本征磁性拓扑绝缘体的高压输运研究

本征磁性拓扑绝缘体MnBi₂Te₄(Bi₂Te₃)_n异质结蕴含着磁性与拓扑序的奇异相互作用，与量子反常霍尔效应等量子现象密切相关。随着非磁性Bi₂Te₃层的层数n增多，实验表明MnBi₂Te₄(Bi₂Te₃)_n的磁基态由A型反铁磁（A-AFM）过渡为铁磁（FM），然而层内都展现了比较稳定的铁磁耦合。本论文主要通过高压原位输运测量手段，系统性地探究了等静水压对MnBi₄Te₇（n=1），MnBi₆Te₁₀（n = 2）磁基态的调控。随着压力的增大，我们发现MnBi₄Te₇和MnBi₆Te₁₀的磁转变温度均有下降，MnBi₄Te₇保持在A型反铁磁基态，而MnBi₆Te₁₀在1.98GPa时发生了由A型反铁磁体转变至准二维铁磁体的相变。高压磁性测量进一步证实了1.98GPa时MnBi₆Te₁₀发生了压力诱导的相变。

结合第一性原理分析，我们认为层内晶格压缩诱导的层内反铁磁序与原有铁磁序的竞争抑制了层内磁性，层内磁性的下降将削弱层间耦合；另一方面，层间晶格压缩增强了层间耦合。层间耦合较弱的体系的磁基态（n>1）很大程度取决于层内耦合，因而MnBi₆Te₁₀的磁性被等静水压抑制，甚至在1.98GPa时发生了层间脱耦。进一步的Sb掺杂研究显示，x = 0.2时Mn(Bi_1-xSb_x)₆Te₁₀已进入准二维铁磁态，我们认为Sb掺杂诱导的相变同样源于层内晶格收缩。

我们还研究了准二维铁磁体MnBi₈Te₁₃（n=3）的高压输运特性。在高达3.15GPa的压力范围内，MnBi₈Te₁₃的磁性被压力显著削弱。特别地，反常霍尔电阻率在1.64GPa时出现了反号，并且反号被压力进一步增强。反号出现的同时还伴随着驼峰状非单调凸起。我们认为该反常行为可能来源于两个反常霍尔信号的叠加。我们的研究显示等静水压能够有效调控MnBi₂Te₄(Bi₂Te₃)_n的磁基态。其丰富的高压相图蕴藏着拓扑性质与磁性之间复杂的相互作用。

In intrinsic magnetic topological insulator MnBi₂Te₄(Bi₂Te₃)_n heterostructures, the interplay between nontrivial band topology and magnetic order produces intriguing states of matter, such as quantum anomalous Hall effect, etc. With the number of nonmagnetic Bi₂Te₃ spacer layer n increases, it was experimentally shown that the magnetic ground state of MnBi₂Te₄(Bi₂Te₃)_n goes through a transition from A-type antiferromagnetic (A-AFM) to ferromagnetic (FM), while the intralayer exchange coupling stays FM state. By performing in-situ high pressure magneto-transport measurements, this thesis presents a systematic study of the hydrostatic pressure tuning of both the intralayer and interlayer exchange coupling of MnBi₄Te₇ (n = 1 ) and MnBi₆Te₁₀ (n = 2 ) up to 3.5GPa. We find the intralayer coupling strength of MnBi₄Te₇ and MnBi₆Te₁₀ is reduced by increasing pressure. The magnetic ground state of MnBi₄Te₇ stays a robust A-AFM state, while MnBi₆Te₁₀ undergoes a phase transition from A-type AFM state to quasi-two-dimensional (quasi-2D) FM state at 1.98GPa. The phase transition is further determined by high pressure magnetic measurements.

Through the first-principles calculations analysis, we propose the suppression of the intralayer exchange coupling is rooted in the competition between in-plane-lattice-compression-induced AFM order and intralayer FM order. The suppression of intralayer exchange magnetism will further inhibit the interlayer coupling. On the contrary, the lattice compression along the c axis enhances the interlayer exchange coupling. Intralayer exchange coupling plays an important role in determining the magnetic ground state of weakly coupled magnetic topological insulators (n > 1 ). Thus, the net magnetism of MnBi₆Te₁₀ decreases with pressure and adjacent layers are decoupled at 1.98GPa. In addition, we have studied the magnetic properties of Mn(Bi_1-xSb_x)₆Te₁₀. Through Sb doping, we find the magnetic ground state of Mn(Bi_1-xSb_x)₆Te₁₀ emerged as quasi-2D FM state when x = 0.2. The phase transition induced by Sb doping is similarly attributed to in-plane-lattice-compression.

Furthermore, we have studied the high pressure transport properties of quasi-2D ferromagnet MnBi₈Te₁₃ (n = 3 ). The net ferromagnetism of MnBi₈Te₁₃ is suppressed by pressure up to 3.15GP. In particular, the polarity of the anomalous Hall resistivity is reversed under 1.64GPa. The reversed Hall signal is enhanced by increasing pressure. The sign reversal is accompanied by the emergence of two nonmonotonic humps. We propose the sign reversal could be attributed to the co-existence of two anomalous Hall effect. Our study indicates hydrostatic pressure could be an effective method for the tuning of the magnetic ground state of MnBi₂Te₄(Bi₂Te₃)_n, in whose high pressure phase diagram the complicated interplay between topology and magnetic order embedded.

[1] KLITZING K V, DORDA G, PEPPER M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance[J]. Physical review letters, 1980, 45(6): 494.
[2] THOULESS D J, KOHMOTO M, NIGHTINGALE M P, et al. Quantized Hall conductance in a two-dimensional periodic potential[J]. Physical review letters, 1982, 49(6): 405.
[3] TSUI D C, STORMER H L, GOSSARD A C. Two-dimensional magnetotransport in the extreme quantum limit[J]. Physical review letters, 1982, 48(22): 1559.
[4] WEN X-G. Topological orders and edge excitations in fractional quantum Hall states[J]. Advances in Physics, 1995, 44(5): 405-473.
[5] NAKAHARA M. Geometry, topology and physics[M]. CRC press, 2018.
[6] HASAN M Z, KANE C L. Colloquium: topological insulators[J]. Reviews of modern physics, 2010, 82(4): 3045.
[7] HALDANE F D M. Model for a quantum Hall effect without Landau levels: Condensed-matter realization of the" parity anomaly"[J]. Physical review letters, 1988, 61(18): 2015.
[8] NOVOSELOV K S, GEIM A K, MOROZOV S V, et al. Electric field effect in atomically thin carbon films[J]. science, 2004, 306(5696): 666-669.
[9] NETO A C, GUINEA F, PERES N M, et al. The electronic properties of graphene[J]. Reviews of modern physics, 2009, 81(1): 109.
[10] KANE C L, MELE E J. Z 2 topological order and the quantum spin Hall effect[J]. Physical review letters, 2005, 95(14): 146802.
[11] MURAKAMI S. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase[J]. New Journal of Physics, 2007, 9(9): 356.
[12] SHENG D, WENG Z, SHENG L, et al. Quantum spin-Hall effect and topologically invariant Chern numbers[J]. Physical review letters, 2006, 97(3): 036808.
[13] HUERTAS-HERNANDO D, GUINEA F, BRATAAS A. Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps[J]. Physical Review B, 2006, 74(15): 155426.
[14] BOETTGER J, TRICKEY S. First-principles calculation of the spin-orbit splitting in graphene[J]. Physical Review B, 2007, 75(12): 121402.108
[15] BERGMAN D L, LE HUR K. Near-zero modes in condensate phases of the Dirac theory on the honeycomb lattice[J]. Physical Review B, 2009, 79(18): 184520.
[16] BERNEVIG B A, HUGHES T L, ZHANG S-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells[J]. science, 2006, 314(5806): 1757-1761.
[17] KONIG M, WIEDMANN S, BRUNE C, et al. Quantum spin Hall insulator state in HgTe quantum wells[J]. science, 2007, 318(5851): 766-770.
[18] ROTH A, BRüNE C, BUHMANN H, et al. Nonlocal transport in the quantum spin Hall state[J]. science, 2009, 325(5938): 294-297.
[19] BüTTIKER M. Absence of backscattering in the quantum Hall effect in multiprobe conductors[J]. Physical Review B, 1988, 38(14): 9375.
[20] LIU C, HUGHES T L, QI X-L, et al. Quantum spin Hall effect in inverted type-II semiconductors[J]. Physical review letters, 2008, 100(23): 236601.
[21] DU L, KNEZ I, SULLIVAN G, et al. Robust helical edge transport in gated InAs/GaSb bilayers[J]. Physical review letters, 2015, 114(9): 096802.
[22] QI X-L, ZHANG S-C. Topological insulators and superconductors[J]. Reviews of modern physics, 2011, 83(4): 1057.
[23] ANDO Y. Topological insulator materials[J]. Journal of the Physical Society of Japan, 2013, 82(10): 102001.
[24] VERGNIORY M, ELCORO L, FELSER C, et al. A complete catalogue of high-quality topological materials[J]. Nature, 2019, 566(7745): 480-485.
[25] TANG F, PO H C, VISHWANATH A, et al. Comprehensive search for topological materials using symmetry indicators[J]. Nature, 2019, 566(7745): 486-489.
[26] ZHANG T, JIANG Y, SONG Z, et al. Catalogue of topological electronic materials[J]. Nature, 2019, 566(7745): 475-479.
[27] FU L, KANE C L. Topological insulators with inversion symmetry[J]. Physical Review B, 2007, 76(4): 045302.
[28] NAGAO T, SADOWSKI J, SAITO M, et al. Nanofilm Allotrope and Phase Transformation of Ultrathin Bi Film on S i (111)− 7× 7[J]. Physical review letters, 2004, 93(10): 105501.
[29] WADA M, MURAKAMI S, FREIMUTH F, et al. Localized edge states in two-dimensional topological insulators: Ultrathin Bi films[J]. Physical Review B, 2011, 83(12): 121310.
[30] HSIEH D, QIAN D, WRAY L, et al. A topological Dirac insulator in a quantum spin Hall phase[J]. Nature, 2008, 452(7190): 970-974.
[31] HSIEH D, XIA Y, QIAN D, et al. Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi 2 Te 3 and Sb 2 Te 3[J]. Physical review letters, 2009, 103(14): 146401.
[32] XIA Y, QIAN D, HSIEH D, et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface[J]. Nature Physics, 2009, 5(6): 398-402.
[33] ZHANG H, LIU C-X, QI X-L, et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface[J]. Nature Physics, 2009, 5(6): 438-442.
[34] CHEN Y, ANALYTIS J G, CHU J-H, et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3[J]. science, 2009, 325(5937): 178-181.
[35] HSIEH D, XIA Y, QIAN D, et al. A tunable topological insulator in the spin helical Dirac transport regime[J]. Nature, 2009, 460(7259): 1101-1105.
[36] ROY R. Topological phases and the quantum spin Hall effect in three dimensions[J]. Physical Review B, 2009, 79(19): 195322.
[37] SUZUURA H, ANDO T. Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice[J]. Physical review letters, 2002, 89(26): 266603.
[38] NOMURA K, KOSHINO M, RYU S. Topological delocalization of two-dimensional massless Dirac fermions[J]. Physical review letters, 2007, 99(14): 146806.
[39] LI C, VAN‘T ERVE O, LI Y, et al. Electrical detection of the helical spin texture in a p-type topological insulator Sb2Te3[J]. Scientific reports, 2016, 6(1): 1-7.
[40] KONG D, CHEN Y, CHA J J, et al. Ambipolar field effect in the ternary topological insulator (BixSb1–x) 2Te3 by composition tuning[J]. Nature nanotechnology, 2011, 6(11): 705-709.
[41] DUAN J, TANG N, HE X, et al. Identification of helicity-dependent photocurrents from topological surface states in Bi2Se3 gated by ionic liquid[J]. Scientific reports, 2014, 4(1): 1-4.
[42] NGABONZIZA P, STEHNO M P, MYOREN H, et al. Gate‐Tunable Transport Properties of In Situ Capped Bi2Te3 Topological Insulator Thin Films[J]. Advanced Electronic Materials, 2016, 2(8): 1600157.
[43] ZHANG T, HA J, LEVY N, et al. Electric-field tuning of the surface band structure of topological insulator Sb 2 Te 3 thin films[J]. Physical review letters, 2013, 111(5): 056803.
[44] WANG Y, XIU F, CHENG L, et al. Gate-controlled surface conduction in Na-doped Bi2Te3 topological insulator nanoplates[J]. Nano letters, 2012, 12(3): 1170-1175.
[45] DZERO M, SUN K, GALITSKI V, et al. Topological kondo insulators[J]. Physical review letters, 2010, 104(10): 106408.
[46] RAGHU S, QI X-L, HONERKAMP C, et al. Topological mott insulators[J]. Physical review letters, 2008, 100(15): 156401.
[47] YU R, ZHANG W, ZHANG H-J, et al. Quantized anomalous Hall effect in magnetic topological insulators[J]. science, 2010, 329(5987): 61-64.
[48] XU S-Y, NEUPANE M, LIU C, et al. Hedgehog spin texture and Berry’s phase tuningin a magnetic topological insulator[J]. Nature Physics, 2012, 8(8): 616-622.
[49] LIU C-X, QI X-L, DAI X, et al. Quantum anomalous Hall effect in Hg 1− y Mn y Te quantum wells[J]. Physical review letters, 2008, 101(14): 146802.
[50] BUDEWITZ A, BENDIAS K, LEUBNER P, et al. Quantum anomalous Hall effect in Mn doped HgTe quantum wells[J]. arXiv preprint arXiv:170605789, 2017
[51] NOMURA K, NAGAOSA N. Surface-quantized anomalous Hall current and the magnetoelectric effect in magnetically disordered topological insulators[J]. Physical review letters, 2011, 106(16): 166802.
[52] ZHANG S-B, LU H-Z, SHEN S-Q. Edge states and integer quantum Hall effect in topological insulator thin films[J]. Scientific reports, 2015, 5(1): 1-10.
[53] CHANG C-Z, ZHANG J, FENG X, et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator[J]. science, 2013, 340(6129): 167-170.
[54] DENG Y, YU Y, SHI M Z, et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4[J]. science, 2020, 367(6480): 895-900.
[55] TOKURA Y, YASUDA K, TSUKAZAKI A. Magnetic topological insulators[J]. Nature Reviews Physics, 2019, 1(2): 126-143.
[56] CHEN Y, CHU J-H, ANALYTIS J, et al. Massive Dirac fermion on the surface of a magnetically doped topological insulator[J]. science, 2010, 329(5992): 659-662.
[57] KHVESHCHENKO D, WIEGMANN P B. Physical realization of the parity anomaly and quantum Hall effect[J]. Physics Letters B, 1989, 225(3): 279-283.
[58] LIU C-X, ZHANG S-C, QI X-L. The quantum anomalous Hall effect: Theory and experiment[J]. Annual Review of Condensed Matter Physics, 2016, 7: 301-321.
[59] QI X-L, WU Y-S, ZHANG S-C. Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors[J]. Physical Review B, 2006, 74(8): 085308.
[60] FU L, KANE C L, MELE E J. Topological insulators in three dimensions[J]. Physical review letters, 2007, 98(10): 106803.
[61] REDLICH A N. Parity violation and gauge noninvariance of the effective gauge field action in three dimensions[J]. Physical Review D, 1984, 29(10): 2366.
[62] DESER S, GRIGUOLO L, SEMINARA D. Gauge invariance, finite temperature, and parity anomaly in D= 3[J]. Physical review letters, 1997, 79(11): 1976.
[63] LIU T, HE J J, NORI F. Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor[J]. Physical Review B, 2018, 98(24): 245413.
[64] LI Q, HAN Y, ZHANG K, et al. Multiple Majorana edge modes in magnetic topological insulator–superconductor heterostructures[J]. Physical Review B, 2020, 102(20): 205402.111
[65] PENG Y, XU Y. Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators[J]. Physical Review B, 2019, 99(19): 195431.
[66] XU Y, SONG Z, WANG Z, et al. Higher-order topology of the axion insulator EuIn 2 As 2[J]. Physical review letters, 2019, 122(25): 256402.
[67] MOGI M, KAWAMURA M, TSUKAZAKI A, et al. Tailoring tricolor structure of magnetic topological insulator for robust axion insulator[J]. Science advances, 2017, 3(10): eaao1669.
[68] LIU C, WANG Y, LI H, et al. Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator[J]. Nature materials, 2020, 19(5): 522-527.
[69] YU X, KOSHIBAE W, TOKUNAGA Y, et al. Transformation between meron and skyrmion topological spin textures in a chiral magnet[J]. Nature, 2018, 564(7734): 95-98.
[70] QI X-L, HUGHES T L, ZHANG S-C. Topological field theory of time-reversal invariant insulators[J]. Physical Review B, 2008, 78(19): 195424.
[71] QI X-L, LI R, ZANG J, et al. Inducing a magnetic monopole with topological surface states[J]. science, 2009, 323(5918): 1184-1187.
[72] WANG J, LIAN B, QI X-L, et al. Quantized topological magnetoelectric effect of the zero-plateau quantum anomalous Hall state[J]. Physical Review B, 2015, 92(8): 081107.
[73] MORIMOTO T, FURUSAKI A, NAGAOSA N. Topological magnetoelectric effects in thin films of topological insulators[J]. Physical Review B, 2015, 92(8): 085113.
[74] ESSIN A M, MOORE J E, VANDERBILT D. Magnetoelectric polarizability and axion electrodynamics in crystalline insulators[J]. Physical review letters, 2009, 102(14): 146805.
[75] WILCZEK F. Two applications of axion electrodynamics[J]. Physical review letters, 1987, 58(18): 1799.
[76] OKADA Y, DHITAL C, ZHOU W, et al. Direct observation of broken time-reversal symmetry on the surface of a magnetically doped topological insulator[J]. Physical review letters, 2011, 106(20): 206805.
[77] CHANG C Z, ZHANG J, LIU M, et al. Thin films of magnetically doped topological insulator with carrier‐independent long‐range ferromagnetic order[J]. Advanced materials, 2013, 25(7): 1065-1070.
[78] YE M, LI W, ZHU S, et al. Carrier-mediated ferromagnetism in the magnetic topological insulator Cr-doped (Sb, Bi) 2Te3[J]. Nature communications, 2015, 6(1): 1-7.
[79] FAN Y, KOU X, UPADHYAYA P, et al. Electric-field control of spin–orbit torque in a magnetically doped topological insulator[J]. Nature nanotechnology, 2016, 11(4): 352-359.
[80] KIM J, JHI S-H. Magnetic phase transition in Fe-doped topological insulator B i 2 S e 3[J]. Physical Review B, 2015, 92(10): 104405.
[81] LANG M, MONTAZERI M, ONBASLI M C, et al. Proximity induced high-temperature magnetic order in topological insulator-ferrimagnetic insulator heterostructure[J]. Nano letters, 2014, 14(6): 3459-3465.
[82] EREMEEV S, MEN'SHOV V, TUGUSHEV V, et al. Magnetic proximity effect at the three-dimensional topological insulator/magnetic insulator interface[J]. Physical Review B, 2013, 88(14): 144430.
[83] 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[J]. Nature communications, 2016, 7(1): 1-6.
[84] LI J, LI Y, DU S, et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials[J]. Science advances, 2019, 5(6): eaaw5685.
[85] OTROKOV M M, KLIMOVSKIKH I I, BENTMANN H, et al. Prediction and observation of an antiferromagnetic topological insulator[J]. Nature, 2019, 576(7787): 416-422.
[86] XU Y, MIOTKOWSKI I, LIU C, et al. Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator[J]. Nature Physics, 2014, 10(12): 956-963.
[87] ZHU T, BISHOP A J, ZHOU T, et al. Synthesis, Magnetic Properties, and Electronic Structure of Magnetic Topological Insulator MnBi2Se4[J]. Nano letters, 2021, 21(12): 5083-5090.
[88] HU C, DING L, GORDON K N, et al. Realization of an intrinsic ferromagnetic topological state in MnBi8Te13[J]. Science advances, 2020, 6(30): eaba4275.
[89] SESSI P, REIS F, BATHON T, et al. Signatures of Dirac fermion-mediated magnetic order[J]. Nature communications, 2014, 5(1): 1-8.
[90] CHECKELSKY J G, YE J, ONOSE Y, et al. Dirac-fermion-mediated ferromagnetism in a topological insulator[J]. Nature Physics, 2012, 8(10): 729-733.
[91] KOU X, LANG M, FAN Y, et al. Interplay between different magnetisms in Cr-doped topological insulators[J]. ACS Nano, 2013, 7(10): 9205-9212.
[92] LI M, CHANG C-Z, WU L, et al. Experimental verification of the van Vleck nature of long-range ferromagnetic order in the vanadium-doped three-dimensional topological insulator Sb 2 Te 3[J]. Physical review letters, 2015, 114(14): 146802.
[93] KACMAN P. Spin interactions in diluted magnetic semiconductors and magnetic semiconductor structures[J]. Semiconductor Science and Technology, 2001, 16(4): R25.
[94] HOR Y, ROUSHAN P, BEIDENKOPF H, et al. Development of ferromagnetism in thedoped topological insulator Bi 2− x Mn x Te 3[J]. Physical Review B, 2010, 81(19): 195203.
[95] LEE I, KIM C K, LEE J, et al. Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Crx (Bi0. 1Sb0. 9) 2-xTe3[J]. Proceedings of the National Academy of Sciences, 2015, 112(5): 1316-1321.
[96] CHANG C-Z, ZHAO W, KIM D Y, et al. High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator[J]. Nature materials, 2015, 14(5): 473-477.
[97] BESTWICK A, FOX E, KOU X, et al. Precise quantization of the anomalous Hall effect near zero magnetic field[J]. Physical review letters, 2015, 114(18): 187201.
[98] CHANG C-Z, ZHAO W, KIM D Y, et al. Zero-field dissipationless chiral edge transport and the nature of dissipation in the quantum anomalous Hall state[J]. Physical review letters, 2015, 115(5): 057206.
[99] WANG J, LIAN B, ZHANG H, et al. Anomalous edge transport in the quantum anomalous Hall state[J]. Physical review letters, 2013, 111(8): 086803.
[100] WU X, LI J, MA X-M, et al. Distinct topological surface states on the two terminations of MnBi 4 Te 7[J]. Physical Review X, 2020, 10(3): 031013.
[101] MOGI M, YOSHIMI R, TSUKAZAKI A, et al. Magnetic modulation doping in topological insulators toward higher-temperature quantum anomalous Hall effect[J]. Applied Physics Letters, 2015, 107(18): 182401.
[102] WATANABE R, YOSHIMI R, KAWAMURA M, et al. Quantum anomalous Hall effect driven by magnetic proximity coupling in all-telluride based heterostructure[J]. Applied Physics Letters, 2019, 115(10): 102403.
[103] OU Y, LIU C, JIANG G, et al. Enhancing the quantum anomalous Hall effect by magnetic codoping in a topological insulator[J]. Advanced materials, 2018, 30(1): 1703062.
[104] OTROKOV M M, MENSHCHIKOVA T V, VERGNIORY M G, et al. Highly-ordered wide bandgap materials for quantized anomalous Hall and magnetoelectric effects[J]. 2D Materials, 2017, 4(2): 025082.
[105] LEE D S, KIM T-H, PARK C-H, et al. Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi 2 MnTe 4[J]. CrystEngComm, 2013, 15(27): 5532-5538.
[106] SASS P M, GE W, YAN J, et al. Magnetic imaging of domain walls in the antiferromagnetic topological insulator MnBi2Te4[J]. Nano letters, 2020, 20(4): 2609-2614.
[107] OTROKOV M, RUSINOV I P, BLANCO-REY M, et al. Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi 2 Te 4 films[J]. Physical review letters, 2019, 122(10): 107202.
[108] LI Z, LI J, HE K, et al. Tunable interlayer magnetism and band topology in van der Waals heterostructures of Mn Bi 2 Te 4-family materials[J]. Physical Review B, 2020, 102(8): 081107.
[109] LI J, WANG C, ZHANG Z, et al. Magnetically controllable topological quantum phase transitions in the antiferromagnetic topological insulator MnBi 2 Te 4[J]. Physical Review B, 2019, 100(12): 121103.
[110] ZEUGNER A, NIETSCHKE F, WOLTER A U, et al. Chemical aspects of the candidate antiferromagnetic topological insulator MnBi2Te4[J]. Chemistry of Materials, 2019, 31(8): 2795-2806.
[111] CUI J, SHI M, WANG H, et al. Transport properties of thin flakes of the antiferromagnetic topological insulator MnB i 2 T e 4[J]. Physical Review B, 2019, 99(15): 155125.
[112] YAN J-Q, ZHANG Q, HEITMANN T, et al. Crystal growth and magnetic structure of MnBi 2 Te 4[J]. Physical Review Materials, 2019, 3(6): 064202.
[113] CHEN B, FEI F, ZHANG D, et al. Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes[J]. Nature communications, 2019, 10(1): 1-8.
[114] GONG Y, GUO J, LI J, et al. Experimental realization of an intrinsic magnetic topological insulator[J]. Chinese Physics Letters, 2019, 36(7): 076801.
[115] LEE S H, ZHU Y, WANG Y, et al. Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnB i 2 T e 4[J]. Physical Review Research, 2019, 1(1): 012011.
[116] HOU F, YAO Q, ZHOU C-S, et al. Te-vacancy-induced surface collapse and reconstruction in antiferromagnetic topological insulator MnBi2Te4[J]. ACS Nano, 2020, 14(9): 11262-11272.
[117] HU Y, XU L, SHI M, et al. Universal gapless Dirac cone and tunable topological states in (MnB i 2 T e 4) m (B i 2 T e 3) n heterostructures[J]. Physical Review B, 2020, 101(16): 161113.
[118] ZHONG H, BAO C, WANG H, et al. Light-tunable surface state and hybridization gap in magnetic topological insulator MnBi8Te13[J]. Nano letters, 2021, 21(14): 6080-6086.
[119] DENG H, CHEN Z, WOŁOŚ A, et al. High-temperature quantum anomalous Hall regime in a MnBi2Te4/Bi2Te3 superlattice[J]. Nature Physics, 2021, 17(1): 36-42.
[120] VIDAL R C, ZEUGNER A, FACIO J I, et al. Topological electronic structure and intrinsic magnetization in MnBi 4 Te 7: a Bi 2 Te 3 derivative with a periodic Mn sublattice[J]. Physical Review X, 2019, 9(4): 041065.
[121] TIAN S, GAO S, NIE S, et al. Magnetic topological insulator MnBi 6 Te 10 with a zero-field ferromagnetic state and gapped Dirac surface states[J]. Physical Review B,2020, 102(3): 035144.
[122] ROSENBERG G, FRANZ M. Surface magnetic ordering in topological insulators with bulk magnetic dopants[J]. Physical Review B, 2012, 85(19): 195119.
[123] DIETL T, OHNO H. Dilute ferromagnetic semiconductors: Physics and spintronic structures[J]. Reviews of modern physics, 2014, 86(1): 187.
[124] KOU X, FAN Y, LANG M, et al. Magnetic topological insulators and quantum anomalous hall effect[J]. Solid State Communications, 2015, 215: 34-53.
[125] YANKOWITZ M, JUNG J, LAKSONO E, et al. Dynamic band-structure tuning of graphene moiré superlattices with pressure[J]. Nature, 2018, 557(7705): 404-408.
[126] NISHIOKA T, SATO N K. New type of magnetization equipment using a commercial Hall sensor[J]. Journal of Magnetism and Magnetic Materials, 2004, 272: 2305-2306.
[127] KRESSE G, FURTHMüLLER J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[J]. Physical Review B, 1996, 54(16): 11169.
[128] PERDEW J P, BURKE K, ERNZERHOF M. Generalized gradient approximation made simple[J]. Physical review letters, 1996, 77(18): 3865.
[129] GRIMME S, ANTONY J, EHRLICH S, et al. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[J]. The Journal of chemical physics, 2010, 132(15): 154104.
[130] GE J, LIU Y, LI J, et al. High-Chern-number and high-temperature quantum Hall effect without Landau levels[J]. National science review, 2020, 7(8): 1280-1287.
[131] DING L, HU C, YE F, et al. Crystal and magnetic structures of magnetic topological insulators MnBi 2 Te 4 and MnBi 4 Te 7[J]. Physical Review B, 2020, 101(2): 020412.
[132] YAN J-Q, LIU Y, PARKER D, et al. A-type antiferromagnetic order in MnBi 4 Te 7 and MnBi 6 Te 10 single crystals[J]. Physical Review Materials, 2020, 4(5): 054202.
[133] HU C, GORDON K N, LIU P, et al. A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling[J]. Nature communications, 2020, 11(1): 1-8.
[134] SUN H, XIA B, CHEN Z, et al. Rational design principles of the quantum anomalous Hall effect in superlatticelike magnetic topological insulators[J]. Physical review letters, 2019, 123(9): 096401.
[135] WU J, LIU F, SASASE M, et al. Natural van der Waals heterostructural single crystals with both magnetic and topological properties[J]. Science advances, 2019, 5(11): eaax9989.
[136] SHI M, LEI B, ZHU C, et al. Magnetic and transport properties in the magnetic topological insulators MnB i 2 T e 4 (B i 2 T e 3) n (n= 1, 2)[J]. Physical Review B, 2019, 100(15): 155144.
[137] JIA B, ZHANG S, YING Z, et al. Unconventional anomalous Hall effect in magnetic topological insulator MnBi4Te7 device[J]. Applied Physics Letters, 2021, 118(8):083101.
[138] HU C, LIEN S-W, FENG E, et al. Tuning magnetism and band topology through antisite defects in Sb-doped MnBi 4 Te 7[J]. Physical Review B, 2021, 104(5): 054422.
[139] DU M H, YAN J, COOPER V R, et al. Tuning Fermi levels in intrinsic antiferromagnetic topological insulators MnBi2Te4 and MnBi4Te7 by defect engineering and chemical doping[J]. Advanced Functional Materials, 2021, 31(3): 2006516.
[140] KLIMOVSKIKH I I, OTROKOV M M, ESTYUNIN D, et al. Tunable 3D/2D magnetism in the (MnBi2Te4)(Bi2Te3) m topological insulators family[J]. npj Quantum Materials, 2020, 5(1): 1-9.
[141] JO N H, WANG L-L, SLAGER R-J, et al. Intrinsic axion insulating behavior in antiferromagnetic MnBi 6 Te 10[J]. Physical Review B, 2020, 102(4): 045130.
[142] XIE H, FEI F, FANG F, et al. Charge carrier mediation and ferromagnetism induced in MnBi6Te10 magnetic topological insulators by antimony doping[J]. Journal of Physics D: Applied Physics, 2021, 55(10): 104002.
[143] KE F, CHEN Y, YIN K, et al. Large bandgap of pressurized trilayer graphene[J]. Proceedings of the National Academy of Sciences, 2019, 116(19): 9186-9190.
[144] ZHAO Z, ZHANG H, YUAN H, et al. Pressure induced metallization with absence of structural transition in layered molybdenum diselenide[J]. Nature communications, 2015, 6(1): 1-8.
[145] RIFLIKOVá M, MARTOŇáK R, TOSATTI E. Pressure-induced gap closing and metallization of Mo Se 2 and Mo Te 2[J]. Physical Review B, 2014, 90(3): 035108.
[146] RODIN A, CARVALHO A, NETO A C. Strain-induced gap modification in black phosphorus[J]. Physical review letters, 2014, 112(17): 176801.
[147] KIRSHENBAUM K, SYERS P, HOPE A, et al. Pressure-induced unconventional superconducting phase in the topological insulator Bi 2 Se 3[J]. Physical review letters, 2013, 111(8): 087001.
[148] ZHANG C, SUN L, CHEN Z, et al. Phase diagram of a pressure-induced superconducting state and its relation to the Hall coefficient of Bi 2 Te 3 single crystals[J]. Physical Review B, 2011, 83(14): 140504.
[149] LI T, JIANG S, SIVADAS N, et al. Pressure-controlled interlayer magnetism in atomically thin CrI3[J]. Nature materials, 2019, 18(12): 1303-1308.
[150] SONG T, FEI Z, YANKOWITZ M, et al. Switching 2D magnetic states via pressure tuning of layer stacking[J]. Nature materials, 2019, 18(12): 1298-1302.
[151] YANKOWITZ M, CHEN S, POLSHYN H, et al. Tuning superconductivity in twisted bilayer graphene[J]. science, 2019, 363(6431): 1059-1064.
[152] FüLöP B, MáRFFY A, ZIHLMANN S, et al. Boosting proximity spin–orbit coupling in graphene/WSe2 heterostructures via hydrostatic pressure[J]. npj 2D Materials andApplications, 2021, 5(1): 1-6.
[153] CHEN K, WANG B, YAN J-Q, et al. Suppression of the antiferromagnetic metallic state in the pressurized MnB i 2 T e 4 single crystal[J]. Physical Review Materials, 2019, 3(9): 094201.
[154] ZHAO Z, HU C, KAVNER A, et al. Phase Transition and Raman Evolution in Pressurized Antiferromagnetism van der Waals Topological Insulator; proceedings of the 2020 Conference on Lasers and Electro-Optics (CLEO), F, 2020 [C]. IEEE.
[155] PEI C, XIA Y, WU J, et al. Pressure-induced topological and structural phase transitions in an antiferromagnetic topological insulator[J]. Chinese Physics Letters, 2020, 37(6): 066401.
[156] GUO W-T, HUANG L, YANG Y, et al. Pressure-induced topological quantum phase transition in the magnetic topological insulator MnBi2Te4[J]. New Journal of Physics, 2021, 23(8): 083030.
[157] YIN Y, MA X, YAN D, et al. Pressure-driven electronic and structural phase transition in intrinsic magnetic topological insulator Mn Sb 2 Te 4[J]. Physical Review B, 2021, 104(17): 174114.
[158] XU Z, YE M, LI J, et al. Hydrostatic pressure-induced magnetic and topological phase transitions in the MnBi 2 Te 4 family of materials[J]. Physical Review B, 2022, 105(8): 085129.
[159] ALIEV Z S, AMIRASLANOV I R, NASONOVA D I, et al. Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: Synthesis and crystal structure[J]. Journal of Alloys and Compounds, 2019, 789: 443-450.
[160] GOODENOUGH J B. Theory of the role of covalence in the perovskite-type manganites [La, M (II)] Mn O 3[J]. Physical Review, 1955, 100(2): 564.
[161] ANDERSON P W. New approach to the theory of superexchange interactions[J]. Physical Review, 1959, 115(1): 2.
[162] TURNER A M, ZHANG Y, MONG R S, et al. Quantized response and topology of magnetic insulators with inversion symmetry[J]. Physical Review B, 2012, 85(16): 165120.
[163] ONO S, WATANABE H. Unified understanding of symmetry indicators for all internal symmetry classes[J]. Physical Review B, 2018, 98(11): 115150.
[164] LU R, SUN H, KUMAR S, et al. Half-magnetic topological insulator with magnetization-induced Dirac gap at a selected surface[J]. Physical Review X, 2021, 11(1): 011039.
[165] YAN J-Q, OKAMOTO S, MCGUIRE M A, et al. Evolution of structural, magnetic, and transport properties in MnBi 2− x Sb x Te 4[J]. Physical Review B, 2019, 100(10): 104409.
[166] CHEN B, WANG D, JIANG Z, et al. Coexistence of ferromagnetism and topology by charge carrier engineering in the intrinsic magnetic topological insulator Mn Bi 4 Te 7[J]. Physical Review B, 2021, 104(7): 075134.
[167] LIU Y, WANG L-L, ZHENG Q, et al. Site mixing for engineering magnetic topological insulators[J]. Physical Review X, 2021, 11(2): 021033.
[168] YUAN Y, WANG X, LI H, et al. Electronic states and magnetic response of MnBi2Te4 by scanning tunneling microscopy and spectroscopy[J]. Nano letters, 2020, 20(5): 3271-3277.
[169] DING L, HU C, FENG E, et al. Neutron diffraction study of magnetism in van der Waals layered MnBi2n Te3n+ 1[J]. Journal of Physics D: Applied Physics, 2021, 54(17): 174003.
[170] ZHANG J, CHANG C-Z, TANG P, et al. Topology-driven magnetic quantum phase transition in topological insulators[J]. science, 2013, 339(6127): 1582-1586.
[171] ZHENG G, WANG M, ZHU X, et al. Tailoring Dzyaloshinskii–Moriya interaction in a transition metal dichalcogenide by dual-intercalation[J]. Nature communications, 2021, 12(1): 1-7.
[172] KURUMAJI T, NAKAJIMA T, HIRSCHBERGER M, et al. Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet[J]. science, 2019, 365(6456): 914-918.
[173] NEUBAUER A, PFLEIDERER C, BINZ B, et al. Topological Hall effect in the A phase of MnSi[J]. Physical review letters, 2009, 102(18): 186602.
[174] LIU C, ZANG Y, RUAN W, et al. Dimensional crossover-induced topological Hall effect in a magnetic topological insulator[J]. Physical review letters, 2017, 119(17): 176809.
[175] SüRGERS C, FISCHER G, WINKEL P, et al. Large topological Hall effect in the non-collinear phase of an antiferromagnet[J]. Nature communications, 2014, 5(1): 1-8.
[176] DENISOV K, ROZHANSKY I, AVERKIEV N, et al. General theory of the topological Hall effect in systems with chiral spin textures[J]. Physical Review B, 2018, 98(19): 195439.
[177] SKOROPATA E, NICHOLS J, OK J M, et al. Interfacial tuning of chiral magnetic interactions for large topological Hall effects in LaMnO3/SrIrO3 heterostructures[J]. Science advances, 2020, 6(27): eaaz3902.
[178] SHAO Q, LIU Y, YU G, et al. Topological Hall effect at above room temperature in heterostructures composed of a magnetic insulator and a heavy metal[J]. Nature Electronics, 2019, 2(5): 182-186.
[179] GAREL T, DONIACH S. Phase transitions with spontaneous modulation-the dipolar Ising ferromagnet[J]. Physical Review B, 1982, 26(1): 325.
[180] OKUBO T, CHUNG S, KAWAMURA H. Multiple-q states and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields[J]. Physical review letters, 2012, 108(1): 017206.
[181] WANG L, FENG Q, LEE H G, et al. Controllable thickness inhomogeneity and berry curvature engineering of anomalous Hall effect in SrRuO3 ultrathin films[J]. Nano letters, 2020, 20(4): 2468-2477.
[182] ZHANG S, WANG R, WANG X, et al. Experimental observation of the gate-controlled reversal of the anomalous Hall effect in the intrinsic magnetic topological insulator MnBi2Te4 device[J]. Nano letters, 2019, 20(1): 709-714.
[183] JIA B, ZHANG S, YING Z, et al. Unconventional anomalous Hall effect in magnetic topological insulator MnBi4Te7 device[J]. Applied Physics Letters, 2021, 118(8): 083101.
[184] LIU N, TENG J, LI Y. Two-component anomalous Hall effect in a magnetically doped topological insulator[J]. Nature communications, 2018, 9(1): 1-8.
[185] DENG H, CHEN Z, WOŁOŚ A, et al. High-temperature quantum anomalous Hall regime in a MnBi2Te4/Bi2Te3 superlattice[J]. Nature Physics, 2021, 17(1): 36-42.
[186] TAI L, LI J, CHONG S K, et al. Distinguishing two-component anomalous Hall effect from topological Hall effect in magnetic topological insulator MnBi2Te4[J]. arXiv preprint arXiv:210309878, 2021
[187] NAGAOSA N, SINOVA J, ONODA S, et al. Anomalous hall effect[J]. Reviews of modern physics, 2010, 82(2): 1539.
[188] ROUT P K, MADDURI P P, MANNA S K, et al. Field-induced topological Hall effect in the noncoplanar triangular antiferromagnetic geometry of Mn 3 Sn[J]. Physical Review B, 2019, 99(9): 094430.