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Cyclotron resonance in Cd1–xFexS and Ga1–xMnxAs at megagauss magnetic fields
Physica B 256±258 (1998) 565±568
Cyclotron resonance in Cd1±xFexS and Ga1±xMnxAs at megagauss magnetic ®elds Y.H. Matsuda
a,* ,
H. Arimoto a, N. Miura a, A. Twardowski b, H. Ohno c, A. Shen c, F. Matsukura c
a
c
Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8666, Japan b Institute of Experimental Physics, Warsaw University, Hoza 69, 00681, Warsaw, Poland Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku University, Sendai 980-77, Japan
Abstract We have performed infrared and far-infrared magneto-transmission experiments for Cd1±x Fex S (x 0.05) and Ga1±x Mnx As (x 0.00004, 0.053) at very high magnetic ®elds up to 500 T. The cyclotron mass of electrons in Cd1±x Fex S (x 0.05) was found to be larger than that in CdS when we applied magnetic ®elds parallel to the c-axis of the crystal; the relative increase of the cyclotron mass shows anomalous temperature dependence at 85±300 K. Hole cyclotron resonance was observed in Ga1±x Mnx As (x 0.00004) at 119 lm and 70.5 lm. In Ga1±x Mnx As (x 0.053) far-infrared transmission does not show any resonance but a rapid decrease of transmission with magnetic ®eld; the magneto-transmission spectrum depends strongly on temperature. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Megagauss magnetic ®elds; Cyclotron resonance; Infrared magneto-transmission; Diluted magnetic semiconductor
There has been only a little information available about the eect of the sp±d exchange interaction on the intra-band transition in wide-gap diluted magnetic semiconductors as compared to the interband transition. One may envisage that the cyclotron motion of electrons and holes would be in¯uenced by the exchange interaction with local magnetic moments. The in¯uence of the exchange interaction would depend on the magnetization of the crystal and the radius of the cyclotron orbit rCR , if rCR becomes comparable with the average distance between transition metal ions. Hence a high ®eld cyclotron resonance exper* Corresponding author. Tel.: 81 3 3478 5472; fax: 81 3 3478 5472; e-mail: [email protected].
iment would give us crucial information about the eect of the exchange interaction on the eective mass in diluted magnetic systems. We perform the transmission experiments using CO, CO2 , H2 O, and optically pumped far-infrared lasers. Pulsed high magnetic ®elds are generated by the electromagnetic ¯ux compression up to 500 T and the single turn coil technique up to 200 T. The single crystals of Cd1±x Fex S (x 0.05) were grown by a modi®ed Bridgman method. The Ga1±x Mnx As thin ®lms were grown by molecular beam epitaxy at 250°C for the crystal with x 0.053, and at 550°C for x 0.00004. The magneto-transmission in Cd1±x Fex S (x 0.05) at a wavelength of 5.53 lm is shown in Fig. 1 (a) and at 16.9 lm in Fig. 1(b) for various
0921-4526/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 6 7 3 - 5
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Y.H. Matsuda et al. / Physica B 256±258 (1998) 565±568
Fig. 1. Magneto-transmission spectra in Cd1±x Fex S (x 0.05) at 5.53 lm (a); and at 16.9 lm (b), at several temperatures.
temperatures. The magnetic ®eld is applied parallel to the c-axis of the crystal. At room temperature electron cyclotron resonance was observed at around 350 and 100 T for 5.53 and 16.9 lm, respectively. These resonance peaks diminish due to the carrier freeze-out with decreasing temperature, while other resonance peaks appeared at lower ®elds which correspond to impurity cyclotron resonance and/or phonon-assisted cyclotron resonance. In this paper we would like to focus on the free electron cyclotron resonance observed at higher temperatures in the range 80±300 K. Fig. 2(a) shows the temperature dependence of the cyclotron mass in Cd1±x Fex S (x 0.05). Compared with the cyclotron mass in CdS obtained by Imanaka et al. [1], it can be seen that the cyclotron mass in Cd1±x Fex S is larger than that in CdS at each temperature and depends strongly on temperature especially at 16.9 lm. The obtained
Fig. 2. (a) Temperature dependence of the cyclotron mass in Cd1±x Fex S (x 0.05) and CdS. Open and closed squares denote the results in Cd1±x Fex S (x 0.05) at 5.53 and 16.9 lm, respectively. Open and closed circles denote the results given in Ref. [1] for CdS at 5.53 and 16.9 lm, respectively. Open triangles show the results at 16.9 lm obtained in this work for CdS. (b) Energy dependence of the cyclotron mass in Cd1±x Fex S (x 0.05) and CdS. The solid curve gives the energy dependence of the eective mass due to the non-parabolicity of the conduction band calculated in terms of the two-band model. The dashed line gives the LO-phonon energy in CdS (37.8 meV).
relative increase of the cyclotron mass at 16.9 lm is 7 2% at room temperature; it shows a gradual increase at ®rst with decreasing temperature to 12 2% at 120 K and shows a rapid decrease to 3 2% at 85 K. Because the relative increase of the energy gap of Cd1±x Fex S (x 0.05) to that of CdS is estimated at less than about 3%, the estimated relative change in the band-edge bare mass is less than 1%. Fig. 2(b) shows the energy dependence of the cyclotron mass at room temperature. The resonant polaron eect is observed for Cd1±x Fex S as well as for CdS. The dashed line
Y.H. Matsuda et al. / Physica B 256±258 (1998) 565±568
shows the LO phonon energy (37.8 meV in CdS). The solid curve gives the energy dependence of the eective mass due to the non-parabolicity of the conduction band, which is calculated in terms of the two-band model using the band-edge bare mass m* 0.168m0 in CdS [1]. Since the cyclotron mass is in¯uenced strongly by the LO phonon, the temperature dependence of the cyclotron mass in CdS is likely to be strongly related to the electron±phonon interaction. If we assume that the effect of the electron±phonon interaction on the cyclotron mass in Cd1±x Fex S is nearly the same as that in CdS, we can expect that the increase of the cyclotron mass is due to the s±d exchange interaction. The value of the s±d exchange constant in Cd1±x Fex S is about 200 meV [2]. We can imagine a magnetic polaron mass in contrast to the polaron mass in this case. When all local spins of Fe-ions are forced to align at high ®elds at low temperature, electrons in the cyclotron motion would not feel any potential ¯uctuation induced by the s±d exchange interaction. Moreover, because the radius of the cyclotron orbit rCR at megagauss ®elds is comparable to the distance between isolated Fe at 350 T), the number of local ions (rCR 14 A spins in the cyclotron orbit would decrease with increasing magnetic ®eld. The decrease of relative enhancement of the cyclotron mass with magnetic ®eld (in Fig. 2 (b)) and with lowering temperature at 16.9 lm from 120 to 85 K (in Fig. 2 (a)) is consistent qualitatively with the picture of a magnetic polaron mass. In order to obtain more clear evidence concerning the in¯uence of the magnetic ions on the cyclotron mass in a diluted magnetic system, further experiments and theoretical investigations are necessary. The magneto-transmission spectra in Ga1±x Mnx As (x 0.00004) at several temperatures are shown in Fig. 3. The magnetic ®eld is applied parallel to á1 0 0ñ direction. The far-infrared laser line at 119 lm is used. The cyclotron resonance peak is observed at 40 T for all temperatures used in this study. It is found that the mobility of the sample is not high enough above 270 K and that the carrier freeze-out occurs below 140 K. The mobility given by the resonance peak at 220 K is 780 cm2 /V s. The temperature dependence of the resonance peak at 70.5 lm (not shown) is
567
Fig. 3. Magneto-transmission spectra in Ga1±x Mnx As (x 0.00004) at 119 lm. The inset shows the temperature dependence of the cyclotron mass obtained at 119 (closed squares) and 70.5 lm (closed circles). The open square and the open circle give the cyclotron mass in p-type GaAs at 119 and 70.5 lm, respectively.
similar to that at 119 lm. In the inset of Fig. 3 the cyclotron mass obtained at 119 and 70.5 lm is plotted as a function of temperature together with the cyclotron mass in p-type GaAs at room temperature. The cyclotron mass in Ga1±x Mnx As (x 0.00004) is found to be 0.42 0.04 m0 at 119 lm and 0.47 0.04 m0 at 70.5 lm which is smaller than that of GaAs in the megagauss range. The origin of the weak temperature dependence of the cyclotron mass is not clear yet. Fig. 4 shows the magneto-transmission in Ga1±x Mnx As (x 0.053) at several temperatures for 119 lm. The magnetic ®eld is applied perpendicular to the surface of the ®lm. This sample is ferromagnetic at low temperature below Tc 88 K. [3] The thickness and the carrierconcentration is 1500 A and 2.2 ´ 1019 cmÿ3 at 10 K. No resonance peak appeared in the magneto-transmission due to a lack of mobility or of the number of free carriers.
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Y.H. Matsuda et al. / Physica B 256±258 (1998) 565±568
dency to saturate around 33 T at 21 K, 54 T at 40 K, and 104 T at 70 K, as indicated by arrows. Since several tens of percent of Mn spins do not contribute to the ferromagnetic component even below Tc [4], magnetization shows paramagnetic behavior at high ®elds. The calculated spin áSñ of the Mn-ions is shown in the inset of Fig. 4. We used the modi®ed Brillouin function for the calculation. We found that the decrease of the transmission saturates at magnetic ®elds at which áSñ is nearly saturated as shown by the solid circles. This fact indicates that the magneto-transmission is strongly related to the alignment of the local moments in the crystal and to the magnitude of the exchange interaction between holes and Mn-ions. Acknowledgements
Fig. 4. Magneto-transmission spectra in Ga1±x Mnx As (x 0.053) at 119 lm. The inset shows the spin áSñ of the Mn- ions, which is calculated using the modi®ed Brillouin function.
A rapid decrease of the transmission with magnetic ®eld is observed; this decrease depends strongly on temperature. The observed temperature- and magnetic ®eld-dependence of the transmission is quite similar to that of the DC conductivity of Ga1±x Mnx As reported in recent literature [3,4]. In Fig. 4, the decrease of transmission shows a ten-
This work was partially supported by a Grantin-Aid for Scienti®c Research on the Priority Area `Spin-Controlled Semiconductor Nanostructures' (No.10138205) from the Ministry of Education, Science, Sports, and Culture. References [1] Y. Imanaka, Thesis, University of Tokyo, 1997, in Japanese; Y. Imanaka, N. Miura, Physica B 201 (1994) 284. [2] A. Twardowski et al., Solid State Commun. 82 (1992) 229. [3] F. Matsukura et al., Phys. Rev. B 57 (1998) R2037. [4] A. Oiwa et al., Solid State Commun. 103 (1997) 209.
Cyclotron resonance in Cd1±xFexS and Ga1±xMnxAs at megagauss magnetic ®elds Y.H. Matsuda
a,* ,
H. Arimoto a, N. Miura a, A. Twardowski b, H. Ohno c, A. Shen c, F. Matsukura c
a
c
Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8666, Japan b Institute of Experimental Physics, Warsaw University, Hoza 69, 00681, Warsaw, Poland Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku University, Sendai 980-77, Japan
Abstract We have performed infrared and far-infrared magneto-transmission experiments for Cd1±x Fex S (x 0.05) and Ga1±x Mnx As (x 0.00004, 0.053) at very high magnetic ®elds up to 500 T. The cyclotron mass of electrons in Cd1±x Fex S (x 0.05) was found to be larger than that in CdS when we applied magnetic ®elds parallel to the c-axis of the crystal; the relative increase of the cyclotron mass shows anomalous temperature dependence at 85±300 K. Hole cyclotron resonance was observed in Ga1±x Mnx As (x 0.00004) at 119 lm and 70.5 lm. In Ga1±x Mnx As (x 0.053) far-infrared transmission does not show any resonance but a rapid decrease of transmission with magnetic ®eld; the magneto-transmission spectrum depends strongly on temperature. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Megagauss magnetic ®elds; Cyclotron resonance; Infrared magneto-transmission; Diluted magnetic semiconductor
There has been only a little information available about the eect of the sp±d exchange interaction on the intra-band transition in wide-gap diluted magnetic semiconductors as compared to the interband transition. One may envisage that the cyclotron motion of electrons and holes would be in¯uenced by the exchange interaction with local magnetic moments. The in¯uence of the exchange interaction would depend on the magnetization of the crystal and the radius of the cyclotron orbit rCR , if rCR becomes comparable with the average distance between transition metal ions. Hence a high ®eld cyclotron resonance exper* Corresponding author. Tel.: 81 3 3478 5472; fax: 81 3 3478 5472; e-mail: [email protected].
iment would give us crucial information about the eect of the exchange interaction on the eective mass in diluted magnetic systems. We perform the transmission experiments using CO, CO2 , H2 O, and optically pumped far-infrared lasers. Pulsed high magnetic ®elds are generated by the electromagnetic ¯ux compression up to 500 T and the single turn coil technique up to 200 T. The single crystals of Cd1±x Fex S (x 0.05) were grown by a modi®ed Bridgman method. The Ga1±x Mnx As thin ®lms were grown by molecular beam epitaxy at 250°C for the crystal with x 0.053, and at 550°C for x 0.00004. The magneto-transmission in Cd1±x Fex S (x 0.05) at a wavelength of 5.53 lm is shown in Fig. 1 (a) and at 16.9 lm in Fig. 1(b) for various
0921-4526/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 6 7 3 - 5
566
Y.H. Matsuda et al. / Physica B 256±258 (1998) 565±568
Fig. 1. Magneto-transmission spectra in Cd1±x Fex S (x 0.05) at 5.53 lm (a); and at 16.9 lm (b), at several temperatures.
temperatures. The magnetic ®eld is applied parallel to the c-axis of the crystal. At room temperature electron cyclotron resonance was observed at around 350 and 100 T for 5.53 and 16.9 lm, respectively. These resonance peaks diminish due to the carrier freeze-out with decreasing temperature, while other resonance peaks appeared at lower ®elds which correspond to impurity cyclotron resonance and/or phonon-assisted cyclotron resonance. In this paper we would like to focus on the free electron cyclotron resonance observed at higher temperatures in the range 80±300 K. Fig. 2(a) shows the temperature dependence of the cyclotron mass in Cd1±x Fex S (x 0.05). Compared with the cyclotron mass in CdS obtained by Imanaka et al. [1], it can be seen that the cyclotron mass in Cd1±x Fex S is larger than that in CdS at each temperature and depends strongly on temperature especially at 16.9 lm. The obtained
Fig. 2. (a) Temperature dependence of the cyclotron mass in Cd1±x Fex S (x 0.05) and CdS. Open and closed squares denote the results in Cd1±x Fex S (x 0.05) at 5.53 and 16.9 lm, respectively. Open and closed circles denote the results given in Ref. [1] for CdS at 5.53 and 16.9 lm, respectively. Open triangles show the results at 16.9 lm obtained in this work for CdS. (b) Energy dependence of the cyclotron mass in Cd1±x Fex S (x 0.05) and CdS. The solid curve gives the energy dependence of the eective mass due to the non-parabolicity of the conduction band calculated in terms of the two-band model. The dashed line gives the LO-phonon energy in CdS (37.8 meV).
relative increase of the cyclotron mass at 16.9 lm is 7 2% at room temperature; it shows a gradual increase at ®rst with decreasing temperature to 12 2% at 120 K and shows a rapid decrease to 3 2% at 85 K. Because the relative increase of the energy gap of Cd1±x Fex S (x 0.05) to that of CdS is estimated at less than about 3%, the estimated relative change in the band-edge bare mass is less than 1%. Fig. 2(b) shows the energy dependence of the cyclotron mass at room temperature. The resonant polaron eect is observed for Cd1±x Fex S as well as for CdS. The dashed line
Y.H. Matsuda et al. / Physica B 256±258 (1998) 565±568
shows the LO phonon energy (37.8 meV in CdS). The solid curve gives the energy dependence of the eective mass due to the non-parabolicity of the conduction band, which is calculated in terms of the two-band model using the band-edge bare mass m* 0.168m0 in CdS [1]. Since the cyclotron mass is in¯uenced strongly by the LO phonon, the temperature dependence of the cyclotron mass in CdS is likely to be strongly related to the electron±phonon interaction. If we assume that the effect of the electron±phonon interaction on the cyclotron mass in Cd1±x Fex S is nearly the same as that in CdS, we can expect that the increase of the cyclotron mass is due to the s±d exchange interaction. The value of the s±d exchange constant in Cd1±x Fex S is about 200 meV [2]. We can imagine a magnetic polaron mass in contrast to the polaron mass in this case. When all local spins of Fe-ions are forced to align at high ®elds at low temperature, electrons in the cyclotron motion would not feel any potential ¯uctuation induced by the s±d exchange interaction. Moreover, because the radius of the cyclotron orbit rCR at megagauss ®elds is comparable to the distance between isolated Fe at 350 T), the number of local ions (rCR 14 A spins in the cyclotron orbit would decrease with increasing magnetic ®eld. The decrease of relative enhancement of the cyclotron mass with magnetic ®eld (in Fig. 2 (b)) and with lowering temperature at 16.9 lm from 120 to 85 K (in Fig. 2 (a)) is consistent qualitatively with the picture of a magnetic polaron mass. In order to obtain more clear evidence concerning the in¯uence of the magnetic ions on the cyclotron mass in a diluted magnetic system, further experiments and theoretical investigations are necessary. The magneto-transmission spectra in Ga1±x Mnx As (x 0.00004) at several temperatures are shown in Fig. 3. The magnetic ®eld is applied parallel to á1 0 0ñ direction. The far-infrared laser line at 119 lm is used. The cyclotron resonance peak is observed at 40 T for all temperatures used in this study. It is found that the mobility of the sample is not high enough above 270 K and that the carrier freeze-out occurs below 140 K. The mobility given by the resonance peak at 220 K is 780 cm2 /V s. The temperature dependence of the resonance peak at 70.5 lm (not shown) is
567
Fig. 3. Magneto-transmission spectra in Ga1±x Mnx As (x 0.00004) at 119 lm. The inset shows the temperature dependence of the cyclotron mass obtained at 119 (closed squares) and 70.5 lm (closed circles). The open square and the open circle give the cyclotron mass in p-type GaAs at 119 and 70.5 lm, respectively.
similar to that at 119 lm. In the inset of Fig. 3 the cyclotron mass obtained at 119 and 70.5 lm is plotted as a function of temperature together with the cyclotron mass in p-type GaAs at room temperature. The cyclotron mass in Ga1±x Mnx As (x 0.00004) is found to be 0.42 0.04 m0 at 119 lm and 0.47 0.04 m0 at 70.5 lm which is smaller than that of GaAs in the megagauss range. The origin of the weak temperature dependence of the cyclotron mass is not clear yet. Fig. 4 shows the magneto-transmission in Ga1±x Mnx As (x 0.053) at several temperatures for 119 lm. The magnetic ®eld is applied perpendicular to the surface of the ®lm. This sample is ferromagnetic at low temperature below Tc 88 K. [3] The thickness and the carrierconcentration is 1500 A and 2.2 ´ 1019 cmÿ3 at 10 K. No resonance peak appeared in the magneto-transmission due to a lack of mobility or of the number of free carriers.
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Y.H. Matsuda et al. / Physica B 256±258 (1998) 565±568
dency to saturate around 33 T at 21 K, 54 T at 40 K, and 104 T at 70 K, as indicated by arrows. Since several tens of percent of Mn spins do not contribute to the ferromagnetic component even below Tc [4], magnetization shows paramagnetic behavior at high ®elds. The calculated spin áSñ of the Mn-ions is shown in the inset of Fig. 4. We used the modi®ed Brillouin function for the calculation. We found that the decrease of the transmission saturates at magnetic ®elds at which áSñ is nearly saturated as shown by the solid circles. This fact indicates that the magneto-transmission is strongly related to the alignment of the local moments in the crystal and to the magnitude of the exchange interaction between holes and Mn-ions. Acknowledgements
Fig. 4. Magneto-transmission spectra in Ga1±x Mnx As (x 0.053) at 119 lm. The inset shows the spin áSñ of the Mn- ions, which is calculated using the modi®ed Brillouin function.
A rapid decrease of the transmission with magnetic ®eld is observed; this decrease depends strongly on temperature. The observed temperature- and magnetic ®eld-dependence of the transmission is quite similar to that of the DC conductivity of Ga1±x Mnx As reported in recent literature [3,4]. In Fig. 4, the decrease of transmission shows a ten-
This work was partially supported by a Grantin-Aid for Scienti®c Research on the Priority Area `Spin-Controlled Semiconductor Nanostructures' (No.10138205) from the Ministry of Education, Science, Sports, and Culture. References [1] Y. Imanaka, Thesis, University of Tokyo, 1997, in Japanese; Y. Imanaka, N. Miura, Physica B 201 (1994) 284. [2] A. Twardowski et al., Solid State Commun. 82 (1992) 229. [3] F. Matsukura et al., Phys. Rev. B 57 (1998) R2037. [4] A. Oiwa et al., Solid State Commun. 103 (1997) 209.