References
- Yu R, Zhang W, Zhang H-J, et al. Quantized anomalous hall effect in magnetic topological insulators. Science. 2010;329:61.
- Liu C-X, Qi X-L, Dai X, et al. Quantum anomalous hall effect inHg1 y Mny tequantum wells. Phys Rev Lett. 2008;101:146802.
- He K, Wang Y, Xue Q-K. Quantum anomalous Hall effect. Natl Sci Rev. 2014;1:38–24.
- Chang C-Z, Zhang J, Feng X, et al. Experimental observation of the quantum anomalous hall effect in a magnetic topological Insulator. Science. 2013;340:167.
- Chang C-Z, Zhao W, Kim DY, et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator. Nat Mater. 2015;14:473–477.
- Feng Y, Feng X, Ou Y, et al. Observation of the zero hall plateau in a quantum anomalous hall insulator. Phys Rev Lett. 2015;115:126801.
- Beidenkopf H, Roushan P, Seo J, et al. Spatial fluctuations of helical Dirac fermions on the surface of topological insulators. Nat Phys. 2011;7:939–943.
- Mogi M, Kawamura M, Yoshimi R, et al. A magnetic heterostructure of topological insulators as a candidate for an axion insulator. Nat Mater. 2017;16:516–521.
- He QL, Kou X, Grutter AJ, et al. Tailoring exchange couplings in magnetic topological-insulator/antiferromagnet heterostructures. Nat Mater. 2017;16:94–100.
- Fan Y, Upadhyaya P, Kou X, et al. Magnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructure. Nat Mater. 2014;13:699–704.
- Zhang J-M, Zhu W, Zhang Y, et al. tailoring magnetic doping in the topological insulato Bi2Se3. Phys Rev Lett. 2012;109:266405.
- Jiang Z, Chang C-Z, Tang C, et al. AIP Adv. 2016;6: 055809. https://aip.scitation.org/doi/full/10.1063/1.4943061.
- He K, Wang Y, Xue Q-K. Topological materials: quantum anomalous hall system. Ann Rev Condens Matter Phys. 2018;9:329–344.
- Himpsel FJ, Ortega JE, Mankey GJ, et al. Magnetic nanostructures. Adv Phys. 1998;47:511–597.
- Kou X, Guo S-T, Fan Y, et al. Scale-invariant quantum anomalous hall effect in magnetic topological insulators beyond the two-dimensional Limit. Phys Rev Lett. 2014;113:137201.
- Wang J, Lian B, Qi X-L, et al. Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state. Phys Rev B. 2015;92:081107.
- Li P, Yu J, Xu J, et al. Topological-magnetic proximity effect in Sb2Te3/CrI3 heterostructures. Phys B Condens Matter. 2019;573:77-μ.
- Klitzing KV, Dorda G, Pepper M. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys Rev Lett. 1980;45:494–497.
- Kou X, Fan,K Y, Wang L. Review of Quantum Hall Trio. J Phys Chem Solids. 2019;128:2–23.
- Yasuda K, Morimoto T, Yoshimi R, et al. Large non-reciprocal charge transport mediated by quantum anomalous Hall edge states. Nat Nanotechnol. 2020;15:831–835.
- Chen L, Shi C, Jiang C, et al. Realization of quantized anomalous Hall effect by inserting CrI3layer in Bi2 Se3 m. New J Phys. 2020;22:073005.
- Nagaosa N, Sinova J, Onoda S, et al. Anomalous Hall effect. Rev Mod Phys. 2010;82:1539–1592.
- Haldane FDM. Model for a quantum hall effect without landau levels: condensed-matter realization of the “Parity Anomaly”. Phys Rev Lett. 1988;61:2015–2018.
- Onoda, M, Nagaosa N. Quantized anomalous hall effect in two-dimensional ferromagnets: quantum hall effect in metals. Phys Rev Lett. 2003;90:206601.
- Bernevig BA, Hughes TL, Zhang S-C. Quantum spin hall effect and topological phase transition in hgte quantum wells. Science. 2006;314:1757.
- Chang C-Z, Zhang J, Liu M, et al. Thin films of magnetically doped topological insulator with carrier-independent long-range ferromagnetic order. Adv Mater. 2013;25:1065–1070.
- Checkelsky JG, Yoshimi R, Tsukazaki A, et al. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat Phys. 2014;10:731–736.
- Grauer S, Fijalkowski KM, Schreyeck S, et al. Scaling of the quantum anomalous hall effect as an indicator of axion electrodynamics. Phys Rev Lett. 2017;118:246801.
- Kandala A, Richardella A, Kempinger S, et al. Giant anisotropic magnetoresistance in a quantum anomalous Hall insulator. Nat Commun. 2015;6:7434.
- Ou Y, Liu C, Jiang G, et al. Enhancing the quantum anomalous hall effect by magnetic codoping in a topological insulator. Adv Mater. 2018;30:1703062.
- Qi S, Qiao Z, Deng X, et al. High-temperature quantum anomalous hall effect in n p Codoped Topological Insulators . Phys Rev Lett. 2016;117:056804.
- Lee I, Kim CK, Lee J, et al. Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx(Bi 0.1Sb 0.9)2-xTe 3 . Proc Nat Acad Sci. 2015;112:1316.
- Lachman EO, Young AF, Richardella A, et al. Visualization of superparamagnetic dynamics in magnetic topological insulators. Sci Adv. 2015;1:e1500740.
- Feng X, Feng Y, Wang J, et al. Thickness dependence of the quantum anomalous hall effect in magnetic topological insulator films. Adv Mater. 2016;28:6386–6390.
- Liu M, Wang W, Richardella AR, et al. Large discrete jumps observed in the transition between Chern states in a ferromagnetic topological insulator. Sci Adv. 2016;2:e1600167.
- Grauer S, Schreyeck S, Winnerlein M, et al. Coincidence of superparamagnetism and perfect quantization in the quantum anomalous Hall state. Physical Review B. 2015;92:201304.
- Chen YL, Chu J-H, Analytis JG, et al. Massive dirac fermion on the surface of a magnetically doped topological insulator. Science. 2010;329:659.
- Zhang J, Chang C-Z, Tang P, et al. Topology-Driven magnetic quantum phase transition in topological Insulators. Science. 2013;339:1582.
- Ou Y, Liu C, Zhang L, et al. Heavily Cr-doped (Bi,Sb)2Te3as a ferromagnetic insulator with electrically tunable conductivity. APL Mater. 2016;4:086101.
- McCray WP. MBE deserves a place in the history books. Nat Nanotechnol. 2007;2:259–261.
- Panish MB. Molecular Beam Epitaxy. Science. 1980;208:916.
- Kou X, He L, Lang M, et al. Manipulating surface-related ferromagnetism in modulation-doped topological Insulators. Nano Lett. 2013;13:4587–4593.
- Mogi M, Yoshimi R, Tsukazaki A, et al. Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect. Appl Phys Lett. 2015;107:182401.
- Pan L, Liu X, He QL, et al. Probing the low-temperature limit of the quantum anomalous Hall effect. Sci Adv. 2020;6:eaaz3595.
- Xiao D, Jiang J, Shin J-H, et al. Realization of the axion insulator state in quantum anomalous hall sandwich Heterostructures. Phys Rev Lett. 2018;120:056801.
- Yoshimi R., Yasuda K., Tsukazaki A., Takahashi K.S., Nagaosa N., Kawasaki M., and Tokura Y., Quantum Hall states stablilized in semi-magnetic bilayers of topological insulators, Nature Communicaitons 6:8530 (2015). https://www.nature.com/articles/ncomms9530
- He QL, Pan L, Stern AL, et al. Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure. Science. 2017;357:294.
- Zhou Z, Chien Y-J, Uher C. Thin film dilute ferromagnetic semiconductors Sb2x Cr x Te 3with a Curie temperature up to 190K . Physical Review B. 2006;74:224418.
- Fanchiang YT, Chen KHM, Tseng CC, et al. Strongly exchange-coupled and surface-state-modulated magnetization dynamics in Bi2Se3/yttrium iron garnet heterostructures. Nat Commun. 2018;9:223.
- Jiang Z, Chang C-Z, Tang C, et al. Independent tuning of electronic properties and induced ferromagnetism in topological insulators with heterostructure approach. Nano Lett. 2015;15:5835–5840.
- Lang M, Montazeri M, Onbasli MC, et al. Proximity induced high-temperature magnetic order in topological insulator - ferrimagnetic insulator heterostructure. Nano Lett. 2014;14:3459–3465.
- Katmis F, Lauter V, Nogueira FS, et al. A high-temperature ferromagnetic topological insulating phase by proximity coupling. Nature. 2016;533:513–516.
- Lee C, Katmis F, Jarillo-Herrero P, et al. Direct measurement of proximity-induced magnetism at the interface between a topological insulator and a ferromagnet. Nat Commun. 2016;7:12014 .
- Li M, Chang C-Z, Kirby BJ, et al. Proximity-driven enhanced magnetic order at ferromagnetic-insulator–magnetic-topological-insulator interface. Phys Rev Lett. 2015;115:087201.
- Wei P, Katmis F, Assaf BA, et al. Exchange-coupling-induced symmetry breaking in topological Insulators. Phys Rev Lett. 2013;110:186807.
- Tang C, Chang C-Z, Zhao G, et al. Above 400-K robust perpendicular ferromagnetic phase in a topological insulator. Sci Adv. 2017;3:e1700307.
- Figueroa AI, Bonell F, Cuxart MG, et al. Absence of magnetic proximity effect at the interface of Bi2Se3andBi Sb 2 Te3with EuS. Phys Rev Lett. 2020;125:226801.
- Eremeev SV, Men׳shov VN, Tugushev VV, et al. Interface induced states at the boundary between a 3D topological insulator Bi 2 Se 3 and a ferromagnetic insulator EuS. J Magn Magn Mater. 2015;383:30–33.
- Kim J, Kim K-W, Wang H, et al. Understanding the giant enhancement of exchange interaction inb2se3 euSHeterostructures. Phys Rev Lett. 2017;119:027201.
- Chen P, Zhang Y, Yao Q, et al. Tailoring the hybrid anomalous hall response in engineered magnetic topological insulator heterostructures. Nano Lett. 2020;20:1731–1737.
- Che X, Murata K, Pan L, et al. Proximity-induced magnetic order in a transferred topological insulator thin film on a magnetic insulator. ACS Nano. 2018;12:5042–5050.
- Lee JS, Richardella A, Fraleigh RD et al. Engineering the breaking of time-reversal symmetry in gate-tunable hybrid ferromagnet/topological insulator heterostructures. npj Quantum Materials. 3:2018; DOI: https://doi.org/10.1038/s41535-018-0123-2
- Mogi M, Nakajima T, Ukleev V, et al. Large anomalous hall effect in topological insulators with proximitized ferromagnetic insulators. Phys Rev Lett. 2019;123:016804.
- He QL, Yin G, Yu L, et al. Topological Transitions Induced by Antiferromagnetism in a Thin-Film Topological Insulator. Phys Rev Lett. 2018;121:096802.
- Pan L, Grutter A, Zhang P, et al. Observation of quantum anomalous hall effect and exchange interaction in topological insulator/antiferromagnet heterostructure. Adv Mater. 2020;32:2001460.
- Watanabe R, Yoshimi R, Kawamura M, et al. Quantum anomalous Hall effect driven by magnetic proximity coupling in all-telluride based heterostructure. Appl Phys Lett. 2019;115:102403.
- Jiang G, Feng Y, Wu W, et al. Quantum Anomalous Hall Multilayers Grown by Molecular Beam Epitaxy. Chin Phys Lett. 2018;35:076802.
- Wang KL, Kou X, Upadhyaya P, et al. Electric-Field Control of Spin-Orbit Interaction for Low-Power Spintronics. Proc IEEE. 2016;104:1974–2008.
- Kuroda K, Arita M, Miyamoto K, et al. hexagonally deformed fermi surface of the 3D Topological InsulatorBi 2Se 3. Phys Rev Lett. 2010;105:076802.
- Yasuda K, Tsukazaki A, Yoshimi R, et al. Large unidirectional magnetoresistance in a magnetic topological insulator. Phys Rev Lett. 2016;117:127202.
- Yasuda K, Tsukazaki A, Yoshimi R, et al. Current-nonlinear hall effect and spin-orbit torque magnetization switching in a magnetic topological insulator. Phys Rev Lett. 2017;119:137204.
- He P, Zhang SS-L, Zhu D, et al. Bilinear magnetoelectric resistance as a probe of three-dimensional spin texture in topological surface states. Nat Phys. 2018;14:495–499.
- Li CH, van ‘T Erve OMJ, Robinson JT, et al. Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in Bi2Se3. Nat Nanotechnol. 2014;9:218–224.
- Tang J, Chang L-T, Kou X, et al. Electrical detection of spin-polarized surface states conduction in (Bi0.53Sb 0.47)2 Te 3Topological Insulator. Nano Lett. 2014;14:5423–5429.
- Lee JS, Richardella A, Hickey DR, et al. Mapping the chemical potential dependence of current-induced spin polarization in a topological insulator. Phys Rev B. 2015;92:155312.
- Liu L, Pai C-F, Li Y, et al. Spin-torque switching with the giant spin hall effect of tantalum. Science. 2012;336:555.
- Sánchez JCR, Vila L, Desfonds G, et al. Spin-to-charge conversion using Rashba coupling at the interface between non-magnetic materials. Nat Commun. 2013;4:2944.
- Lesne E, Fu Y, Oyarzun S, et al. Highly efficient and tunable spin-to-charge conversion through Rashba coupling at oxide interfaces. Nat Mater. 2016;15:1261–1266.
- Mellnik AR, Lee JS, Richardella A, et al. Spin-transfer torque generated by a topological insulator. Nature. 2014;511:449–451.
- Liu L, Moriyama T, Ralph DC, et al. Spin-torque ferromagnetic resonance induced by the spin hall effect. Phys Rev Lett. 2011;106:036601.
- Pai C-F, Liu L, Li Y, et al. Spin transfer torque devices utilizing the giant spin Hall effect of tungsten. Appl Phys Lett. 2012;101:122404.
- Deorani P, Son J, Banerjee K, et al. Observation of inverse spin Hall effect in bismuth selenide. Phys Rev B. 2014;90:094403.
- Tang C, Song Q, Chang C-Z, et al. Dirac surface state–modulated spin dynamics in a ferrimagnetic insulator at room temperature. Sci Adv. 2018;4:eaas8660.
- Wang Y, Deorani P, Banerjee K, et al. Topological surface states originated spin-orbit torques inBi 2Se 3. Phys Rev Lett. 2015;114:257202.
- Fan Y, Kou X, Upadhyaya P, et al. Electric-field control of spin–orbit torque in a magnetically doped topological insulator. Nat Nanotechnol. 2016;11:352–359.
- Jiang Z, Chang C-Z, Masir MR, et al. Enhanced spin Seebeck effect signal due to spin-momentum locked topological surface states. Nat Commun. 2016;7:11458.
- Dankert A, Geurs J, Kamalakar MV, et al. Room Temperature Electrical Detection of Spin Polarized Currents in Topological Insulators. Nano Lett. 2015;15:7976–7981.
- Liu L, Richardella A, Garate I, et al. Spin-polarized tunneling study of spin-momentum locking in topological insulators. Phys Rev B. 2015;91:235437.
- Wang Y, Zhu D, Wu Y, et al. Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques. Nat Commun. 2017;8:1364.
- Wu H, Zhang P, Deng P, et al. Room-Temperature Spin-Orbit Torque from Topological Surface States. Phys Rev Lett. 2019;123:207205.
- Shao Q, Wu H, Pan Q, et al., presented at the 2018 IEEE International Electron Devices Meeting (IEDM), 2018 (unpublished), San Francisco, CA, USA. https://ieeexplore.ieee.org/document/8614499.
- Han J, Richardella A, Siddiqui SA, et al. Room-Temperature Spin-Orbit Torque Switching Induced by a Topological Insulator. Phys Rev Lett. 2017;119:077702.
- Dc M, Grassi R, Chen J-Y, et al. Room-temperature high spin–orbit torque due to quantum confinement in sputtered BixSe(1–x) films. Nat Mater. 2018;17:800–807.
- Bahramy MS, King PDC, de la Torre A, et al. Emergent quantum confinement at topological insulator surfaces. Nat Commun. 2012;3:1159.
- Park BC, Kim T-H, Sim KI, et al. Terahertz single conductance quantum and topological phase transitions in topological insulator Bi2Se3 ultrathin films. Nat Commun. 2015;6:6552.
- Kondou K, Yoshimi R, Tsukazaki A, et al. Fermi-level-dependent charge-to-spin current conversion by Dirac surface states of topological insulators. Nat Phys. 2016;12:1027–1031.
- Khang NHD, Ueda,P Y, Hai N. A conductive topological insulator with large spin Hall effect for ultralow power spin–orbit torque switching. Nat Mater. 2018;17:808–813.
- Fert A, Cros V, Sampaio J. Skyrmions on the track. Nat Nanotechnol. 2013;8:152–156.
- Wu H, Gross F, Dai B, et al. Ferrimagnetic Skyrmions in Topological Insulator/Ferrimagnet Heterostructures. Adv Mater. 2020;32:e2003380.
- Yasuda K, Wakatsuki R, Morimoto T, et al. Geometric Hall effects in topological insulator heterostructures. Nat Phys. 2016;12:555–559.
- Zhang S, Kronast F, van der Laan G, et al. Real-Space Observation of Skyrmionium in a Ferromagnet-Magnetic Topological Insulator Heterostructure. Nano Lett. 2018;18:1057–1063.
- He QL, Yin G, Grutter AJ, et al. Exchange-biasing topological charges by antiferromagnetism. Nat Commun. 2018;9:2767.
- Deng Y, Yu Y, Shi MZ, et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi 2 Te 4 . Science. 2020;367:895–900.
- He K, Xue Q-K. The Road to High-Temperature Quantum Anomalous Hall Effect in Magnetic Topological Insulators. SPIN. 2019;09:1940016.