磁斯格明子拓扑特性及其动力学微磁学模拟研究进展

孔令尧

doi:10.7498/aps.67.20180235

摘要

具有非平庸拓扑性的新型磁结构斯格明子，由于其拓扑稳定性、尺寸小、低电流驱动等方面的显著优势，有望应用于自旋电子学储存器件.拓扑和凝聚态物理学的结合，使得斯格明子展现出很多有趣的拓扑物理现象，吸引了众多的研究兴趣，同时这些性质也是其电流驱动下动力学特点的重要影响因素.本文从斯格明子的拓扑物理学基础及其自旋电子学器件应用相关动力学两个方面介绍了相关研究进展.在拓扑物理基础方面，介绍了斯格明子的拓扑霍尔效应、斯格明子霍尔效应以及自旋轨道转矩等拓扑性质，由此讨论了斯格明子的动力学性质及其计算方法；在动力学方面，从非均匀电流驱动生成斯格明子、电流驱动下的稳定输运、产生湮灭过程的人工控制几个赛道存储应用关心的问题简要地介绍了相关微磁学模拟研究最新进展.

关键词:

Abstract

Skyrmions, as a nontrivial topological magnetic structure, have the advantages of topological stability, small size and low driving electrical current, showing potential applications in spintronic memory device. There are several mechanisms for skyrmion formation in magnets. One major mechanism is, in chiral-lattice ferromagnets, the competition between the Dzyaloshinskii-Moriya and ferromagnetic exchange interactions, due to the lack of spatial inversion symmetry. The combination of topology and condensed physics demonstrates various new topological phenomena of skyrmions, which also determine their dynamics. In this review, recent progress on the topological physics foundation of Skyrmions, as well as their dynamics of application in spintronics devices, is reviewed. The topological physics foundations of skyrmions is introduced. Firstly, the structure of skyrmions, which shows a special nontrivial topology in the real space, is presented accompanied with the formation of skyrmions caused by Dzyaloshinskii Moriya interactions in chiral magnets. Secondly, due to the importance of the describable method of the topology of a skyrmion, the topological charge, that characterize the topology, as well as the calculation method are introduced. Also, the arising topological stability is discussed here. Then, the typical topological effects arising from the topology of a skyrmion, including topological Hall effect and the skyrmion Hall effect are reviewed. The next is the introduction of the helical and the spiral spin configuration, the alternatives for Bloch and Nal type skyrmions respectively, which show up under lower external magnetic field with the same interaction. Also the phase transition of the helical/spiral state to skyrmions and the Monte Carlo method to simulate the spin configuration of a chiral magnet are introduced. At last, the spin orbital torque and the spin transfer torque, that describe the driven effect of a skyrmion by an electrical current or a thermal field, are reviewed. The consequence dynamics of skyrmions, the Landau-LifshitzGilbert equation, are also introduced. The recent progress of typical dynamics of skyrmions on several concerned problems in practical applications are reviewed. The applications in spintronics memory require skyrmions have steady transportation driven by electrical current and controllable creation and annihilation process. Firstly, skyrmion can be generated by the spatial nonuniform electric current with a certain geometry constrain. Especially for the Nal type skyrmion, nonuniformity of the spin orbital torque, come from the non-uniform electric current, play an important role in the skyrmion generation process. Secondly, skyrmion moves with a perpendicular velocity under an electrical current, because of the skyrmion Hall effect. So the elimination of skyrmion Hall effect is practically concerned to make the transportation steady. The anti-ferromagnetic skyrmion and antiferromagnetic coupled skyrmion bilayer are found with no skyrmion Hall effect by have two opposite component cancel out. Finally, with topological stability, skyrmions are hard to convert from and to a nontrivial topological spin configuration at low temperature. So the manipulation of skyrmion creation and annihilation are discussed accompanied with their difference of Bloch and Nal type skyrmiom.

Keywords:

作者及机构信息

孔令尧

1.
中国工程物理研究院流体物理研究所, 绵阳 621900

通信作者: 孔令尧, LingyaoKong@163.com

基金项目: 国家自然科学基金（批准号：11504351）资助的课题.

Authors and contacts

Kong Ling-Yao

1.
Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China

Corresponding author: Kong Ling-Yao, LingyaoKong@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11504351).

参考文献

[1]	Skyrme T 1962 Nucl. Phys. 31 556
[2]	Polyakov A M, Belavin A A 1975 Jetp Lett. 22 503
[3]	Muhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Boni P 2009 Science 323 915
[4]	Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 465 901
[5]	Thiaville A, Rohart S, Ju , Cros V, Fert A 2012 Europhys. Lett. 100 57002
[6]	Hoffmann A 2013 IEEE Trans. Magn. 49 5172
[7]	Fert A, Cros V, Sampaio J 2013 Nat. Nanotechnol. 8 152
[8]	Hellman F, Hoffmann A, Tserkovnyak Y, Beach G S, Fullerton E E, Leighton C, MacDonald A H, Ralph D C, Arena D A, Drr H A, Fischer P, Grollier J, Heremans J P, Jungwirth T, Kimel A V, Koopmans B, Krivorotov I N, May S J, Petford L A K, Rondinelli J M, Samarth N, Schuller I K, Slavin A N, Stiles M D, Tchernyshyov O, Thiaville A, Zink B L 2017 Rev. Mod. Phys. 89 025006
[9]	Schulz T, Ritz R, Bauer A, Halder M, Wagner M, Franz C, Pfleiderer C, Everschor K, Garst M, Rosch A 2012 Nat. Phys. 8 301
[10]	Yi S D, Onoda S, Nagaosa N, Han J H 2009 Phys. Rev. B 80 054416
[11]	Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Bni P 2009 Phys. Rev. Lett. 102 186602
[12]	Zang J, Mostovoy M, Han J H, Nagaosa N 2011 Phys. Rev. Lett. 107 136804
[13]	Litzius K, Lemesh I, Krger B, Bassirian P, Caretta L, Richter K, Bttner F, Sato K, Tretiakov O A, Frster J, Reeve R M, Weigand M, Bykova I, Stoll H, Schtz G, Beach G S D, Klui M 2016 Nat. Phys. 13 170
[14]	Woo S, Litzius K, Krger B, Im M Y, Caretta L, Richter K, Mann M, Krone A, Reeve R M, Weigand M, Agrawal P, Lemesh I, Mawass M A, Fischer P, Klui M, Beach G S D 2016 Nat. Mater. 15 501
[15]	Jiang W, Zhang X, Yu G, Zhang W, Wang X, Jungfleisch M B, Pearson J E, Cheng X, Heinonen O, Wang K L, Zhou Y, Hoffmann A, te Velthuis S G E 2016 Nat. Phys. 13 162
[16]	Liu L, Pai C F, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Science 336 555
[17]	Lin S Z, Reichhardt C, Batista C D, Saxena A 2013 Phys. Rev. B 87 214419
[18]	Kang W, Huang Y, Zhang X, Zhou Y, Zhao W 2016 Proc. IEEE 104 2040
[19]	Kang W, Zheng C, Huang Y, Zhang X, Zhou Y, Lv W, Zhao W 2016 IEEE Electron Dev. Lett. 37 924
[20]	Parkin S S P, Hayashi M, Thomas L 2008 Science 320 190
[21]	Parkin S, Yang S H 2015 Nat. Nanotechnol. 10 195
[22]	Pfleiderer C, Rosch A 2010 Nature 465 880
[23]	Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2010 Nat. Mater. 10 106
[24]	Huang S X, Chien C L 2012 Phys. Rev. Lett. 108 267201
[25]	Kanazawa N, Onose Y, Arima T, Okuyama D, Ohoyama K, Wakimoto S, Kakurai K, Ishiwata S, Tokura Y 2011 Phys. Rev. Lett. 106 156603
[26]	Kanazawa N, Kim J H, Inosov D S, White J S, Egetenmeyer N, Gavilano J L, Ishiwata S, Onose Y, Arima T, Keimer B, Tokura Y 2012 Phys. Rev. B 86 134425
[27]	Makarova O L, Tsvyashchenko A V, Andre G, Porcher F, Fomicheva L N, Rey N, Mirebeau I 2012 Phys. Rev. B 85 205205
[28]	Seki S, Yu X Z, Ishiwata S, Tokura Y 2012 Science 336 198
[29]	Adams T, Chacon A, Wagner M, Bauer A, Brandl G, Pedersen B, Berger H, Lemmens P, Pfleiderer C 2012 Phys. Rev. Lett. 108 237204
[30]	Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[31]	Landau L D, Lifshitz E M, Sykes J B, Bell J S, Dill E H 1961 Electrodynamics of Continuous Media (2nd Ed.) (Oxford: Pergamon) pp178-179
[32]	Moriya T 1960 Phys. Rev. 120 91
[33]	Han J H, Zang J, Yang Z, Park J H, Nagaosa N 2010 Phys. Rev. B 82 094429
[34]	Rler U K, Leonov A A, Bogdanov A N 2011 J. Phys. Conf. Ser. 303 012105
[35]	Yu X, Mostovoy M, Tokunaga Y, Zhang W, Kimoto K, Matsui Y, Kaneko Y, Nagaosa N, Tokura Y 2012 Proc. Nat. Acad. Sci. USA 109 8856
[36]	Everschor S K, Sitte M 2014 J. Appl. Phys. 115 172602
[37]	Rajaraman R 1987 Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory (Oxford: Elsevier Science Technology) pp31-32
[38]	Nagaosa N, Tokura Y 2013 Nat. Nanotechnol. 8 899
[39]	Berg B, Lscher M 1981 Nucl. Phys. B 190 412
[40]	Hou W T, Yu J X, Daly M, Zang J 2017 Phys. Rev. B 96 140403
[41]	Yin G, Li Y, Kong L, Lake R K, Chien C L, Zang J 2016 Phys. Rev. B 93 174403
[42]	Kong L, Zang J 2013 Phys. Rev. Lett. 111 067203
[43]	Milde P, Kohler D, Seidel J, Eng L M, Bauer A, Chacon A, Kindervater J, Muhlbauer S, Pfleiderer C, Buhrandt S, Schutte C, Rosch A 2013 Science 340 1076
[44]	Tokunaga Y, Yu X Z, White J S, Rnnow H M, Morikawa D, Taguchi Y, Tokura Y 2015 Nat. Commun. 6 7638
[45]	Oike H, Kikkawa A, Kanazawa N, Taguchi Y, Kawasaki M, Tokura Y, Kagawa F 2015 Nat. Phys. 12 62
[46]	Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, Tokura Y 2010 Science 329 297
[47]	Ding J, Yang X, Zhu T 2015 IEEE Trans. Magn. 51 1
[48]	Zhang X, Mller J, Xia J, Garst M, Liu X, Zhou Y 2017 New J. Phys. 19 065001
[49]	Jin C, Li Z A, Kovcs A, Caron J, Zheng F, Rybakov F N, Kiselev N S, Du H, Blgel S, Tian M, Zhang Y, Farle M, Dunin B R E 2017 Nat. Commun. 8 15569
[50]	Laarhoven P J M, Aarts E H L 1987 Simulated Annealing: Theory and Applications (Dordrecht: Reidel) pp7-15
[51]	Metropolis N, Ulam S 1949 J. Am. Stat. Assoc. 44 335
[52]	Creutz M 1987 Phys. Rev. D 36 515
[53]	Rybakov F N, Borisov A B, Blgel S, Kiselev N S 2015 Phys. Rev. Lett. 115 117201
[54]	Han J H 2017 Skyrmions in Condensed Matter (Charm: Springer) pp67-68
[55]	Jonietz F, Muhlbauer S, Pfleiderer C, Neubauer A, Munzer W, Bauer A, Adams T, Georgii R, Boni P, Duine R A, Everschor K, Garst M, Rosch A 2010 Science 330 1648
[56]	Zhang S, Li Z 2004 Phys. Rev. Lett. 93 127204
[57]	Tatara G, Kohno H 2004 Phys. Rev. Lett. 92 086601
[58]	Sinova J, Valenzuela S O, Wunderlich J, Back C, Jungwirth T 2015 Rev. Mod Phys. 87 1213
[59]	Emori S, Bauer U, Ahn S M, Martinez E, Beach G S D 2013 Nat. Mater. 12 611
[60]	Gambardella P, Miron I M 2011 Philosoph. Trans. Roy. Soc. A: Math. Phys. Engin. Sci. 369 3175
[61]	Ryu K S, Thomas L, Yang S H, Parkin S 2013 Nat. Nanotechnol. 8 527
[62]	Yu G, Upadhyaya P, Shao Q, Wu H, Yin G, Li X, He C, Jiang W, Han X, Amiri P K, Wang K L 2016 Nano Lett. 17 261
[63]	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 2015 Science 349 283
[64]	Jiang W, Chen G, Liu K, Zang J, te Velthuis S G, Hoffmann A 2017 Phys. Reports 704 1
[65]	Mochizuki M, Yu X Z, Seki S, Kanazawa N, Koshibae W, Zang J, Mostovoy M, Tokura Y, Nagaosa N 2014 Nat. Mater. 13 241
[66]	Tserkovnyak Y, Mecklenburg M 2008 Phys. Rev. B 77 134407
[67]	Garca P J L, Lzaro F J 1998 Phys. Rev. B 58 14937
[68]	Hinzke D, Nowak U 2011 Phys. Rev. Lett. 107 027205
[69]	Vansteenkiste A, Leliaert J, Dvornik M, Helsen M, Garcia Sanchez F, Waeyenberge B V 2014 AIP Adv. 4 107133
[70]	Donahue M J, Porter D P 1999 OOMMF User's Guide (Version 1.0) (Gaithersburg: National Institute of Standards and Technology) pp1-83
[71]	Romming N, Hanneken C, Menzel M, Bickel J E, Wolter B, von Bergmann K, Kubetzka A, Wiesendanger R 2013 Science 341 636
[72]	Hsu P J, Kubetzka A, Finco A, Romming N, von Bergmann K, Wiesendanger R 2016 Nat. Nanotechnol. 12 123
[73]	Yuan H Y, Wang X R 2016 Sci. Rep. 6 22638
[74]	Finazzi M, Savoini M, Khorsand A R, Tsukamoto A, Itoh A, Du L, Kirilyuk A, Rasing T, Ezawa M 2013 Phys. Rev. Lett. 110 177205
[75]	Fujita H, Sato M 2017 Phys. Rev. B 95 054421
[76]	Flovik V, Qaiumzadeh A, Nandy A K, Heo C, Rasing T 2017 Phys. Rev. B 96 140411
[77]	Koshibae W, Nagaosa N 2014 Nat. Commun. 5 5148
[78]	Tomasello R, Ricci M, Burrascano P, Puliafito V, Carpentieri M, Finocchio G 2017 AIP Adv. 7 056022
[79]	Di K, Zhang V L, Lim H S, Ng S C, Kuok M H, Yu J, Yoon J, Qiu X, Yang H 2015 Phys. Rev. Lett. 114 047201
[80]	Liu Y, Yan H, Jia M, Du H, Du A 2016 Appl. Phys. Lett. 109 102402
[81]	Lin S Z 2016 Phys. Rev. B 94 205205
[82]	Zhang X, Zhou Y, Ezawa M 2016 Nat. Commun. 7 10293
[83]	Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[84]	Purnama I, Gan W L, Wong D W, Lew W S 2015 Sci. Reports 5 10620
[85]	Zhang X, Zhou Y, Ezawa M 2016 Sci. Reports 6 24795
[86]	Zhang X, Ezawa M, Zhou Y 2016 Phys. Rev. B 94 064406
[87]	Reichhardt C, Ray D, Reichhardt C J O 2015 New J. Phys. 17 073034
[88]	Zhang X, Xia J, Zhou Y, Wang D, Liu X, Zhao W, Ezawa M 2016 Phys. Rev. B 94 094420
[89]	Reichhardt C, Ray D, Reichhardt C O 2015 Phys. Rev. Lett. 114 217202
[90]	Wu J, Carlton D, Park J S, Meng Y, Arenholz E, Doran A, Young A T, Scholl A, Hwang C, Zhao H W, Bokor J, Qiu Z Q 2011 Nat. Phys. 7 303
[91]	Rohart S, Miltat J, Thiaville A 2016 Phys. Rev. B 93 214412
[92]	Du H, Che R, Kong L, Zhao X, Jin C, Wang C, Yang J, Ning W, Li R, Jin C, Chen X, Zang J, Zhang Y, Tian M 2015 Nat. Commun. 6 8504

施引文献

[1]	Skyrme T 1962 Nucl. Phys. 31 556
[2]	Polyakov A M, Belavin A A 1975 Jetp Lett. 22 503
[3]	Muhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Boni P 2009 Science 323 915
[4]	Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 465 901
[5]	Thiaville A, Rohart S, Ju , Cros V, Fert A 2012 Europhys. Lett. 100 57002
[6]	Hoffmann A 2013 IEEE Trans. Magn. 49 5172
[7]	Fert A, Cros V, Sampaio J 2013 Nat. Nanotechnol. 8 152
[8]	Hellman F, Hoffmann A, Tserkovnyak Y, Beach G S, Fullerton E E, Leighton C, MacDonald A H, Ralph D C, Arena D A, Drr H A, Fischer P, Grollier J, Heremans J P, Jungwirth T, Kimel A V, Koopmans B, Krivorotov I N, May S J, Petford L A K, Rondinelli J M, Samarth N, Schuller I K, Slavin A N, Stiles M D, Tchernyshyov O, Thiaville A, Zink B L 2017 Rev. Mod. Phys. 89 025006
[9]	Schulz T, Ritz R, Bauer A, Halder M, Wagner M, Franz C, Pfleiderer C, Everschor K, Garst M, Rosch A 2012 Nat. Phys. 8 301
[10]	Yi S D, Onoda S, Nagaosa N, Han J H 2009 Phys. Rev. B 80 054416
[11]	Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Bni P 2009 Phys. Rev. Lett. 102 186602
[12]	Zang J, Mostovoy M, Han J H, Nagaosa N 2011 Phys. Rev. Lett. 107 136804
[13]	Litzius K, Lemesh I, Krger B, Bassirian P, Caretta L, Richter K, Bttner F, Sato K, Tretiakov O A, Frster J, Reeve R M, Weigand M, Bykova I, Stoll H, Schtz G, Beach G S D, Klui M 2016 Nat. Phys. 13 170
[14]	Woo S, Litzius K, Krger B, Im M Y, Caretta L, Richter K, Mann M, Krone A, Reeve R M, Weigand M, Agrawal P, Lemesh I, Mawass M A, Fischer P, Klui M, Beach G S D 2016 Nat. Mater. 15 501
[15]	Jiang W, Zhang X, Yu G, Zhang W, Wang X, Jungfleisch M B, Pearson J E, Cheng X, Heinonen O, Wang K L, Zhou Y, Hoffmann A, te Velthuis S G E 2016 Nat. Phys. 13 162
[16]	Liu L, Pai C F, Li Y, Tseng H W, Ralph D C, Buhrman R A 2012 Science 336 555
[17]	Lin S Z, Reichhardt C, Batista C D, Saxena A 2013 Phys. Rev. B 87 214419
[18]	Kang W, Huang Y, Zhang X, Zhou Y, Zhao W 2016 Proc. IEEE 104 2040
[19]	Kang W, Zheng C, Huang Y, Zhang X, Zhou Y, Lv W, Zhao W 2016 IEEE Electron Dev. Lett. 37 924
[20]	Parkin S S P, Hayashi M, Thomas L 2008 Science 320 190
[21]	Parkin S, Yang S H 2015 Nat. Nanotechnol. 10 195
[22]	Pfleiderer C, Rosch A 2010 Nature 465 880
[23]	Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2010 Nat. Mater. 10 106
[24]	Huang S X, Chien C L 2012 Phys. Rev. Lett. 108 267201
[25]	Kanazawa N, Onose Y, Arima T, Okuyama D, Ohoyama K, Wakimoto S, Kakurai K, Ishiwata S, Tokura Y 2011 Phys. Rev. Lett. 106 156603
[26]	Kanazawa N, Kim J H, Inosov D S, White J S, Egetenmeyer N, Gavilano J L, Ishiwata S, Onose Y, Arima T, Keimer B, Tokura Y 2012 Phys. Rev. B 86 134425
[27]	Makarova O L, Tsvyashchenko A V, Andre G, Porcher F, Fomicheva L N, Rey N, Mirebeau I 2012 Phys. Rev. B 85 205205
[28]	Seki S, Yu X Z, Ishiwata S, Tokura Y 2012 Science 336 198
[29]	Adams T, Chacon A, Wagner M, Bauer A, Brandl G, Pedersen B, Berger H, Lemmens P, Pfleiderer C 2012 Phys. Rev. Lett. 108 237204
[30]	Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[31]	Landau L D, Lifshitz E M, Sykes J B, Bell J S, Dill E H 1961 Electrodynamics of Continuous Media (2nd Ed.) (Oxford: Pergamon) pp178-179
[32]	Moriya T 1960 Phys. Rev. 120 91
[33]	Han J H, Zang J, Yang Z, Park J H, Nagaosa N 2010 Phys. Rev. B 82 094429
[34]	Rler U K, Leonov A A, Bogdanov A N 2011 J. Phys. Conf. Ser. 303 012105
[35]	Yu X, Mostovoy M, Tokunaga Y, Zhang W, Kimoto K, Matsui Y, Kaneko Y, Nagaosa N, Tokura Y 2012 Proc. Nat. Acad. Sci. USA 109 8856
[36]	Everschor S K, Sitte M 2014 J. Appl. Phys. 115 172602
[37]	Rajaraman R 1987 Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory (Oxford: Elsevier Science Technology) pp31-32
[38]	Nagaosa N, Tokura Y 2013 Nat. Nanotechnol. 8 899
[39]	Berg B, Lscher M 1981 Nucl. Phys. B 190 412
[40]	Hou W T, Yu J X, Daly M, Zang J 2017 Phys. Rev. B 96 140403
[41]	Yin G, Li Y, Kong L, Lake R K, Chien C L, Zang J 2016 Phys. Rev. B 93 174403
[42]	Kong L, Zang J 2013 Phys. Rev. Lett. 111 067203
[43]	Milde P, Kohler D, Seidel J, Eng L M, Bauer A, Chacon A, Kindervater J, Muhlbauer S, Pfleiderer C, Buhrandt S, Schutte C, Rosch A 2013 Science 340 1076
[44]	Tokunaga Y, Yu X Z, White J S, Rnnow H M, Morikawa D, Taguchi Y, Tokura Y 2015 Nat. Commun. 6 7638
[45]	Oike H, Kikkawa A, Kanazawa N, Taguchi Y, Kawasaki M, Tokura Y, Kagawa F 2015 Nat. Phys. 12 62
[46]	Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N, Tokura Y 2010 Science 329 297
[47]	Ding J, Yang X, Zhu T 2015 IEEE Trans. Magn. 51 1
[48]	Zhang X, Mller J, Xia J, Garst M, Liu X, Zhou Y 2017 New J. Phys. 19 065001
[49]	Jin C, Li Z A, Kovcs A, Caron J, Zheng F, Rybakov F N, Kiselev N S, Du H, Blgel S, Tian M, Zhang Y, Farle M, Dunin B R E 2017 Nat. Commun. 8 15569
[50]	Laarhoven P J M, Aarts E H L 1987 Simulated Annealing: Theory and Applications (Dordrecht: Reidel) pp7-15
[51]	Metropolis N, Ulam S 1949 J. Am. Stat. Assoc. 44 335
[52]	Creutz M 1987 Phys. Rev. D 36 515
[53]	Rybakov F N, Borisov A B, Blgel S, Kiselev N S 2015 Phys. Rev. Lett. 115 117201
[54]	Han J H 2017 Skyrmions in Condensed Matter (Charm: Springer) pp67-68
[55]	Jonietz F, Muhlbauer S, Pfleiderer C, Neubauer A, Munzer W, Bauer A, Adams T, Georgii R, Boni P, Duine R A, Everschor K, Garst M, Rosch A 2010 Science 330 1648
[56]	Zhang S, Li Z 2004 Phys. Rev. Lett. 93 127204
[57]	Tatara G, Kohno H 2004 Phys. Rev. Lett. 92 086601
[58]	Sinova J, Valenzuela S O, Wunderlich J, Back C, Jungwirth T 2015 Rev. Mod Phys. 87 1213
[59]	Emori S, Bauer U, Ahn S M, Martinez E, Beach G S D 2013 Nat. Mater. 12 611
[60]	Gambardella P, Miron I M 2011 Philosoph. Trans. Roy. Soc. A: Math. Phys. Engin. Sci. 369 3175
[61]	Ryu K S, Thomas L, Yang S H, Parkin S 2013 Nat. Nanotechnol. 8 527
[62]	Yu G, Upadhyaya P, Shao Q, Wu H, Yin G, Li X, He C, Jiang W, Han X, Amiri P K, Wang K L 2016 Nano Lett. 17 261
[63]	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 2015 Science 349 283
[64]	Jiang W, Chen G, Liu K, Zang J, te Velthuis S G, Hoffmann A 2017 Phys. Reports 704 1
[65]	Mochizuki M, Yu X Z, Seki S, Kanazawa N, Koshibae W, Zang J, Mostovoy M, Tokura Y, Nagaosa N 2014 Nat. Mater. 13 241
[66]	Tserkovnyak Y, Mecklenburg M 2008 Phys. Rev. B 77 134407
[67]	Garca P J L, Lzaro F J 1998 Phys. Rev. B 58 14937
[68]	Hinzke D, Nowak U 2011 Phys. Rev. Lett. 107 027205
[69]	Vansteenkiste A, Leliaert J, Dvornik M, Helsen M, Garcia Sanchez F, Waeyenberge B V 2014 AIP Adv. 4 107133
[70]	Donahue M J, Porter D P 1999 OOMMF User's Guide (Version 1.0) (Gaithersburg: National Institute of Standards and Technology) pp1-83
[71]	Romming N, Hanneken C, Menzel M, Bickel J E, Wolter B, von Bergmann K, Kubetzka A, Wiesendanger R 2013 Science 341 636
[72]	Hsu P J, Kubetzka A, Finco A, Romming N, von Bergmann K, Wiesendanger R 2016 Nat. Nanotechnol. 12 123
[73]	Yuan H Y, Wang X R 2016 Sci. Rep. 6 22638
[74]	Finazzi M, Savoini M, Khorsand A R, Tsukamoto A, Itoh A, Du L, Kirilyuk A, Rasing T, Ezawa M 2013 Phys. Rev. Lett. 110 177205
[75]	Fujita H, Sato M 2017 Phys. Rev. B 95 054421
[76]	Flovik V, Qaiumzadeh A, Nandy A K, Heo C, Rasing T 2017 Phys. Rev. B 96 140411
[77]	Koshibae W, Nagaosa N 2014 Nat. Commun. 5 5148
[78]	Tomasello R, Ricci M, Burrascano P, Puliafito V, Carpentieri M, Finocchio G 2017 AIP Adv. 7 056022
[79]	Di K, Zhang V L, Lim H S, Ng S C, Kuok M H, Yu J, Yoon J, Qiu X, Yang H 2015 Phys. Rev. Lett. 114 047201
[80]	Liu Y, Yan H, Jia M, Du H, Du A 2016 Appl. Phys. Lett. 109 102402
[81]	Lin S Z 2016 Phys. Rev. B 94 205205
[82]	Zhang X, Zhou Y, Ezawa M 2016 Nat. Commun. 7 10293
[83]	Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[84]	Purnama I, Gan W L, Wong D W, Lew W S 2015 Sci. Reports 5 10620
[85]	Zhang X, Zhou Y, Ezawa M 2016 Sci. Reports 6 24795
[86]	Zhang X, Ezawa M, Zhou Y 2016 Phys. Rev. B 94 064406
[87]	Reichhardt C, Ray D, Reichhardt C J O 2015 New J. Phys. 17 073034
[88]	Zhang X, Xia J, Zhou Y, Wang D, Liu X, Zhao W, Ezawa M 2016 Phys. Rev. B 94 094420
[89]	Reichhardt C, Ray D, Reichhardt C O 2015 Phys. Rev. Lett. 114 217202
[90]	Wu J, Carlton D, Park J S, Meng Y, Arenholz E, Doran A, Young A T, Scholl A, Hwang C, Zhao H W, Bokor J, Qiu Z Q 2011 Nat. Phys. 7 303
[91]	Rohart S, Miltat J, Thiaville A 2016 Phys. Rev. B 93 214412
[92]	Du H, Che R, Kong L, Zhao X, Jin C, Wang C, Yang J, Ning W, Li R, Jin C, Chen X, Zang J, Zhang Y, Tian M 2015 Nat. Commun. 6 8504

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