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Possible s–d hybridization effect on the cyclotron mass in II–VI diluted magnetic semiconductors at megagauss fields
Physica B 294}295 (2001) 467}470
Possible s}d hybridization e!ect on the cyclotron mass in II}VI diluted magnetic semiconductors at megagauss "elds Y.H. Matsuda *, N. Miura , S. Kuroda, M. Shibuya, K. Takita, A. Twardowski Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Institute of Experimental Physics, Warsaw University, Hoza 69, PL 00681, Warsaw, Poland
Abstract Cyclotron resonance of electrons in Cd Fe S (x"0, 0.05) and Cd Mn Te (x"0, 0.064, 0.097, 0.11) has been \V \V V studied at very high magnetic "elds up to 500 T. It has been found that the cyclotron mass increases due to the presence of magnetic ions. The mass enhancement is remarkably larger than expected from the increase of the band gap. The e!ect of the d states of magnetic ions on the sp band structure of the host crystal plays an important role for understanding the unusual mass enhancement. The s}d hybridization as well as the p}d hybridization becomes important at very large cyclotron energy. 2001 Elsevier Science B.V. All rights reserved. Keywords: Diluted magnetic semiconductors; Cyclotron resonance; sp}d hybridization; Megagauss "elds
1. Introduction Band electrons coupled strongly with localized magnetic moments give rise to a variety of interesting physical phenomena as can be seen in heavy fermion systems or high-¹ superconductors. Since the e!ective mass of these highly correlated electrons is strongly in#uenced by the exchange interaction between band electrons and magnetic moments, cyclotron resonance (CR) has attracted much interest. However, the CR of such materials is generally very di$cult to observe because of their high carrier concentration and low carrier mobility. In diluted magnetic semiconductors (DMS), band * Corresponding author. Tel.: #81-471-36-3338; fax: #81471-35-1221. E-mail address: [email protected] (Y.H. Matsuda).
electrons and magnetic ions are coupled strongly by the sp}d exchange interaction. The electronic structure without magnetic "eld is very similar to that of their host (nonmagnetic) semiconductors [1]. In applied magnetic "elds DMSs show very large magneto-optical e!ects due to the giant spin Zeeman splitting of the conduction and valence bands through the s}d and p}d exchange interactions [1]. Recently, cooperative phenomena including ferromagnetic transitions in doped p-type DMS have been reported [2,3]. We can envisage that the e!ective masses of band electrons in DMS are signi"cantly in#uenced by magnetic ions from the analogy of other strongly correlated materials. However, only few CR studies in DMS have been reported so far, because the mobility of DMS is generally too low for CR to be observed. In the present study we have measured the CR in a wide gap II}VI DMS at very high magnetic "elds to see
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 7 0 1 - 8
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Y.H. Matsuda et al. / Physica B 294}295 (2001) 467}470
the e!ect of the magnetic ions on the conduction electrons.
2. Experiment Magnetic "elds are generated by electromagnetic #ux compression and the single turn coil technique up to 500 and 200 T, respectively. Single crystals of Cd Fe S (x"0.05) were grown by the modi"ed \V V Bridgman method and Cd Mn Te (x"0, 0.064, \V V 0.097, 0.11) epilayers were grown by molecular beam epitaxy. We used CO, CO and H O lasers as light sources for wavelengths of 5.53, 10.6 m, and 16.9 and 28 m, respectively.
3. Results and discussion The magneto-transmission spectra of Cd Fe S (x"0.05) and Cd Mn Te (x"0.11) \V V \V V are shown in Fig. 1. The magnetic "eld (B) is applied parallel or perpendicular to the c-axis of the wurtzite structure for Cd Fe S, and parallel to \V V the growth direction (1 0 0) of Cd Mn Te. Near \V V room temperature, we see only a broad absorption peak due to the electron CR in each spectrum. The electron mobility obtained from the resonance peak width at around 100 T is 170 cm/(Vs) in Cd Fe S and 320 cm/(Vs) in Cd Mn Te. \V V \V V The absorption band due to the impurity cyclotron resonance (ICR) is observed on the lower "eld side at low temperatures, while the intensity of the free electron CR absorption decreases with decreasing temperature due to carrier freeze-out. The resonance "eld and hence the cyclotron mass do not depend on the carrier concentration of samples when B is very high. Almost all carriers are populated in the lowest Landau level (N"0) near k "0. In other words, the CR obtained in this work is the quantum CR corresponding to the inter-Landau level transition from N"0 to 1. Fig. 2 shows the plot of the photon energy (cyclotron energy) as a function of the resonance "eld B of the CR peaks. We can obtain the e!ective mass from the least-squares "t of the plot using a relation m* "m*(1#2E/E ), where m* is the !0 !0 cyclotron mass, m* is the band edge e!ective mass,
Fig. 1. Magneto-transmission spectra of Cd Fe S and \V V Cd Mn Te at various photon energies. \V V
Fig. 2. Photon energies (electron cyclotron energy) versus magnetic "eld in CdS and Cd Fe S. The insets show the temper\V V ature dependence of the cyclotron mass at 73.4 meV.
E and E denote the photon energy and the band gap, respectively. The mass m* in Cd Fe S is \V V found to be larger than in CdS by 4% for Bc, while an increase of the mass expected from the increase
Y.H. Matsuda et al. / Physica B 294}295 (2001) 467}470
of the band gap is smaller than 2.7%. We assume that the band gap of FeS is smaller than 4 eV, and use linear interpolation between CdS and hypothetical FeS. Although the Fe spin disorder e!ect induces the band bending [4], the increase of the band gap induced by this e!ect seems to be smaller than expected from the virtual crystal approximation. Since the electron}phonon interaction is not taken into account, there is some error in the obtained masses. Nevertheless, we believe that the error is not very large because the photon energies used in this work are much larger than the LOphonon energy in CdS (37.8 meV). According to a theoretical prediction [5], the sp}d hybridization enlarges the e!ective mass of conduction electrons in DMS. The electron mass can be larger by about 4% than that without the hybridization e!ect (only the band gap e!ect) in Cd Mn Te (x"0.1). We presume that more de\V V tailed theoretical work is required for a quantitative comparison between the theory and the present results of Cd Fe S. However, it is likely that the \V V hybridization e!ect can be one of the most promising mechanisms for the large enhancement of the cyclotron mass. Although the mass change is not so large in the case of BNc, we imagine that the sp}d hybridization makes the conduction band anisotropic, and the m* depends signi"cantly on the !0 magnetic "eld direction. The temperature dependence of m* at 73.4 meV !0 is shown in the insets of Fig. 2. It is found that the temperature dependence of the mass enhancement is much di!erent between Bc and BNc. For Bc, we can see a strong temperature dependence of the mass enhancement. This suggests that the cyclotron motion is strongly in#uenced by the magnetization of magnetic ions thorough the sp}d exchange interaction. The small temperature dependence for BNc probably arises from the anisotropic s}d exchange constant at the large cyclotron energy. Fig. 3 shows the photon energy (cyclotron energy) as a function of the resonant "eld B in Cd Mn Te (x"0, 0.064, 0.11). The e!ective \V V masses (m*) have been obtained by a least-squares "t using the same formula as that for Cd Fe S. \V V This gives m*"0.091 m , 0.100 m , and 0.105 m , for x"0, 0.064 and 0.11, respectively. The relative increase of m* and cyclotron masses obtained at
469
Fig. 3. Photon energies (electron cyclotron energy) versus magnetic "eld in CdTe and Cd Mn Te. The solid curve, are the \V V results of the least-squares "t using the 2 band-k ) p formula. The inset shows the relative increase of the electron e!ective masses obtained from the photon energy versus B plot (closed circles) and the cyclotron masses at 117 meV (open triangles). The solid and dashed lines in the inset denote the calculated relative increase of the e!ective mass with and without the sp}d hybridization e!ect, respectively (after Ref. [5]).
117 meV are shown in the inset. The solid and dashed lines in the inset denote the Mn concentration dependence of the e!ective mass of electrons in Cd Mn Te calculated by Hui et al. including \V V and excluding the sp}d hybridization, respectively [5]. Although the masses obtained from the CR are in approximate agreement with a calculation including the sp}d hybridization, there is a small discrepancy between the theory and experiment. As the calculation in Ref. [5] is for the point of the conduction band, the hybridization between the s-like conduction band and the d band (the s}d hybridization) has not been taken into account. Since the p-like component admixes to the conduction band at wavevectors away from the Brillouin zone center, the band mixing between the conduction band and the d band becomes signi"cant due to the p}d hybridization. (The e!ective s}d hybridization attains a considerable size.) [6,7]. The cyclotron masses obtained from the present study should re#ect the band structure in#uenced by the s}d hybridization in the case of large cyclotron energy. We imagine that the energy dispersion of the conduction band near the anti-crossing point of
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Y.H. Matsuda et al. / Physica B 294}295 (2001) 467}470
mean "eld approximation are problems left for the future study. 4. Summary
Fig. 4. Schematic diagram of the electronic band structure in Cd Mn Te. E , ;, , and denote the valence band top, \V V > \ the e!ective Coulomb repulsion of Mn, the upper, and the lower Hubbard levels of the Mn d-state, respectively. N is the Landau level index. The s}d hybridization can lead to a signi"cant change in the energy dispersion of the conduction band away from the bottom of the conduction band. The s}d exchange constant can be changed by the hybridization.
the s and d bands becomes very small. Hence, we can obtain a very large e!ective mass at a high energy. Moreover, according to the recent report [7], the s}d kinetic exchange interaction can switch on at a "nite energy from the bottom of the conduction band; the s}d exchange constant depends on the energy and even changes its sign. Then we propose that the discrepancy between experiment and theory originates from the s}d hybridization e!ect and from the change in the s}d exchange constant at large cyclotron energy. A schematic diagram of the band structure of the conduction band mixed with the d band at a high energy is shown in Fig. 4. More detailed discussion requires the calculation of the Landau levels. The magnetic polaron or other many body-e!ects beyond the
The electron e!ective masses obtained from high "eld cyclotron resonance in Cd Fe S (x"0.05) \V V and Cd Mn Te (x"0.064, 0.097, 0.11) are found \V V to be signi"cantly larger than expected from the increase of the band gap. The s}d as well as the p}d hybridization can play an important role for the large enhancement of the mass. The present results provide the "rst experimental evidence of the e!ective mass in#uenced signi"cantly by the d states of the magnetic ions in DMS. Acknowledgements This work was partially supported by Grant-inAid for Scienti"c Research on Priority Area `Spin Controlled Semiconductor Nanostructuresa (No. 11125205) from the Ministry of Education, Science, Sports, and Culture. References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Appl. Phys. Lett. 69 (1996) 363. [3] H. Ohno, Science 281 (1998) 951. [4] W.C. Chou, S.S. Kou, F.R. Chen, A. Twardowski, J. Tworzydlo, Y.F. Chen, Phys. Stat. Sol. B 193 (1996) 125. [5] P.M. Hui, H. Ehrenreich, K.C. Hass, Phys. Rev. B 40 (1989) 12346. [6] Y.D. Kim, S.L. Cooper, M.V. Klein, B.T. Jonker, Phys. Rev. B 49 (1994) 1732. [7] I.A. Merkulov, D.R. Yakovlev, A. Keller, W. Ossau, J. Geurts, A. Waag, G. Landwehr, G. Karczewski, T. Wojtowicz, J. Kossut, Phys. Rev. Lett. 83 (1999) 1431.
Possible s}d hybridization e!ect on the cyclotron mass in II}VI diluted magnetic semiconductors at megagauss "elds Y.H. Matsuda *, N. Miura , S. Kuroda, M. Shibuya, K. Takita, A. Twardowski Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan Institute of Experimental Physics, Warsaw University, Hoza 69, PL 00681, Warsaw, Poland
Abstract Cyclotron resonance of electrons in Cd Fe S (x"0, 0.05) and Cd Mn Te (x"0, 0.064, 0.097, 0.11) has been \V \V V studied at very high magnetic "elds up to 500 T. It has been found that the cyclotron mass increases due to the presence of magnetic ions. The mass enhancement is remarkably larger than expected from the increase of the band gap. The e!ect of the d states of magnetic ions on the sp band structure of the host crystal plays an important role for understanding the unusual mass enhancement. The s}d hybridization as well as the p}d hybridization becomes important at very large cyclotron energy. 2001 Elsevier Science B.V. All rights reserved. Keywords: Diluted magnetic semiconductors; Cyclotron resonance; sp}d hybridization; Megagauss "elds
1. Introduction Band electrons coupled strongly with localized magnetic moments give rise to a variety of interesting physical phenomena as can be seen in heavy fermion systems or high-¹ superconductors. Since the e!ective mass of these highly correlated electrons is strongly in#uenced by the exchange interaction between band electrons and magnetic moments, cyclotron resonance (CR) has attracted much interest. However, the CR of such materials is generally very di$cult to observe because of their high carrier concentration and low carrier mobility. In diluted magnetic semiconductors (DMS), band * Corresponding author. Tel.: #81-471-36-3338; fax: #81471-35-1221. E-mail address: [email protected] (Y.H. Matsuda).
electrons and magnetic ions are coupled strongly by the sp}d exchange interaction. The electronic structure without magnetic "eld is very similar to that of their host (nonmagnetic) semiconductors [1]. In applied magnetic "elds DMSs show very large magneto-optical e!ects due to the giant spin Zeeman splitting of the conduction and valence bands through the s}d and p}d exchange interactions [1]. Recently, cooperative phenomena including ferromagnetic transitions in doped p-type DMS have been reported [2,3]. We can envisage that the e!ective masses of band electrons in DMS are signi"cantly in#uenced by magnetic ions from the analogy of other strongly correlated materials. However, only few CR studies in DMS have been reported so far, because the mobility of DMS is generally too low for CR to be observed. In the present study we have measured the CR in a wide gap II}VI DMS at very high magnetic "elds to see
0921-4526/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 7 0 1 - 8
468
Y.H. Matsuda et al. / Physica B 294}295 (2001) 467}470
the e!ect of the magnetic ions on the conduction electrons.
2. Experiment Magnetic "elds are generated by electromagnetic #ux compression and the single turn coil technique up to 500 and 200 T, respectively. Single crystals of Cd Fe S (x"0.05) were grown by the modi"ed \V V Bridgman method and Cd Mn Te (x"0, 0.064, \V V 0.097, 0.11) epilayers were grown by molecular beam epitaxy. We used CO, CO and H O lasers as light sources for wavelengths of 5.53, 10.6 m, and 16.9 and 28 m, respectively.
3. Results and discussion The magneto-transmission spectra of Cd Fe S (x"0.05) and Cd Mn Te (x"0.11) \V V \V V are shown in Fig. 1. The magnetic "eld (B) is applied parallel or perpendicular to the c-axis of the wurtzite structure for Cd Fe S, and parallel to \V V the growth direction (1 0 0) of Cd Mn Te. Near \V V room temperature, we see only a broad absorption peak due to the electron CR in each spectrum. The electron mobility obtained from the resonance peak width at around 100 T is 170 cm/(Vs) in Cd Fe S and 320 cm/(Vs) in Cd Mn Te. \V V \V V The absorption band due to the impurity cyclotron resonance (ICR) is observed on the lower "eld side at low temperatures, while the intensity of the free electron CR absorption decreases with decreasing temperature due to carrier freeze-out. The resonance "eld and hence the cyclotron mass do not depend on the carrier concentration of samples when B is very high. Almost all carriers are populated in the lowest Landau level (N"0) near k "0. In other words, the CR obtained in this work is the quantum CR corresponding to the inter-Landau level transition from N"0 to 1. Fig. 2 shows the plot of the photon energy (cyclotron energy) as a function of the resonance "eld B of the CR peaks. We can obtain the e!ective mass from the least-squares "t of the plot using a relation m* "m*(1#2E/E ), where m* is the !0 !0 cyclotron mass, m* is the band edge e!ective mass,
Fig. 1. Magneto-transmission spectra of Cd Fe S and \V V Cd Mn Te at various photon energies. \V V
Fig. 2. Photon energies (electron cyclotron energy) versus magnetic "eld in CdS and Cd Fe S. The insets show the temper\V V ature dependence of the cyclotron mass at 73.4 meV.
E and E denote the photon energy and the band gap, respectively. The mass m* in Cd Fe S is \V V found to be larger than in CdS by 4% for Bc, while an increase of the mass expected from the increase
Y.H. Matsuda et al. / Physica B 294}295 (2001) 467}470
of the band gap is smaller than 2.7%. We assume that the band gap of FeS is smaller than 4 eV, and use linear interpolation between CdS and hypothetical FeS. Although the Fe spin disorder e!ect induces the band bending [4], the increase of the band gap induced by this e!ect seems to be smaller than expected from the virtual crystal approximation. Since the electron}phonon interaction is not taken into account, there is some error in the obtained masses. Nevertheless, we believe that the error is not very large because the photon energies used in this work are much larger than the LOphonon energy in CdS (37.8 meV). According to a theoretical prediction [5], the sp}d hybridization enlarges the e!ective mass of conduction electrons in DMS. The electron mass can be larger by about 4% than that without the hybridization e!ect (only the band gap e!ect) in Cd Mn Te (x"0.1). We presume that more de\V V tailed theoretical work is required for a quantitative comparison between the theory and the present results of Cd Fe S. However, it is likely that the \V V hybridization e!ect can be one of the most promising mechanisms for the large enhancement of the cyclotron mass. Although the mass change is not so large in the case of BNc, we imagine that the sp}d hybridization makes the conduction band anisotropic, and the m* depends signi"cantly on the !0 magnetic "eld direction. The temperature dependence of m* at 73.4 meV !0 is shown in the insets of Fig. 2. It is found that the temperature dependence of the mass enhancement is much di!erent between Bc and BNc. For Bc, we can see a strong temperature dependence of the mass enhancement. This suggests that the cyclotron motion is strongly in#uenced by the magnetization of magnetic ions thorough the sp}d exchange interaction. The small temperature dependence for BNc probably arises from the anisotropic s}d exchange constant at the large cyclotron energy. Fig. 3 shows the photon energy (cyclotron energy) as a function of the resonant "eld B in Cd Mn Te (x"0, 0.064, 0.11). The e!ective \V V masses (m*) have been obtained by a least-squares "t using the same formula as that for Cd Fe S. \V V This gives m*"0.091 m , 0.100 m , and 0.105 m , for x"0, 0.064 and 0.11, respectively. The relative increase of m* and cyclotron masses obtained at
469
Fig. 3. Photon energies (electron cyclotron energy) versus magnetic "eld in CdTe and Cd Mn Te. The solid curve, are the \V V results of the least-squares "t using the 2 band-k ) p formula. The inset shows the relative increase of the electron e!ective masses obtained from the photon energy versus B plot (closed circles) and the cyclotron masses at 117 meV (open triangles). The solid and dashed lines in the inset denote the calculated relative increase of the e!ective mass with and without the sp}d hybridization e!ect, respectively (after Ref. [5]).
117 meV are shown in the inset. The solid and dashed lines in the inset denote the Mn concentration dependence of the e!ective mass of electrons in Cd Mn Te calculated by Hui et al. including \V V and excluding the sp}d hybridization, respectively [5]. Although the masses obtained from the CR are in approximate agreement with a calculation including the sp}d hybridization, there is a small discrepancy between the theory and experiment. As the calculation in Ref. [5] is for the point of the conduction band, the hybridization between the s-like conduction band and the d band (the s}d hybridization) has not been taken into account. Since the p-like component admixes to the conduction band at wavevectors away from the Brillouin zone center, the band mixing between the conduction band and the d band becomes signi"cant due to the p}d hybridization. (The e!ective s}d hybridization attains a considerable size.) [6,7]. The cyclotron masses obtained from the present study should re#ect the band structure in#uenced by the s}d hybridization in the case of large cyclotron energy. We imagine that the energy dispersion of the conduction band near the anti-crossing point of
470
Y.H. Matsuda et al. / Physica B 294}295 (2001) 467}470
mean "eld approximation are problems left for the future study. 4. Summary
Fig. 4. Schematic diagram of the electronic band structure in Cd Mn Te. E , ;, , and denote the valence band top, \V V > \ the e!ective Coulomb repulsion of Mn, the upper, and the lower Hubbard levels of the Mn d-state, respectively. N is the Landau level index. The s}d hybridization can lead to a signi"cant change in the energy dispersion of the conduction band away from the bottom of the conduction band. The s}d exchange constant can be changed by the hybridization.
the s and d bands becomes very small. Hence, we can obtain a very large e!ective mass at a high energy. Moreover, according to the recent report [7], the s}d kinetic exchange interaction can switch on at a "nite energy from the bottom of the conduction band; the s}d exchange constant depends on the energy and even changes its sign. Then we propose that the discrepancy between experiment and theory originates from the s}d hybridization e!ect and from the change in the s}d exchange constant at large cyclotron energy. A schematic diagram of the band structure of the conduction band mixed with the d band at a high energy is shown in Fig. 4. More detailed discussion requires the calculation of the Landau levels. The magnetic polaron or other many body-e!ects beyond the
The electron e!ective masses obtained from high "eld cyclotron resonance in Cd Fe S (x"0.05) \V V and Cd Mn Te (x"0.064, 0.097, 0.11) are found \V V to be signi"cantly larger than expected from the increase of the band gap. The s}d as well as the p}d hybridization can play an important role for the large enhancement of the mass. The present results provide the "rst experimental evidence of the e!ective mass in#uenced signi"cantly by the d states of the magnetic ions in DMS. Acknowledgements This work was partially supported by Grant-inAid for Scienti"c Research on Priority Area `Spin Controlled Semiconductor Nanostructuresa (No. 11125205) from the Ministry of Education, Science, Sports, and Culture. References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Appl. Phys. Lett. 69 (1996) 363. [3] H. Ohno, Science 281 (1998) 951. [4] W.C. Chou, S.S. Kou, F.R. Chen, A. Twardowski, J. Tworzydlo, Y.F. Chen, Phys. Stat. Sol. B 193 (1996) 125. [5] P.M. Hui, H. Ehrenreich, K.C. Hass, Phys. Rev. B 40 (1989) 12346. [6] Y.D. Kim, S.L. Cooper, M.V. Klein, B.T. Jonker, Phys. Rev. B 49 (1994) 1732. [7] I.A. Merkulov, D.R. Yakovlev, A. Keller, W. Ossau, J. Geurts, A. Waag, G. Landwehr, G. Karczewski, T. Wojtowicz, J. Kossut, Phys. Rev. Lett. 83 (1999) 1431.