- Email: [email protected]
Ferromagnetic (Ga, Mn)As and its heterostructures
Physica E 2 (1998) 904—908
Ferromagnetic (Ga, Mn)As and its heterostructures H. Ohno*, F. Matsukura, A. Shen, Y. Sugawara, N. Akiba, T. Kuroiwa Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku University, Sendai 980-77, Japan
Abstract Magnetotransport measurements have been performed to clarify the origin of ferromagnetism in a new III—V-based diluted magnetic semiconductor, (Ga, Mn)As. Hall resistance was dominated by the anomalous Hall effect proportional to the magnetization, allowing one to determine the magnetic properties such as Curie temperature and Curie constant as well as the conduction type (p-type) and carrier concentration. Negative resistance above Curie temperature was shown to be well accounted for by the spin disorder scattering, from which the exchange between conduction holes and localized Mn moments was determined. This exchange interaction is shown to be responsible for the observed ferromagnetism in (Ga, Mn)As through the RKKY interaction. The magnetic coupling between two ferromagnetic (Ga, Mn)As films separated by a nonmagnetic (Al, Ga)As layer was controlled by the composition of the intermediary layer, indicating the critical role of the holes in the intermediary layer on the coupling. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: (Ga, Mn)As; Ferromagnetism; RKKY interaction
1. Introduction Recently, we have successfully grown a new diluted magnetic semiconductor (DMS) (Ga, Mn)As, an alloy of a III—V compound GaAs and a transition element Mn, by low-temperature molecular-beam epitaxy (MBE) [1]. Magnetization measurements showed that (Ga, Mn)As is ferromagnetic with Curie temperature ¹ as high as C 110 K [2]. Although ferromagnetic interaction has been reported not only in (Ga, Mn)As but also in (In, Mn)As and has been suggested as hole induced [3], no experimental substantiation has been made * Corresponding author. Tel. & fax: #81-22-217-5553; e-mail: [email protected].
so far. Here we report results of magnetotransport measurements of (Ga, Mn)As epitaxial films done to clarify the origin of the ferromagnetism in this new III—V-based DMS (Ga, Mn)As. We also examined the magnetic coupling between the ferromagnetic (Ga, Mn)As layers with intermediary nonmagnetic layer in (Ga, Mn)As heterostructures.
2. Experimental All the samples were grown by MBE at low substrate temperature of 250°C to prevent Mn surface segregation and second-phase MnAs formation. Details of growth was reported elsewhere [1]. Judging from the linear dependence of lattice
1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 1 8 4 - 2
H. Ohno et al. / Physica E 2 (1998) 904—908
constant on Mn composition, x, and good agreement between the extrapolated lattice constant of x"1 with the one extrapolated from the previous (In, Mn)As work [4] together with recently extended X-ray-absorption fine-structure results on (In, Mn)As [5], Mn is believed to be incorporated into the group III sublattice. The maximum Mn concentration so far is 0.071, above which the formation of MnAs takes place at the surface during MBE growth even at low substrate temperatures. Temperature ¹ (2—300 K) and magnetic field B (up to 7 T) dependence of sheet resistance R 4)%%5 and Hall resistance R of 200 nm (Ga, Mn)As H!-layers grown on (Al, Ga)As buffer layer/(0 0 1) GaAs substrates were measured using a standard DC transport measurement setup. Temperature dependence of R of samples with intermediate 4)%%5 Mn composition x (0.035—0.053) showed that they were on the metal side of the metal—insulator transition, whereas low and high x samples were on the insulator side. Although measurements were done on a number of metallic as well as insulating samples, to avoid complication arising from the localization effects, we concentrate here on the metallic samples especially the one with x"0.043; results for other metallic samples were essentially the same. As reported in Ref. [1], R can be expressed as H!-R R R " 0 B# S M, H!-d d
905
3. Results on (Ga, Mn)As layers and discussion Fig. 1 summarizes the results of the magnetotransport measurements on a sample with x" 0.043. Note that since R /R "cM, the vertiH!-- 4)%%5 cal axis of Fig. 1 is proportional to M. Using Arrot plots, where (R /R )2 is plotted against H!-- 4)%%5 (B/R /R ) (not shown), one can obtain the temH!-- 4)%%5 perature dependence of the saturation magnetization M and Curie temperature ¹ ; for the present S C sample thus determined ¹ "91 K. The temperC ature dependence of M can be fitted with a stanS dard Brillouin function curve assuming spin of Mn, S "5, indicating that ferromagnetism observed M/ 2 in (Ga, Mn)As can be understood in the framework of a simple mean field theory, at least to the first approximation. The saturation magnetization at low temperature agreed with the value expected from the nominal concentration of Mn with S " M/ 5. The paramagnetic Curie temperature h was ob2 tained from the temperature dependence of the inverse of the zero field slope of R /R (proporH!-- 4)%%5 tional to susceptibility s). As shown in Fig. 2,
(1)
where R is the ordinary (normal) Hall coefficient, 0 R the anomalous Hall coefficient, d the sample S thickness, and M the magnetization of the sample. R can be shown to be proportional to R in the S 4)%%5 present samples and thus R /d"cR , where c is S 4)%%5 a constant, indicating that the skew scattering is responsible for the anomalous Hall effect [6]. Since the anomalous Hall term is the dominant term even up to room temperature, one can determine M of the sample from R . In order to determine the H!-conduction type and the carrier concentration, one has to measure the ordinary Hall coefficient as a slope of the R —B curve at low temperature unH!-der high magnetic field, where M is saturated and constant.
Fig. 1. Magnetic field B dependence of R /R (Hall resistH!-- 4)%%5 ance/sheet resistance) with temperature ¹ as a parameter of 20 nm (Ga, Mn)As (Mn composition 0.043) grown on a (Al, Ga)As buffer layer/(1 0 0) GaAs substrate structure. When the ordinary Hall term is negligible, which is the case in the present sample, R /R is proportional to magnetization. H!-- 4)%%5
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H. Ohno et al. / Physica E 2 (1998) 904—908
Fig. 2. 1/s—¹ curve for the same sample as in Fig. 1. s determined from the zero field slope of R /R follows the H!-- 4)%%5 Curie—Weiss law and paramagnetic Curie temperature can be determined.
a straight line characteristic of Curie—Weiss law was obtained. For all the samples, h was very close to ¹ . The effective Bohr magneton deduced from C the Curie constant was consistent with S "5. M/ 2 The slope of R —B measured at 10 K revealed H!-that the conduction type was p-type with hole concentration of 1.0]1020 cm~3. The R —¹ curve showed a maximum at 4)%%5 around ¹ , which moved to higher temperature C with increasing B, as shown in Fig. 3. This critical behavior of R is known to be due to the scatter4)%%5 ing of carriers by magnetic fluctuation via exchange interaction and has been observed in magnetic semiconductors [7]. The observed negative resistance can be understood as the reduction of scattering by aligning the spins by B. Well above ¹ , one C can fit the B dependence of R to the following 4)%%5 critical scattering resistivity formula: k m2C2 o "2p2 F n [S(S#1)!SST2], 4 ne2 h3 4
(2)
where k is the Fermi wave vector, n the hole F concentration, m the effective mass, C the p—d ex-
Fig. 3. Temperature dependence of sheet resitivity R of the 4)%%5 sample shown in Fig. 1. Critical behavior of R is clearly 4)%%5 observed together with negative magnetoresistance in the all temperature range investigated.
change, n the Mn concentration, S"5, and SST 2 4 the average spin on Mn [8]. Other symbols have their usual meanings. By using the measured hole concentration and the effective mass of 0.5 m (m 0 0 the free electron mass), the fit of Eq. (2) to experimental results yields C"150$40 eV A_ 3 or N b+3 eV in terms of N b commonly used to 0 0 describe p—d interaction in DMSs [9]. Essentially, the same exchange was obtained from other metallic (Ga, Mn)As samples. This rather large C should be compared to the typical p—d exchange in II—VIbased DMSs which is 1 eV at most. Although the origin of this enhancement is not clear at the moment, similar p—d exchange in GaAs doped with Mn was reported by Szczytko et al. [10], who investigated magneto-optical properties of Mndoped GaAs. Since the magnetic interaction between Mn in cation sublattice in zinc blende structure is known to be antiferromagnetic [11], the ferromagnetic interaction responsible for the observed ferromagnetism in (Ga, Mn)As is most likely carrier-induced. The Curie temperature can be calculated using the exchange constant and the hole concentration determined above assuming that the RKKY
H. Ohno et al. / Physica E 2 (1998) 904—908
907
interaction, the carrier mediated magnetic interaction, is responsible for the interaction between Mn ions. Although the result depend slightly on the cut-off length of the RKKY interaction, i.e. magnetic mean free path, the calculated Curie temperature was 65 K, in good agreement with experimentally determined Curie temperature of 91 K. Because of the quantitative agreement, we conclude that the RKKY interaction is responsible for the appearance of ferromagnetism in (Ga, Mn)As.
4. (Ga, Mn)As heterostructures In order to further examine the presence of carrier-mediated magnetic interaction, we have used (Ga, Mn)As-based heterostructures. High-quality (Ga, Mn)As superlattice structures of 24 nm period (12 nm (Ga, Mn)As and 12 nm GaAs) have already been demonstrated and shown to exhibit ferromagnetism [12]. We have grown a series of structures with a 30 nm (Ga, Mn)As (x"0.04) layer and a 30 nm (Ga, Mn)As (x"0.02) layer separated by a nonmagnetic (Al, Ga)As layer and examined the magnetic coupling between the two magnetic layers. Fig. 4 shows typical results of magnetic measurements (M—B curves, B applied in the plane), where two different (Al, Ga)As intermediary layers were inserted between the two magnetic layers. The thickness of the intermediary layer was fixed to 10 monolayers and the Al composition was varied (x "0.16, 0.29), hence the barrier in the Avalence band (see schematic diagram of Fig. 4a). For x "0.29, the two layers were magnetically Adecoupled and the M—B curve was a simple addition of the two individual M—B curves measured on separately grown samples; the (Ga, Mn)As (x"0.02) layer had a larger coersive force and “softer” magnetization curve than those of the x" 0.04 sample resulting in two-step magnetization of the dashed curve in Fig. 4b. On the other hand, for x "0.16, the magnetization curve showed only Aone step (solid curve in Fig. 4b), indicating that the two magnetic layers were now ferromagnetically coupled. The magnetic coupling between the two ferromagnetic (Ga, Mn)As films separated by a nonmagnetic GaAs layer was also shown to be a function of thickness of the intermediary GaAs
Fig. 4. (a) Schematic diagram of relative energy of the barrier of the intermediary layer and the Fermi level of the two (Ga, Mn)As layers. (b) The dashed line shows the M—B curve with the high barrier nonmagnetic layer measured at 5 K. The two-step magnetization curve is a result of magnetic decoupling. The solid line is with the low barrier height. Because of the coupling, the magnetization curve shows only one step.
layer (not shown here). Both sets of results indicate the critical role of the holes in the intermediary layer on the magnetic coupling. This is consistent with the RKKY interaction being the origin of the magnetic coupling in the present material system. Detailed analysis is in progress and will be reported in a separate article.
5. Conclusion We have shown that the interaction responsible for the appearance of ferromagnetism in
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H. Ohno et al. / Physica E 2 (1998) 904—908
(Ga, Mn)As is the RKKY interaction via p—d exchange. The p—d exchange constant has been determined from the transport measurements to be about 3 eV. We also showed that control of magnetic interaction between the two ferromagnetic (Ga, Mn)As layers is possible using intermediary nonmagnetic layers in (Ga, Mn)As heterostructures.
Acknowledgements This work has been partly supported by a Grant-in-Aid for Scientific Research on Priority Area “Spin Controlled Semiconductor Nanostructures” (No. 09244103) from the Ministry of Education, Science, Sports and Culture, Japan, the “Research for the Future” Program from the Japan Society for the Promotion of Science, and the Mitsubishi Foundation. The early stage of the present work was supported by Japan Science and Technology Corporation under the PRESTO (Sakigake 21) Program.
References [1] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Appl. Phys. Lett. 69 (1996) 363. [2] H. Ohno, F. Matsukura, A. Shen, Y. Sugawara, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Proc. 23rd. Int. Conf. Physics of Semiconductors, Berlin, Germany, 1996, p. 405; F. Matsukura, H. Ohno, A. Shen, Y. Sugawara, unpublished. [3] H. Ohno, H. Munekata, T. Penney, S. von Molna´r, L.L. Chang, Phys. Rev. Lett. 68 (1992) 2664. [4] H. Munekata, H. Ohno, S. von Molna´r, A. Segmu¨ller, L.L. Chang, L. Esaki, Phys. Rev. Lett. 63 (1989) 1849. [5] Y.L. Soo, S.W. Huang, Z.H. Ming, Y.H. Kao, H. Munekata, L.L. Chang, Phys. Rev. B 53 (1996) 4905. [6] C.L. Chien, C.W. Westgate (Eds.), The Hall Effect and its applications, Plenum, New York, 1980, pp. 43—51. [7] S. von Mona´r, T. Kasuya, Phys. Rev. Lett. 21 (1968) 1757. [8] T. Kasuya, Prog. Theor. Phys. 16 (1956) 45. [9] J.K. Furdyna, J. Kossut (Eds.), Semiconductors and Semimetals, vol. 25, Academic Press, Boston, 1986, pp. 293—296. [10] J. Szczytko, W. Mac, A. Stachow, A. Twardowski, P. Becla, J. Tworzydlo, Solid State Commun. 99 (1996) 927. [11] J.K. Furdyna, J. Kossut (Eds.), Semiconductors and Semimetals, vol. 25, Academic Press, Boston, 1986, p. 100. [12] A. Shen, H. Ohno, F. Matsukura, Y. Sugawara, Y. Ohno, N. Akiba, T. Kuroiwa, Jpn. J. Appl. Phys. 36 (1997) L73.
Ferromagnetic (Ga, Mn)As and its heterostructures H. Ohno*, F. Matsukura, A. Shen, Y. Sugawara, N. Akiba, T. Kuroiwa Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku University, Sendai 980-77, Japan
Abstract Magnetotransport measurements have been performed to clarify the origin of ferromagnetism in a new III—V-based diluted magnetic semiconductor, (Ga, Mn)As. Hall resistance was dominated by the anomalous Hall effect proportional to the magnetization, allowing one to determine the magnetic properties such as Curie temperature and Curie constant as well as the conduction type (p-type) and carrier concentration. Negative resistance above Curie temperature was shown to be well accounted for by the spin disorder scattering, from which the exchange between conduction holes and localized Mn moments was determined. This exchange interaction is shown to be responsible for the observed ferromagnetism in (Ga, Mn)As through the RKKY interaction. The magnetic coupling between two ferromagnetic (Ga, Mn)As films separated by a nonmagnetic (Al, Ga)As layer was controlled by the composition of the intermediary layer, indicating the critical role of the holes in the intermediary layer on the coupling. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: (Ga, Mn)As; Ferromagnetism; RKKY interaction
1. Introduction Recently, we have successfully grown a new diluted magnetic semiconductor (DMS) (Ga, Mn)As, an alloy of a III—V compound GaAs and a transition element Mn, by low-temperature molecular-beam epitaxy (MBE) [1]. Magnetization measurements showed that (Ga, Mn)As is ferromagnetic with Curie temperature ¹ as high as C 110 K [2]. Although ferromagnetic interaction has been reported not only in (Ga, Mn)As but also in (In, Mn)As and has been suggested as hole induced [3], no experimental substantiation has been made * Corresponding author. Tel. & fax: #81-22-217-5553; e-mail: [email protected].
so far. Here we report results of magnetotransport measurements of (Ga, Mn)As epitaxial films done to clarify the origin of the ferromagnetism in this new III—V-based DMS (Ga, Mn)As. We also examined the magnetic coupling between the ferromagnetic (Ga, Mn)As layers with intermediary nonmagnetic layer in (Ga, Mn)As heterostructures.
2. Experimental All the samples were grown by MBE at low substrate temperature of 250°C to prevent Mn surface segregation and second-phase MnAs formation. Details of growth was reported elsewhere [1]. Judging from the linear dependence of lattice
1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 1 8 4 - 2
H. Ohno et al. / Physica E 2 (1998) 904—908
constant on Mn composition, x, and good agreement between the extrapolated lattice constant of x"1 with the one extrapolated from the previous (In, Mn)As work [4] together with recently extended X-ray-absorption fine-structure results on (In, Mn)As [5], Mn is believed to be incorporated into the group III sublattice. The maximum Mn concentration so far is 0.071, above which the formation of MnAs takes place at the surface during MBE growth even at low substrate temperatures. Temperature ¹ (2—300 K) and magnetic field B (up to 7 T) dependence of sheet resistance R 4)%%5 and Hall resistance R of 200 nm (Ga, Mn)As H!-layers grown on (Al, Ga)As buffer layer/(0 0 1) GaAs substrates were measured using a standard DC transport measurement setup. Temperature dependence of R of samples with intermediate 4)%%5 Mn composition x (0.035—0.053) showed that they were on the metal side of the metal—insulator transition, whereas low and high x samples were on the insulator side. Although measurements were done on a number of metallic as well as insulating samples, to avoid complication arising from the localization effects, we concentrate here on the metallic samples especially the one with x"0.043; results for other metallic samples were essentially the same. As reported in Ref. [1], R can be expressed as H!-R R R " 0 B# S M, H!-d d
905
3. Results on (Ga, Mn)As layers and discussion Fig. 1 summarizes the results of the magnetotransport measurements on a sample with x" 0.043. Note that since R /R "cM, the vertiH!-- 4)%%5 cal axis of Fig. 1 is proportional to M. Using Arrot plots, where (R /R )2 is plotted against H!-- 4)%%5 (B/R /R ) (not shown), one can obtain the temH!-- 4)%%5 perature dependence of the saturation magnetization M and Curie temperature ¹ ; for the present S C sample thus determined ¹ "91 K. The temperC ature dependence of M can be fitted with a stanS dard Brillouin function curve assuming spin of Mn, S "5, indicating that ferromagnetism observed M/ 2 in (Ga, Mn)As can be understood in the framework of a simple mean field theory, at least to the first approximation. The saturation magnetization at low temperature agreed with the value expected from the nominal concentration of Mn with S " M/ 5. The paramagnetic Curie temperature h was ob2 tained from the temperature dependence of the inverse of the zero field slope of R /R (proporH!-- 4)%%5 tional to susceptibility s). As shown in Fig. 2,
(1)
where R is the ordinary (normal) Hall coefficient, 0 R the anomalous Hall coefficient, d the sample S thickness, and M the magnetization of the sample. R can be shown to be proportional to R in the S 4)%%5 present samples and thus R /d"cR , where c is S 4)%%5 a constant, indicating that the skew scattering is responsible for the anomalous Hall effect [6]. Since the anomalous Hall term is the dominant term even up to room temperature, one can determine M of the sample from R . In order to determine the H!-conduction type and the carrier concentration, one has to measure the ordinary Hall coefficient as a slope of the R —B curve at low temperature unH!-der high magnetic field, where M is saturated and constant.
Fig. 1. Magnetic field B dependence of R /R (Hall resistH!-- 4)%%5 ance/sheet resistance) with temperature ¹ as a parameter of 20 nm (Ga, Mn)As (Mn composition 0.043) grown on a (Al, Ga)As buffer layer/(1 0 0) GaAs substrate structure. When the ordinary Hall term is negligible, which is the case in the present sample, R /R is proportional to magnetization. H!-- 4)%%5
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H. Ohno et al. / Physica E 2 (1998) 904—908
Fig. 2. 1/s—¹ curve for the same sample as in Fig. 1. s determined from the zero field slope of R /R follows the H!-- 4)%%5 Curie—Weiss law and paramagnetic Curie temperature can be determined.
a straight line characteristic of Curie—Weiss law was obtained. For all the samples, h was very close to ¹ . The effective Bohr magneton deduced from C the Curie constant was consistent with S "5. M/ 2 The slope of R —B measured at 10 K revealed H!-that the conduction type was p-type with hole concentration of 1.0]1020 cm~3. The R —¹ curve showed a maximum at 4)%%5 around ¹ , which moved to higher temperature C with increasing B, as shown in Fig. 3. This critical behavior of R is known to be due to the scatter4)%%5 ing of carriers by magnetic fluctuation via exchange interaction and has been observed in magnetic semiconductors [7]. The observed negative resistance can be understood as the reduction of scattering by aligning the spins by B. Well above ¹ , one C can fit the B dependence of R to the following 4)%%5 critical scattering resistivity formula: k m2C2 o "2p2 F n [S(S#1)!SST2], 4 ne2 h3 4
(2)
where k is the Fermi wave vector, n the hole F concentration, m the effective mass, C the p—d ex-
Fig. 3. Temperature dependence of sheet resitivity R of the 4)%%5 sample shown in Fig. 1. Critical behavior of R is clearly 4)%%5 observed together with negative magnetoresistance in the all temperature range investigated.
change, n the Mn concentration, S"5, and SST 2 4 the average spin on Mn [8]. Other symbols have their usual meanings. By using the measured hole concentration and the effective mass of 0.5 m (m 0 0 the free electron mass), the fit of Eq. (2) to experimental results yields C"150$40 eV A_ 3 or N b+3 eV in terms of N b commonly used to 0 0 describe p—d interaction in DMSs [9]. Essentially, the same exchange was obtained from other metallic (Ga, Mn)As samples. This rather large C should be compared to the typical p—d exchange in II—VIbased DMSs which is 1 eV at most. Although the origin of this enhancement is not clear at the moment, similar p—d exchange in GaAs doped with Mn was reported by Szczytko et al. [10], who investigated magneto-optical properties of Mndoped GaAs. Since the magnetic interaction between Mn in cation sublattice in zinc blende structure is known to be antiferromagnetic [11], the ferromagnetic interaction responsible for the observed ferromagnetism in (Ga, Mn)As is most likely carrier-induced. The Curie temperature can be calculated using the exchange constant and the hole concentration determined above assuming that the RKKY
H. Ohno et al. / Physica E 2 (1998) 904—908
907
interaction, the carrier mediated magnetic interaction, is responsible for the interaction between Mn ions. Although the result depend slightly on the cut-off length of the RKKY interaction, i.e. magnetic mean free path, the calculated Curie temperature was 65 K, in good agreement with experimentally determined Curie temperature of 91 K. Because of the quantitative agreement, we conclude that the RKKY interaction is responsible for the appearance of ferromagnetism in (Ga, Mn)As.
4. (Ga, Mn)As heterostructures In order to further examine the presence of carrier-mediated magnetic interaction, we have used (Ga, Mn)As-based heterostructures. High-quality (Ga, Mn)As superlattice structures of 24 nm period (12 nm (Ga, Mn)As and 12 nm GaAs) have already been demonstrated and shown to exhibit ferromagnetism [12]. We have grown a series of structures with a 30 nm (Ga, Mn)As (x"0.04) layer and a 30 nm (Ga, Mn)As (x"0.02) layer separated by a nonmagnetic (Al, Ga)As layer and examined the magnetic coupling between the two magnetic layers. Fig. 4 shows typical results of magnetic measurements (M—B curves, B applied in the plane), where two different (Al, Ga)As intermediary layers were inserted between the two magnetic layers. The thickness of the intermediary layer was fixed to 10 monolayers and the Al composition was varied (x "0.16, 0.29), hence the barrier in the Avalence band (see schematic diagram of Fig. 4a). For x "0.29, the two layers were magnetically Adecoupled and the M—B curve was a simple addition of the two individual M—B curves measured on separately grown samples; the (Ga, Mn)As (x"0.02) layer had a larger coersive force and “softer” magnetization curve than those of the x" 0.04 sample resulting in two-step magnetization of the dashed curve in Fig. 4b. On the other hand, for x "0.16, the magnetization curve showed only Aone step (solid curve in Fig. 4b), indicating that the two magnetic layers were now ferromagnetically coupled. The magnetic coupling between the two ferromagnetic (Ga, Mn)As films separated by a nonmagnetic GaAs layer was also shown to be a function of thickness of the intermediary GaAs
Fig. 4. (a) Schematic diagram of relative energy of the barrier of the intermediary layer and the Fermi level of the two (Ga, Mn)As layers. (b) The dashed line shows the M—B curve with the high barrier nonmagnetic layer measured at 5 K. The two-step magnetization curve is a result of magnetic decoupling. The solid line is with the low barrier height. Because of the coupling, the magnetization curve shows only one step.
layer (not shown here). Both sets of results indicate the critical role of the holes in the intermediary layer on the magnetic coupling. This is consistent with the RKKY interaction being the origin of the magnetic coupling in the present material system. Detailed analysis is in progress and will be reported in a separate article.
5. Conclusion We have shown that the interaction responsible for the appearance of ferromagnetism in
908
H. Ohno et al. / Physica E 2 (1998) 904—908
(Ga, Mn)As is the RKKY interaction via p—d exchange. The p—d exchange constant has been determined from the transport measurements to be about 3 eV. We also showed that control of magnetic interaction between the two ferromagnetic (Ga, Mn)As layers is possible using intermediary nonmagnetic layers in (Ga, Mn)As heterostructures.
Acknowledgements This work has been partly supported by a Grant-in-Aid for Scientific Research on Priority Area “Spin Controlled Semiconductor Nanostructures” (No. 09244103) from the Ministry of Education, Science, Sports and Culture, Japan, the “Research for the Future” Program from the Japan Society for the Promotion of Science, and the Mitsubishi Foundation. The early stage of the present work was supported by Japan Science and Technology Corporation under the PRESTO (Sakigake 21) Program.
References [1] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Appl. Phys. Lett. 69 (1996) 363. [2] H. Ohno, F. Matsukura, A. Shen, Y. Sugawara, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, Proc. 23rd. Int. Conf. Physics of Semiconductors, Berlin, Germany, 1996, p. 405; F. Matsukura, H. Ohno, A. Shen, Y. Sugawara, unpublished. [3] H. Ohno, H. Munekata, T. Penney, S. von Molna´r, L.L. Chang, Phys. Rev. Lett. 68 (1992) 2664. [4] H. Munekata, H. Ohno, S. von Molna´r, A. Segmu¨ller, L.L. Chang, L. Esaki, Phys. Rev. Lett. 63 (1989) 1849. [5] Y.L. Soo, S.W. Huang, Z.H. Ming, Y.H. Kao, H. Munekata, L.L. Chang, Phys. Rev. B 53 (1996) 4905. [6] C.L. Chien, C.W. Westgate (Eds.), The Hall Effect and its applications, Plenum, New York, 1980, pp. 43—51. [7] S. von Mona´r, T. Kasuya, Phys. Rev. Lett. 21 (1968) 1757. [8] T. Kasuya, Prog. Theor. Phys. 16 (1956) 45. [9] J.K. Furdyna, J. Kossut (Eds.), Semiconductors and Semimetals, vol. 25, Academic Press, Boston, 1986, pp. 293—296. [10] J. Szczytko, W. Mac, A. Stachow, A. Twardowski, P. Becla, J. Tworzydlo, Solid State Commun. 99 (1996) 927. [11] J.K. Furdyna, J. Kossut (Eds.), Semiconductors and Semimetals, vol. 25, Academic Press, Boston, 1986, p. 100. [12] A. Shen, H. Ohno, F. Matsukura, Y. Sugawara, Y. Ohno, N. Akiba, T. Kuroiwa, Jpn. J. Appl. Phys. 36 (1997) L73.