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Cd1−TxMnxTe multiple quantum wells under high magnetic fields
PHYSICA[ Physica B 201 (1994) 415-418
ELSEVIER
Magneto-optical study of CdTe/Cdl - xMnxTe multiple quantum wells under high magnetic fields Shinji Kuroda a'*, Kazutoshi Kojima a, K6ji Kobayashi a, Yutaka Shirai a'l, K6ki Takita a, Kazuhito Uchida b, Noboru Miura b aInstitute of Materials Science, University of Tsukuba, Tsukuba, lbaraki 305, Japan b Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
Abstract
The magneto-optical properties of CdTe/Cdl_xMnxTe multiple quantum wells (MQW's) with high Mn contents of about 30% were studied through absorption measurements at high magnetic fields up to 40 T. Absorption peaks due to the heavy-hole and light-hole related excitons exhibit large Zeeman splitting. The Zeeman splitting energy of the heavy-hole excitons was compared with a variational calculation. Reduced antiferromagnetic coupling of Mn 2 ÷ spins at the M Q W heterointerface and the interdiffusion are discussed as a possible origin of the discrepancy between experiment and theory.
1. Introduction
Semiconductor heterostructures of diluted magnetic semiconductor (DMS) have attracted much attention because of a variety of interesting and novel phenomena 1-1] originating from the spatially modulated s p - d exchange interaction between mobile carriers and localized magnetic moments. CdTe/Cdl_xMn~Te multiple quantum well (MQW) is typical system of this kind, where electrons and holes are confined in the non-magnetic CdTe layer (type I) and are affected by the exchange interaction through the penetration of wavefunction into the Cd~_xMnxTe layers. Magneto-optical properties of this system have been studied extensively through measurements of photoluminescence (PL) [2], PL excitation spectroscopy [3-5] and reflectivity [6].
* Corresponding author. ~Present address: Toshiba Corporation.
In the present work, we performed a study of the magneto-absorption spectroscopy. Though measurement of absorption spectra is a powerful experimental method, especially in pulsed high magnetic fields, there was a experimental difficulty arising from the fundamental absorption of substrate materials with smaller band-gaps, which masks the absorption in the quantum wells. Recently it has become possible to remove GaAs substrates using a selective etching technique I-7, 8]. In a previous paper [8], we reported on absorption measurements in CdTe/Cdl_xMnxTe MQW's with intermediate range of Mn contents (12-14%), and revealed that the quantized level structure at high magnetic fields is influenced significantly by the valence-band mixing effect. This paper reports a study on a series of MQW's with relatively high Mn contents of about 30%. We make quantitative analysis of observed absorption peaks due to heavy-hole related excitons, in comparison with calculations using a variational approach.
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 1 0 2 - 2
416
S. Kuroda et al./Physica B 201 (1994) 415-418
2. Experimental procedures Procedures of sample preparation and magnetooptical measurement are the same as described in Ref. [8]. M Q W samples were grown by the M B E method; a CdTe buffer layer ( ~ 2000 ,~), a Cd~_xMn~Te cladding layer ( ~ 8000 ~), an M Q W structure of alternating CdTe and Cdt_~Mn~Te layers and finally a Cd~_xMn~Te cap layer ( ~ 2000,~) were grown successively on the (100) surface of a GaAs substrate. After the growth, the GaAs substrate was removed by grinding and selective etching using N H 4 O H : H 2 0 2 solution. The widths of the well and barrier layers Lw, LB and M n content x of the cap and cladding layers were determined from the results of the X-ray diffraction and the PL measurement at zero magnetic field. In the absorption measurement, magnetic fields up to 40 T were applied using a non-destructive pulsed magnet. The sample was mounted in the Faraday configuration and absorption spectra for circularly polarized light a ÷ or a were measured. The measurement was done at T = 4.2 K.
a result on sample # 2 with an intermediate well width (Lw = 50/~, LB = 131 /~, x = 0.27) for the cr÷ (open symbols) and a (closed symbols) polarizations. At zero magnetic field, peaks at around 1.67, 1.71 and 1.89 eV are assigned to the absorptions due to heavy-hole exciton of n = 1 subband (E1H1), light-hole exciton of n = 1 subband (ELL0 and heavy-hole exciton of n = 2 subband (E2H2), 1.80
i
1.75 > & o
~
w m ~ m.--m-'~''~" 3 4 / 1 5 5
(
1.70
. . . . . . . . . . . . #2 ~
(50/131)
1.6.=
~
(67/163)'
2'0
•
4'0
a) J
i
E2H2
1.90
3'0
Magnetic Field (T)
1.95
Sample #2 (50/131)
#1
)
[] = o
1.60
1.95
n
0
3. Experimental results Fig. 1 shows a typical example of absorption peak positions plotted against applied magnetic fields. This is
n
EIH1
,
, ..
,
.......
1.90
Ui ig r
> (~02/131 )
q~l]~l~]l~E]r-'nr'n
>
[]
I-I n
e~o
1.85
1.85 •
1.80
............. "-::'-":"-
O q "dmea._ _
0
¢)
#.
1.75
0
.o8
o o •
oo
o
1.70 o , ~ 1 ~ o o ~ = .
_
1.80 '~"~oo..o9 o o o
17
•
1'0
2'0
O
20
(67/163)
s'0
Magnetic Field (T)
.65
;o
20
3'0
4'0
so
b)
Magnetic Field (T) Fig. 1. The magnetic field dependence of absorption peak energies of CdTe/Cd~ xMn~Te MQW of sample #2 (Lw = 50 ~, L B = 131 ~ and x = 0.27) for the tr + (open symbols) and it(closed symbols) polarizations. Circles, triangles and squares represent the E~H1, E~L~ and EzH2 excitons, respectively. Peaks other than these excitons are plotted by diamonds.
Fig. 2. The magnetic field dependence of the (a) EIH~ and (b) E2H2 excitons of samples #1 (Lw=34/~, LB=155~, x = 0.30), # 2 and # 3 (Lw = 67 ,~, Ls = 163/~, x = 0.32) (Lw and L B of the respective samples are shown in the figure as (Lw/LB) under the sample numbers). The solid and broken lines show the calculated exciton energies when valence-band offset ratio Qv is assumed to be 20% and 10%, respectively.
S. Kuroda et al./Physica B 201 (1994) 415-418
respectively (in the figure, they are represented by circles, triangles and squares). With the application of magnetic field, these exciton peaks exhibit large Zeeman splitting; the Zeeman splitting is enhanced by the sp-d exchange interaction with Mn 2+ spins located in the barrier layers through the penetration of wavefunction into the barrier layers, and the lower- (upper-) branch of the split states is observed in the absorption spectra of the a + (a-) polarization. The amount of the splitting becomes larger in the order of the E,L1, E~H~ and E2H2 excitons. This tendency can be understood qualitatively when one estimates the degree of the penetration of the electron and hole wavefunctions on the basis of simple Kronig-Penney model. Absorption peaks observed other than these excitons are represented by diamonds in the figure. Among them, peaks which appear at the higher energy side of the ElL1 peaks above 10 T are interpreted as the absorption due to transitions between higher Landau levels of the conduction and heavy-hole bands. On the other hand, peaks which appear between the E~H~ and E~L~ peaks below 15 T are considered to be the absorption due to the 2s state of the E1H1 exciton. Here we concentrate our attention on the behavior of the heavy-hole exciton under magnetic fields. Fig. 2 shows the magnetic field dependence of the E1H1 (a) and E2H2 (b) exciton energies including those of other samples with various well widths. It is clearly seen that the amount of Zeeman splitting becomes larger for a sample with a narrower well width. This can also be understood easily since the electron and hole wavefunctions penetrate into the barrier layers to a greater degree when the well width becomes narrower with the same barrier height.
4. Discussion
For a quantitative analysis, we made a calculation of exciton energies under magnetic fields by a variational approach, following the procedure in Ref. I-9]. In the calculation, the valence-band mixing effect was neglected. This is considered to be justified since in a CdTe/Cd~_xMnxTe QW with high Mn contents of about 30% the energy separation between heavy- and light-hole subbands is large enough due to a relatively large barrier height and energy splitting caused by strain. Furthermore, we took account of additional confinement of heavy holes along the growth axis due to the Coloumb interaction with electrons confined in the well [6]. Mn 2 ÷ spins in the barrier layers were assumed to behave in a way similar to those in bulk Cd~_xMnxTe; the average alignment of Mn 2 ÷ spins (sz) should be expressed by the sum of a modified Brillouin function and an additional term linear to magnetic fields [10].
417
In Fig. 2, calculated exciton energies are plotted against magnetic field by solid and dotted lines with the valence-band offset ratio Qv as a parameter. The calculated exciton energies at zero field deviate from the observed peak positions by a few meV. When plotting calculated lines in Fig. 2, we added an offset to the exciton energies under magnetic fields in order for the energies at zero field to fit the observed peak positions. When Qv is assumed to be 20%, general features of the calculated lines of the E1HI exciton have tendencies similar to the observed peak positions, such as direction of the energy shift with increasing magnetic field. However the Zeeman splitting energies in the calculation are found to be too small compared to the observation. If Qv is assumed to be 10%, the calculated splitting energies become larger but the exciton energies of the lower branch decrease rapidly above about 20 T due to the type I ~ II transition, which is contrary to the observation. Therefore, we can conclude that the fit is better for Qv = 20 o/o than for 10% in the overall feature. Even in that case, however, there remains a quantitative disagreement between the calculation and the observation. In the calculation, the Zeeman splitting energies continue to increase up to the highest field, reflecting the field dependence of the Mn 2÷ spin alignment (sz) in bulk Cdl-xMnxTe; that is, the contribution of the field-linear term is considerably large in the expression of (sz) in Cdl -xMnxTe with Mn contents as high as 30% [10]. On the other hand, the observed splitting energies increase rapidly at low fields and saturates at about 10 T. A similar discrepancy is found in the field dependence of the E2H2 exciton energies. The observed splitting energies showed a Brillouin-function-like field dependence while the calculated ones behave more linearly. Therefore, quantitative agreement in the whole range of magnetic field cannot be achieved either for Qv = 10% or 20%. Recently Ossau et al. pointed out that an anomalous behavior of Mn 2 + spins located at the heterointerface between the CdTe and Cdl-xMnxTe layers affects the Zeeman splitting of the excitons [11]. According to their suggestion, the probability of the antiferromagnetic coupling in Mn clusters is reduced for Mn 2 + spins at the heterointerface because nearest-neighboring Mn 2+ spins are missing at the side of the CdTe layer. Then the contribution of the Brillouin function term is considered to be larger in (sz) of Mn 2 + spins at the heterointerface than in bulk Cd~ _xMnxTe; that is, (sz) increases rapidly at low magnetic fields and saturates with a further increase of field. The Zeeman splitting of excitons, which is strongly influenced by the exchange interaction with Mn 2+ spins at the heterointerface, is expected to show a Brillouin-function-like field dependence, rather than a linear dependence. Hence, this picture is favorable to
418
S. Kuroda et al./Physica B 201 (1994) 415-418
explain the discrepancy between the calculation and the observation [7]. Another possible origin of the discrepancy is the interdiffusion at the heterointerface. Assuming that the change of Mn concentration along the growth axis is not abrupt at the heterointerface due to the interdiffusion during the growth process, Mn 2 + spins in the interdiffusion layer are expected to play a similar role to that of Mn 2+ spins at the heterointerface in the above picture; that is, the Zeeman splitting is considered to be strongly affected by the alignment of Mn 2 + spins in the interdiffusion layer, which have a more Brillouin-function-like field dependence due to diluted Mn contents.
5. Summary We performed the absorption measurement of CdTe/Cdl_xMnxTe MQW's with relatively high Mn contents of about 30% at high magnetic fields up to 40 T. We observed absorption peaks due to the E1H1, E~L1 and E2Hz excitons, transitions between the conduction and heavy-hole Landau levels and the 2s state of the E1Ha exciton. The observed energies of the ExH1, E~L~ and EzH2 excitons exhibit the large Zeeman splitting. We calculated heavy-hole exciton energies by a variational approach and compared them with the observed peak energies. The calculated Zeeman splitting energies are smaller than the experimental data and increase almost linearly with magnetic field, while the observed splitting energies have Brillouin-function-like dependence on magnetic field. This discrepancy can be explained qualitatively by the influence of Mn 2+ spins located near the QW heterointerface, which are expected to show a Brillouin-function-like magnetization under
magnetic fields due to the reduced antiferromagnetic coupling of Mn 2 + spins at the heterointerface and/or the formation of diluted Mn-content regions near the heterointerface by the interdiffusion.
Acknowledgement This work is supported in part by Iketani Science and Technology Foundation.
References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] A.V. Nurmikko, X.-C. Zhang, S.-K. Chang, L.A. Kolodziejski, R.L. Gunshor and S. Datta, J. Lumin. 34 (1985) 89. I-3] J. Warnock, A. Petrou, R.N. Bicknell,N.C. Giles-Taylor, D.K. Blanks and J.F. Schetzina, Phys. Rev. B 32 (1985) 8116. [4] E. Deleporte, J.M. Berroir, G. Bastard, C. Delalande, J.M. Hong and L.L. Chang, Phys. Rev. B 42 (1990) 5891. [5] M.J. Lawless, R.J. Nicholas, M.J. McNamee, W. Hayes, D.E. Ashenford and B. Lunn, Surf. Sci. 267 (1992) 354. 1-6] E.L. Ivchenko, A.V. Kavokin, V.P. Kochereshko, G.R. Posina, I.N. Uraltsev, D.R. Yakovlev, R.N. Bicknell-Tassius, A. Waag and G. Landwehr, Phys. Rev. B 46 (1992) 7713. [7] H. Akinaga, T. Abe, K. Ando, S. Yoshida, K. Uchida, S. Sasaki and N. Miura. Phys. Rev. B 47 (1993) 15954. 1-8] S. Kuroda, Y. Shirai, K. Kojima, K. Uchida, N. Miura and K. Takita, Jpn. J. Appl. Phys. 32 (1993) Suppl. 32-3 364. [9] K.-S. Lee, Y. Aoyagi and T. Sugano, Phys. Rev. B 46 (1992) 10269. [10] D. Heiman, E.D. Isaacs, P. Becla and S. Foner, Phys. Rev. B 35 (1987) 3307. [11] W. Ossau and B. Kuhn-Heinrich, Physica B 184 (1993) 422.
ELSEVIER
Magneto-optical study of CdTe/Cdl - xMnxTe multiple quantum wells under high magnetic fields Shinji Kuroda a'*, Kazutoshi Kojima a, K6ji Kobayashi a, Yutaka Shirai a'l, K6ki Takita a, Kazuhito Uchida b, Noboru Miura b aInstitute of Materials Science, University of Tsukuba, Tsukuba, lbaraki 305, Japan b Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106, Japan
Abstract
The magneto-optical properties of CdTe/Cdl_xMnxTe multiple quantum wells (MQW's) with high Mn contents of about 30% were studied through absorption measurements at high magnetic fields up to 40 T. Absorption peaks due to the heavy-hole and light-hole related excitons exhibit large Zeeman splitting. The Zeeman splitting energy of the heavy-hole excitons was compared with a variational calculation. Reduced antiferromagnetic coupling of Mn 2 ÷ spins at the M Q W heterointerface and the interdiffusion are discussed as a possible origin of the discrepancy between experiment and theory.
1. Introduction
Semiconductor heterostructures of diluted magnetic semiconductor (DMS) have attracted much attention because of a variety of interesting and novel phenomena 1-1] originating from the spatially modulated s p - d exchange interaction between mobile carriers and localized magnetic moments. CdTe/Cdl_xMn~Te multiple quantum well (MQW) is typical system of this kind, where electrons and holes are confined in the non-magnetic CdTe layer (type I) and are affected by the exchange interaction through the penetration of wavefunction into the Cd~_xMnxTe layers. Magneto-optical properties of this system have been studied extensively through measurements of photoluminescence (PL) [2], PL excitation spectroscopy [3-5] and reflectivity [6].
* Corresponding author. ~Present address: Toshiba Corporation.
In the present work, we performed a study of the magneto-absorption spectroscopy. Though measurement of absorption spectra is a powerful experimental method, especially in pulsed high magnetic fields, there was a experimental difficulty arising from the fundamental absorption of substrate materials with smaller band-gaps, which masks the absorption in the quantum wells. Recently it has become possible to remove GaAs substrates using a selective etching technique I-7, 8]. In a previous paper [8], we reported on absorption measurements in CdTe/Cdl_xMnxTe MQW's with intermediate range of Mn contents (12-14%), and revealed that the quantized level structure at high magnetic fields is influenced significantly by the valence-band mixing effect. This paper reports a study on a series of MQW's with relatively high Mn contents of about 30%. We make quantitative analysis of observed absorption peaks due to heavy-hole related excitons, in comparison with calculations using a variational approach.
0921-4526/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 4 ) 0 0 1 0 2 - 2
416
S. Kuroda et al./Physica B 201 (1994) 415-418
2. Experimental procedures Procedures of sample preparation and magnetooptical measurement are the same as described in Ref. [8]. M Q W samples were grown by the M B E method; a CdTe buffer layer ( ~ 2000 ,~), a Cd~_xMn~Te cladding layer ( ~ 8000 ~), an M Q W structure of alternating CdTe and Cdt_~Mn~Te layers and finally a Cd~_xMn~Te cap layer ( ~ 2000,~) were grown successively on the (100) surface of a GaAs substrate. After the growth, the GaAs substrate was removed by grinding and selective etching using N H 4 O H : H 2 0 2 solution. The widths of the well and barrier layers Lw, LB and M n content x of the cap and cladding layers were determined from the results of the X-ray diffraction and the PL measurement at zero magnetic field. In the absorption measurement, magnetic fields up to 40 T were applied using a non-destructive pulsed magnet. The sample was mounted in the Faraday configuration and absorption spectra for circularly polarized light a ÷ or a were measured. The measurement was done at T = 4.2 K.
a result on sample # 2 with an intermediate well width (Lw = 50/~, LB = 131 /~, x = 0.27) for the cr÷ (open symbols) and a (closed symbols) polarizations. At zero magnetic field, peaks at around 1.67, 1.71 and 1.89 eV are assigned to the absorptions due to heavy-hole exciton of n = 1 subband (E1H1), light-hole exciton of n = 1 subband (ELL0 and heavy-hole exciton of n = 2 subband (E2H2), 1.80
i
1.75 > & o
~
w m ~ m.--m-'~''~" 3 4 / 1 5 5
(
1.70
. . . . . . . . . . . . #2 ~
(50/131)
1.6.=
~
(67/163)'
2'0
•
4'0
a) J
i
E2H2
1.90
3'0
Magnetic Field (T)
1.95
Sample #2 (50/131)
#1
)
[] = o
1.60
1.95
n
0
3. Experimental results Fig. 1 shows a typical example of absorption peak positions plotted against applied magnetic fields. This is
n
EIH1
,
, ..
,
.......
1.90
Ui ig r
> (~02/131 )
q~l]~l~]l~E]r-'nr'n
>
[]
I-I n
e~o
1.85
1.85 •
1.80
............. "-::'-":"-
O q "dmea._ _
0
¢)
#.
1.75
0
.o8
o o •
oo
o
1.70 o , ~ 1 ~ o o ~ = .
_
1.80 '~"~oo..o9 o o o
17
•
1'0
2'0
O
20
(67/163)
s'0
Magnetic Field (T)
.65
;o
20
3'0
4'0
so
b)
Magnetic Field (T) Fig. 1. The magnetic field dependence of absorption peak energies of CdTe/Cd~ xMn~Te MQW of sample #2 (Lw = 50 ~, L B = 131 ~ and x = 0.27) for the tr + (open symbols) and it(closed symbols) polarizations. Circles, triangles and squares represent the E~H1, E~L~ and EzH2 excitons, respectively. Peaks other than these excitons are plotted by diamonds.
Fig. 2. The magnetic field dependence of the (a) EIH~ and (b) E2H2 excitons of samples #1 (Lw=34/~, LB=155~, x = 0.30), # 2 and # 3 (Lw = 67 ,~, Ls = 163/~, x = 0.32) (Lw and L B of the respective samples are shown in the figure as (Lw/LB) under the sample numbers). The solid and broken lines show the calculated exciton energies when valence-band offset ratio Qv is assumed to be 20% and 10%, respectively.
S. Kuroda et al./Physica B 201 (1994) 415-418
respectively (in the figure, they are represented by circles, triangles and squares). With the application of magnetic field, these exciton peaks exhibit large Zeeman splitting; the Zeeman splitting is enhanced by the sp-d exchange interaction with Mn 2+ spins located in the barrier layers through the penetration of wavefunction into the barrier layers, and the lower- (upper-) branch of the split states is observed in the absorption spectra of the a + (a-) polarization. The amount of the splitting becomes larger in the order of the E,L1, E~H~ and E2H2 excitons. This tendency can be understood qualitatively when one estimates the degree of the penetration of the electron and hole wavefunctions on the basis of simple Kronig-Penney model. Absorption peaks observed other than these excitons are represented by diamonds in the figure. Among them, peaks which appear at the higher energy side of the ElL1 peaks above 10 T are interpreted as the absorption due to transitions between higher Landau levels of the conduction and heavy-hole bands. On the other hand, peaks which appear between the E~H~ and E~L~ peaks below 15 T are considered to be the absorption due to the 2s state of the E1H1 exciton. Here we concentrate our attention on the behavior of the heavy-hole exciton under magnetic fields. Fig. 2 shows the magnetic field dependence of the E1H1 (a) and E2H2 (b) exciton energies including those of other samples with various well widths. It is clearly seen that the amount of Zeeman splitting becomes larger for a sample with a narrower well width. This can also be understood easily since the electron and hole wavefunctions penetrate into the barrier layers to a greater degree when the well width becomes narrower with the same barrier height.
4. Discussion
For a quantitative analysis, we made a calculation of exciton energies under magnetic fields by a variational approach, following the procedure in Ref. I-9]. In the calculation, the valence-band mixing effect was neglected. This is considered to be justified since in a CdTe/Cd~_xMnxTe QW with high Mn contents of about 30% the energy separation between heavy- and light-hole subbands is large enough due to a relatively large barrier height and energy splitting caused by strain. Furthermore, we took account of additional confinement of heavy holes along the growth axis due to the Coloumb interaction with electrons confined in the well [6]. Mn 2 ÷ spins in the barrier layers were assumed to behave in a way similar to those in bulk Cd~_xMnxTe; the average alignment of Mn 2 ÷ spins (sz) should be expressed by the sum of a modified Brillouin function and an additional term linear to magnetic fields [10].
417
In Fig. 2, calculated exciton energies are plotted against magnetic field by solid and dotted lines with the valence-band offset ratio Qv as a parameter. The calculated exciton energies at zero field deviate from the observed peak positions by a few meV. When plotting calculated lines in Fig. 2, we added an offset to the exciton energies under magnetic fields in order for the energies at zero field to fit the observed peak positions. When Qv is assumed to be 20%, general features of the calculated lines of the E1HI exciton have tendencies similar to the observed peak positions, such as direction of the energy shift with increasing magnetic field. However the Zeeman splitting energies in the calculation are found to be too small compared to the observation. If Qv is assumed to be 10%, the calculated splitting energies become larger but the exciton energies of the lower branch decrease rapidly above about 20 T due to the type I ~ II transition, which is contrary to the observation. Therefore, we can conclude that the fit is better for Qv = 20 o/o than for 10% in the overall feature. Even in that case, however, there remains a quantitative disagreement between the calculation and the observation. In the calculation, the Zeeman splitting energies continue to increase up to the highest field, reflecting the field dependence of the Mn 2÷ spin alignment (sz) in bulk Cdl-xMnxTe; that is, the contribution of the field-linear term is considerably large in the expression of (sz) in Cdl -xMnxTe with Mn contents as high as 30% [10]. On the other hand, the observed splitting energies increase rapidly at low fields and saturates at about 10 T. A similar discrepancy is found in the field dependence of the E2H2 exciton energies. The observed splitting energies showed a Brillouin-function-like field dependence while the calculated ones behave more linearly. Therefore, quantitative agreement in the whole range of magnetic field cannot be achieved either for Qv = 10% or 20%. Recently Ossau et al. pointed out that an anomalous behavior of Mn 2 + spins located at the heterointerface between the CdTe and Cdl-xMnxTe layers affects the Zeeman splitting of the excitons [11]. According to their suggestion, the probability of the antiferromagnetic coupling in Mn clusters is reduced for Mn 2 + spins at the heterointerface because nearest-neighboring Mn 2+ spins are missing at the side of the CdTe layer. Then the contribution of the Brillouin function term is considered to be larger in (sz) of Mn 2 + spins at the heterointerface than in bulk Cd~ _xMnxTe; that is, (sz) increases rapidly at low magnetic fields and saturates with a further increase of field. The Zeeman splitting of excitons, which is strongly influenced by the exchange interaction with Mn 2+ spins at the heterointerface, is expected to show a Brillouin-function-like field dependence, rather than a linear dependence. Hence, this picture is favorable to
418
S. Kuroda et al./Physica B 201 (1994) 415-418
explain the discrepancy between the calculation and the observation [7]. Another possible origin of the discrepancy is the interdiffusion at the heterointerface. Assuming that the change of Mn concentration along the growth axis is not abrupt at the heterointerface due to the interdiffusion during the growth process, Mn 2 + spins in the interdiffusion layer are expected to play a similar role to that of Mn 2+ spins at the heterointerface in the above picture; that is, the Zeeman splitting is considered to be strongly affected by the alignment of Mn 2 + spins in the interdiffusion layer, which have a more Brillouin-function-like field dependence due to diluted Mn contents.
5. Summary We performed the absorption measurement of CdTe/Cdl_xMnxTe MQW's with relatively high Mn contents of about 30% at high magnetic fields up to 40 T. We observed absorption peaks due to the E1H1, E~L1 and E2Hz excitons, transitions between the conduction and heavy-hole Landau levels and the 2s state of the E1Ha exciton. The observed energies of the ExH1, E~L~ and EzH2 excitons exhibit the large Zeeman splitting. We calculated heavy-hole exciton energies by a variational approach and compared them with the observed peak energies. The calculated Zeeman splitting energies are smaller than the experimental data and increase almost linearly with magnetic field, while the observed splitting energies have Brillouin-function-like dependence on magnetic field. This discrepancy can be explained qualitatively by the influence of Mn 2+ spins located near the QW heterointerface, which are expected to show a Brillouin-function-like magnetization under
magnetic fields due to the reduced antiferromagnetic coupling of Mn 2 + spins at the heterointerface and/or the formation of diluted Mn-content regions near the heterointerface by the interdiffusion.
Acknowledgement This work is supported in part by Iketani Science and Technology Foundation.
References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] A.V. Nurmikko, X.-C. Zhang, S.-K. Chang, L.A. Kolodziejski, R.L. Gunshor and S. Datta, J. Lumin. 34 (1985) 89. I-3] J. Warnock, A. Petrou, R.N. Bicknell,N.C. Giles-Taylor, D.K. Blanks and J.F. Schetzina, Phys. Rev. B 32 (1985) 8116. [4] E. Deleporte, J.M. Berroir, G. Bastard, C. Delalande, J.M. Hong and L.L. Chang, Phys. Rev. B 42 (1990) 5891. [5] M.J. Lawless, R.J. Nicholas, M.J. McNamee, W. Hayes, D.E. Ashenford and B. Lunn, Surf. Sci. 267 (1992) 354. 1-6] E.L. Ivchenko, A.V. Kavokin, V.P. Kochereshko, G.R. Posina, I.N. Uraltsev, D.R. Yakovlev, R.N. Bicknell-Tassius, A. Waag and G. Landwehr, Phys. Rev. B 46 (1992) 7713. [7] H. Akinaga, T. Abe, K. Ando, S. Yoshida, K. Uchida, S. Sasaki and N. Miura. Phys. Rev. B 47 (1993) 15954. 1-8] S. Kuroda, Y. Shirai, K. Kojima, K. Uchida, N. Miura and K. Takita, Jpn. J. Appl. Phys. 32 (1993) Suppl. 32-3 364. [9] K.-S. Lee, Y. Aoyagi and T. Sugano, Phys. Rev. B 46 (1992) 10269. [10] D. Heiman, E.D. Isaacs, P. Becla and S. Foner, Phys. Rev. B 35 (1987) 3307. [11] W. Ossau and B. Kuhn-Heinrich, Physica B 184 (1993) 422.