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斯格明子是一种拓扑稳定的手性自旋结构，凭借其在磁性赛道存储器和自旋电子器件方面的巨大应用潜力而受到研究人员的广泛关注.为了使斯格明子能够更好地应用于磁性赛道存储器，研究斯格明子在纳米条带中的运动行为就变得非常重要.本文主要研究了存在周期性应变的纳米条带中铁磁斯格明子和反铁磁斯格明子在电流驱动下的运动行为.研究结果表明：周期性应变使得驱动电流存在一个临界电流密度，只有当电流密度大于临界电流密度时斯格明子才能够在纳米条带中连续移动.临界电流密度随应变振幅的增加而增加，随应变周期的增加而减小.铁磁斯格明子在周期性应变的调制下会产生周期性运动，轨迹为波浪式，其横向速度受到边界的影响，而纵向速度则与应变梯度成正比.反铁磁斯格明子在周期性应变调控下运动方向不变，但其移动速度则剧烈变化.Magnetic skyrmions are a topologically stable and particle-like chiral spin configuration. They are appealing because of their potential applications in racetrack memory and other spintronic devices. These applications are strongly dependent on the skyrmion motion in confined geometry. Therefore, it is important to study the moving behaviors of skyrmions in a nanotrack to make them have more practical applications. Mechanical strain and stress have been demonstrated theoretically and experimentally to be able to effectively control the skyrmion phase. It can stabilize the skyrmion lattice in a broad range, and change the shape of the skyrmion crystal. In this paper, we study the moving behaviors of ferromagnetic skyrmions and antiferromagnetic skyrmions under the action of sinusoidally distributed strain in a nanotrack by using micromagnetic simulation. We assume that strain is uniaxial and perpendicular to the plane of the nanotrack. Its strength varies sinusoidally along the x-axis. Meanwhile, we apply an in-pane current along the nanotrack to drive the skyrmion moving towards the right side. We first find that there is a threshold current density that is defined as the minimum current that can drive skyrmion moving continuously. When the current density is larger than the threshold current density, the skyrmion can move continuously in the nanotrack. The threshold current density increases with the amplitude of strain increasing, but decreases with the period of strain increasing. Second, we find that the trajectory of skyrmion changes under the action of the sinusoidal distributed strains. For ferromagnetic skyrmion, its trajectory changes from straight line to periodic wavy line. Also, we find that the longitudinal velocity of skyrmion is affected by the boundary of the nanotrack. When the skyrmion is close to the upper boundary of the nanotrack, the longitudinal velocity increases sharply and it will form a peak in the velocity curve, but when the skyrmion is close to the lower boundary of the nanotrack, the longitudinal velocity decreases and it will form a valley in the velocity curve. The transverse velocity of skyrmion relates to the strain gradient. It is inversely proportional to the strain gradient. For antiferromagnetic skyrmion, we find that the movement trajectory of antiferromagnetic skyrmion does not change under the stress control. However, its diameter and velocity change periodically. Its velocity can vary between 103 m/s and 0. Our results demonstrate that the sinusoidal strain can control the skyrmion motion. This work may provide guidance in designing and developing of the spintronic devices based on magnetic skyrmions.
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[1] Mhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Bni P 2009 Science 323 915
[2] Yu X Z, Onose Y, Kanazawa N, Park J H, Han J H, Matsui Y, Nagaosa N, Tokura Y 2010 Nature 465 901
[3] Shibata K, Yu X Z, Hara T, Morikawa D, Kanazawa N, Kimoto K, Ishiwata S, Matsui Y, Tokura Y 2013 Nat. Nanotechnol. 8 723
[4] Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2011 Nat. Mater. 10 106
[5] Franz C, Freimuth F, Bauer A, Ritz R, Schnarr C, Duvinage C, Adams T, Blgel S, Rosch A, Mokrousov Y, Pfleiderer C 2014 Phys. Rev. Lett. 112 186601
[6] Tokunaga Y, Yu X Z, White J S, Rnnow H M, Morikawa D, Taguchi Y, Tokura Y 2015 Nat. Commun. 6 7638
[7] Tanigaki T, Shibata K, Kanazawa N, Yu X, Onose Y, Park H S, Shindo D, Tokura Y 2015 Nano Lett. 15 5438
[8] Heinze S, von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blgel S 2011 Nat. Phys. 7 713
[9] Sonntag A, Hermenau J, Krause S, Wiesendanger R 2014 Phys. Rev. Lett. 113 077202
[10] Chen G, Mascaraque A, N'Diaye A T, Schmid A K 2015 Appl. Phys. Lett. 106 242404
[11] Peng L, Zhang Y, Wang W, He M, Li L, Ding B, Li J, Sun Y, Zhang X G, Cai J, Wang S, Wu G, Shen B 2017 Nano Lett. 17 7075
[12] 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 Y, Stashkevich A, Mourad Chrif S, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M, Gaudin G 2016 Nat. Nanotechnol. 11 449
[13] Yu G, Upadhyaya P, Li X, Li W, Kim S K, Fan Y, Wong K L, Tserkovnyak Y, Amiri P K, Wang K L 2016 Nano Lett. 16 1981
[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] Yu G, Jenkins A, Ma X, Razavi S A, He C, Yin G, Shao Q, He Q L, Wu H, Li W, Jiang W, Han X, Li X E, Bleszynski Jayich A C, Amiri P K, Wang K L 2018 Nano Lett. 18 980
[16] Karube K, White J S, Morikawa D, Bartkowiak M, Kikkawa A, Tokunaga Y, Arima T, Rnnow H M, Tokura Y, Taguchi Y 2017 Phys. Rev. Mater. 1 074405
[17] Sampaio J, Cros V, Rohart S, Thiaville A, Fert A 2013 Nat. Nanotechnol. 8 839
[18] Iwasaki J, Mochizuki M, Nagaosa N 2013 Nat. Nanotechnol. 8 742
[19] Iwasaki J, Mochizuki M, Nagaosa N 2013 Nat. Commun. 4 1463
[20] Koshibae W, Nagaosa N 2014 Nat. Commun. 5 5148
[21] Nayak A K, Kumar V, Ma T, Werner P, Pippel E, Sahoo R, Damay F, Rler U K, Felser C, Parkin S S P 2017 Nature 548 561
[22] Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[23] Tomasello R, Martinez E, Zivieri R, Torres L, Carpentieri M, Finocchio G 2014 Sci. Rep. 4 6784
[24] Kang W, Huang Y, Zheng C, L W, Lei N, Zhang Y, Zhang X, Zhou Y, Zhao W 2016 Sci. Rep. 6 23164
[25] Kang W, Zheng C, Huang Y, Zhang X, Zhou Y, L W, Zhao W 2016 IEEE Electron Device Lett. 37 924
[26] Parkes D E, Cavill S A, Hindmarch A T, Wadley P, McGee F, Staddon C R, Edmonds K W, Campion R P, Gallagher B L, Rushforth A W 2012 Appl. Phys. Lett. 101 072402
[27] Cavill S A, Parkes D E, Miguel J, Dhesi S S, Edmonds K W, Campion R P, Rushforth A W 2013 Appl. Phys. Lett. 102 032405
[28] Jger J V, Scherbakov A V, Linnik T L, Yakovlev D R, Wang M, Wadley P, Holy V, Cavill S A, Akimov A V, Rushforth A W, Bayer M 2013 Appl. Phys. Lett. 103 032409
[29] Lei N, Devolder T, Agnus G, Aubert P, Daniel L, Kim J V, Zhao W, Trypiniotis T, Cowburn R P, Chappert C, Ravelosona D, Lecoeur P 2013 Nat. Commun. 4 1378
[30] Ostler T A, Cuadrado R, Chantrell R W, Rushforth A W, Cavill S A 2015 Phys. Rev. Lett. 115 067202
[31] Shibata K, Iwasaki J, Kanazawa N, Aizawa S, Tanigaki T, Shirai M, Nakajima T, Kubota M, Kawasaki M, Park H S, Shindo D, Nagaosa N, Tokura Y 2015 Nat. Nanotechnol. 10 589
[32] Nii Y, Nakajima T, Kikkawa A, Yamasaki Y, Ohishi K, Suzuki J, Taguchi Y, Arima T, Tokura Y, Iwasa Y 2015 Nat. Commun. 6 8539
[33] Liu Y, Lei N, Zhao W, Liu W, Ruotolo A, Braun H B, Zhou Y 2017 Appl. Phys. Lett. 111 022406
[34] Zhang X, Zhou Y, Ezawa M 2016 Sci. Rep. 6 24795
[35] Yuan H Y, Wang X R 2016 Sci. Rep. 6 22638
[36] Donahue M J, Porter D G 1999 OOMMF User's Guid. Version 1.0 Gaithersburg, MD: Interag. Rep. NISTIR 6376, NIST
[37] Saiki K 1972 J. Phys. Soc. Jpn. 33 1284
[38] Kittle C 1949 Rev. Mod. Phys. 19 541
[39] Hu Y, Wang B 2017 New J. Phys. 19 123002
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