磁斯格明子在钉扎作用下的动力学研究进展
西交利物浦大学, 物理系, 江苏苏州 215123
| 摘 要： | 磁斯格明子由于其具有拓扑保护、尺寸小、驱动电流低的优势，有望应用于下一代存储和计算器件，例如赛道存储、逻辑计算和神经计算器件。室温下磁斯格明子的发现也为实现基于磁斯格明子的计算和存储器件奠定了基础。缺陷和杂质等在真实材料中不可避免，这些天然的钉扎中心会对磁斯格明子的动力学，包括临界驱动电流、霍尔角度等产生重要影响。关于薄膜中室温磁斯格明子的工作表明，钉扎的影响在室温下会非常大。因此，研究不同温度下的钉扎效应和磁斯格明子-钉扎间的相互作用，对研究磁斯格明子在实际器件中的动力学和实现室温磁斯格明子自旋器件非常重要。此外，利用这些作用也可人工引入钉扎中心以操控磁斯格明子的运动。本文介绍了磁斯格明子的动力学模型，特别是在有限温环境、钉扎作用下的理论模型，以及数值模拟。同时，简要综述了最近关于钉扎和磁斯格明子相互作用的一些研究工作；并展望了该领域的研究方向。通过替换或增加原子、设置空缺、改变材料厚度或弯曲度、改变磁性参数等方式引入钉扎时，可使磁斯格明子运动时的霍尔角发生变化，也可将磁斯格明子固定在某一区域，或沿着特定轨道运动，克服室温下热扰动，有助于实现室温下磁斯格明子自旋器件。 |
| 关 键 词： | 磁斯格明子; 钉扎; 动力学 |
| DOI： | 10.57237/j.se.2022.01.005 |
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收稿日期: 2022-09-28
接受日期: 2022-10-24
在线出版日期: 2023-01-05
Research Progress on Dynamics of Skyrmions Under the Effect of Pinning
Department of Physics, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China
| Abstract: | Magnetic skyrmions offer the potential as an information carrier for the next-generation storage and computing devices such as racetrack memory devices, logic gates, and even neurocomputing owing to the topology-protected structure, nano-scale size and relatively low driving current compared to traditional devices. The discovery of magnetic skyrmions at room temperature also lays the foundation for realizing room-temperature magnetic skyrmion spintronic devices. Defects and impurities are unavoidable in real materials. These pinning centers significantly affect the dynamics of the skyrmion, including the critical driving current, and the Hall angle, etc. The study on room-temperature magnetic skyrmions in thin films has shown that the effect of pinning can be dominant at room temperature. Hence, the study of pinning effects and the skyrmion-pinning interaction is significant to the motion of magnetic skyrmions at room temperature and the realization of room-temperature magnetic skyrmion spin devices Magnetic skyrmion motion can be strongly modified under the effect of pinning (defects and purities). Moreover, these effects can inspire us to utilize artificial pinning centers to manipulate the dynamics of skyrmions. In this article, we introduce the models for skyrmion motion and pinning effect at room temperature and gives an overview of the methods for creating different types of pinning and their impact on the skyrmions. When pinning is induced by replacing or adding atoms, setting vacancies, changing the material thickness or curvature, or changing magnetic parameters, the skyrmions hall angle will vary. Moreover, the magnetic skyrmions can be fixed in a particular region, move along a specific orbit and overcome thermal perturbations at room temperature under the effect of pinning, which helps to realize magnetic skyrmion spin devices at room temperature. |
| Keywords: | Skyrmion; Pinning; Dynamics |
基金
| 1. | 西交利物浦大学Key Programme Special Fund (Grant No. KSF-E-22) |
| 2. | Research Enhancement Fund (Grant No. REF17-1-7). |
参考文献
| [1] | Bogdanov A, Hubert A. Thermodynamically stable magnetic vortex states in magnetic crystals [J]. J. Magn. Magn. Mater., 1994, 138: 255-269. |
| [2] | Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Böni P. Skyrmion lattice in a chiral magnet [J]. Science, 2009, 323: 915-919. |
| [3] | Nagaosa N, Tokura Y. Topological properties and dynamics of magnetic skyrmions [J]. Nat. Nanotechnol., 2013, 8: 899-911. |
| [4] | Yu X, Liu Y. Formation and annihilation of skyrmions in a bucket-shaped nanotube [J]. Phys. Lett. A, 2021, 415 (127656). |
| [5] | Guo J, Xia J, Zhang X, Pong P W, Zhou Y. A ferromagnetic skyrmion-based nano-oscillator with modified perpendicular magnetic anisotropy [J]. Phys. Lett. A, 2021, 392 (127157). |
| [6] | Fert A, Reyren N, Cros V. Magnetic skyrmions: advances in physics and potential applications [J]. Nat. Rev. Mater., 2017, 2 (17031). |
| [7] | Dzyaloshinskii I. A thermodynamic theory of ‘weak’ ferromagnetism of antiferromagnetics [J]. J. Phys. Chem. Solids, 1958, 4: 241-255. |
| [8] | Moriya T. Anisotropic superexchange interaction and weak ferromagnetism [J]. Phys. Rev., 1960, 120: 91–98. |
| [9] | Rajaraman R. Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory [M]. Oxford: Elsevier Science & Technology, 1987: 31–32. |
| [10] | Skyrme T. A unified field theory of mesons and baryons [J]. Nucl. Phys., 1962, 31 (556). |
| [11] | Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y. Real-space observation of a two-dimensional skyrmion crystal [J]. Nature, 2010, 465: 901-904. |
| [12] | Heinze S, Bergmann K, Menzel M, Brede J, Ku-betzka A, Wiesendanger R, Bihlmayer G, Bl ̈ugel S. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions [J]. Nature Phys., 2011, 7: 713-718. |
| [13] | Jiang W, Upadhyaya P, Zhang W, Yu G, Jungfleisch M B, Fradin F Y, Pearson J E, Tserkovnyak Y, Wang K L, Heinonen O, Te Velthuis S G E, Hoffmann A. Blowing magnetic skyrmion bubbles [J]. Science, 2018, 349: 283-286. |
| [14] | Wang L, Feng Q, Kim Y, Kim R, Lee K H, Pollard S D, Shin Y J, Zhou H, Peng W, Lee D, Meng W, Yang H, Han J H, Kim M, Lu Q, Noh T W. Ferro-electrically tunable magnetic skyrmions in ultrathin oxideheterostructures [J]. Nature Materials, 2018, 17: 1087-1094. |
| [15] | Nagaosa N, Tokura Y. Topological propertiesand dynamics of magnetic skyrmions [J]. Nature Nanotechnol., 2013, 8 (899). |
| [16] | Boulle O, Vogel J, Yang H, Pizzini S, De Souza Chaves D, Locatelli A, Mentes T O, Sala A, Buda-Prejbeanu L D, Klein O, Belmeguenai M, Roussign ́e Y, Stashkevich A, Ch ́erif S M, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M, and Gaudin G. Room-temperaturechiral magnetic skyrmions in ultrathin magnetic nanostruc-tures [J]. Nature Nanotechnol., 2016, 11: 449-454. |
| [17] | Jonietz F, M ̈uhlbauer S, Pfleiderer C, Neubauer A, M ̈unzer W, Bauer A, Adams T, Georgii R, B ̈oni P, Duine R A, Everschor K, Garst M, Rosch A. Spintransfer torques in MnSi at ultralow current densities [J]. Science, 2010, 330 (1648). |
| [18] | 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 chiralmagnet [J]. Nature Phys., 2012, 8 (301). |
| [19] | Woo S, Song K M, Zhang X C, Zhou Y, Ezawa M, Liu X X, Finizio S, Raabe J, Lee N J, Kim S I, Park S Y, Kim Y, Kim J Y, Lee D, Lee O, Choi J W, Min B C, Koo H C, Chang J. Current-driven dynamicsand inhibition of the skyrmion Hall effect of ferrimagneticskyrmions in GdFeCo films [J]. Nature Commun., 2018, 9 (959). |
| [20] | Hrabec A, Sampaio J, Belmeguenai M, Gross I, Weil R, Ch ́erif S M, Stashkevich A, Jacques V, Thiaville A, Rohart S. Current-induced skyrmion generationand dynamics in symmetric bilayers [J]. Nature Commun., 2017, 8 (15765). |
| [21] | Kong L, Zang J. Dynamics of an insulatingskyrmion under a temperature gradient [J]. Phys. Rev. Lett., 2013, 111 (067203). |
| [22] | Shen L C, Xia J, Zhao G P, Zhang X C, Ezawa M, Tretiakov O A, Liu X X, Zhou Y. Dynamicsof the antiferromagnetic skyrmion induced by a magneticanisotropy gradient [J]. Phys. Rev. B, 2018, 98 (134448). |
| [23] | Kruchkov A J, White J S, Bartkowiak M, Zivkovi ́c I, Magrez A, Rønnow H M. Direct electricfield control of the skyrmion phase in a magnetoelectricinsulator [J]. Sci. Rep., 2018, 8 (10466). |
| [24] | Wang W, Beg M, Zhang B, Kuch W, Fan-gohr H. Driving magnetic skyrmions with microwavefields [J]. Phys. Rev. B, 2015, 92 (020403). |
| [25] | Shen M, Zhang Y, Ou-Yang J, Yang X, You L. Motion of a skyrmionium driven by spin wave [J]. Appl. Phys. Lett., 2018, 112 (062403). |
| [26] | Nepal R, G¨ung¨ord¨u U, Kovalev A A. Magnetic skyrmion bubble motion driven by surface acoustic waves [J]. Appl. Phys. Lett., 2018, 112 (112404). |
| [27] | Psaroudaki C, Loss D. Skyrmions driven by intrinsic magnons [J]. Phys. Rev. Lett., 2018, 120 (237203). |
| [28] | Jonietz F et al. Spin transfer torques in MnSi at ultralow current densities [J]. Science, 2010, 330:1648-1651. |
| [29] | Yu X Z et al. Skyrmion flow near room temperature in an ultralow current density [J]. Nat. Commun., 2012, 3 (988). |
| [30] | Jiang W, Chen G, Liu K, Zang J, te Velthuis S G, Hoffmann A. Skyrmions in magnetic multilayers [J]. Phys. Reports, 2017, 704 (1). |
| [31] | Thiele A A. Steady-state motion of magnetic domains [J]. Phys. Rev. Lett., 1973, 30: 230-233. |
| [32] | Iwasaki J, Mochizuki M, Nagaosa N. Universal current-velocity relation of skyrmion motion in chiral magnets [J]. Nat. Commun., 2013, 4 (1463). |
| [33] | Litzius K et al. Skyrmion Hall effect revealed by direct time‑resolved X‑ray microscopy [J]. Nat. Phys., 2017, 13: 170-175. |
| [34] | Miltat J, Rohart S, Thiaville A. Brownian motion of magnetic domain walls and skyrmions and their diffusion constants [J]. Phys. Rev. B, 2018: 97 (214426). |
| [35] | Schütte C, Iwasaki J, Rosch A, Nagaosa N. Inertia, diffusion, and dynamics of a driven skyrmion [J]. Phys. Rev. B, 2014, 90 (174434). |
| [36] | Weißenhofer M, Rózsa L, Nowak U. Skyrmion dynamics at finite temperatures: Beyond thiele’s equation [J]. Phys. Rev. Lett., 2021, 127 (047203). |
| [37] | Liu Y H, Li Y Q. A mechanism to pin skyrmions in chiral magnets [J]. J. Phys., 2013, 25 (076005). |
| [38] | Iwasaki J, Mochizuki M, Nagaosa N. Current-induced skyrmion dynamics in constricted geometries [J]. Nature Nanotechnol., 2013, 8: 742-747. |
| [39] | Kim J V, Yoo M W. Current-driven skyrmion dynamics in disordered films [J]. Appl. Phys. Lett., 2017, 110 (132404). |
| [40] | Legrand W et al. Room temperature current induced generation and motion of sub-100 nm skyrmions [J]. Nano Lett., 2017, 17: 2703-2712. |
| [41] | Jiang Y X, Xuan C, Yu H. Current-driven dynamics of skyrmions in the presence of pinning at finite temperatures [J]. J. Magn. Magn. Mater., 2022, 562 (169786). |
| [42] | Jiang W et al. Direct observation of the skyrmion Hall effect. Nature Phys., 2017, 13 (162). |
| [43] | Zhao L et al. Topology-dependent Brownian gyromotion of a single skyrmion [J]. Phys. Rev. Lett., 2020, 125 (027206). |
| [44] | Reichhardt C, Reichhardt C J O. Statics and Dynamics of Skyrmions Interacting with Pinning: A Review [Z]. |
| [45] | Reichhardt C, Reichhardt C J O. Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: A review [J]. Rep. Prog. Phys., 2017, 80 (026501). |
| [46] | Choi H C, Lin S Z, and Zhu J X. Density functional theory study of skyrmion pinning by atomic defects in MnSi [J]. Phys. Rev. B, 2016, 93 (115112). |
| [47] | Lima Fernandes I, Bouaziz J, Blügel S, and Lounis S. Universality of defect skyrmion interaction profiles [J]. Nat. Commun., 2018, 9 (4395). |
| [48] | Potkina M, Lobanov I, and Uzdin V. Nonmagnetic impurities in skyrmion racetrack memory [J]. Nanosyst.: Phys., Chem., Math., 2020, 11 (628). |
| [49] | Stosic D, Ludermir T B, and Milosevic M V. Pinning of magnetic skyrmions in a monolayer Co film on Pt(111): Theoretical characterization and exemplified utilization [J]. Phys. Rev. B, 2017, 96 (214403). |
| [50] | Müller J and Rosch A. Capturing of a magnetic skyrmion with a hole [J]. Phys. Rev. B, 2015, 91 (054410). |
| [51] | Iwasaki J, Mochizuki M, and Nagaosa N. Current-induced skyrmion dynamics in constricted geometries [J]. Nat. Nanotechnol., 2013, 8, (742). |
| [52] | Suess D, Vogler C, Bruckner F, Heistracher P, Slanovc F, and Abert C. Spin torque efficiency and analytic error rate estimates of skyrmion racetrack memory [J]. Sci. Rep., 2019, 9 (4827). |
| [53] | Pathak S A and Hertel R. Geometrically constrained skyrmions [J]. Magnetochemistry, 2021, 7 (26). |
| [54] | Kravchuk V P et al. Topoogically stable magnetization states on a spherical shell: Curvature-stabilized skyrmions [J]. Phys. Rev. B, 2016, 94 (144402). |
| [55] | Streubel R et al. Magnetism in curved geometries [J]. Phys. D: Appl. Phys., 2016, 49 (363001). |
| [56] | Yang J, Abert C, Suess D, and Kim S K. Intrinsic DMI-free skyrmion formation and robust dynamic behaviors in magnetic hemispherical shells [J]. Sci. Rep., 2021, 11 (3886). |
| [57] | Kravchuk V P et al. Multiplet of skyrmion states on a curvilinear defect: Reconfigurable skyrmion lattices [J]. Phys. Rev. Lett., 2018, 120 (067201). |
| [58] | Carvalho-Santos V L et al. Skyrmion propagation along curved race tracks [J]. Appl. Phys. Lett., 2021, 118 (172407). |
| [59] | Toscano D et al. Building traps for skyrmions by the incorporation of magnetic defects into nanomagnets: Pinning and scattering traps by magnetic properties engineering [J]. J. Magn. Magn. Mater., 2019, 480 (171). |
| [60] | Sampaio J et al. Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures [J]. Nat. Nanotechnol., 2013, 8 (839). |
| [61] | Mulkers J, Waeyenberge B V, and Milosevic M V. Effects of spatially engineered Dzyaloshinskii-Moriya interaction in ferromagnetic films [J]. Phys. Rev. B, 2017, 95 (144401). |
| [62] | Castell-Queralt J et al. Accelerating, guiding, and compressing skyrmions by defect rails [J]. Nanoscale, 2019, 11 (12589). |
| [63] | 梁雪, 赵莉, 邱雷, 李双, 丁丽红, 丰友华, 张溪超, 周艳, 赵国平. 磁性磁斯格明子的赛道存储 [J]. Acta Physica Sinica, 2018, 67 (137510). |
