Dilute Magnetic Semiconductor - i-Explore International Research ...

International Journal of IT, Engineering and Applied Sciences Research (IJIEASR) Volume 3, No. 1, January 2014

ISSN: 2319-4413

Dilute Magnetic Semiconductor: A Review of Theoretical Status H. S. Kaushik, Department of Humanities and Applied Sciences, YMCA University of Science and Technology, Faridabad Anuradha Sharma, Department of Humanities and Applied Sciences, YMCA University of Science and Technology, Faridabad Mamta Sharma, Department of Materials and Metallurgical Engineering, PEC University of Technology, Chandigarh

ABSTRACT Dilute Magnetic semiconductors has been attracting researchers due to their wide range of applications like spintronics devices such as spin-FET, spin-LED, nanoscale integrated magnetic memories & sensors etc. But most of practical applications requires curie temperature for DMS to be around room temperature or more. Hence different studies had been done world-wide for controlling the electrical & magnetic properties of DMS. Zener model has been the basic model for understanding the carrier mediated ferromagnetism & different exchange interactions in the DMS lattice . Based on zener model dependence of Curie temperature on carrier concentration structural defects & impurity parameters has been analyzed. Anomalous Hall effect is also another important property of DMS which has been studied to understand the differences from normal hall effect and their cause.

Keywords DMS, Curie Temperature , Room Temperature Ferromagnetism, Zener model, Anomalous Hall Effect etc.

1. INTRODUCTION In most of semiconductor devices like the Bipolar junction transistors, FETs, MOSFETs etc electronic charge is controlled by doping with acceptor or donor impurities [15]. The electronic spin can also be utilized for expanding the scope of their applications. In order to achieve such devices, the electrons must be spin-polarized and their polarization largely preserved as they travel through the semiconductor material. The spin polarized carriers can be created by doping ferromagnetic impurities e.g. transition metals like Mn, Co, Cr and rare-earth metals such as Pd, Eu etc. [6-9].The variety of such semiconductors is called Dilute Magnetic Semiconductors which have combination of both magnetic and semiconducting properties. Such a compound is an alloy between a non-magnetic semiconductor and a magnetic element like the transition and rare-earth elements. The interesting room temperature Ferromagnetism in many diluted semiconductor oxide systems (O-DMS), has opened up a route for spintronic

devices. Dilute Magnetic semiconductors have been studied by the researchers for identifying DMSs which have strong ferromagnetism at room temperature. Initially II-VI semiconductor alloys like Zn1-xMnxTe and Cd1-xMnxTe were studied but they showed very weak ferromagnetism and low Curie temperature (Tc). More recently, the Mndoped III–V semiconductors like In1-xMnxAs and Ga1has been studied and they have shown xMnxAs ferromagnetism at higher Curie temperature. The temperature is still too low for practical applications [10]. In all these materials ferromagnetism has been proven to be carrier mediated, which enables the modification of magnetic behavior through charge manipulation. It has motivated a continuous search for materials with even higher Tc and carrier mediated ferromagnetism. It has led to discovery of oxide-based DMSs like ZnO,SnO2,Cu2O and In1.8Sn0.8O3 etc. which are wide band gap semiconductors (>3eV) and can add an optoelectronic dimension to the new generation of spintronic devices [1113]. 1.1 LATTICE STRUCTURE OF DMS The Dilute Magnetic Semiconductors have two types of lattice structure hexagonal wurtzite and cubic zinc blende. Wurtzite is the more common and stable form for II-VI DMS's under ambient conditions. Whereas the zinc blende structure is more common in III-V semiconductor based DMSs. The zincblende crystal consists of two identical interpenetrating face centered cubic (fcc) sublattices. The different sublattices occupied by the different group III and group V element ions are shifted by the fourth of the cubic diagonal relative to each other.In this configuration each ion is surrounded by four nearest neighbor ions of the different sublattice forming an equilateral tetrahedron . The lack of inversion symmetry in both wurtzite and the zinc blende lattice structure results in piezoelectricity and pyroelectricity in some of oxide based DMS's and it also contributes to the spin orbit interaction which contributes in spin transport phenomena. Zinc blende crystal with Cr as transition metal dopant and Wurtzite crystal with Mn as dopant has been shown in Figure 1. Transition metal dopant ions may replace the II or III atoms in host semiconductor and contribute to magnetic spin or they can occupy

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interstitial sites and act as defects i.e. they can act as substitutional as well as interstitial impurity [14-17].

Figure 2 Interaction between itinerant carrier and Magnetic Ions

Figure 1 (A) Cubic Zinc-Blende structure. (B) Hexagonal Wurtzite Structure 1.2 ORIGIN OF FERROMAGNETISM III-V semiconductors when doped with Mn or any other transition metal, the Mn2+ ions mostly substitute III atoms in host semiconductor. These Mn2+ ions provide angular momemtum L = 0 and S = 5/2 magnetic moments due to their half filled 3d shells. Depending on their concentration and energetic position within the band gap the Mn2+ states can either form an impurity band or they act as an impurity level, creating valence band holes. Besides, Mn can also occupy interstitial positions in the zinc blende lattice. These Mn ions act as donors, and tend to passivate substitutional Mn acceptors therefore they do not contribute to the ferromagnetism. The effective magnetic interaction between the distant Mn2+ ions is mediated by the valence band holes in a two step process. The magnetic 3d electrons remain localized at the magnetic ion therefore they do not contribute to the charge transport. If the energetic position of the Mn3+ states is well below the top of the valence band and Mn+ levels are well above the bottom of the conduction band, the valence fluctuations of the Mn2+ state are virtual and can be characterized by single phenomenological exchange coupling constant Jpd . The resulting spindependent exchange between the top of the valence band and the lower lying half filled Mn d shell takes place through the 3d6 configuration and favors antiferromagnetic p − d coupling . The valence band is formed from the hybridized anion p and cation d states, thus the Hpd local exchange between the hole and the Mn2+ spins is determined by the • exchange integral of the corresponding wave functions in the form of Hpd = −2Jpd 𝐬𝐬. S

(1)

where Jpd = N0 β is the p − d coupling constant with N0 being the concentration of the cation sites. Here s and S represents the spin operators of the hole and the Mn2+ ion, respectively.

Above figure shows the example of interaction between the magnetic ions with S=5/2 and itinerant carriers with s=1/2 in DMS. The spin state of the Mn ion is mediated to the neighbor sites by the propagating spin-polarized carriers which tend to align the whole ensemble of the localized spins. The dependence of the energy of the system on the relative orientation of Mn moments is generally referred to as an exchange interaction. [16, 18]. Some of exchange interaction mechanisms which are dominated in DMS’s are: (i) Direct or potential exchange interaction based on the Coulomb interaction between Spins (s-d interaction). (ii) Kinetic exchange interaction involving hybridization effects (p-d coupling). (iii) Indirect exchange of the type of super exchange (d-d interaction). 1.2.1 s-d INTERACTION The s-d interaction is interaction between conduction s band electron spins and magnetic ion spins resulting from the Coulomb interaction .These interactions are ferromagnetic in nature and their exchange energy value is close to N0α ≈ 0.2 eV almost for all DMS’s. This interaction is described by Kondo-like Hamiltonian: (2) Hex = −J(r − R i )𝐬𝐬. Si where s is a spin operator of the band electron, Si is a spin operator of the magnetic ion which is localized in the crystal lattice point Ri and J(r – Ri) is the exchange integral. For electrons from conduction band (s electrons) and from valence band (p electrons) the matrix elements of the exchange integrals are denoted as [16]. (3) N0 α = N0 ⟨S|J|S⟩ (4) N0 β = N0 ⟨X|J|X⟩

1.2.2 p-d INTERACTION The interaction between valence charge carriers and localized magnetic ion spins are termed as p-d interactions. These interactions are anti-ferromagnetic (negative exchange energy • ) in nature.The exchange energy value N0• is six to eight times greater than s-d interaction N0α . Kodo Model does not predict such large value of the p-d interaction . Then Dietl , Bhattacharjee and Larson explained the experimentally observed values and the sign



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of the p-d interaction for Mn based DMS by the p-d hybridization effects. [17]. The model Hamiltonian of the multisite Anderson Hamiltonian consists of Hamiltonian term H0 of the s, p energy bands ε n(k) of the crystal, Hubbard Hamiltonian Hd of Mn d electrons on site i with linearized electron – electron interaction, the Mn 3d – Te 5p hybridization Hamiltonian Hpd ( kinetic part of H) and Mn d – sp-band potential exchange Hamiltonian Hχ . H = H0 + Hd + Hpd + Hχ (5)

1.2.3 d-d INTERACTION The direct interaction between localized magnetic ion spins is termed as d-d interactions. This interaction is also known as Heisenberg exchange interaction and is given by following Hamiltonian ��⃗𝑖𝑖 . 𝑆𝑆 ��⃗𝑗𝑗 𝐻𝐻𝑖𝑖𝑖𝑖 = −2𝐽𝐽𝑖𝑖𝑖𝑖 . 𝑆𝑆 (6) It is much smaller than the sp-d interaction. The d-d mediated super exchange interaction between two Mn spins in II-VI DMS has been studied by Larson. It appears that this process is dominated in Mn-Mn interaction. The theory was developed in the frame of the band picture of MnTe and CdMnTe compounds. The Mn-Mn interaction has been described by Heisenberg Hamiltonian ��⃗𝑖𝑖 . 𝑆𝑆 ��⃗𝑗𝑗 𝐻𝐻𝑁𝑁 = − ∑𝑖𝑖≠𝑗𝑗 𝐽𝐽𝑑𝑑𝑑𝑑 ( 𝑅𝑅𝑖𝑖𝑖𝑖 ). 𝑆𝑆 (7) To calculate the exchange integral Jdd Larson took into account the effect of the Hpd Hamiltonian on an intermediate states in which the occupation of Mn d states is different from five. Apart from above interaction spin orbit interaction also plays critical role in understanding magnetic transport properties of Dilute Magnetic Semiconductors. 1.2.4 SPIN ORBIT INTERACTION In order to develop spintronics as a practical technology it is necessary to have a functional DMS whose magnetic property is controllable by changing the external field. According to Dirac spin motion of electron is coupled to its orbital motion in the presence of an external electric potential. The Hamiltonian for describing spin orbit interaction can be given by following Hamiltonian 𝐻𝐻𝑆𝑆𝑆𝑆 =

1

2𝑚𝑚 0 𝑐𝑐 2

𝒔𝒔. (𝛻𝛻𝛻𝛻 × 𝒑𝒑)

(8)

Where V is the external potential acting on the electron, m0 is the bare mass of the electron, 𝒔𝒔 = ћ𝜎𝜎/2 is its spin operator, 𝜎𝜎 is the vector of the Pauli matrices and p is the momentum operator. Due to the large Dirac gap (2𝑚𝑚0 𝑐𝑐 2 ≈ 1𝑀𝑀𝑀𝑀𝑀𝑀) in the denominator HSO is small for electrons moving slowly (v/c < 1) in the vacuum. However, in case of charge carriers propagating in a crystal the SO coupling is strongly enhanced because the coupling is enhanced by the fast electron motion in the strong electric field of the nuclei. Moreover, the lack of inversion symmetry in the zinc blende lattice lifts the two-fold degeneracy of the |k↑

ISSN: 2319-4413

and |k↓ states throughout the Brillouin zone except for some high symmetry lines and planes. As a result, new terms appear in the electron Hamiltonian which mixes the spin and momentum degrees of freedom and thus further contribute to the effect of SO coupling [19-21].

2. ZENER MODEL DESCRIPTION OF FERROMAGNETISM 2.1 ZENER’S DOUBLE-EXCHANGE MECHANISM It assumes an intermediate nonmagnetic atom and interaction occurs when the two isolated magnetic atoms have a different number of electrons in the magnetic shell and hopping through the intermediate nonmagnetic atom involves magnetic-shell electrons. Combined with the onshell Hund’s rule, double exchange couples magnetic moments ferromagnetically. Parallel spin alignment is favored because it increases the hopping probability and therefore decreases the kinetic energy of spin-polarized electrons. Another form of double exchange interaction, in which Mn acceptor states form an impurity band with mixed spd character has been observed for DMSs where Mn-Mn exchange coupling are realized through hopping within an impurity band. According to Sato et al. [22-23] the origin of stability of ferromagnetic state by hole doping treatment is a double-exchange mechanism in Mn- doped ZnO. 2.2 ZENER’S KINETIC-EXCHANGE OR INDIRECT-EXCHANGE INTERACTION. It arises in models with local, usually d-shell or f-shell, moments whose coupling is mediated by s- or p-band itinerant carriers. The local moments can have a ferromagnetic direct-exchange interaction with band electrons on the same site and/or an antiferromagnetic interaction due to hybridization between the local moment and band electrons on neighboring sites .Polarization of band electrons due to the interaction at one site is propagated to neighboring sites [10].The coupling of the hole spin to the localized Mn spins is described by Hamiltonian given in equation 8 By substituting magnetization of the localized spins 𝑀𝑀(𝑟𝑟) = −𝑆𝑆𝑆𝑆𝜇𝜇𝐵𝐵 where g = 2.0 and S = 5/2. The magnetic field dependence of the magnetization is parametrized in the absence of carriers by the BS Brillouin function 𝑀𝑀0 (𝐻𝐻) = −𝑆𝑆𝑆𝑆𝜇𝜇𝐵𝐵 𝑁𝑁0 𝑥𝑥𝑒𝑒𝑒𝑒𝑒𝑒 𝐵𝐵𝑆𝑆 [

𝑔𝑔𝜇𝜇 𝐵𝐵 𝐻𝐻

]

𝑘𝑘 𝐵𝐵 (𝑇𝑇+𝑇𝑇𝐴𝐴𝐴𝐴 )

(9)

The effective Mn concentration xeff < x reflects the effect of compensation due to anti-sites and interstitial double donors. The other empirical parameter TAF accounts for the short range anti-ferromagnetic super-exchange between the Mn ions. This interaction also arises from the p − d hybridization and is mediated by the spin-polarization of the occupied electron bands. In (III,Mn)V semiconductors, however, this coupling is overcompensated by the long



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range ferromagnetic interaction and plays a minor role. The mean-field approach utilizes a variational method in which the magnetization dependent F[M] Ginzburg-Landau freeenergy functional is minimized. The Fc[M] hole related contribution was calculated by diagonalizing the k · p matrix together with the p − d exchange Hamiltonian . The contribution of the localized spins is given by 𝑀𝑀

𝐹𝐹𝑆𝑆 (𝑀𝑀) = ∫0 𝑑𝑑𝑀𝑀0 𝐻𝐻(𝑀𝑀0 )

(10)

The minimization of the total free-energy functional yields to the solution of the mean-field equation.

𝑀𝑀0 (𝐻𝐻) = −𝑆𝑆𝑆𝑆𝜇𝜇𝐵𝐵 𝑁𝑁0 𝑥𝑥𝑒𝑒𝑒𝑒𝑒𝑒 𝐵𝐵𝑆𝑆 �

𝜕𝜕𝜕𝜕𝑐𝑐 (𝑀𝑀) � + 𝐻𝐻 𝜕𝜕𝜕𝜕 � 𝑘𝑘𝐵𝐵 (𝑇𝑇 + 𝑇𝑇𝐴𝐴𝐴𝐴 )

𝑔𝑔𝜇𝜇𝐵𝐵 �−

(11)

As temperature approaches to curie temperature Fc[M] is parameterized by the small variable M2 as given by Fc [M] = Fc [0] − AF ρs β2 M 2 /8g 2 μB 2

(12)

taking the relation of the ρs spin density of states to the carrier magnetic susceptibility into account, according to χs = AF ρs g 2 μB 2 /4 . The effect of the carrier-carrier interactions is included in the AF Fermi-liquid parameter. By expanding the Brillouin function in powers of M, the leading term supplies the mean-field expression for the transition temperature in the form of TC =

x eff S(S+1)J 2pd A F ρ s (T C ) 12N 0 k B

− TAF

(13)

As expected TC is proportional to concentration and spin of the magnetic ions, to the density of states of the mediating holes and (due to the double exchange process) to the square of the local coupling constant. On the other hand, with increasing exchange interaction or valence band density of states the validity of the mean-field theory breaks down the strong exchange coupling or the large effective mass tend to localize the holes so that they can not couple Mn ions located at different lattice sites. Furthermore, the electron-electron correlations at higher densities lead to interactions which vary rapidly in space and also act against higher Curie temperature (Figure 3), [24].

Figure 3 - (A) High carrier density: Carrier (electrons or holes) mediated interaction leads to ferromagnetism.(B) Low carrier density: Percolation network is formed, carriers hop from site to site freely, aligning Mn moments within the cluster network. Zener model neglects the Friedel oscillations, the effect of the spin-orbit interaction. Later the phenomenon of the carrier mediated magnetic coupling in Dilute magnetic semiconductors was explained by Rudermann, Kittel, Kasuya and Yosida which is also known as RKKY theory. [25-26]. The RKKY theory also takes the oscillations of the electron spin-polarization around the localized spins into account, therefore the resulting J(r) effective coupling is also an oscillatory function of the distance between the magnetic ions. 2 (sin(2k F r) − 2k F rcos(2k F r))/(2k F r)4 J(r) ∝ Jpd

(14)

where kF is the length of the Fermi wave vector. ( 14this ) interaction is type of double exchange due to presence of the square of the Jpd local coupling.

3. ANOMALOUS HALL EFFECT In a magnetic sample the off-diagonal resistivity is conventionally written as the sum of two terms ρH = R 0 B + R S M (15)

The first term is the normal Hall effect, which is due to the deflecting Lorentz force, thus linear in B. This term is directly related to the charge carrier density. In a ferromagnetic system an additional term, the anomalous Hall effect (AHE) appears, which is often found to be simply proportional to the magnetization. In the scattering scheme, such a relation reflects that the AHE is due to the spin polarization of the charge carriers. In DMSs the spinpolarization arises from the exchange coupling between the holes and the Mn2+ ions.




The microscopic origin of the AHE is hidden in the coefficient RS and is still very far from being fully explored. Earlier studies were focused towards understanding the extrinsic mechanisms for AHE assuming a spin-asymmetric impurity scattering of spin-polarized carriers. Recently, much efforts have been done for understanding intrinsic mechanisms for origin of AHE in Dilute magnetic semiconductors. [24, 27]. 3.1 EXTRINSIC ANOMALOUS HALL EFFECT The extrinsic theories of the AHE start from the potential scattering of the charge carriers which becomes spindependent in the presence of spin-orbit coupling. In a paramagnet such scattering processes may result in a nonzero transversal spin current while the total transversal charge current is zero due to the equal number of carriers with up and down spin. This leads to the recently proposed spin Hall effect. In a ferromagnet, however, the spin subbands are differently populated and the arising spin current is accompanied with a net transversal charge current. This is proportional to the spin-polarization and hence to the magnetization. As the extrinsic AHE stems from scattering it is intimately related also to the diagonal resistivity, ρ . Depending on the specific scattering mechanism the model calculations predict a ρAH ∝ ρα , with α = 1 for skew-scattering and α = 2 for side-jump. [24, 28]. 3.2 INTRINSIC ANOMALOUS HALL EFFECT The development of the intrinsic AHE theories was initiated by R. Karplus and J. M. Luttinger in 1954. They considered the band structure in the ferromagnetic state taking into account the spin-orbit interaction perturbatively. Their calculation revealed that moving beyond the conventional Boltzmann transport theory the interband matrix element of the current operator gives rise to an anomalous velocity that is essential to the AHE. The resulting anomalous Hall resistivity obeys ρAH ∝ ρ2 the scaling law. This theory was criticized by Smit and Berger pointing out the role of the impurity scatterings in the steady state equilibrium and hence in the AHE. Based on their suggestions, the extrinsic skew-scattering and the side-jump mechanisms have became generally accepted as the main sources of the AHE. Recent advances in the understanding of the AHE exhibit an intensive interest in the reinterpretation of the intrinsic theory based on the Berry phase formulation [24,28].

4. APPLICATIONS OF DMS Since the discovery of the giant magnetoresistance (GMR) in 1988 in thin film structures consisting of alternating ferromagnetic and nonmagnetic layers, increasing efforts have been made to combine the spin and charge degrees of freedom of the electrons in commercial microelectronic elements. Utilizing the electron’s spin combined with, or

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without its charge has the potential advantage of nonvolatility, increased data processing speed, decreased electric power consumption, and increased integration densities compared with conventional semiconductor based integrated circuits. The proposed multifunctional spintronic device concepts envisions spin field effect transistors with ultra low power use, magnetic diodes with gain, integrated reprogrammable logic and memory chips and light emitting spin diodes with polarized output. The most fundamental challenges in the realization of practical spintronic devices address the achievement of sufficiently long spin lifetimes, injection of spin-polarized carriers across hetero-interfaces and the detection of spin coherence in nanoscale structures, which are preferably compatible with the fabrication methods and well understood semiconductor compounds applied by now a days microelectronic industry. In the spin-FET (Figure 4) source and drain constitute Dilute magnetic semiconductor, connected by a narrow semiconductor channel. The spins of electrons injected into the semiconductor, are set parallel to the magnetization source. Thus, from its source to the drain spin-polarized current flows if the drain and source are magnetized in one direction. In the spin-LED spin-polarized carriers are injected from the contact, combined with composite materials such as nanowires Ga1-xMnxN. Spin-LED can be used to transmit information using the spin-codes. Emitting light of a certain polarization depending on the orientation of the spin, spin-LED allows you to encode the information carried by polarized light.

Figure 4 - Schematic diagram of Spin FET based Light Emitting Diode The spin-polarized light emission can be utilized to detect spin injection efficiency in ferromagnetic semiconductor heterostructures and also to detect spin-polarized Zener tunneling in (Ga,Mn)As based p − n diodes. The discovery of the giant planar Hall effect in bulk (Ga,Mn)As epilayers can be used to detect in-plane magnetization.



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Recently strength of ferromagnetic exchange coupling has been controlled without changing the carrier concentration by applying hydrostatic pressure on DMS which may open new scope of applications in strain engineering [13, 28]. Some applications can directly utilize the bulk property of the carrier mediated ferromagnetism in (In,Mn)As based DMS. The magnetic state of the (In,Mn)As layer embedded in a FET structure can be modified electrically by applying a gate voltage while it is detected by the AHE signal in a small perpendicular magnetic field. The electrical manipulation of the coercive field not only enables the switching between the different magnetic phases leading to demagnetization but also enables reversible electrically induced magnetization reversal. These features offer all the required functionalities of a rewritable nanoscale magnetic memory element for ultra high density information storage.[29-37].

5. CONCLUSIONS The finding of Diluted Magnetic semiconductor is significant in the sense that it it opens up a completely new paradigm for next generation microelectronics which takes advantage of the spin properties in addition to the charge transport property. The material will be really useful if it works at room temperature.

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[12] K. Ueda, H. Tabata and T. Kawai. 2001, Applied Physics, Vol. 79, p. 988. [13] M. CSONTOS, G. MIHÁLY, B. JANKÓ, T. WOJTOWICZ, X. LIU AND J. K. FURDYNA. June 2005, Nature Materials, Vol. 4, pp. 447-449. [14] R Shioda, K Ando, T Hayashi, M Tanaka, Phys. Rev. B 58, 1100–1102 (1998) [15] Amol Rahane, Mrinalini Deshpande , Ravindra Pandey, J Nanopart Res, DOI 10.1007/s11051-010-9871-z. [16] T. Jungwirth, Jairo Sinova ,J. Mašek ,J. Kučera,A. H. MacDonald. 2006, Condensed Matter, Vol. 78, pp. 802830]. [17] M. Kuzma, I. Stefaniuk and M. Bester. 2009, Symmetry and Structural Properties of Condensed Matter, pp. 1-12. [18] K. Sato, P. H. Dederichsa, H. Katayama-Yoshida, J. Kudrnovsky, Physica B 340–342 (2003) 863–869. [19] Spin Physics in Semiconductors, edited by Mikhail I. Dyakonov, Springer. [20] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L.Roukes, A. Y. Chtchelkanova and D. M. Treger. 2001, Science, Vol. 94, pp. 1488-1495. [21] A.-M. Nili, M. A. Majidi, P. Reis,1 J. Moreno, and M. Jarrell, Condensed matter structure, July, 2010. [22]. K Sato, H Katayama-Yoshida, Physica B, 308-310 (2001), 904-907. [23] K Sato, H Katayama-Yoshida, Physica E 10 (2001) 251-255. [24] CSONTOS, Mikl´os. High pressure magnetotransport study of (III,Mn)V dilute magnetic semiconductors. Institute of Physics. 2007. Ph.D. THESIS. [25] E Kolley et al 1998 J. Phys.: Condens. Matter 10 657. [26] Lihui Zhou, Jens Wiebe, Samir Lounis, Elena Vedmedenko, Focko Meier , Stefan Blüge, Peter H. Dederichs & Roland Wiesendanger Nature Physics 6, 187 191 (2010). [27] Hideo Ohno, Journal of Magnetism and Magnetic Materials 200 (1999) 110}129. [28] Magnetic and electric properties of transition metal doped ZnO films. K. Ueda, H. Tabata and T. Kawai. 2001, Applied Physics, Vol. 79, p. 988. [29]Diluted Magnetic Semiconductors By Mukesh Kumar Jain, World Scientific] [30] Dietl, T., Ohno, H., Matsukura, F., Cibert, J. & Ferrand, D. Science, 287, 1019–1022 (2000) [31] Furdyna, J. J. App. Phys. 64, R29–R56 (1988).], [Ohno, H. et al. Appl. Phys Lett. 69, 363–365 (1996). [32] Wang, M. et al. Appl. Phys. Lett. 93, 132103 (2008)]. [33] Zener, C. Phys. Rev. 81, 440–444 (1951).], [34] Ohno, H. et al. Nature 408, 944–946 (2000).] [35] Dietl, T. Nature Mater. 9, 965-974 (2010). [36] Richardella, A. et al. Science 327, 665–669 (2010) [37] Zunger, A., Lany, S. & Raebiger, H. Physics 3, 53 (2010)



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