pulse width of the xenon flash lamp is about 1 It s and a temperature rise of sample is less than 0.5K at 4.2K. The signal was detected by Sb doped Ge and Putley type n-InSb detectors. The magnetic field was applied up to 10T in Faraday configuration. The absorption spectra were obtained by use of a two channel boxcar integrator with 0.5 Its aperture. The change in the absorption coefficient, A ~t, between resonant and non-resonant conditions is obtained by
101
•
•
"''''1
•
"
"''''1
n-GaAs
[] O
1s-2p+l
<>
A
.-.
[] <>
10o
r" O 220~m o zx
$
1721tm zx 9 119~rn [] <> 84p.m
•._! --- 1 0 -1
4.2K Illuminated
10-2
d.A a=ln (IJI,) where d is the sample thickness, and I, and I= are the intensities of the transmitted FIR laser beams under the resonant and non-resonant conditions.
"
Vol. 93, No. 5
....... '
1015
Donor
........ '
1016
........
Concentration
' 1017
(cm-3)
Fig. 2 The dependence on the donor concentration of the line-width for ls-2p,~ transition in GaAs at 4.2K.
3. EXPERIMENTAL RESULTS Figure 1 shows the absorption spectra for ls-2p,~ transition for hydrogenic shallow donors in n-GaAs with various doping levels. The absorption spectra with the wavelength of 119itm were obtained for the delay-time of -50/z s after the intrinsic photoexcitation of a xenon flash lamp at 4.2K. We confirmed that the donor-acceptor recombination lifetime is more than 1ms for all employed GaAs samples after the photoexcitation. The shallow donors were almost completely neutralized by illuminating the samples by a xenon flash lamp to eliminate the Stark broadening. In addition, we confirmed from the experimental results on the temperature dependence that the phonon effect did not influence the line-widths at 4.2K cO i-
T=4.2K
GaAs
" ~
~.=119~.m Nd=
for all employed samples. We neglect the effect of acceptors because all employed samples are n-types and the effective Bohr radius of acceptor is -5 times less than that of donor in GaAs. Accordingly, the line-broadening is dominated by increasing of the donor concentration. The peak shift to higher magnetic field is also observed with the increment of the donor concentration. Figure 2 shows the dependence on the donor concentration of the linewidth of ls-2p+~ transition. The line-widths are seen to be proportional to NDx(X : 1.2-1.3, ND: donor concentration) except that of sample GaAs-E. The magnetic field dependence of the absorption spectra is shown in Fig. 3 for sample GaAs-B at 4.2K for
09 t-
GaAs-B T=4.2K
. m
J5
Nd= 2.3xl 01~cm3
g
Illuminated
L
v
016
?:
c
xl ~ / k.~_
C
4.8xl 0
.
TM
4~m
c 0 O_ 0 o9 ..0
~2.3xl
0 TM }..
<
1.5x10 is
O o9
< (
I
0
I
I
I
I
6.0 8.0 2.0 4.0 Magnetic Field ( T )
Fig. 1 The absorption spectra for ls-2p, 1 transition in various n-GaAs samples at 4.2K for the wavelength of 119 Itm.
0
I
I
2.0
I
I
4.0
Magnetic
I
1
I
6.0 Field
I
8.0 (T)
Fig. 3 The absorption spectra for ls-2p, 1 transition in sample GaAs-B at 4.2K for the wavelengths of 220, 172, 119 and 84 It m.
101
365
MAGNETIC-FIELD-INDUCED NARROWING
Vol. 93, No. 5 ,
......
•
•
•
•
•
••=|
,5
"
"
'
1
'
'
'
1
'
'
=
|
n-GaAs
-----
[]
t-
,, o
$ _J
E
C,
D
1
"
'
'
'
"
v
2.0 "o n"
[]
.m
•-
v O
10o
'
ls_2p+ 1
O
I--
'
Kohn-LuRinger ~ p e
n't
v
O
'
[]
z~ o
1.5
[]
C
o
z~
B
o >
o
A
z~
1 0 -1 0
1.0
4.2K Illuminated •
=
•
•1||
1 0 -2
•
1
.
.
•
.
. . , l
10
0.0
Magnetic Field (T) Fig. 4 The dependence on the magnetic field of the line-width for ls-2p,l transition in GaAs at 4.2K.
various FIR wavelengths. The narrowing of the linewidth is observed with increasing magnetic field. We show in Fig. 4 the dependence on the magnetic field of the line-width for ls-2p, 1 transition. The line-widths are seen to vary as BY(Y : -0.64--0.73, B : magnetic field) except that of sample GaAs-E.
=
0.5
.
=
I
=
=
=
0.2
I
=
,
0.4
,
I
=
.
.
0.6
I
,
=
=
0.8
1.0
Fig. 5 The dependence on the magnetic field strength 7 of the effective Bohr radii of ls and 2p, 1states in the unit of that of l s state in the absence of magnetic field.
~bls~ (p, z) = C is exp [- ( p 2/av12s + z 2 / ap 12s) 1 / 2 ] and KL ~b2p+1 (p, Z) = C2p+1 e iq~p x exp [ - ( p 2/av ~+1 + z 2 / ap ~p+l ) 1 / 2 ],
4. DISCUSSIONS In this section, we will qualitatively discuss the dependence of the line-width of the absorption spectrum for ls-2p,1 transition on the concentration and the magnetic field. Baltensperger [3] (1953) has calculated the extent of the ls, 2s and 2p bands of hydrogenie shallow donor in the absence of the magnetic field, using the Wigner-Seitz method for donors arranged in a regular close-packed lattice. The calculation shows that the hydrogenic Is and 2p states begin to broaden at r~=(3/4 zcNn)V3/%" = -6, and -12, respectively, where N D is the donor concentration and a s' the effective Bohr radius for donors. If as" for GaAs is taken as 99A, the concentration broadening for l s and 2p states starts from the concentration of 1.1x10 ~5 and 1.4x10 14c r n 3, respectively. Accordingly, the broadening for ls-2p, 1 optical transition is considered to be dominated by that of 2p,1 state. Since the concentrations of GaAs samples employed in this experiment are Nn=l.5xl0 15-..6.0x10 16an",3 and the Stark as well as phonon broadening is ineffectual in our experimental situations, the line-widths are thought to be dominated by the concentration broadening for 2P,1 state. Next we consider the magnetic field effect on the hydrogenic donor. When ~"=$icod'2Ry" (o~¢: cyclotron frequency, Ry': effective Rydberg energy of a hydrogenic impurity) is less than 1, the Kohn-Luttinger type (hydrogen type ) [6] wavefunctions give the approximately good variational functions for l s and 2p,1 states. When the magnetic field is applied along z-axis, the wavefunctions for ls and 2p, 1 states are given as
where /92 = x2 + y2, C1* and C~1 are the normalization factors, av and ap are the Bohr radii for the directions vertical and parallel to the magnetic field, respectively. Using the Kohn-Luttinger type wavefunctions, we carried out the variational calculations and obtained the 7 dependence of the effective Bohr radii for l s and 2p.1 states and show in Fig,5. As for our experiments, T ranges from 0.14 to 0.92. As seen in Fig.5, the effective Bohr radii of 2p,1 state are strongly affected by the magnetic field. At 9"=0.92, the effective Bohr radii of 2p,1 state shrink about up to the half of that in the absent of magnetic field. On the other hand, those of ls state have weak dependence on the magnetic field compared with 2p. 1state. Consequently, the narrowing of the line-width induced by the magnetic field is considered mainly to arise from the strong shrinkage of 2p.~ state for our experiments.
5. CONCLUSIONS Both the donor concentration and the magnetic field dependence for the absorption spectrum of 1s-2p.l transition of hydrogenic shallow donors have been studied for the concentration broadening through the FIR magnetoabsorption measurements. The magnetic-field-induced narrowing of the line-width was observed and explained qualitatively. The narrowing due to the magnetic field is considered to come from the strong shrinkage of 2p, 1state.
366
MAGNETIC-FIELD-INDUCED NARROWING
Vol. 93, No. 5
6. REFERENCES
1. T. Ohyama, Phys. Star. Solidi A98,373 (1980), 2. H. Navarro, E. E. Hailer and F. K¢ilmann Phys. Rev. B37, 10822 (1987) 3. W. Baltensperger, Pldl. Mag. 44, 1355 (1953),
4. R. Newman, Phys. Rev. 103 103 (1956), 5. D. Romero, S. Liu, H. D. Drew and K. Ploog, Phys. Rev. B42 3179 (1990) 6. W. Kohn and J. M. Luttinger, Phys. Rev. 98 915 (1955)