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Electric field manipulation of magnetic skyrmions

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Abstract

Magnetic skyrmions are vortex-like swirling spin textures that are promising candidates for carrying information bits in future magnetic memories or logic circuits. To build skyrmionic devices, researchers must electrically manipulate magnetic skyrmions to enable easy integration into modern semiconductor technology. This operation generally uses a spin-polarized current, which unavoidably causes high energy dissipation and Joule heating. Thus, the electric-field strategy is a hopeful alternative for electrically manipulating the skyrmions due to the strategy’s negligible Joule heating and low energy cost. In this review, we systematically summarize the theoretical and experimental development of the electrical-field manipulation of magnetic skyrmions over the past decade. We review the following magnetic systems and physical mechanisms: (i) ultra-thin multilayer films with accumulation and release of interfacial charge, (ii) single-phase multiferroic material with magneto-electric coupling, (iii) ferromagnetic/ferroelectric (FM/FE) multiferroic heterostructure with magneto-elastic coupling. Finally, we consider future developmental trends in the electric-field manipulation of magnetic skyrmions and other topological magnetic domain structures.

Graphical abstract

摘要

磁斯格明子是一种类涡旋的自旋结构, 因其具有拓扑保护性、纳米级尺寸以及优异的磁电特性, 有望成为未来磁性存储器或逻辑器件中的信息载体。为使斯格明子器件易集成于现代半导体技术, 磁性斯格明子需要能通过电学手段操纵。目前主要采用自旋极化的电流操控斯格明子, 这种方法不可避免地会带来高能耗和高焦耳热问题。相比之下, 电场操控方式可以大大降低能耗引起的焦耳热可以忽略不计, 极具应用潜力。本文根据物理机理和材料体系, 从具有界面电荷积累和释放的超薄多层膜、具有磁电耦合的单相多铁材料、具有磁弹性耦合的铁磁/铁电(FM/FE)多铁异质结构三类材料体系系统地总结了**十年来电场操纵磁斯格明子的理论和实验方面的研究进展。最后, 我们对电场操控磁斯格明子和其他拓扑磁畴结构的发展趋势进行了展望。

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Fig. 1

Reproduced with permission from Ref. [76]. Copyright 2017, Springer Nature. b Schematic of skyrmion creation and annihilation in Pt/Co/oxide structure via application of electric field with opposite sign. c Evolution of magnetic skyrmion bubbles density in Pt/Co/oxide trilayer with different electric fields under a 0.15 mT perpendicular magnetic field. Reproduced with permission from Ref. [78]. Copyright 2017, American Chemical Society. d Device structure with current contacts and voltage contacts; e electric field non-volatile create and delete skyrmions measured by magnetic force microscope (MFM). Reproduced with permission from Ref. [79]. Copyright 2020, Springer Nature

Fig. 2

Reproduced with permission from Ref. [80]. Copyright 2018, Royal Society of Chemistry. c Schematic of voltage-controlled magnetic anisotropy gradient; d anisotropy gradient effect on skyrmion velocities. Reproduced with permission from Ref. [81]. Copyright 2018, American Physical Society

Fig. 3

Reproduced with permission from Ref. [82]. Copyright 2019, American Chemical Society. d, e Schematic illustration of sectional view and top view of Pt/CoNi/Pt/CoNi/Pt multilayer experiment sample, where gate voltage (VG) is applied between multilayer and ITO as indicated; f MOKE microscopy images of electric field-induced evolution of magnetic domains. Reproduced with permission from Ref. [83]. Copyright 2019, American Chemical Society

Fig. 4

Reproduced with permission from Ref. [84]. Copyright 2021, American Physical Society. d Illustration of experiment set of ionic gel gating modification; e schematic of voltage manipulation of skyrmion based on Ta/CoFeB/TaOx/MgO/Ta/IL/Pt structure; f magnetic domains evolution by gating voltage at flat state (Hz remaining at 2.5 × 10–4 T); g magnetic domains evolution by gating voltage at bent state (Hz remaining at 6.72 × 10–4 T). Reproduced with permission from Ref. [85]. Copyright 2020, John Wiley & Sons

Fig. 5

Reproduced with permission from Ref. [89]. Copyright 2012, American Physical Society

Fig. 6

Reproduced with permission from Ref. [90]. Copyright 2015, AIP Publishing. b Magnetic phase diagram of Cu2OSeO3 near transition temperature under electric fields of + 30 (blue), 0 (black), and –30 kV·cm−1 (red); c a.c. susceptibility as a function of electric field at 54 (blue), 55.5 (green), and 56.5 K (red), and 0.035 T fixed magnetic field. Reproduced with permission from Ref. [91]. Copyright 2016, Springer Nature. d Schematic illustration of sample configuration; e LTEM image before applied electric field (E); f LTEM image at E =  + 3.6 V·μm−2; f LTEM image at E =  − 3.6 V·μm−2 and (inset) corresponding direction of electric fields, magnetic field, and spontaneous electric polarization in LTEM images, where measurements were performed at 24.7 K with an magnetic field (B) of 0.0254 T (directions of E, B, and spontaneous P of skyrmion phase are shown on left with correspondence to LTEM images. Reproduced with permission from Ref. [92]. Copyright 2018, American Chemical Society

Fig. 7

Reproduced with permission from Ref. [105]. Copyright 2018, Elsevier. c Sketch ferromagnetic/piezoelectric heterostructure and strain the centerline (x-axis) of ferromagnetic nanostripe. Reproduced with permission from Ref. [103]. Copyright 2019, AIP Publishing. d Skyrmion speed as a function of either current density (blue) or strain gradient (red); e, f temporal evolution of skyrmion creation and deletion with different strains, where mz is volume average of normalized perpendicular magnetization, Q is topological charge number, and Δfintrin is change of intrinsic magnetic free energy density, Δfintrin(t) = fintrin(t)–fintrin(t = 0). Reproduced with permission from Ref. [102]. Copyright 2018, Springer Nature

Fig. 8

Reproduced with permission from Ref. [100]. Copyright 2020, Springer Nature. d–i Illustration isolated skyrmion morphology switch under different magnitude and orientation electric fields. Reproduced with permission from Ref. [101]. Copyright 2020, Springer Nature

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References

  1. Thouless DJ, Kohmoto M, Nightingale MP, den Nijs M. Quantized Hall conductance in a two-dimensional periodic potential. Phys Rev Lett. 1982;49(6):405. https://doi.org/10.1103/PhysRevLett.49.405.

    Article  CAS  Google Scholar 

  2. Haldane FDM. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the "parity anomaly". Phys Rev Lett. 1988;61(18):2015. https://doi.org/10.1103/PhysRevLett.61.2015.

    Article  CAS  Google Scholar 

  3. Nelson DR, Kosterlitz J. Universal jump in the superfluid density of two-dimensional superfluids. Phys Rev Lett. 1977;39(19):1201. https://doi.org/10.1103/PhysRevLett.39.1201.

    Article  CAS  Google Scholar 

  4. Yu XZ, Onose Y, Kanazawa N, Park JH, Han JH, Matsui Y, Nagaosa N, Tokura Y. Real-space observation of a two-dimensional skyrmion crystal. Nature. 2010;465(7300):901. https://doi.org/10.1038/nature09124.

    Article  CAS  Google Scholar 

  5. Yu XZ, Kanazawa N, Onose Y, Kimoto K, Zhang WZ, Ishiwata S, Matsui Y, Tokura Y. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat Mater. 2011;10(2):106. https://doi.org/10.1038/nmat2916.

    Article  CAS  Google Scholar 

  6. Das S, Tang YL, Hong Z, Goncalves MAP, McCarter MR, Klewe C, Nguyen KX, Gomez-Ortiz F, Shafer P, Arenholz E, Stoica VA, Hsu SL, Wang B, Ophus C, Liu JF, Nelson CT, Saremi S, Prasad B, Mei AB, Schlom DG, Iniguez J, Garcia-Fernandez P, Muller DA, Chen LQ, Junquera J, Martin LW, Ramesh R. Observation of room-temperature polar skyrmions. Nature. 2019;568(7752):368. https://doi.org/10.1038/s41586-019-1092-8.

    Article  CAS  Google Scholar 

  7. Bogdanov AN, Yablonskii D. Thermodynamically stable “vortices” in magnetically ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz. 1989; 95(1):178. http://jetp.ac.ru/cgibin/dn/e_068_01_0101.pdf.

  8. Bogdanov A, Hubert A. Thermodynamically stable magnetic vortex states in magnetic crystals. J Magn Magn Mater. 1994;138(3):255. https://doi.org/10.1016/03048853(94)90046-9.

    Article  CAS  Google Scholar 

  9. Roessler UK, Bogdanov A, Pfleiderer C. Spontaneous skyrmion ground states in magnetic metals. Nature. 2006;442(7104):797. https://doi.org/10.1038/nature05056.

    Article  CAS  Google Scholar 

  10. Yu XZ, Koshibae W, Tokunaga Y, Shibata K, Taguchi Y, Nagaosa N, Tokura Y. Transformation between meron and skyrmion topological spin textures in a chiral magnet. Nature. 2018;564(7734):95. https://doi.org/10.1038/s41586-018-0745-3.

    Article  CAS  Google Scholar 

  11. Kharkov Y, Sushkov O, Mostovoy M. Bound states of skyrmions and merons near the Lifshitz point. Phys Rev Lett. 2017;119(20):207201. https://doi.org/10.1103/PhysRevLett.119.207201.

    Article  CAS  Google Scholar 

  12. Göbel B, Mook A, Henk J, Mertig I, Tretiakov OA. Magnetic bimerons as skyrmion analogues in in-plane magnets. Phys Rev B. 2019;99(6):060407. https://doi.org/10.1103/PhysRevB.99.060407.

    Article  Google Scholar 

  13. Gao N, Je SG, Im MY, Choi JW, Yang M, Li QC, Wang T, Lee S, Han HS, Lee KS. Creation and annihilation of topological meron pairs in in-plane magnetized films. Nat Commun. 2019;10(1):5603. https://doi.org/10.1038/s41467-019-13642-z.

  14. Shinjo T, Okuno T, Hassdorf R, Shigeto K, Ono T. Magnetic vortex core observation in circular dots of permalloy. Science. 2000;289(5481):930. https://doi.org/10.1126/science.289.5481.930.

    Article  CAS  Google Scholar 

  15. Wachowiak A, Wiebe J, Bode M, Pietzsch O, Morgenstern M, Wiesendanger R. Direct observation of internal spin structure of magnetic vortex cores. Science. 2002;298(5593):577. https://doi.org/10.1126/science.1075302.

    Article  CAS  Google Scholar 

  16. Yadav AK, Nelson CT, Hsu SL, Hong Z, Clarkson JD, Schleputz CM, Damodaran AR, Shafer P, Arenholz E, Dedon LR, Chen D, Vishwanath A, Minor AM, Chen LQ, Scott JF, Martin LW, Ramesh R. Observation of polar vortices in oxide superlattices. Nature. 2016;530(7589):198. https://doi.org/10.1126/science.1075302.

    Article  CAS  Google Scholar 

  17. Kim KE, Jeong S, Chu K, Lee JH, Kim GY, Xue F, Koo TY, Chen LQ, Choi SY, Ramesh R, Yang CH. Configurable topological textures in strain graded ferroelectric nanoplates. Nat Commun. 2018;9(1):403. https://doi.org/10.1038/s41467-017-02813-5.

    Article  CAS  Google Scholar 

  18. Bruno P, Dugaev V, Taillefumier M. Topological Hall effect and Berry phase in magnetic nanostructures. Phys Rev Lett. 2004;93(9):096806. https://doi.org/10.1103/PhysRevLett.93.096806.

    Article  CAS  Google Scholar 

  19. Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P, Böni P. Topological Hall effect in the A phase of MnSi. Phys Rev Lett. 2009;102(18):186602. https://doi.org/10.1103/PhysRevLett.102.186602.

    Article  CAS  Google Scholar 

  20. Lee M, Kang W, Onose Y, Tokura Y, Ong NP. Unusual Hall effect anomaly in MnSi under pressure. Phys Rev Lett. 2009;102(18):186601. https://doi.org/10.1103/PhysRevLett.102.186602.

    Article  CAS  Google Scholar 

  21. Zang J, Mostovoy M, Han JH, Nagaosa N. Dynamics of skyrmion crystals in metallic thin films. Phys Rev Lett. 2011;107(13):136804. https://doi.org/10.1103/PhysRevLett.107.136804.

    Article  CAS  Google Scholar 

  22. Jiang W, Zhang X, Yu G, Zhang W, Wang X, Jungfleisch MB, Pearson JE, Cheng X, Heinonen O, Wang KL. Direct observation of the skyrmion Hall effect. Nat Phys. 2017;13(2):162. https://doi.org/10.1038/nphys3883.

    Article  CAS  Google Scholar 

  23. Litzius K, Lemesh I, Krüger B, Bassirian P, Caretta L, Richter K, Büttner F, Sato K, Tretiakov OA, Förster J. Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy. Nat Phys. 2017;13(2):170. https://doi.org/10.1038/nphys3883.

    Article  CAS  Google Scholar 

  24. Sampaio J, Cros V, Rohart S, Thiaville A, Fert A. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures. Nat Nanotechnol. 2013;8(11):839. https://doi.org/10.1038/nnano.2013.210.

    Article  CAS  Google Scholar 

  25. Fert A, Cros V, Sampaio J. Skyrmions on the track. Nat Nanotechnol. 2013;8(3):152. https://doi.org/10.1038/nnano.2013.29.

    Article  CAS  Google Scholar 

  26. Yu G, Upadhyaya P, Shao Q, Wu H, Yin G, Li X, He C, Jiang W, Han X, Amiri PK. Room-temperature skyrmion shift device for memory application. Nano Lett. 2017;17(1):261. https://doi.org/10.1021/acs.nanolett.6b04010.

    Article  CAS  Google Scholar 

  27. Jonietz F, Mühlbauer S, Pfleiderer C, Neubauer A, Münzer W, Bauer A, Adams T, Georgii R, Böni P, Duine RA. Spin transfer torques in MnSi at ultralow current densities. Science. 2010;330(6011):1648. https://doi.org/10.1126/science.1195709.

    Article  CAS  Google Scholar 

  28. Nagaosa N, Tokura Y. Topological properties and dynamics of magnetic skyrmions. Nat Nanotechnol. 2013;8(12):899. https://doi.org/10.1038/nnano.2013.243.

    Article  CAS  Google Scholar 

  29. Jiang W, Upadhyaya P, Zhang W, Yu G, Jungfleisch MB, Fradin FY, Pearson JE, Tserkovnyak Y, Wang KL, Heinonen O. Blowing magnetic skyrmion bubbles. Science. 2015;349(6245):283. https://doi.org/10.1126/science.aaa1442.

    Article  CAS  Google Scholar 

  30. Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Böni P. Skyrmion lattice in a chiral magnet. Science. 2009;323(5916):915. https://doi.org/10.1126/science.1166767.

    Article  CAS  Google Scholar 

  31. Tonomura A, Yu X, Yanagisawa K, Matsuda T, Onose Y, Kanazawa N, Park HS, Tokura Y. Real-space observation of skyrmion lattice in helimagnet MnSi thin samples. Nano Lett. 2012;12(3):1673. https://doi.org/10.1021/nl300073m.

    Article  CAS  Google Scholar 

  32. Fujishiro Y, Kanazawa N, Nakajima T, Yu X, Ohishi K, Kawamura Y, Kakurai K, Arima T, Mitamura H, Miyake A. Topological transitions among skyrmion-and hedgehog-lattice states in cubic chiral magnets. Nat Commun. 2019;10(1):1059. https://doi.org/10.1038/s41467-019-08985-6.

    Article  CAS  Google Scholar 

  33. Yu X, Kanazawa N, Onose Y, Kimoto K, Zhang W, Ishiwata S, Matsui Y, Tokura Y. Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. Nat Mater. 2011;10(2):1237. https://doi.org/10.1038/nmat2916.

    Article  CAS  Google Scholar 

  34. Yu XZ, Kanazawa N, Zhang WZ, Nagai T, Hara T, Kimoto K, Matsui Y, Onose Y, Tokura Y. Skyrmion flow near room temperature in an ultralow current density. Nat Commun. 2012;3(1):988. https://doi.org/10.1038/ncomms1990.

    Article  CAS  Google Scholar 

  35. Shibata K, Yu X, Hara T, Morikawa D, Kanazawa N, Kimoto K, Ishiwata S, Matsui Y, Tokura Y. Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit coupling. Nat Nanotechnol. 2013;8(10):723. https://doi.org/10.1038/nnano.2013.174.

    Article  CAS  Google Scholar 

  36. Seki S, Kim J-H, Inosov D, Georgii R, Keimer B, Ishiwata S, Tokura Y. Formation and rotation of skyrmion crystal in the chiral-lattice insulator Cu2OSeO3. Phys Rev B. 2012;85(22):198. https://doi.org/10.1103/PhysRevB.85.220406.

    Article  CAS  Google Scholar 

  37. Adams T, Chacon A, Wagner M, Bauer A, Brandl G, Pedersen B, Berger H, Lemmens P, Pfleiderer C. Long-wavelength helimagnetic order and skyrmion lattice phase in Cu2OSeO3. Phys Rev Lett. 2012;108(23):237204. https://doi.org/10.1103/PhysRevLett.108.237204.

    Article  CAS  Google Scholar 

  38. Karube K, White J, Reynolds N, Gavilano J, Oike H, Kikkawa A, Kagawa F, Tokunaga Y, Rønnow HM, Tokura Y. Robust metastable skyrmions and their triangular–square lattice structural transition in a high-temperature chiral magnet. Nat Mater. 2016;15(12):1237. https://doi.org/10.1038/nmat4752.

    Article  CAS  Google Scholar 

  39. Tokunaga Y, Yu X, White J, Rønnow HM, Morikawa D, Taguchi Y, Tokura Y. A new class of chiral materials hosting magnetic skyrmions beyond room temperature. Nat Commun. 2015;6(1):7638. https://doi.org/10.1038/ncomms8638.

    Article  CAS  Google Scholar 

  40. Heinze S, Von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blügel S. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat Phys. 2011;7(9):713. https://doi.org/10.1038/nphys2045.

    Article  CAS  Google Scholar 

  41. Wang L, Liu C, Mehmood N, Han G, Wang YD, Xu XL, Feng C, Hou ZP, Peng Y, Gao XS, Yu GH. Construction of a room-temperature Pt/Co/Ta multilayer film with ultrahigh-density skyrmions for memory application. ACS Appl Mater Interfaces. 2019;11(12):12098. https://doi.org/10.1021/acsami.9b00155.

    Article  CAS  Google Scholar 

  42. Woo S, Litzius K, Krüger B, Im MY, Caretta L, Richter K, Mann M, Krone A, Reeve RM, Weigand M. Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. Nat Mater. 2016;15(5):501. https://doi.org/10.1038/nmat4593.

    Article  CAS  Google Scholar 

  43. Boulle O, Vogel J, Yang H, Pizzini S, de Souza CD, Locatelli A, Menteş TO, Sala A, Buda-Prejbeanu LD, Klein O. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat Nanotechnol. 2016;11(5):449. https://doi.org/10.1038/nnano.2015.315.

    Article  CAS  Google Scholar 

  44. Moreau-Luchaire C, Moutafis C, Reyren N, Sampaio J, Vaz C, Van Horne N, Bouzehouane K, Garcia K, Deranlot C, Warnicke P. Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature. Nat Nanotechnol. 2016;11(5):444. https://doi.org/10.1038/nnano.2015.313.

    Article  CAS  Google Scholar 

  45. Soumyanarayanan A, Raju M, Oyarce AG, Tan AK, Im MY, Petrović A, Ho P, Khoo K, Tran M, Gan C. Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers. Nat Mater. 2017;16(9):898. https://doi.org/10.1038/nmat4934.

    Article  CAS  Google Scholar 

  46. Casiraghi A, Corte-León H, Vafaee M, Garcia-Sanchez F, Durin G, Pasquale M, Jakob G, Kläui M, Kazakova O. Individual skyrmion manipulation by local magnetic field gradients. Commun Phys. 2019;2(1):145. https://doi.org/10.1038/s42005-019-0242-5.

    Article  Google Scholar 

  47. Rohart S, Thiaville A. Skyrmion confinement in ultrathin film nanostructures in the presence of Dzyaloshinskii-Moriya interaction. Phys Rev B. 2013;88(18):184422. https://doi.org/10.1103/PhysRevB.88.184422.

    Article  CAS  Google Scholar 

  48. Everschor K, Garst M, Duine R, Rosch A. Current-induced rotational torques in the skyrmion lattice phase of chiral magnets. Phys Rev B. 2011;84(6):064401. https://doi.org/10.1103/PhysRevB.84.064401.

    Article  CAS  Google Scholar 

  49. Tchoe Y, Han JH. Skyrmion generation by current. Phys Rev B. 2012;85(17):174416. https://doi.org/10.1103/PhysRevB.85.174416.

    Article  CAS  Google Scholar 

  50. Zhou Y, Ezawa M. A reversible conversion between a skyrmion and a domain-wall pair in a junction geometry. Nat Commun. 2014;5(1):4652. https://doi.org/10.1038/ncomms5652.

    Article  CAS  Google Scholar 

  51. Heinonen O, Jiang W, Somaily H, Te Velthuis SG, Hoffmann A. Generation of magnetic skyrmion bubbles by inhomogeneous spin Hall currents. Phys Rev B. 2016;93(9):094407. https://doi.org/10.1103/PhysRevB.93.094407.a.

    Article  Google Scholar 

  52. Lin SZ. Edge instability in a chiral stripe domain under an electric current and skyrmion generation. Phys Rev B. 2016;94(2):020402. https://doi.org/10.1103/PhysRevB.93.094407.

    Article  CAS  Google Scholar 

  53. Liu Y, Yan H, Jia M, Du H, Du A. Topological analysis of spin-torque driven magnetic skyrmion formation. Appl Phys Lett. 2016;109(10):102402. https://doi.org/10.1063/1.4962452.

    Article  CAS  Google Scholar 

  54. Yuan H, Wang X. Skyrmion creation and manipulation by nano-second current pulses. Sci Rep. 2016;6(1):22638. https://doi.org/10.1038/srep22638.

    Article  CAS  Google Scholar 

  55. Yin G, Li Y, Kong L, Lake RK, Chien CL, Zang J. Topological charge analysis of ultrafast single skyrmion creation. Phys Rev B. 2016;93(17):174403. https://doi.org/10.1103/PhysRevB.93.174403.

    Article  CAS  Google Scholar 

  56. Hrabec A, Sampaio J, Belmeguenai M, Gross I, Weil R, Chérif SM, Stashkevich A, Jacques V, Thiaville A, Rohart S. Current-induced skyrmion generation and dynamics in symmetric bilayers. Nat Commun. 2017;8(1):15765. https://doi.org/10.1038/ncomms15765.

    Article  CAS  Google Scholar 

  57. Finizio S, Zeissler K, Wintz S, Mayr S, Weßels T, Huxtable AJ, Burnell G, Marrows CH, Raabe J. Deterministic field-free skyrmion nucleation at a nanoengineered injector device. Nano Lett. 2019;19(10):7246. https://doi.org/10.1021/acs.nanolett.9b02840.

    Article  CAS  Google Scholar 

  58. De Lucia A, Litzius K, Krüger B, Tretiakov OA, Kläui M. Multiscale simulations of topological transformations in magnetic-skyrmion spin structures. Phys Rev B. 2017;96(2):020405. https://doi.org/10.1103/PhysRevB.96.020405.

    Article  Google Scholar 

  59. Schulz T, Ritz R, Bauer A, Halder M, Wagner M, Franz C, Pfleiderer C, Everschor K, Garst M, Rosch A. Emergent electrodynamics of skyrmions in a chiral magnet. Nat Phys. 2012;8(4):301. https://doi.org/10.1038/nphys2231.

    Article  CAS  Google Scholar 

  60. Legrand W, Maccariello D, Reyren N, Garcia K, Moutafis C, Moreau-Luchaire C, Collin S, Bouzehouane K, Cros V, Fert A. Room-temperature current-induced generation and motion of sub-100 nm skyrmions. Nano Lett. 2017;17(4):2703. https://doi.org/10.1021/acs.nanolett.7b00649.

    Article  CAS  Google Scholar 

  61. Woo S, Song KM, Han HS, Jung MS, Im MY, Lee KS, Song KS, Fischer P, Hong JI, Choi JW. Spin-orbit torque-driven skyrmion dynamics revealed by time-resolved X-ray microscopy. Nat Commun. 2017;8(1):15573. https://doi.org/10.1038/ncomms15573.

  62. Lemesh I, Litzius K, Böttcher M, Bassirian P, Kerber N, Heinze D, Zázvorka J, Büttner F, Caretta L, Mann M. Current-induced Skyrmion generation through morphological thermal transitions in chiral ferromagnetic heterostructures. Adv Mater. 2018;30(49):1805461. https://doi.org/10.1002/adma.201805461.

    Article  CAS  Google Scholar 

  63. Büttner F, Lemesh I, Schneider M, Pfau B, Günther CM, Hessing P, Geilhufe J, Caretta L, Engel D, Krüger B. Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques. Nat Nanotechnol. 2017;12(11):1040. https://doi.org/10.1038/nnano.2017.178.

    Article  CAS  Google Scholar 

  64. Woo S, Song KM, Zhang X, Ezawa M, Zhou Y, Liu X, Weigand M, Finizio S, Raabe J, Park MC. Deterministic creation and deletion of a single magnetic skyrmion observed by direct time-resolved X-ray microscopy. Nat Electron. 2018;1(5):288. https://doi.org/10.1038/s41928-018-0070-8.

    Article  Google Scholar 

  65. Iwasaki J, Mochizuki M, Nagaosa N. Current-induced skyrmion dynamics in constricted geometries. Nat Nanotechnol. 2013;8(10):742. https://doi.org/10.1038/nnano.2013.176.

    Article  CAS  Google Scholar 

  66. Xu C, Chen P, Tan H, Yang Y, **ang H, Bellaiche L. Electric-field switching of magnetic topological charge in type-I multiferroics. Phys Rev Lett. 2020;125(3):037203. https://doi.org/10.1103/PhysRevLett.125.037203.

    Article  CAS  Google Scholar 

  67. Ikeda S, Miura K, Yamamoto H, Mizunuma K, Gan H, Endo M, Kanai S, Hayakawa J, Matsukura F, Ohno H. A perpendicular-anisotropy CoFeB/MgO magnetic tunnel junction. Nat Mater. 2010;9(9):721. https://doi.org/10.1038/nmat2804.

    Article  CAS  Google Scholar 

  68. Worledge D, Hu G, Abraham DW, Sun J, Trouilloud P, Nowak J, Brown S, Gaidis M, O’sullivan E, Robertazzi R. Spin torque switching of perpendicular Ta/CoFeB/MgO-based magnetic tunnel junctions. Appl Phys Lett. 2011;98(2):022501. https://doi.org/10.1063/1.3536482.

    Article  CAS  Google Scholar 

  69. Sinha J, Hayashi M, Kellock AJ, Fukami S, Yamanouchi M, Sato H, Ikeda S, Mitani S, Yang SH, Parkin SS. Enhanced interface perpendicular magnetic anisotropy in Ta/CoFeB/MgO using nitrogen doped Ta underlayers. Appl Phys Lett. 2013;102(24):242405. https://doi.org/10.1063/1.4811269.

    Article  CAS  Google Scholar 

  70. Liu T, Cai J, Sun L. Large enhanced perpendicular magnetic anisotropy in CoFeB/MgO system with the typical Ta buffer replaced by an Hf layer. AIP Adv. 2012;2(3):032151. https://doi.org/10.1063/1.4748337.

    Article  CAS  Google Scholar 

  71. Pai C-F, Nguyen MH, Belvin C, Vilela-Leão LH, Ralph D, Buhrman R. Enhancement of perpendicular magnetic anisotropy and transmission of spin-Hall-effect-induced spin currents by a Hf spacer layer in W/Hf/CoFeB/MgO layer structures. Appl Phys Lett. 2014;104(8):082407. https://doi.org/10.1063/1.4866965.

    Article  CAS  Google Scholar 

  72. Lee DS, Chang HT, Cheng CW, Chern G. Perpendicular magnetic anisotropy in MgO/CoFeB/Nb and a comparison of the cap layer effect. IEEE Trans Magn. 2014;50(7):3201904. https://doi.org/10.1109/TMAG.2014.2298243.

    Article  CAS  Google Scholar 

  73. Skowroński W, Nozaki T, Shiota Y, Tamaru S, Yakushiji K, Kubota H, Fukushima A, Yuasa S, Suzuki Y. Perpendicular magnetic anisotropy of Ir/CoFeB/MgO trilayer system tuned by electric fields. Appl Phys Express. 2015;8(5):053003. https://doi.org/10.7567/APEX.8.053003.

    Article  CAS  Google Scholar 

  74. Oh YW, Lee KD, Jeong JR, Park BG. Interfacial perpendicular magnetic anisotropy in CoFeB/MgO structure with various underlayers. J Appl Phys. 2014;115(17):17C724. https://doi.org/10.1063/1.4864047.

  75. Liu T, Zhang Y, Cai J, Pan H. Thermally robust Mo/CoFeB/MgO trilayers with strong perpendicular magnetic anisotropy. Sci Rep. 2014;4(1):5895. https://doi.org/10.1038/srep05895.

    Article  CAS  Google Scholar 

  76. Hsu PJ, Kubetzka A, Finco A, Romming N, von Bergmann K, Wiesendanger R. Electric-field-driven switching of individual magnetic skyrmions. Nat Nanotechnol. 2017;12(2):123. https://doi.org/10.1038/nnano.2016.234.

    Article  CAS  Google Scholar 

  77. Jaiswal S, Litzius K, Lemesh I, Büttner F, Finizio S, Raabe J, Weigand M, Lee K, Langer J, Ocker B. Investigation of the Dzyaloshinskii-Moriya interaction and room temperature skyrmions in W/CoFeB/MgO thin films and microwires. Appl Phys Lett. 2017;111(2):022409. https://doi.org/10.1063/1.4991360.

    Article  CAS  Google Scholar 

  78. Schott M, Bernand-Mantel A, Ranno L, Pizzini S, Vogel J, Bea H, Baraduc C, Auffret S, Gaudin G, Givord D. The Skyrmion switch: turning magnetic Skyrmion bubbles on and off with an electric field. Nano Lett. 2017;17(5):3006. https://doi.org/10.1021/acs.nanolett.7b00328.

    Article  CAS  Google Scholar 

  79. Bhattacharya D, Razavi SA, Wu H, Dai B, Wang KL, Atulasimha J. Creation and annihilation of non-volatile fixed magnetic skyrmions using voltage control of magnetic anisotropy. Nat Electron. 2020;3(9):539. https://doi.org/10.1038/s41928-020-0432-x.

    Article  Google Scholar 

  80. Wang X, Gan WL, Martinez JC, Tan FN, Jalil MBA, Lew WS. Efficient skyrmion transport mediated by a voltage controlled magnetic anisotropy gradient. Nanoscale. 2018;10(2):733. https://doi.org/10.1039/c7nr06482a.

    Article  CAS  Google Scholar 

  81. Shen L, **a J, Zhao G, Zhang X, Ezawa M, Tretiakov OA, Liu X, Zhou Y. Dynamics of the antiferromagnetic skyrmion induced by a magnetic anisotropy gradient. Phys Rev B. 2018;98(13):134448. https://doi.org/10.1103/PhysRevB.98.134448.

    Article  CAS  Google Scholar 

  82. Liu Y, Lei N, Wang C, Zhang X, Kang W, Zhu D, Zhou Y, Liu X, Zhang Y, Zhao W. Voltage-driven high-speed skyrmion motion in a skyrmion-shift device. Phys Rev Appl. 2019;11(1):014004. https://doi.org/10.1103/PhysRevApplied.11.014004.

    Article  CAS  Google Scholar 

  83. Ma C, Zhang X, **a J, Ezawa M, Jiang W, Ono T, Piramanayagam SN, Morisako A, Zhou Y, Liu X. Electric field-induced creation and directional motion of domain walls and skyrmion bubbles. Nano Lett. 2019;19(1):353. https://doi.org/10.1021/acs.nanolett.8b03983.

    Article  CAS  Google Scholar 

  84. Zhang Y, Dubuis G, Doyle C, Butler T, Granville S. Nonvolatile and volatile skyrmion generation engineered by ionic liquid gating in ultrathin films. Phys Rev Appl. 2021;16(1):014030. https://doi.org/10.1103/PhysRevApplied.16.014030.

    Article  CAS  Google Scholar 

  85. Yang Q, Cheng Y, Li Y, Zhou Z, Liang J, Zhao X, Hu Z, Peng R, Yang H, Liu M. Voltage control of skyrmion bubbles for topological flexible spintronic devices. Adv Electron Mater. 2020;6(8):2000246. https://doi.org/10.1002/aelm.202000246.

    Article  CAS  Google Scholar 

  86. Choi T, Lee S, Choi Y, Kiryukhin V, Cheong SW. Switchable ferroelectric diode and photovoltaic effect in BiFeO3. Science. 2009;324(5923):63. https://doi.org/10.1126/science.1168636.

    Article  CAS  Google Scholar 

  87. Seki S, Yu XZ, Ishiwata S, Tokura Y. Observation of skyrmions in a multiferroic material. Science. 2012;336(6078):198. https://doi.org/10.1126/science.1214143.

    Article  CAS  Google Scholar 

  88. Mochizuki M, Seki S. Magnetoelectric resonances and predicted microwave diode effect of the skyrmion crystal in a multiferroic chiral-lattice magnet. Phys Rev B. 2013;87(13):134403. https://doi.org/10.1103/PhysRevB.87.134403.

    Article  CAS  Google Scholar 

  89. Seki S, Ishiwata S, Tokura Y. Magnetoelectric nature of skyrmions in a chiral magnetic insulator Cu2OSeO3. Phys Rev B. 2012;86(6):060403. https://doi.org/10.1103/PhysRevB.86.060403.

    Article  CAS  Google Scholar 

  90. Mochizuki M, Watanabe Y. Writing a skyrmion on multiferroic materials. Appl Phys Lett. 2015;107(8):082409. https://doi.org/10.1063/1.4929727.

    Article  CAS  Google Scholar 

  91. Okamura Y, Kagawa F, Seki S, Tokura Y. Transition to and from the skyrmion lattice phase by electric fields in a magnetoelectric compound. Nat Commun. 2016;7(1):12669. https://doi.org/10.1038/ncomms12669.

    Article  CAS  Google Scholar 

  92. Huang P, Cantoni M, Kruchkov A, Rajeswari J, Magrez A, Carbone F, Ronnow HM. In Situ electric field skyrmion creation in magnetoelectric Cu2OSeO3. Nano Lett. 2018;18(8):5167. https://doi.org/10.1021/acs.nanolett.8b02097.

    Article  CAS  Google Scholar 

  93. Deng L, Wu HC, Litvinchuk AP, Yuan NF, Lee JJ, Dahal R, Berger H, Yang HD, Chu CW. Room-temperature skyrmion phase in bulk Cu2OSeO3 under high pressures. Proc Natl Acad Sci. 2020;117(16):8783. https://doi.org/10.1073/pnas.1922108117.

  94. Kézsmárki I, Bordács S, Milde P, Neuber E, Eng L, White J, Rønnow HM, Dewhurst C, Mochizuki M, Yanai K. Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8. Nat Mater. 2015;14(11):1116. https://doi.org/10.1038/nmat4402.

    Article  CAS  Google Scholar 

  95. Ruff E, Widmann S, Lunkenheimer P, Tsurkan V, Bordács S, Kézsmárki I, Loidl A. Multiferroicity and skyrmions carrying electric polarization in GaV4S8. Sci Adv. 2015;1(10):e1500916. https://doi.org/10.1126/sciadv.1500916.

    Article  CAS  Google Scholar 

  96. Fujima Y, Abe N, Tokunaga Y, Arima T. Thermodynamically stable skyrmion lattice at low temperatures in a bulk crystal of lacunar spinel GaV4S8. Phys Rev B. 2017;95(18):180410. https://doi.org/10.1103/PhysRevB.95.180410.

    Article  Google Scholar 

  97. Nii Y, Nakajima T, Kikkawa A, Yamasaki Y, Ohishi K, Suzuki J, Taguchi Y, Arima T, Tokura Y, Iwasa Y. Uniaxial stress control of skyrmion phase. Nat Commun. 2015;6(1):8539. https://doi.org/10.1038/ncomms9539.

    Article  CAS  Google Scholar 

  98. Liu M, Howe BM, Grazulis L, Mahalingam K, Nan T, Sun NX, Brown GJ. Voltage-impulse-induced non-volatile ferroelastic switching of ferromagnetic resonance for reconfigurable magnetoelectric microwave devices. Adv Mater. 2013;25(35):4886. https://doi.org/10.1002/adma.201301989.

    Article  CAS  Google Scholar 

  99. Yang Y, Li J, Peng X, Hong B, Wang X, Ge H, Wang D, Du Y. Surface-effect enhanced magneto-electric coupling in FePt/PMN-PT multiferroic heterostructures. AIP Adv. 2017;7(5):055833. https://doi.org/10.1063/1.4978588.

    Article  CAS  Google Scholar 

  100. Wang Y, Wang L, **a J, Lai Z, Tian G, Zhang X, Hou Z, Gao X, Mi W, Feng C, Zeng M, Zhou G, Yu G, Wu G, Zhou Y, Wang W, Zhang XX, Liu J. Electric-field-driven non-volatile multi-state switching of individual skyrmions in a multiferroic heterostructure. Nat Commun. 2020;11(1):3577. https://doi.org/10.1038/s41467-020-17354-7.

    Article  CAS  Google Scholar 

  101. Ba Y, Zhuang S, Zhang Y, Wang Y, Gao Y, Zhou H, Chen M, Sun W, Liu Q, Chai G, Ma J, Zhang Y, Tian H, Du H, Jiang W, Nan C, Hu JM, Zhao Y. Electric-field control of skyrmions in multiferroic heterostructure via magnetoelectric coupling. Nat Commun. 2021;12(1):322. https://doi.org/10.1038/s41467-020-20528-y.

    Article  CAS  Google Scholar 

  102. Hu JM, Yang T, Chen LQ. Strain-mediated voltage-controlled switching of magnetic skyrmions in nanostructures. npj Comput Mater. 2018;4(1):62. https://doi.org/10.1038/s41524-018-0119-2.

    Article  Google Scholar 

  103. Yanes R, Garcia-Sanchez F, Luis R, Martinez E, Raposo V, Torres L, Lopez-Diaz L. Skyrmion motion induced by voltage-controlled in-plane strain gradients. Appl Phys Lett. 2019;115(13):132401. https://doi.org/10.1063/1.5119085.

    Article  CAS  Google Scholar 

  104. Schleicher B, Niemann R, Diestel A, Hühne R, Schultz L, Fähler S. Epitaxial Ni-Mn-Ga-Co thin films on PMN-PT substrates for multicaloric applications. J Appl Phys. 2015;118(5):053906. https://doi.org/10.1063/1.4927850.

    Article  CAS  Google Scholar 

  105. Li Z, Zhang Y, Huang Y, Wang C, Zhang X, Liu Y, Zhou Y, Kang W, Koli SC, Lei N. Strain-controlled skyrmion creation and propagation in ferroelectric/ ferromagnetic hybrid wires. J Magn Magn Mater. 2018;455:19. https://doi.org/10.1016/j.jmmm.2017.07.008.

    Article  CAS  Google Scholar 

  106. Jungwirth T, Marti X, Wadley P, Wunderlich J. Antiferromagnetic spintronics. Nat Nanotechnol. 2016;11(3):231. https://doi.org/10.1038/nnano.2016.18.

    Article  CAS  Google Scholar 

  107. Duine R, Lee K-J, Parkin SS, Stiles MD. Synthetic antiferromagnetic spintronics. Nat Phys. 2018;14(3):217. https://doi.org/10.1038/s41567-018-0050-y.

    Article  CAS  Google Scholar 

  108. Šmejkal L, Mokrousov Y, Yan B, MacDonald AH. Topological antiferromagnetic spintronics. Nat Phys. 2018;14(3):242. https://doi.org/10.1038/s41567-018-0064-5.

    Article  CAS  Google Scholar 

  109. Yan H, Feng Z, Shang S, Wang X, Hu Z, Wang J, Zhu Z, Wang H, Chen Z, Hua H, Lu W, Wang J, Qin P, Guo H, Zhou X, Leng Z, Liu Z, Jiang C, Coey M, Liu Z. A piezoelectric, strain-controlled antiferromagnetic memory insensitive to magnetic fields. Nat Nanotechnol. 2019;14(2):131. https://doi.org/10.1038/s41565-018-0339-0.

    Article  CAS  Google Scholar 

  110. Liu ZQ, Chen H, Wang JM, Liu JH, Wang K, Feng ZX, Yan H, Wang XR, Jiang CB, Coey JMD, MacDonald AH. Electrical switching of the topological anomalous Hall effect in a non-collinear antiferromagnet above room temperature. Nature Electron. 2018;1(3):172. https://doi.org/10.1038/s41928-018-0040-1.

    Article  CAS  Google Scholar 

  111. Liu Z, Feng Z, Yan H, Wang X, Zhou X, Qin P, Guo H, Yu R, Jiang C. Antiferromagnetic piezospintronics. Adv Electron Mater. 2019;5(7):1900176. https://doi.org/10.1002/aelm.201900176.

    Article  CAS  Google Scholar 

  112. Qin P, Yan H, Wang X, Feng Z, Guo H, Zhou X, Wu H, Zhang X, Leng Z, Chen H, Liu Z. Noncollinear spintronics and electric-field control: a review. Rare Met. 2020;39(2):95. https://doi.org/10.1007/s12598-019-01352-w.

    Article  CAS  Google Scholar 

  113. Legrand W, Maccariello D, Ajejas F, Collin S, Vecchiola A, Bouzehouane K, Reyren N, Cros V, Fert A. Room-temperature stabilization of antiferromagnetic skyrmions in synthetic antiferromagnets. Nat Mater. 2020;19(1):34. https://doi.org/10.1038/s41563-019-0468-3.

    Article  CAS  Google Scholar 

  114. Gao S, Rosales H, Gómez Albarracín FA, Tsurkan V, Kaur G, Fennell T, Steffens P, Boehm M, Čermák P, Schneidewind A. Fractional antiferromagnetic skyrmion lattice induced by anisotropic couplings. Nature. 2020;586(7827):37. https://doi.org/10.1038/s41586-020-2716-8.

    Article  CAS  Google Scholar 

  115. Barker J, Tretiakov OA. Static and dynamical properties of antiferromagnetic skyrmions in the presence of applied current and temperature. Phys Rev Lett. 2016;116(14):147203. https://doi.org/10.1103/PhysRevLett.116.147203.

    Article  CAS  Google Scholar 

  116. Zhang X, Zhou Y, Ezawa M. Magnetic bilayer-skyrmions without skyrmion Hall effect. Nat Commun. 2016;7(1):10293. https://doi.org/10.1038/ncomms10293.

    Article  CAS  Google Scholar 

  117. Göbel B, Henk J, Mertig I. Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk. Sci Rep. 2019;9(1):9521. https://doi.org/10.1038/s41598-019-45965-8.

    Article  CAS  Google Scholar 

  118. Yu X, Tokunaga Y, Kaneko Y, Zhang W, Kimoto K, Matsui Y, Taguchi Y, Tokura Y. Biskyrmion states and their current-driven motion in a layered manganite. Nat Commun. 2014;5(1):3198. https://doi.org/10.1038/ncomms4198.

    Article  CAS  Google Scholar 

  119. Zhang X, **a J, Zhou Y, Wang D, Liu X, Zhao W, Ezawa M. Control and manipulation of a magnetic skyrmionium in nanostructures. Phys Rev B. 2016;94(9):094420. https://doi.org/10.1103/PhysRevB.94.094420.

    Article  CAS  Google Scholar 

  120. Zhang S, Kronast F, van der Laan G, Hesjedal T. Real-space observation of skyrmionium in a ferromagnet-magnetic topological insulator heterostructure. Nano Lett. 2018;18(2):1057. https://doi.org/10.1021/acs.nanolett.7b04537.

    Article  CAS  Google Scholar 

  121. Göbel B, Schäffer AF, Berakdar J, Mertig I, Parkin SSP. Electrical writing, deleting, reading, and moving of magnetic skyrmioniums in a racetrack device. Sci Rep. 2019;9(1):121. https://doi.org/10.1038/s41598-019-48617-z.

    Article  CAS  Google Scholar 

  122. Ishida Y, Kondo K. Theoretical comparison between skyrmion and skyrmionium motions for spintronics applications. Jpn J Appl Phys. 2020;59(SG):SGGI04. https://doi.org/10.7567/1347-4065/ab5b6b.

    Article  CAS  Google Scholar 

  123. Udalov OG, Beloborodov IS, Sapozhnikov MV. Magnetic skyrmions and bimerons in films with anisotropic interfacial Dzyaloshinskii-Moriya interaction. Phys Rev B. 2021;103(17):174416. https://doi.org/10.1103/PhysRevB.103.174416.

    Article  CAS  Google Scholar 

  124. Zhang X, **a J, Shen L, Ezawa M, Tretiakov OA, Zhao GP, Liu XX, Zhou Y. Static and dynamic properties of bimerons in a frustrated ferromagnetic monolayer. Phys Rev B. 2020;101(14):144435. https://doi.org/10.1103/PhysRevB.101.144435.

    Article  CAS  Google Scholar 

  125. Tan A, Li J, Scholl A, Arenholz E, Young AT, Li Q, Hwang C, Qiu ZQ. Topology of spin meron pairs in coupled Ni/Fe/Co/Cu(0 0 1) disks. Phys Rev B. 2016;94(1):014433. https://doi.org/10.1103/PhysRevB.94.014433.

    Article  CAS  Google Scholar 

  126. Zheng F, Rybakov FN, Borisov AB, Song D, Wang S, Li Z-A, Du H, Kiselev NS, Caron J, Kovács A. Experimental observation of chiral magnetic bobbers in B20-type FeGe. Nat Nanotechnol. 2018;13(6):451. https://doi.org/10.1038/s41565-018-0093-3.

    Article  CAS  Google Scholar 

  127. Ahmed AS, Rowland J, Esser BD, Dunsiger SR, McComb DW, Randeria M, Kawakami KK. Chiral bobbers and skyrmions in epitaxial FeGe/Si (111) films. Phys Rev Mater. 2018;2(4): 041401. https://doi.org/10.1103/PhysRevMaterials.2.041401.

    Article  CAS  Google Scholar 

  128. Wang X, Qaiumzadeh A, Brataas A. Current-driven dynamics of magnetic hopfions. Phys Rev Lett. 2019;123(14):147203. https://doi.org/10.1103/PhysRevLett.123.147203.

    Article  CAS  Google Scholar 

  129. Kent N, Reynolds N, Raftrey D, Campbell IT, Virasawmy S, Dhuey S, Chopdekar RV, Hierro-Rodriguez A, Sorrentino A, Pereiro E. Creation and observation of Hopfions in magnetic multilayer systems. Nat Commun. 2021;12(1):1562. https://doi.org/10.1038/s41467-021-21846-5.

    Article  CAS  Google Scholar 

  130. Pershoguba SS, Andreoli D, Zang J. Electronic scattering off a magnetic hopfion. Phys Rev B. 2021;104(7):075102. https://doi.org/10.1103/PhysRevB.104.075102.

    Article  CAS  Google Scholar 

  131. Zarzuela R, Ochoa H, Tserkovnyak Y. Hydrodynamics of three-dimensional skyrmions in frustrated magnets. Phys Rev B. 2019;100(5):054426. https://doi.org/10.1103/PhysRevB.100.054426.

    Article  CAS  Google Scholar 

  132. Liu Y, Lake RK, Zang J. Binding a hopfion in a chiral magnet nanodisk. Phys Rev B. 2018;98(17):174437. https://doi.org/10.1103/PhysRevB.98.174437.

    Article  CAS  Google Scholar 

  133. Qiu L, **a J, Feng Y, Shen L, Morvan FJ, Zhang X, Liu X, **e L, Zhou Y, Zhao G. Dynamics of antiskyrmions induced by the voltage-controlled magnetic anisotropy gradient. J Magn Magn Mater. 2020;496:165922. https://doi.org/10.1016/j.jmmm.2019.165922.

    Article  CAS  Google Scholar 

  134. Mehmood N, Fazal R, Yadong W, Guo T, Zhang Q, Hou Z, **ngsen G, Liu JM. Stability phase diagrams and tuning of magnetic skyrmionium and other states. J Magn Magn Mater. 2021;526:167706. https://doi.org/10.1016/j.jmmm.2020.167706.

    Article  CAS  Google Scholar 

  135. Tang J, Wu Y, Wang W, Kong L, Lv B, Wei W, Zang J, Tian M, Du H. Magnetic skyrmion bundles and their current-driven dynamics. Nat Nanotechnol. 2021;16(10):1086. https://doi.org/10.1038/s41565-021-00985-2.

    Article  CAS  Google Scholar 

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Acknowledgements

This work was financially supported by the National Key Research and Development Program of China (No. 2020YFA0309300), the Natural Science Foundation of Guangdong Province (No. 2016A030308019), the National Natural Science Foundation of China (Nos. 51901081 and 51871161), the Science and Technology Program of Guangzhou (Nos. 2019050001 and 202002030052).

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Wang, YD., Wei, ZJ., Tu, HR. et al. Electric field manipulation of magnetic skyrmions. Rare Met. 41, 4000–4014 (2022). https://doi.org/10.1007/s12598-022-02084-0

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