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在带有垂直各向异性的二维三角晶格磁体中，当同时存在最近邻铁磁性和第三近邻反铁磁性交换作用时，垂直于膜面施加外磁场会使体系内自旋沿着非共面的方向排列，甚至出现拓扑稳定的斯格明子自旋结构.基于蒙特卡罗模拟方法，本文研究了在该二维阻挫磁体中，竞争性交换作用和外磁场对斯格明子直径的影响.与常规非中心对称的手性磁体中的斯格明子性质类似，外磁场会磁化斯格明子外围自旋而减小斯格明子直径.但是，磁体中反铁磁性交换作用的增强会整体压缩斯格明子.本文结合自旋波理论和蒙特卡罗模拟，首次量化了此类阻挫磁体中斯格明子的直径.结果表明：在弱的反铁磁性交换作用磁体中，斯格明子直径随磁场增大而快速线性减小；随着反铁磁性交换作用的增大，斯格明子直径随外磁场增大的减小变得相对平缓，但在强磁场下也会造成斯格明子直径的加速减小；随着反铁磁性交换作用的增强，斯格明子在不同外磁场下的直径的最大值和中值均从逐渐减小到渐趋稳定，而直径的最小值则从快速减小到表现出很大的涨落.这些现象都可以通过分析斯格明子在不同交换作用和外磁场下的构型和磁能变化加以解释.该项工作阐明了在中心对称的阻挫磁体中斯格明子直径的可调节性，不仅完善了我们对斯格明子本身物理机理的认识，同时也为发展基于斯格明子的新一代存储和逻辑器件提供了理论支撑.Magnetic skyrmions were first observed in a bulk B20 chiral magnet where the unit cell of the crystal lacks inversion symmetry, i. e. it is noncentrosymmetric, due to the Dzyaloshinskii-Moriya interaction (DMI). The breaking of structural inversion symmetry can also be achieved artificially in extremely thin FM layers adjacent to heavy elements, to induce a nonzero DMI. Many skyrmion properties in the DMI-based system are revealed such as the skyrmion diameters simply inversely proportional to the DMI constant. On the contrary, the triangular lattice, providing a simple realization of a high-symmetry system with six equivalent orientations for the helix, is centrosymmetric. In a two-dimensional triangular lattice magnet with the magnetocrystalline anisotropy perpendicular to the film plane, the magnetic frustration can arise from the coexistence of a nearest -neighbor ferromagnetic exchange interaction and a third-neighbor antiferromagnetic exchange interaction. When an external magnetic field is applied parallelly to the anisotropy, the non-coplanar alignments of spins are favored and even the topologically protected magnetic skyrmions also appear. Based on the Monte Carlo simulation, the dependence of magnetic-field-induced magnetic phase transitions in such magnetic frustrated magnets, including the magnetic phase of skyrmion crystals, and the skyrmion diameters on competing exchange interaction and magnetic field is studied. The results indicate that the diameters of magnetic skyrmions strongly depend on the competing exchange interactions and external magnetic field. Like the diameter features of magnetic skyrmions observed in the conventional DMI-based chiral magnets, the external magnetic field can magnetize the skyrmion periphery spins to reduce the skyrmion diameters. However, the enhanced antiferromagnetic exchange interaction can compress the entire skyrmions. In the framework of the spin wave theory and Monte Carlo simulation results, the diameters of magnetic skyrmions in exchange-interaction-frustrated systems are quantified. The skyrmion diameter decreases linearly with the increase of magnetic field for weak antiferromagnetic exchange interaction. With the increase of antiferromagnetic exchange interaction, the decrease of the skyrmion diameter with increasing magnetic field becomes slow, while the strong magnetic fields may rapidly reduce the skyrmion diameter. With the increase of antiferromagnetic exchange interaction, the maximum and median skyrmion diameters decrease to level-off roughly, while the minimum skyrmion diameters show a rapid decrease first and a great fluctuation later. The phenomena are explained through discussing the variations of configurations and magnetic energies of skyrmions. This work demonstrates the adjustability of skyrmion diameter in centrosymmetric frustrated magnet, which not only improves the understanding of origin of skyrmions, but also supports theoretically the development of new generation of skyrmion-based storage and logic devices.
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Keywords:
- skyrmion diameter /
- magnetic frustration /
- exchange interaction /
- Monte Carlo method
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[1] Bogdanov A N, Yablonskii D 1989 Zh. Eksp. Teor. Fiz. 95 178
[2] Bogdanov A N, Hubert A 1994 J. Magn. Magn. Mater. 138 255
[3] Mhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Bni P 2009 Science 323 915
[4] Seki S, Yu X Z, Ishiwata S, Tokura Y 2012 Science 336 198
[5] Adams T, Chacon A, Wagner M, Bauer A, Brandl G, Pedersen B, Berger H, Lemmens P, Pfleiderer C 2012 Phys. Rev. Lett. 108 237204
[6] Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2011 Nature Mater. 10 106
[7] Yu X Z, Kanazawa N, Zhang W, Nagai T, Hara T, Kimoto K, Matsui Y, Onose Y, Tokura Y 2012 Nature Commun. 3 988
[8] Onose Y, Okamura Y, Seki S, Ishiwata S, Tokura Y 2012 Phys. Rev. Lett. 109 037603
[9] Romming N, Hanneken C, Menzel M, Bickel J E, Wolter B, von Bergmann K, Kubetzka A, Wiesendanger R 2013 Science 341 636
[10] Fert A, Cros V, Sampaio J 2013 Nature Nanotechnol. 8 152
[11] Ding B, Wang W H 2018 Physics 47 15 (in Chinese) [丁贝,王文洪 2018 物理 47 15]
[12] Dzyaloshinsky I 1958 J. Phys. Chem. Sol. 4 241
[13] Moriya T 1960 Phys. Rev. 120 91
[14] Nagaosa N, Tokura Y 2013 Nature Nanotechnol. 8 899
[15] Hou Z P, Ren W J, Ding B, Xu G Z, Wang Y, Yang B, 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
[16] Hou Z P, Zhang Q, Xu G Z, Gong C, Ding B, Wang Y, Li H, Liu E K, Xu F, Zhang H W, Yao Y, Wu G H, Zhang X X, Wang W H 2018 Nano Lett. 18 1274
[17] Yu X Z, Tokunaga Y, Taguchi Y, Tokura Y 2017 Adv. Mater. 29 1603958
[18] Wang W H, Zhang Y, Xu G, Peng L, Ding B, Wang Y, Hou Z, Zhang X, Li X, Liu E, Wang S, Cai J, Wang F, Li J, Hu F, Wu G, Shen B, Zhang X 2016 Adv. Mater. 28 6887
[19] Phatak C, Heinonen O, Graef M D, Petford-Long A 2016 Nano Lett. 16 4141
[20] Yu X Z, Tokunaga Y, Kaneko Y, Zhang W Z, Kimoto K, Matsui Y, Taguchi Y, Tokura Y 2014 Nature Commun. 5 3198
[21] Ding B, Li Y Q, Xu G Z, Wang Y, Hou Z P, Liu E K, Liu Z Y, Wu G H, Wang W H 2017 Appl. Phys. Lett. 110 092404
[22] Chakraverty S, Matsuda T, Wadati H, Okamoto J, Yamasaki Y, Nakao H, Murakami Y, Ishiwata S, Kawasaki M, Taguchi Y, Tokura Y, Hwang H Y 2013 Phys. Rev. B 88 220405
[23] Rzsa L, Dek A, Simon E, Yanes R, Udvardi L, Szunyogh L, Nowak U 2016 Phys. Rev. Lett. 117 157205
[24] Rzsa L, Palots K, Dek A, Simon E, Yanes R, Udvardi L, Szunyogh L, Nowak U 2017 Phys. Rev. B 95 094423
[25] Okubo T, Chung S, Kawamura H 2012 Phys. Rev. Lett. 108 017206
[26] Hayami S, Lin S Z, Kamiya Y, Batista C D 2016 Phys. Rev. B 93 184413
[27] Hu Y, Chi X D, Li X, Liu Y, Du A 2017 Sci. Rep. 7 16079
[28] Lin S Z, Hayami S 2016 Phys. Rev. B 93 064430
[29] Lin S Z, Hayami S, Batista C D 2016 Phys. Rev. Lett. 116 187202
[30] Hayami S, Lin S Z, Kamiya Y, Batista C D 2016 Phys. Rev. B 94 174420
[31] Leonov A O, Mostovoy M 2015 Nature Commun. 6 8275
[32] Leonov A O, Mostovoy M 2017 Nature Commun. 8 14394
[33] Yuan H Y, Gomonay O, Klui M 2017 Phys. Rev. B 96 134415
[34] Zhang X C, Xia J, Zhou Y, Liu X X, Zhang H, Ezawa M 2017 Nature Commun. 8 1717
[35] Gbel B, Mook A, Henk J, Mertig I 2017 Phys. Rev. B 95 094413
[36] Hamamoto K, Ezawa M, Nagaosa N 2015 Phys. Rev. B 92 115417
[37] Araki Y, Nomura K 2017 Phys. Rev. B 96 165303
[38] Malottki S V, Dup B, Bessarab P F, Delin A, Heinze S 2017 Sci. Rep. 7 12299
[39] Romming N, Kubetzka A, Hanneken C 2015 Phys. Rev. Lett. 114 177203
[40] Simon E, Palots K, Rzsa L, Udvardi L, Szunyogh L 2014 Phys. Rev. B 90 094410
[41] Stoudenmire E M, Trebst S, Balents L 2009 Phys. Rev. B 79 214436
[42] Day P, Dinsdale A, Krausz E R, Robbins D J 1976 J. Phys. C 9 2481
[43] Heim B, Rnnow T F, Isakov S V, Troyer M 2015 Science 348 215
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