Ferromagnetic semiconductor heterostructures

Ferromagnetic semiconductor heterostructures

ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6 Ferromagnetic semiconductor heterostructures Hideo Ohnoa,b,* a Labo...

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Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6

Ferromagnetic semiconductor heterostructures Hideo Ohnoa,b,* a

Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku Univerisity, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan b ERATO Semiconductor Spintronics Project, Japan Science and Technology Agency (JST), Japan

Abstract Ferromagnetic III–V semiconductors made it possible to integrate ferromagnetism with semiconductor heterostructures, allowing access to sturctures that exhibit magnetic/spin-related phenomena not previously accessible. This paper reviews the novel phenomena realized in such heterostructures the electric-field control of ferromagnetism, and a mean-field model developed to describe the ferromagnetism observed in magnetic III–V semiconductors. r 2004 Elsevier B.V. All rights reserved. PACS: 75.70.I; 75.50.Pp; 75.70.Cn Keywords: Ferromagnetic semiconductor; Heterostructure; Mean-field model; Electric-field control

1. Introduction Hole-induced ferromagnetism in transition metal doped III–V compounds [1,2] made it possible to integrate ferromagnetism with existing nonmagnetic III–V heterostructures [3]. These structures have allowed us to explore a new dimension of spin-dependent phenomena in semiconductors (Fig. 1). A mean-field theory based on exchange between carrier spin and Mn spin [4,5] indicated that the properties of ferromagnetism in magnetic III–V’s depend critically on the hole concentration. By the use of insulating-gate field-effect transistor structure to modulate carrier concentration, reversible electrical switching of the ferromagnetic phase transition has been realized [6]. Furthermore, ferromagnetic/nonmagnetic semiconductor multilayers have been shown to exhibit spin-dependent scattering, tunnel magnetoresistance as well as interlayer coupling due to the carrier polarization [7,8]. Electrical spin injection across a ferromagnetic/nonmagnetic junction and into *Corresponding author. Laboratory for Electronic Intelligent Systems, Research Institute of Electrical Communication, Tohoku Univerisity, Katahira 2-1-1, Aoba-ku, Sendai 9808577, Japan. Tel./fax: +81-22-217-5553. E-mail address: [email protected] (H. Ohno).

an InGaAs quantum well has been demonstrated using a ferromagnetic III–V semiconductor as a source of spin polarized holes and a III–V quantum well as a light emitting spin detector [9]; electrical electron spin injection using p-type ferromagnetic semiconductors has also been realized in a spin Esaki diode, where spin polarized electrons are transported across a pn junction via interband tunneling into a nonmagnetic n-type semiconductor layer [10,11]. We are thus beginning to learn and understand how to control and utilize the spin degree of freedom in semiconductor structures [12,13]. Here, I review selected progresses made in the past and discuss about the current issues as well as the prospect of the field.

2. Properties of Mn-based ferromagnetic III–V semiconductors In order to introduce a high concentration of Mn beyond its solubility limit into nonmagnetic III–V hosts (particularly GaAs and InAs), which is necessary to induce magnetic cooperative phenomena, a low-temperature molecular beam epitaxy at substrate temperature of 250 C is employed [14]. Mn introduces magnetic moments as well as holes; Mn produces the shallowest

0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.961

ARTICLE IN PRESS H. Ohno / Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6


200 -doped, Tokyo

TC (K)



Tohoku Tokyo


Penn. State

Nottingham Penn. State







0 1996 1997 1998 1999 2000 2001 2002 2003 2004

year Fig. 2. Ferromagnetic transition temperature of as-grown (open symbols) and annealed (closed) (Ga,Mn) As. Fig. 1. Semiconductor spintronics covers the areas of spin/ magnetism and electronics/optics.



R0 RM Bþ M; ¼ d d

where R0 is the ordinary Hall coefficient, B the magnetic field, RM the anomalous Hall coefficient, M the magnetization perpendicular to the film, and d the thickness of the semiconductor layer. In order to determine R0, one needs to go to low temperature and to high magnetic fields to saturate the second term [18], because of the negative magnetoresistance that persists to high magnetic fields; note that RM is resistivitydependent. The highest TC so far obtained in (Ga,Mn)As, an alloy between GaAs and Mn, in its thin film form is 160 K [19], whereas sheet doping of Mn in a modulation doped GaAs heterostructure with additional Be doping is reported to result in 172 K [20]. Low-temperature annealing has been found effective in raising TC to above-mentioned values [21–23], indicating that diffusion of defects is playing a role in determining TC. The evolution of TC with time is shown in Fig. 2. When grown on GaAs, (Ga,Mn)As shows an in-plane magnetic easy axis. This easy axis is strain-dependent and can be made perpendicular-to-plane by changing the sign of strain. (Ga,Mn)As is under compressive strain on GaAs. A lattice relaxed (In,Ga)As buffer,


5K, B ⊥ plane


5K, B // plane





6 M (mT)

M (mT)

acceptor state in III–V’s among the transition metals and produces high concentration of holes. Thus introduced holes mediate ferromagnetic interaction and make the resulting alloys ferromagnetic [15–17]. Ferromagnetic transition temperature TC can be determined either by direct magnetization measurements or by magnetotransport measurements, using Arrott plots. The latter is possible because the Hall resistance RHall is often dominated by the anomalous Hall effect, i.e.

(Al,Ga,Mn)As 20 y=0.17,x=0.046


-20 -30 -100

0T in plane

4 2 0 0 10 20 30 40 50 T (K)


0 B (mT)



Fig. 3. Magnetization versus magnetic field of an (Al,Ga, Mn)As sample with Al composition y=0.17 at 5 and 20 K. Magnetic field is applied in two different directions, showing that the easy-axis of magnetization of the sample is perpendicular to the sample plane at 5 K and in-plane at 20 K. Inset shows the temperature dependence of in-plane remanent magnetization; a hump seen in the trace is a result of temperature-dependent easy-axis direction.

having a greater lattice constant than the (Ga,Mn)As layer grown on top of it, introduces tensile strain and results in perpendicular anisotropy [24]. A temperaturedependent easy-axis was found in (AlyGa1xyMnx)As [25] and in (Ga,Mn)As [26]; these films show in-plane easy-axis right below TC but at low temperatures the preferred direction becomes perpendicular-to-plane as in the y=0.17 (x=0.046) sample shown in Fig. 3 [25].

3. A mean field model for the ferromagnetism A mean field model based on exchange interactions mediated by delocalized holes in the ensemble of localized spins has been developed, which is described

ARTICLE IN PRESS H. Ohno / Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6

model, such as disorder and the formation of an impurity band, to name a few. The importance of these aspects is now being addressed in a number of theoretical studies [32–45].

4. Ferromagnetic III–V semiconductor heterostructures The epitaxial compatibility of ferromagnetic III–V’s allows integration of ferromagnetism with nonmagnetic III–V semiconductors. This allows exploration of semiconductor heterostructure properties previously inaccessible with nonmagnetic heterostructures alone. Four examples are given in the following. 4.1. Tunnel magnetoresistance in ferromagnetic/ nonmagnetic trilayers made of semiconductors Trilayer structure is a building block of magnetic multilayers and is a powerful tool to study the properties of spin-dependent scattering, tunnel magnetoresistance (TMR), and interlayer coupling. Trilayer structures made of semiconductors alone has been grown and the properties have been studied [7,8]. It is especially interesting to see how high the TMR ratio can be in the structure as this gives a measure of spin polarization in the system. We have found that TMR ratio can be as high as 290% in a (Ga,Mn)As/GaAs/(Ga,Mn)As trilayers as shown in Fig. 4 [46]. Here, 6 nm thick GaAs is used as the nonmagnetic tunnel barrier. Note that there is a potential barrier between (Ga,Mn)As and GaAs (GaAs acting as a barrier for holes) of about 100 meV from the Fermi energy of (Ga,Mn)As [47]. This TMR ratio converts to 77% spin polarization if the 300 300

0.39 K +0.5 mV

200 MR (%)

200 MR (%)

in detail in Ref. [5]. The model uses a parameterized hole-spin exchange interaction, an exchange integral N0b. TC is obtained by minimizing the free-energy functional with respect to M at a given hole concentration p. In short, the presence of magnetization increases the free-energy of localized spin system, whereas spin splitting in the carrier part introduced by the presence of exchange reduces the carrier part of the energy, and at a certain temperature these two terms balance, which is our TC. The carrier contribution part is calculated by solving a 6  6 Luttinger–Kohn Hamiltonian with the presence of exchange. TC for (Ga,Mn)As calculated using N0b=1.2 eV taken from photoemission experiments [27] (negative sign indicates that hole spins align antiferromagnetically with Mn spins), and Mn composition of x=0.053, hole concentration of p=3.5  1020 cm3, and a carrier–carrier interaction enhancement of 1.2 [28], is 130 K, which compares very favorably with the experimental value of 110 K. This model explains not only TC of a (Ga,Mn)As sample but also the strain dependence of the magnetic easy axis and its carrier concentration/temperature dependence. For experimentally relevant carrier concentrations, the model predicts an in-plane easy axis for compressive strain and a perpendicular axis for tensile strain in (Ga,Mn)As in accordance with experimental results. Note that the magnetic anisotropy arises solely from the anisotropy of the valence band in this model. The temperature dependence shown in Fig. 3 can be explained in the following way. The carrier distribution within the spin-subbands of the valence band determines the anisotropy; at low carrier concentration (hence high resistivity) and at low temperatures (where the spin splitting is maximum), only one spin-split subband is occupied and this results in a perpendicular easy axis. At higher temperatures, the spin splitting reduces because of the reduced magnetization and results in multi-band occupation and an in-plane easy axis. Resistivity of (Al,Ga,Mn)As increases with increasing Al composition indicating reduction of carrier concentration. In the y=0.17 sample, the carrier concentration is low enough so that at low temperatures the easy axis becomes perpendicular to the plane because of the single band occupation. At an elevated temperature, the multiband occupation takes place and the easy axis switches its direction producing a hump in remanence shown in the inset of Fig. 3. In addition, this mean-field model is capable of explaining the anomalous magnetic circular dichroism observed in (Ga,Mn)As [29] and the TC’s of holeinduced ferromagnetism observed in II–VI magnetic semiconductor (Zn,Mn)Te [30] as well as in group IV magnetic semiconductor GeMn [31]. The range of experiments this model semi-quantitatively explains is perhaps broader than expected, considering the factors not taken into account in the


0 -50 -25 0 25 50 B (mT)


0 -0.4



0.0 B (T)



Fig. 4. TMR ratio as a function of magnetic field B of a 20 nm (Ga,Mn)As (x ¼ 0:074)/6 nm GaAs/20 nm (Ga,Mn)As (x ¼ 0:044) trilayer structure. The magnetic field is applied along [1 0 0] direction.


H. Ohno / Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6

Julli"ere formula is used. This is close to what we expect from the mean field model described earlier [5]. 4.2. Ferromagnetic resonant tunnel diodes Spontaneous magnetization in ferromagnetic state gives rise to spin splitting in the bands. This spin splitting is expected to manifest itself in current–voltage (I2V ) characteristics of a resonant tunneling diode (RTD) when its emitter is a ferromagnet [48]. Fig. 5 shows the temperature dependence of dI/dV versus V curves of such an RTD in the absence of magnetic field, in which clear spontaneous splitting of resonant peaks labeled HH2 and LH1 were observed below TC of 60 K. Under positive bias, holes are injected from the (Ga,Mn)As side. This result demonstrates that semiconductor quantum structures can be used for spectroscopy of the spin spilt bands in a ferromagnetic material. It is certainly interesting to have a magnetic well. So far the low substrate temperature required for the growth of ferromagnetic alloys has prevented us from obtaining high-quality heterostructures necessary for observing tunnel effects in such structures. 4.3. Electrical spin injection of holes and electrons The imbalance in spin population of the carrier system introduced by ferromagnetic phase can be used as a spin polarized carrier source for spin injection in epitaxially integrated semiconductor heterostructures. Since (Ga,Mn)As is p-type, a hole spin injection was first demonstrated [9,49]. In a spin injection light emitting diode (LED) structure, partially spin polarized holes are

injected from a p-type (Ga,Mn)As layer through an intrinsic GaAs into an (In,Ga)As quantum well in an p– i–n structure, where they recombine with spin unpolarized electrons transported from the backside nonmagnetic n-type GaAs layer. Spin polarization of the recombining holes and hence spin injection are demonstrated by the observation of electroluminescence (EL) polarization, i.e. the LED serves as a spin detector. Two polarization states of EL reflecting the two magnetization directions in (Ga,Mn)As were clearly observed in the absence of an external magnetic field at lowtemperatures. Electrical electron injection is also possible by the use of interband spin tunneling from p-type ferromagnetic semiconductors such as (Ga,Mn)As [10,11]. 4.4. Electric field control of ferromagnetism The magnitude of hole-mediated ferromagnetic interaction can be tuned by changing the hole concentration. This can be done by application of electric fields in a gated structure. Fig. 6 shows that reversible magnetic phase transition is possible in an insulating-gate fieldeffect transistor structure having a 5 nm (In,Mn)As channel (x=0.03) [6,50]. In Fig. 6, the magnetization curves measured through the anomalous Hall effect at three different gate voltages VG (+125, 0, 125 V) are shown. The gate polyimide insulator thickness is 0.8 mm. At 22.5 K under zero gate bias, the channel is weakly ferromagnetic as can be seen from the presence of soft hysteresis. Application of positive gate voltage partially depletes holes and reduces the ferromagnetic interaction, resulting in a paramagnetic magnetization curve with no

50 T = 22.5 K

RHall (Ω)

25 0 0V +125 V -125 V 0V

-25 -50 -1.0

Fig. 5. Differential conductance as a function of bias voltage of a double barrier resonant tunneling diode with a ferromagnetic emitter. Note the spontaneous splitting of HH2 and LH1 in the absence of magnetic field at low-temperature. The structure consists of (from the surface side) 150 nm (Ga0.965Mn0.035)As/ 15 nm undoped GaAs spacer/5 nm undoped AlAs barrier/5 nm undoped GaAs quantum well/5 nm undoped AlAs barrier/5 nm undoped GaAs spacer/150 nm Be doped GaAs (p=5  1017 cm3)/150 nm Be doped GaAs (p=5  1018 cm3)/p+ GaAs substrate.


0 B (mT)



Fig. 6. Hall resistance, RHall, of an insulated gate (In,Mn)As field-effect transistor as a function of magnetic field under three different gate voltages. RHall is proportional to the magnetization of the (In,Mn)As channel. Positive gate voltage of 125 V partially depletes holes and results in weaker ferromagnetic interaction and a paramagnetic response, whereas negative gate voltage produces square hysteresis. Zero gate voltage curves, before and after application of positive and negative gate voltage, are virtually identical.

ARTICLE IN PRESS H. Ohno / Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6

hysteresis. When holes are accumulated by applying negative gate bias, a clear square hysteresis appears. Virtually identical magnetization curve is obtained when the gate voltage returns to 0 V. The 125 V swing gives rise to 76% change in the hole concentration and results in the transition temperature change of 74%. This agrees well with what is expected from the meanfield model. It is worth noting that photogenerated carriers can also be used to modify the ferromagnetic properties [51,52]. We have demonstrated electrically assisted magnetization reversal as well as electrical demagnetization using the electric field control of ferromagnetism [53]. Once the transition temperature of ferromagnetic semiconductors reaches the level required for practical applications, these effects should play a critical role in realizing new functionalities not accesible to conventional magnetism.

5. Summary and outlook III–V semiconductors that exhibit ferromagnetism have brought in unprecedented ways of controlling magnetism through its semiconducting nature. It has also introduced possibilities of using spins and magnetic cooperative phenomena in semiconductor heterostructures. For any spintronic application at room temperature, ferromagnetism in semiconductors well above room temperature is a prerequisite. Although a general chemical trend has been delineated by theoretical studies [4,5,54,55], experimental results reported to date are encouraging yet confusing. This is because of the lack of critical information offered in literatures that report room temperature ferromagnetism. It is no longer adequate to show the presence of ferromagnetism at room temperature, but experimental proof of interaction between magnetism and host band structure has to be presented to minimize the possibility of ferromagnetism coming from precipitates and inclusions. Magnetooptical signatures [56] or the anomalous Hall effect are a good measure of interaction as both of them are a result of carrier polarization). To my knowledge, there is one study that established the presence of ferromagnetism with TC nearly at room temperature; Saito et al. [57] has shown that TC of ferromagnetism in (Zn,Cr)Te is 300 K by magnetization measurement and that the semiconducting host is involved in the ferromagnetism by observing magneto-optical enhancement at an optical critical point of the host. The ferromagnetic interaction responsible for magnetism in this material is very likely ferromagnetic superexchange [58]. There is another direction to go other than magnetoelectronics operating at room temperature, that is spin-based semiconductor quantum information


technology. For this, (effective) single spin manipulation and detection are required and research efforts will be directed in that direction. Here, operating temperature is not an issue. The electric-field control of ferromagnetism together with the new possibilities such as electrical spin injection enabled by ferromagnetic semiconductor heterostructures has unlocked new ways to manipulate the spin degree of freedom in semiconductors. We are thus beginning to learn how to utilize spin and magnetism in semiconductors, which may lead us to a new class of electronics, semiconductor spintronics, where both charge and spin of electrons play a critical role in realizing functions.

Acknowledgements I am grateful to a number of colleagues, especially F. Matsukura, D. Chiba, M. Yamanouchi, Y. Ohno, K. Ohtani, and T. Dietl. This work was partly supported by the IT-Program of Research Revolution 2002 (RR2002) from MEXT.

References [1] H. Ohno, H. Munekata, T. Penney, S. von Moln!ar, L.L. Chang, Phys. Rev. Lett. 68 (1992) 2664. [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] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [5] T. Dietl, H. Ohno, F. Matsukura, Phys. Rev. B 63 (2001) 195205. [6] H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno, K. Ohtani, Nature 408 (2000) 944. [7] D. Chiba, N. Akiba, F. Matsukura, Y. Ohno, H. Ohno, Appl. Phys. Lett. 77 (2000) 1873. [8] M. Tanaka, Y. Higo, Phys. Rev. Lett. 87 (2001) 026602. [9] Y. Ohno, D.K. Young, B. Beschoten, F. Matsukura, H. Ohno, D.D. Awschalom, Nature 402 (1999) 790. [10] M. Kohda, Y. Ohno, K. Takamura, F. Matsukura, H. Ohno, Jpn. J. Appl. Phys. 40 (2001) L1274. [11] E. Johnston-Halperin, D. Lofgreen, R.K. Kawakami, D.K. Young, L. Coldren, A.C. Gossard, D.D. Awschalom, Phys. Rev. B 65 (2002) 041306. [12] H. Ohno, F. Matsukura, Y. Ohno, JSAP International, 5 (2002) 4–13 (available at http://www.jsapi.jsap.or.jp/). [13] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Moln!ar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [14] H. Munekata, H. Ohno, S. von Moln!ar, A. Segmuller, . L.L. Chang, L. Esaki, Phys. Rev. Lett. 63 (1989) 1849. [15] H. Ohno, J. Magn. Magn. Mater. 200 (1999) 110. [16] H. Ohno, F. Matsukura, Solid State Commun. 117 (2001) 179.


H. Ohno / Journal of Magnetism and Magnetic Materials 272-276 (2004) 1–6

[17] F. Matsukura, T. Dietl, H. Ohno, III–V Ferromagnetic semiconductors, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 14, North-Holland, Amsterdam, 2002, pp. 1–87. [18] T. Omiya, F. Matsukura, T. Dietl, Y. Ohno, T. Sakon, M. Motokawa, H. Ohno, Physica E 7 (2000) 976. [19] D. Chiba, K. Takamura, F. Matsukura, H. Ohno, Appl. Phys. Lett. 82 (2003) 3020. [20] A.M. Nazmul, S. Sugahara, M. Tanaka, cond-mat/ 0208299. [21] T. Hayashi, Y. Hashimoto, S. Katsumoto, Y. Iye, Appl. Phys. Lett. 78 (2001) 1691. [22] K.C. Ku, S.J. Potashnik, R.F. Wang, S.H. Chun, P. Schiffer, N. Samarth, M.J. Seong, A. Mascarenhas, E. Johnston-Halperin, R.C. Myers, A.C. Gossar, D.D. Awschalom, Appl. Phys. Lett. 82 (2003) 2302. [23] K.W. Edmonds, K.Y. Wang, R.P. Campion, A.C. Neumann, C.T. Foxon, B.L. Gallagher, P.C. Main, Appl. Phys. Lett. 81 (2002) 3010. [24] H. Ohno, F. Matsukura, A. Shen, Y. Sugawara, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, in: M. Scheffler, R. Zimmermann (Eds.), Proceedings of the 23rd International Conference on Physics of Semiconductors, World Scientific, Singapore, 1996, pp. 405–408. [25] K. Takamura, F. Matsukura, D. Chiba, H. Ohno, Appl. Phys. Lett. 81 (2002) 2590. [26] M. Sawicki, F. Matsukura, T. Dietl, G.M. Schott, C. Ruester, G. Schmidt, L.W. Molenkamp, G. Karczewski, J. Supercond. 16 (2003) 7. [27] J. Okabayashi, A. Kimura, O. Rader, T. Mizokawa, A. Fujimori, T. Hayashi, M. Tanaka, Phys. Rev. B 58 (1998) R4211. [28] T. Jungwirth, W.A. Atkinson, B.H. Lee, A.H. MacDonald, Phys. Rev. B 59 (1999) 9818. [29] B. Beschoten, P.A. Cowell, I. Malajovich, D.D. Awschalom, F. Matsukura, A. Shen, H. Ohno, Phys. Rev. Lett. 83 (1999) 3073. [30] D. Ferrand, J. Cibert, C. Bourgognon, S. Tatarenko, A. Wasiela, G. Fishman, A. Bonanni, H. Sitter, S. Kole!snik, J. Jaroszyn˜ski, A. Barcz, T. Dietl, J. Cryst. Growth 214/215 (2000) 387. [31] Y.D. Park, A.T. Hanbicki, S.C. Erwin, C.S. Hellberg, J.M. Sullivan, J.E. Mattson, T.F. Ambrose, A. Wilson, G. Spanos, B.T. Jonker, Science 295 (2002) 651. [32] H. Akai, Phys. Rev. Lett. 81 (1998) 3002. [33] T. Ogawa, M. Shirai, N. Suzuki, I. Kitagawa, J. Magn. Magn. Mater. 197 (1999) 428. [34] J. Inoue, S. Nonoyama, H. Itoh, Phys. Rev. Lett. 85 (2000) 4610.

[35] O. Sakai, S. Suzuki, K. Nishizawa, J. Phys. Soc. Japan 70 (2001) 1105. [36] M. Berciu, R.N. Bhatt, Phys. Rev. Lett. 87 (2001) 107203. [37] S. Sanvito, P. Ordejon, N.A. Hill, Phys. Rev. B 63 (2001) 165206. [38] M. van Schilfgaarde, O.N. Mryasov, Phys. Rev. B 63 (2001) 233205. [39] M. Yagi, Y. Kayanuma, J. Phys. Soc. Japan 71 (2002) 2010. [40] A. Kaminski, S. Das Sarma, Phys. Rev. Lett. 88 (2002) 247202. [41] J. Schliemann, A.H. MacDonald, Phys. Rev. Lett. 88 (2002) 137201. [42] M. Mayr, G. Alvarez, E. Dagotto, Phys. Rev. B 65 (2002) 241202. [43] G. Zarand, B. Janko, Phys. Rev. Lett. 89 (2002) 047201. [44] C. Timm, F. Sch.afer, F. von Oppen, Phys. Rev. Lett. 89 (2002) 137201. [45] Y.J. Zhao, T. Shishidou, A.J. Freeman, Phys. Rev. Lett. 90 (2003) 047204. [46] D. Chiba, F. Matsukura, H. Ohno, 11th International Conference on Modulated Semiconductor Structures (MSS11), Nara, Japan, July 14–18, 2003. [47] Y. Ohno, I. Arata, F. Matsukura, H. Ohno, Physica E 13 (2002) 521. [48] H. Ohno, N. Akiba, F. Matsukura, A. Shen, K. Ohtani, Y. Ohno, Appl. Phys. Lett. 73 (1998) 363. [49] D.K. Young, E. Johnston-Halperin, D.D. Awschalom, Y. Ohno, H. Ohno, Appl. Phys. Lett. 80 (2002) 1598. [50] D. Chiba, M. Yamanouchi, F. Matsukura, E. Abe, Y. Ohno, K. Ohtani, H. Ohno, J. Supercond. 16 (2003) 179. [51] S. Koshihara, A. Oiwa, M. Hirasawa, S. Katsumoto, Y. Iye, C. Urano, H. Takagi, H. Munekata, Phys. Rev. Lett. 78 (1997) 4617. [52] H. Boukari, P. Kossacki, M. Bertolini, D. Ferrand, J. Cibert, S. Tatarenko, A. Wasiela, J.A. Gaj, T. Dietl, Phys. Rev. Lett. 88 (2002) 207204. [53] D. Chiba, M. Yamanouchi, F. Matsukura, H. Ohno, Science 301 (2003) 943. [54] T. Jungwirth, J. Konig, J. Sinova, J. Kucera, A.H. MacDonald, Phys. Rev. B 66 (2002) 012402. [55] K. Sato, H. Katayama-Yoshida, Semicond. Sci. Technol. 17 (2002) 367. [56] K. Ando, T. Hayashi, M. Tanaka, A. Twardowski, J. Appl. Phys. 83 (1998) 6548. [57] H. Saito, V. Zayets, S. Yamagata, K. Ando, Phys. Rev. Lett. 90 (2003) 207202. [58] J. Blinowski, P. Kacman, J.A. Majewski, Phys. Rev. B 53 (1996) 9524.