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Owing to the topologically protected properties, magnetic skyrmions possess high stability and small critical driving current, thus making them potentially applied to future racetrack memory devices. Skyrmions have been identified in several material systems. One large class contains the centrosymmetric materials, where skyrmions emerge as the competition between perpendicular magnetic anisotropy and magnetic dipolar interactions. The recently reported skyrmion host includes La-Sr-Mn-O, hexagonal MnNiGa, Fe3Sn2, etc. In these systems, due to the isotropic characteristic of the dipolar interaction, magnetic bubble can exhibit various topologies and helicities. The common types of bubbles existing in the materials are the trivial one with n=0 (n is the topological charge) and the non-trivial one with n=1, and the latter is taken to be equivalent to magnetic skyrmion. In this article, we investigate the formation of skyrmions under various magnetic parameters and the role of stripe domain chairity in tuning the bubble topology. The main method we use here is micromagnetic simulation with the Object Oriented MicroMagnetic Framework (OOMMF) code. Also some recent experimental results on MnNiGa and Fe3Sn2 are exhibited and compared with the simulation prediction. Under a fixed magnetization (Ms), by tuning the exchange constant A and magnetic anisotropy Ku, we find that the domains can evolve into a bubble state under a moderate anisotropy value, and to some extent, large anisotropy favors the formation of n=1 topological skyrmion. In the case of the stripe domains, it is found that different initial configuration can lead to different domain wall charity and further change the process of skyrmion formation. When the magnetization in the domain wall orients in the same direction, n=0 bubble will form upon applying magnetic field. While the magnetization in the wall orients alternatively up and down, a topological skyrmion is directly formed. In the stripe domains with inversed 180 Bloch wall, in-plane magnetization dominates and no bubble or skyrmion can form. In addition, the tilt of the magnetic field and uniaxial anisotropy can also change the morphology and topology of the skyrmions, which has been verified in our experiments. According to the above results, we propose to tune the topology of skyrmions in centrosymmetric material through adjusting the ground magnetic state, magnetic anisotropy and in-plane components, which can be realized by element doping at different sites and appropriately designing the sample.
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Keywords:
- magnetic skyrmions /
- domain wall /
- micromagnetic
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[19] Hou Z P, Zhang Q, Xu G Z, Gong C, Ding B, Wang Y, Li H, Liu E K, Xu F, Zhang H, Yao Y, Wu G H, Zhang X X, Wang W H 2018 Nano. Lett. 18 1274
[20] Iwasaki J, Mochizuki M, Nagaosa N 2013 Nat. Nanotech. 8 742
[21] Zhang X C, Zhao G P, Fangohr H, Liu J P, Xia W X, Xia J, Morvan F J 2015 Sci. Rep. 5 7643
[22] Zhang X C, Zhou Y, Ezawa M 2016 Sci. Rep. 6 24795
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[25] Yu X, Tokunaga Y, Taguchi Y, Tokura Y 2017 Adv. Mater. 29 1603958
[26] Jiang W J, Chen G, Liu K, Zang J D, Velthuis S, Hoffmann A 2017 Phys. Rep. 704 1
[27] Nakajima H, Kotani A, Harada K, Ishii Y, Mori S 2016 Phys. Rev. B 94 224427
[28] Nagaosa N, Yu X Z, Tokura Y 2012 Phil. Trans. R. Soc. A 370 5806
[29] Yu X, Mostovoy M, Tokunaga Y, Zhang W, Kimoto K, Matsui Y, Kaneko Y, Nagaosa N, Tokura Y 2012 Proc. Natl. Acad. Sci. USA 109 8856
[30] Han B S 2017 Physics 46 352 (in Chinese) [韩宝善 2017 物理 46 352]
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[33] Donahue M J, Porter D G 1999 OMMFF User's Guide Version 10 (Gaithersburg, MD: NISTIR 6376, National Institute of Standards and Technology)
[34] Zhang Z D 2015 Acta Phys. Sin. 64 67503 (in Chinese) [张志东 2015 64 67503]
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[36] Kotani A, Nakajima H, Harada K, Ishii Y, Mori S 2016 Phys. Rev. B 94 024407
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[1] Rler U K, Bogdanov A N, Pfleiderer C 2006 Nature 442 797
[2] Yu X Z, Kanazawa N, Zhang W Z, Nagai T, Hara T, Kimoto K, Matsui Y, Onose Y, Tokura Y 2012 Nat. Commun. 3 988
[3] Sampaio J, Cros V, Rohart S, Thiaville A, Fert A 2013 Nat. Nanotech. 8 839
[4] Fert A, Cros V, Sampaio J 2013 Nat. Nanotech. 8 152
[5] Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz P G, Bni P 2009 Phys. Rev. Lett. 102 186602
[6] Huang S X, Chien C L 2012 Phys. Rev. Lett. 108 267201
[7] Mnzer W, Neubauer A, Adams T, Mhlbauer S, Franz C, Jonietz F, Georgii R, Bni P, Pedersen B, Schmidt M, Rosch A, Pfleiderer C 2010 Phys. Rev. B 81 041203
[8] Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2011 Nat. Mater. 10 106
[9] Mhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Bni P 2009 Science 323 915
[10] Heinze S, Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blgel S 2011 Nat. Phys. 7 713
[11] Jiang W J, Upadhyaya P, Zhang W, Yu G Q, Jungfleisch M B, Fradin F Y, Pearson J E, Tserkovnyak Y, Wang K L, Heinonen O, Velthuis S G, Hoffmann A 2015 Science 349 283
[12] Boulle O, Vogel J, Yang H X, Pizzini S, de Souza Chaves D, Locatelli A, Mentes T O, Sala A, Buda-Prejbeanu L D, Klein O, Belmeguenai M, Roussign Y, Stashkevich A, Chrif S M, Avalle L, Foerster M, Chshiev M, Auffret S, Miron I M, Gaudin G 2016 Nat. Nanotech. 11 449
[13] Nagaosa N, Tokura Y 2013 Nat. Nanotech. 8 899
[14] Malozemoff A P, Slonczewski J C 1979 Magnetic Domain Walls in Bubble Materials (New York: Academic Press) p1
[15] Grundy P J 1977 Contem. Phys. 18 47
[16] Yu X Z, Tokunaga Y, Kaneko Y, Zhang W Z, Kimoto K, Matsui Y, Taguchi Y, Tokura Y 2014 Nat. Commun. 5 3198
[17] Wang W H, Zhang Y, Xu G Z, Peng L C, Ding B, Wang Y, Hou Z P, Zhang X M, Li X Y, Liu E K, Wang S G, Cai J W, Wang F W, Li J, Hu F, Wu G H, Shen B G, Zhang X X 2016 Adv. Mater. 28 6887
[18] Hou Z P, Ren W J, Ding B, Xu G Z, Wang Y, Yang B C, Zhang Q, Zhang Y, Liu E K, Xu F, Wang W H, Wu G H, Zhang X X, Shen B G, Zhang Z D 2017 Adv. Mater. 29 1701144
[19] Hou Z P, Zhang Q, Xu G Z, Gong C, Ding B, Wang Y, Li H, Liu E K, Xu F, Zhang H, Yao Y, Wu G H, Zhang X X, Wang W H 2018 Nano. Lett. 18 1274
[20] Iwasaki J, Mochizuki M, Nagaosa N 2013 Nat. Nanotech. 8 742
[21] Zhang X C, Zhao G P, Fangohr H, Liu J P, Xia W X, Xia J, Morvan F J 2015 Sci. Rep. 5 7643
[22] Zhang X C, Zhou Y, Ezawa M 2016 Sci. Rep. 6 24795
[23] Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[24] Jin C D, Song C K, Wang J B, Liu Q F 2016 Appl. Phys. Lett. 109 182404
[25] Yu X, Tokunaga Y, Taguchi Y, Tokura Y 2017 Adv. Mater. 29 1603958
[26] Jiang W J, Chen G, Liu K, Zang J D, Velthuis S, Hoffmann A 2017 Phys. Rep. 704 1
[27] Nakajima H, Kotani A, Harada K, Ishii Y, Mori S 2016 Phys. Rev. B 94 224427
[28] Nagaosa N, Yu X Z, Tokura Y 2012 Phil. Trans. R. Soc. A 370 5806
[29] Yu X, Mostovoy M, Tokunaga Y, Zhang W, Kimoto K, Matsui Y, Kaneko Y, Nagaosa N, Tokura Y 2012 Proc. Natl. Acad. Sci. USA 109 8856
[30] Han B S 2017 Physics 46 352 (in Chinese) [韩宝善 2017 物理 46 352]
[31] Iwasaki J, Mochizuki M, Nagaosa N 2013 Nat. Commun. 4 1463
[32] Li J 2017 Physics 46 281 (in Chinese) [栗佳 2017 物理 46 281]
[33] Donahue M J, Porter D G 1999 OMMFF User's Guide Version 10 (Gaithersburg, MD: NISTIR 6376, National Institute of Standards and Technology)
[34] Zhang Z D 2015 Acta Phys. Sin. 64 67503 (in Chinese) [张志东 2015 64 67503]
[35] Du H F, Che R C, Kong L Y, Zhao X B, Jin C M, Wang C, Yang J Y, Ning W, Li R W, Jin C Q, Chen X H, Zang J D, Zhang Y H, Tian M L 2015 Nat. Commun. 6 8504
[36] Kotani A, Nakajima H, Harada K, Ishii Y, Mori S 2016 Phys. Rev. B 94 024407
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