J. Semicond. > Volume 40 > Issue 8 > Article Number: 080301

Families of magnetic semiconductors — an overview

Tomasz Dietl 1, 2, , , Alberta Bonanni 3, , and Hideo Ohno 4, 5, 2, 6, 7, 8, ,

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Abstract: The interplay of magnetic and semiconducting properties has been in the focus for more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magnetic semiconductor families, including europium chalcogenides, chromium spinels, dilute magnetic semiconductors, dilute ferromagnetic semiconductors and insulators, mentioning also sources of non-uniformities in the magnetization distribution, accounting for an apparent high Curie temperature ferromagnetism in many systems. Our survey is carried out from today's perspective of ferromagnetic and antiferromagnetic spintronics as well as of the emerging fields of magnetic topological materials and atomically thin 2D layers.

Key words: magnetic and dilute magnetic semiconductorstopological materials2D systems

Abstract: The interplay of magnetic and semiconducting properties has been in the focus for more than a half of the century. In this introductory article we briefly review the key properties and functionalities of various magnetic semiconductor families, including europium chalcogenides, chromium spinels, dilute magnetic semiconductors, dilute ferromagnetic semiconductors and insulators, mentioning also sources of non-uniformities in the magnetization distribution, accounting for an apparent high Curie temperature ferromagnetism in many systems. Our survey is carried out from today's perspective of ferromagnetic and antiferromagnetic spintronics as well as of the emerging fields of magnetic topological materials and atomically thin 2D layers.

Key words: magnetic and dilute magnetic semiconductorstopological materials2D systems



References:

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Methfessel S, Mattis D C. Magnetic semiconductors. Vol. 18. Springer, 1968, 1

[2]

Baltzer P K, Wojtowicz P J, Robbins M, et al. Exchange interactions in ferromagnetic chromium chalcogenide spinels. Phys Rev, 1966, 151, 367

[3]

Wachter P. Europium chalcogenides: EuO, EuS, EuSe and EuTe. In: Handbook on the Physics and Chemistry of Rare Earth. Vol. 2. Edited by Gschneidner K A Jr, Eyring L. Amsterdam: North-Holland, 1979, 507

[4]

Kasuya T, Yanase A. Anomalous transport phenomena in Eu-chalcogenide alloys. Rev Mod Phys, 1968, 40, 684

[5]

Nagaev E L. Colossal-magnetoresistance materials: manganites and conventional ferromagnetic semiconductors. Phys Rep, 2001, 346, 387

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Žutić I, Matos-Abiague A, Scharf B, et al. Proximitized materials. Mater Today, 2019, 22, 85

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Xu G, Weng H M, Wang Z J, et al. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4. Phys Rev Lett, 2011, 107, 186806

[8]

Jungwirth J, Marti X, Wadley P, et al. Antiferromagnetic spintronics. Nat Nanotech, 2016, 11(9), 231

[9]

Li H, Ruan S C, Zeng Y J. Intrinsic van der Waals magnetic materials from bulk to the 2D limit: New frontiers of spintronics. Adv Mater, 2019, 0, 1900065

[10]

Webster L, Yan J A. Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3. Phys Rev B, 2018, 98, 144411

[11]

Haury A, Wasiela A, Arnoult A, et al. Observation of a ferromagnetic transition induced by two-dimensional hole gas in modulationdoped CdMnTe quantum wells. Phys Rev Lett, 1997, 79, 511

[12]

Huang B, Clark G, Navarro-Moratalla E, et al. Intrinsic van der Waals magnetic materials from bulk to the 2D limit: New frontiers of spintronics. Nature, 2019, 546, 270

[13]

Gałązka R R. Semimagnetic semiconductors. Proceedings 14th International Conference on the Physics of Semiconductors, 1978, 133

[14]

Furdyna J K, Kossut J. Diluted magnetic semiconductors. In: Semiconductors and Semimetals. Vol. 25. New York: Academic Press, 1988

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Dietl T. (Diluted) Magnetic semiconductors. In: Handbook of Semiconductors. Vol. 3B. Edited by Mahajan S. North Holland, Amsterdam, 1994. 1251

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Gaj J A, Kossut J. Introduction to the physics of diluted magnetic semiconductors. Berlin: Springer, 2010

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Król M, Mirek R, Lekenta K, et al. Spin polarized semimagnetic exciton-polariton condensate in magnetic field. Sci Rep, 2018, 8(10), 6694

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Betthausen C, Giudici P, Iankilevitch A, et al. Fractional quantum Hall effect in a dilute magnetic semiconductor. Phys Rev B, 2014, 90, 115302

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Fiederling R, Keim M, Reuscher G, et al. Injection and detection of a spin-polarized current in a light-emitting diode. Nature, 1999, 402, 787

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Dietl T. Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach. Phys Rev B, 2015, 91, 125204

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Dietl T. Hole states in wide band-gap diluted magnetic semiconductors and oxides. Phys Rev B, 2008, 77, 085208

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Pacuski W, Kossacki P, Ferrand D, et al. Observation of strong-coupling effects in a diluted magnetic semiconductor Ga1– xFexN. Phys Rev Lett, 2008, 100, 037204

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Kobak J, Smoleński T, Goryca M, et al. Designing quantum dots for solotronics. Nat Commun, 2014, 5, 3191

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Dietl T, Ohno H, Matsukura F, et al. Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science, 2000, 287, 1019

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Dietl T, Ohno H. Dilute ferromagnetic semiconductors: Physics and spintronic structures. Rev Mod Phys, 2014, 86, 187

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Ohno H. Making nonmagnetic semiconductors ferromagnetic. Science, 1998, 281, 951

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Story T, Gałązka R R, Frankel R B, et al. Carrier-concentration-induced ferromagnetism in PbSnMnTe. Phys Rev Lett, 1986, 56(11), 777

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Ferrand D, Cibert J, Bourgognon C, et al. Carrier-induced ferromagnetic interactions in p-doped Zn1– xMnxTe epilayers. J Cryst Growth, 2000, 214, 387

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Olejník K, Owen M H S, Novák V, et al. Enhanced annealing, high Curie temperature and low-voltage gating in (Ga, Mn)As: A surface oxide control study. Phys Rev B, 2008, 78, 054403

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Wang M, Campion R P, Rushforth A W, et al. Achieving high Curie temperature in (Ga, Mn)As. Appl Phys Lett, 2008, 93, 132103

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Chen L, Yang X, Yang H F, et al. Enhancing the Curie temperature of ferromagnetic semiconductor (Ga, Mn)As to 200 K via nanostructure engineering. Nano Lett, 2011, 11, 2584

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Fukuma Y, Asada H, Miyawaki S, et al. Carrierinduced ferromagnetism in Ge0.92Mn0.08Te epilayers with a Curie temperature up to 190 K. Appl Phys Lett, 2008, 93, 252502

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Hassan M, Springholz G, Lechner R T, et al. Molecular beam epitaxy of single phase GeMnTe with high ferromagnetic transition temperature. J Cryst Growth, 2011, 323, 363

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Zhao K, Chen B J, Zhao G Q, et al. Ferromagnetism at 230K in (Ba0.7K0.3)(Zn0.85Mn0.15)2As2 diluted magnetic semiconductor. Chin Sci Bull, 2014, 59, 2524

[41]

Andrearczyk T, Jaroszyński J, Sawicki M, et al. Ferromagnetic interactions in p- and n-type II–VI diluted magnetic semiconductors. Proceedings of 25th International Conference on Physics of Semiconductors, 2000, 235

[42]

Kazakov A, Simion G, Lyanda-Geller Y, et al. Mesoscopic transport in electrostatically defined spin-full channels in quantum Hall ferromagnets. Phys Rev Lett, 2017, 119, 046803

[43]

Jungwirth T, Wunderlich J, Novák V, et al. Spin-dependent phenomena and device concepts explored in (Ga, Mn)As. Rev Mod Phys, 2014, 86, 855

[44]

Ohno Y, Young D K, Beschoten B, et al. Electrical spin injection in a ferromagnetic semiconductor heterostructure. Nature, 1999, 402, 790

[45]

Ohno H, Chiba D, Matsukura F, et al. Electric-field control of ferromagnetism. Nature, 2000, 408, 944

[46]

Boukari H, Kossacki P, Bertolini M, et al. Light and electricfield control of ferromagnetism in magnetic quantum structures. Phys Rev Lett, 2002, 88, 207204

[47]

Chiba D, Sawicki M, Nishitani Y, et al. Magnetization vector manipulation by electricfields. Nature, 2008, 455, 515

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Yamanouchi M, Chiba D, Matsukura F, et al. Current-induced domain-wall switching in a ferromagnetic semiconductor structure. Nature, 2004, 428, 539

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Yamanouchi M, Chiba D, Matsukura F, et al. Velocity of domain-wall motion induced by electrical current in a ferromagnetic semiconductor (Ga, Mn)As. Phys Rev Lett, 2006, 96, 096601

[50]

Gould C, Rüster C, Jungwirth T, et al. Tunneling anisotropic magnetoresistance: A spin-valve like tunnel magnetoresistance using a single magnetic layer. Phys Rev Lett, 2004, 93, 117203

[51]

Wunderlich J, Jungwirth T, Kaestner B, et al. Coulomb blockade anisotropic magnetoresistance effect in a (Ga, Mn)As single-electron transistor. Phys Rev Lett, 2006, 97, 077201

[52]

Bernevig B A, Vafek O. Piezo-magnetoelectric effects in p-doped semiconductors. Phys Rev B, 2005, 72, 033203

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Chernyshov A, Overby M, Liu X Y, et al. Evidence for reversible control of magnetization in a ferromagnetic material by means of spinorbit magneticfield. Nat Phys, 2009, 5, 656

[54]

Kanai S, Matsukura F, Ikeda S, et al. Spintronics: from basic research to VLSI application. AAPPS Bulletin, 2015, 25(13), 4

[55]

Jungwirth T, Niu Q, MacDonald A H. Anomalous Hall effect in ferromagnetic semiconductors. Phys Rev Lett, 2002, 88, 207208

[56]

Nagaosa N, Sinova J, Onoda S, et al. Anomalous Hall effect. Rev Mod Phys, 2010, 82, 1539

[57]

Ke H, Wang Y Y, Xue Q K. Topological materials: quantum anomalous Hall system. Annu Rev Cond Mat Phys, 2018, 9, 3293449

[58]

Tokura Y, Yasuda K, Tsukazaki A. Magnetic topological insulators. Nat Rev Phys, 2019, 110

[59]

Manchon A, Železné J, Miron I M, et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev Mod Phys, 2019, in press, arXiv:1801.09636

[60]

Stefanowicz S, Kunert G, Simserides C, et al. Phase diagram and critical behavior of a random ferromagnet Ga1– xMnxN. Phys Rev B, 2013, 88(R), 081201

[61]

Bonanni A, Sawicki M, Devillers T, et al. Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga, Mn)N. Phys Rev B, 2011, 84, 035206

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Kunert G, Dobkowska S, Li T, et al. Ga1– xMnxN epitaxial films with high magnetization. Appl Phys Lett, 2012, 101, 022413

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Korenblit I Y, Shender E F, Shklovsky B I. Percolation approach to the phase transition in the very dilute ferromagnetic alloys. Phys Lett A, 1973, 46, 275

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Sztenkiel D, Foltyn M, Mazur G P, et al. Stretching magnetism with an electricfield in a nitride semiconductor. Nat Commun, 2016, 7, 13232

[65]

Chang C Z, Zhang J S, Feng X, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science, 2013, 340, 167

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Yu R, Zhang W, Zhang H J, et al. Quantized anomalous Hall effect in magnetic topological insulators. Science, 2010, 329, 61

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Fan Y B, Kou X F, Upadhyaya P, et al. Electric-field control of spin-orbit torque in a magnetically doped topological insulator. Nat Nanotechnol, 2016, 352

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Bulmash D, Liu C X, Qi X L. Prediction of a Weyl semimetal in Hg1– x yCdxMnyTe. Phys Rev B, 2014, 89, 081106

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Dietl T, Ohno H, Matsukura F. Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors. Phys Rev B, 2001, 63, 195205

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Lewinert C, Bastard G. Indirect exchange interaction in extremely non-parabolic zerogap semiconductors. J Phys C, 1980, 13, 2347

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Gupta S, Kanai S, Matsukura F, et al. Magnetic and transport properties of Sb2Te3 doped with high concentration of Cr. Appl Phys Express, 2017, 10, 103001

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[1]

Methfessel S, Mattis D C. Magnetic semiconductors. Vol. 18. Springer, 1968, 1

[2]

Baltzer P K, Wojtowicz P J, Robbins M, et al. Exchange interactions in ferromagnetic chromium chalcogenide spinels. Phys Rev, 1966, 151, 367

[3]

Wachter P. Europium chalcogenides: EuO, EuS, EuSe and EuTe. In: Handbook on the Physics and Chemistry of Rare Earth. Vol. 2. Edited by Gschneidner K A Jr, Eyring L. Amsterdam: North-Holland, 1979, 507

[4]

Kasuya T, Yanase A. Anomalous transport phenomena in Eu-chalcogenide alloys. Rev Mod Phys, 1968, 40, 684

[5]

Nagaev E L. Colossal-magnetoresistance materials: manganites and conventional ferromagnetic semiconductors. Phys Rep, 2001, 346, 387

[6]

Žutić I, Matos-Abiague A, Scharf B, et al. Proximitized materials. Mater Today, 2019, 22, 85

[7]

Xu G, Weng H M, Wang Z J, et al. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4. Phys Rev Lett, 2011, 107, 186806

[8]

Jungwirth J, Marti X, Wadley P, et al. Antiferromagnetic spintronics. Nat Nanotech, 2016, 11(9), 231

[9]

Li H, Ruan S C, Zeng Y J. Intrinsic van der Waals magnetic materials from bulk to the 2D limit: New frontiers of spintronics. Adv Mater, 2019, 0, 1900065

[10]

Webster L, Yan J A. Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3. Phys Rev B, 2018, 98, 144411

[11]

Haury A, Wasiela A, Arnoult A, et al. Observation of a ferromagnetic transition induced by two-dimensional hole gas in modulationdoped CdMnTe quantum wells. Phys Rev Lett, 1997, 79, 511

[12]

Huang B, Clark G, Navarro-Moratalla E, et al. Intrinsic van der Waals magnetic materials from bulk to the 2D limit: New frontiers of spintronics. Nature, 2019, 546, 270

[13]

Gałązka R R. Semimagnetic semiconductors. Proceedings 14th International Conference on the Physics of Semiconductors, 1978, 133

[14]

Furdyna J K, Kossut J. Diluted magnetic semiconductors. In: Semiconductors and Semimetals. Vol. 25. New York: Academic Press, 1988

[15]

Dietl T. (Diluted) Magnetic semiconductors. In: Handbook of Semiconductors. Vol. 3B. Edited by Mahajan S. North Holland, Amsterdam, 1994. 1251

[16]

Spałek J, Lewicki A, Tarnawski Z, et al. Magnetic susceptibility of semimagnetic semiconductors: The high-temperature regime and the role of superexchange. Phys Rev B, 1986, 33, 3407

[17]

Gałązka R R. II–VI compounds — Polish perspective. Phys Stat Sol B, 2006, 243, 759

[18]

Andresen J C, Katzgraber H G, Oganesyan V, et al. Existence of a thermodynamic spin-glass phase in the zero-concentration limit of anisotropic dipolar systems. Phys Rev X, 2014, 4, 041016

[19]

Gaj J A, Kossut J. Introduction to the physics of diluted magnetic semiconductors. Berlin: Springer, 2010

[20]

Król M, Mirek R, Lekenta K, et al. Spin polarized semimagnetic exciton-polariton condensate in magnetic field. Sci Rep, 2018, 8(10), 6694

[21]

Betthausen C, Giudici P, Iankilevitch A, et al. Fractional quantum Hall effect in a dilute magnetic semiconductor. Phys Rev B, 2014, 90, 115302

[22]

Fiederling R, Keim M, Reuscher G, et al. Injection and detection of a spin-polarized current in a light-emitting diode. Nature, 1999, 402, 787

[23]

Leclercq B, Rigaux C, Mycielski A,et al. Critical dynamics in Cd1– xMnxTe spin glasses. Phys Rev B, 1993, 47, 6169

[24]

Jaroszyński J, Wróbel J, Karczewski G, et al. Magnetoconductance noise and irreversibilities in submicron wires of spin-glass n+-Cd1– xMnxTe. Phys Rev Lett, 1998, 80, 5635

[25]

Dietl T. Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach. Phys Rev B, 2015, 91, 125204

[26]

Dietl T. Hole states in wide band-gap diluted magnetic semiconductors and oxides. Phys Rev B, 2008, 77, 085208

[27]

Pacuski W, Kossacki P, Ferrand D, et al. Observation of strong-coupling effects in a diluted magnetic semiconductor Ga1– xFexN. Phys Rev Lett, 2008, 100, 037204

[28]

Besombes L, Léger Y, Maingault L, et al. Probing the spin state of a single magnetic ion in an individual quantum dot. Phys Rev Lett, 2004, 93, 207403

[29]

Kobak J, Smoleński T, Goryca M, et al. Designing quantum dots for solotronics. Nat Commun, 2014, 5, 3191

[30]

Dietl T, Ohno H, Matsukura F, et al. Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science, 2000, 287, 1019

[31]

Dietl T, Ohno H. Dilute ferromagnetic semiconductors: Physics and spintronic structures. Rev Mod Phys, 2014, 86, 187

[32]

Ohno H. Making nonmagnetic semiconductors ferromagnetic. Science, 1998, 281, 951

[33]

Story T, Gałązka R R, Frankel R B, et al. Carrier-concentration-induced ferromagnetism in PbSnMnTe. Phys Rev Lett, 1986, 56(11), 777

[34]

Ferrand D, Cibert J, Bourgognon C, et al. Carrier-induced ferromagnetic interactions in p-doped Zn1– xMnxTe epilayers. J Cryst Growth, 2000, 214, 387

[35]

Olejník K, Owen M H S, Novák V, et al. Enhanced annealing, high Curie temperature and low-voltage gating in (Ga, Mn)As: A surface oxide control study. Phys Rev B, 2008, 78, 054403

[36]

Wang M, Campion R P, Rushforth A W, et al. Achieving high Curie temperature in (Ga, Mn)As. Appl Phys Lett, 2008, 93, 132103

[37]

Chen L, Yang X, Yang H F, et al. Enhancing the Curie temperature of ferromagnetic semiconductor (Ga, Mn)As to 200 K via nanostructure engineering. Nano Lett, 2011, 11, 2584

[38]

Fukuma Y, Asada H, Miyawaki S, et al. Carrierinduced ferromagnetism in Ge0.92Mn0.08Te epilayers with a Curie temperature up to 190 K. Appl Phys Lett, 2008, 93, 252502

[39]

Hassan M, Springholz G, Lechner R T, et al. Molecular beam epitaxy of single phase GeMnTe with high ferromagnetic transition temperature. J Cryst Growth, 2011, 323, 363

[40]

Zhao K, Chen B J, Zhao G Q, et al. Ferromagnetism at 230K in (Ba0.7K0.3)(Zn0.85Mn0.15)2As2 diluted magnetic semiconductor. Chin Sci Bull, 2014, 59, 2524

[41]

Andrearczyk T, Jaroszyński J, Sawicki M, et al. Ferromagnetic interactions in p- and n-type II–VI diluted magnetic semiconductors. Proceedings of 25th International Conference on Physics of Semiconductors, 2000, 235

[42]

Kazakov A, Simion G, Lyanda-Geller Y, et al. Mesoscopic transport in electrostatically defined spin-full channels in quantum Hall ferromagnets. Phys Rev Lett, 2017, 119, 046803

[43]

Jungwirth T, Wunderlich J, Novák V, et al. Spin-dependent phenomena and device concepts explored in (Ga, Mn)As. Rev Mod Phys, 2014, 86, 855

[44]

Ohno Y, Young D K, Beschoten B, et al. Electrical spin injection in a ferromagnetic semiconductor heterostructure. Nature, 1999, 402, 790

[45]

Ohno H, Chiba D, Matsukura F, et al. Electric-field control of ferromagnetism. Nature, 2000, 408, 944

[46]

Boukari H, Kossacki P, Bertolini M, et al. Light and electricfield control of ferromagnetism in magnetic quantum structures. Phys Rev Lett, 2002, 88, 207204

[47]

Chiba D, Sawicki M, Nishitani Y, et al. Magnetization vector manipulation by electricfields. Nature, 2008, 455, 515

[48]

Yamanouchi M, Chiba D, Matsukura F, et al. Current-induced domain-wall switching in a ferromagnetic semiconductor structure. Nature, 2004, 428, 539

[49]

Yamanouchi M, Chiba D, Matsukura F, et al. Velocity of domain-wall motion induced by electrical current in a ferromagnetic semiconductor (Ga, Mn)As. Phys Rev Lett, 2006, 96, 096601

[50]

Gould C, Rüster C, Jungwirth T, et al. Tunneling anisotropic magnetoresistance: A spin-valve like tunnel magnetoresistance using a single magnetic layer. Phys Rev Lett, 2004, 93, 117203

[51]

Wunderlich J, Jungwirth T, Kaestner B, et al. Coulomb blockade anisotropic magnetoresistance effect in a (Ga, Mn)As single-electron transistor. Phys Rev Lett, 2006, 97, 077201

[52]

Bernevig B A, Vafek O. Piezo-magnetoelectric effects in p-doped semiconductors. Phys Rev B, 2005, 72, 033203

[53]

Chernyshov A, Overby M, Liu X Y, et al. Evidence for reversible control of magnetization in a ferromagnetic material by means of spinorbit magneticfield. Nat Phys, 2009, 5, 656

[54]

Kanai S, Matsukura F, Ikeda S, et al. Spintronics: from basic research to VLSI application. AAPPS Bulletin, 2015, 25(13), 4

[55]

Jungwirth T, Niu Q, MacDonald A H. Anomalous Hall effect in ferromagnetic semiconductors. Phys Rev Lett, 2002, 88, 207208

[56]

Nagaosa N, Sinova J, Onoda S, et al. Anomalous Hall effect. Rev Mod Phys, 2010, 82, 1539

[57]

Ke H, Wang Y Y, Xue Q K. Topological materials: quantum anomalous Hall system. Annu Rev Cond Mat Phys, 2018, 9, 3293449

[58]

Tokura Y, Yasuda K, Tsukazaki A. Magnetic topological insulators. Nat Rev Phys, 2019, 110

[59]

Manchon A, Železné J, Miron I M, et al. Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems. Rev Mod Phys, 2019, in press, arXiv:1801.09636

[60]

Stefanowicz S, Kunert G, Simserides C, et al. Phase diagram and critical behavior of a random ferromagnet Ga1– xMnxN. Phys Rev B, 2013, 88(R), 081201

[61]

Bonanni A, Sawicki M, Devillers T, et al. Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga, Mn)N. Phys Rev B, 2011, 84, 035206

[62]

Kunert G, Dobkowska S, Li T, et al. Ga1– xMnxN epitaxial films with high magnetization. Appl Phys Lett, 2012, 101, 022413

[63]

Korenblit I Y, Shender E F, Shklovsky B I. Percolation approach to the phase transition in the very dilute ferromagnetic alloys. Phys Lett A, 1973, 46, 275

[64]

Sztenkiel D, Foltyn M, Mazur G P, et al. Stretching magnetism with an electricfield in a nitride semiconductor. Nat Commun, 2016, 7, 13232

[65]

Chang C Z, Zhang J S, Feng X, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science, 2013, 340, 167

[66]

Yu R, Zhang W, Zhang H J, et al. Quantized anomalous Hall effect in magnetic topological insulators. Science, 2010, 329, 61

[67]

Fan Y B, Kou X F, Upadhyaya P, et al. Electric-field control of spin-orbit torque in a magnetically doped topological insulator. Nat Nanotechnol, 2016, 352

[68]

Bulmash D, Liu C X, Qi X L. Prediction of a Weyl semimetal in Hg1– x yCdxMnyTe. Phys Rev B, 2014, 89, 081106

[69]

Dietl T, Ohno H, Matsukura F. Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors. Phys Rev B, 2001, 63, 195205

[70]

Lewinert C, Bastard G. Indirect exchange interaction in extremely non-parabolic zerogap semiconductors. J Phys C, 1980, 13, 2347

[71]

Vergniory M G, Otrokov M M, Thonig D, et al. Exchange interaction and its tuning in magnetic binary chalcogenides. Phys Rev B, 2014, 89, 165202

[72]

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T Dietl, A Bonanni, H Ohno, Families of magnetic semiconductors — an overview[J]. J. Semicond., 2019, 40(8): 080301. doi: 10.1088/1674-4926/40/8/080301.

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Manuscript received: Manuscript revised: Online: Accepted Manuscript: 19 June 2019 Uncorrected proof: 09 July 2019 Published: 09 August 2019

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