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In a nanodisk made of soft ferromagnet, the magnetic vortex structure are highly stabilized, and the circulation directions of the vortices are naturally binary (either clockwise (CW) or counter-clockwise (CCW)), which can be associated with one bit of information, and thus the magnetic vortices have been of great interest recently. A vortex-circulation-based memory requires the perfect controllability of the circulation direction. From the circulation point of view, there are four possible ground states in a nanodisk pair: (CCW, CCW), (CCW, CW), (CW, CCW) and (CW, CW). In a perfect circular nanodisk, CW and CCW states are degenerate because of the high symmetry of the system. However, the circulation of the magnetic vortex is known to be controlled by introducing the asymmetry. It has been reported that the magnetic vortices with opposite (the same) circulations are realized in one-side-flat disk pair. That means in one-side-flat nanodisk pair only the control of two of these four ground states is possible, eg., (CCW, CW), (CW, CCW) or (CCW, CCW), (CW, CW). We found that the reversal of the magnetic vortex circulation is affected by the nanodisk thickness as well. By further introducing another asymmetry, different thickness, the control of the four circulation ground states is achieved in a nanodisk pair. In this work, the controllability of the four ground states in a nanodisk pair was numerically investigated via micromagnetic simulations. The results show that in a single one-side-flat nanodisk, there exists a preferred rotational sense at the remanent state after the nanodisk is saturated by the external magnetic field, applied parallel to the flat edge of the nanodisk. The shape anisotropy is the primary cause of this phenomenon. We further found that the obtained rotational senses of the magnetization in the vortex state in nanodisks with the same geometrical parameters but different thickness (20 nm and 50 nm) are opposite for the same direction of the externally applied field. This is attributed to the competition between the demagnetization field energy and the exchange energy during the vortex formation. The method we proposed provides a simple means of controlling the vortex state that can thus become a useful tool for designing vortex-based devices.
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Keywords:
- magnetic vortex /
- circulation reversal /
- magnetic nanodisk /
- micromagnetic simulation
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图 1 厚度t不同的两对切边的纳米盘的形状和尺寸
Figure 1. Geometry and dimension of one-side-flat nanodisk pairs with different thickness t.
图 2 厚度(a) t = 50 nm和(b) t = 20 nm的纳米盘的磁滞回线. 图中的颜色和箭头代表xy平面内的磁化方向, 黑色和白色的点分别代表方向朝下和朝上的磁涡旋核. 当磁感应强度从150 mT减小至0 mT时, 厚度为(c) 50 nm和(d) 20 nm的纳米盘的能量密度的变化
Figure 2. Hysteresis loops of (a) t = 50 nm and (b) t = 20 nm nanodisks. The color map as well as the arrows inside the nanodisks represents the magnetization directions in xy plane, and the black and white dots represent downward and upward magnetic vortex core, respectively. Variation of the energy density for (c) t = 50 nm and (d) t = 20 nm nanodisks when the magnetic filed is swept from 150 mT to 0 mT.
图 3 (a) Pair A和(b) Pair B的磁滞回线. (c) Pair A和(d) Pair B在不同磁感应强度下的磁化分布图
Figure 3. Hysteresis loops of (a) nanodisk Pair A and (b) nanodisk Pair B. The snapshots of local magnetization distribution of nanodisk (c) Pair A and (d) Pair B under different external magnetic field.
图 4 在Pair B中得到旋性相同(CCW, CCW)的两个磁涡旋
Figure 4. Formation of the magnetic vortices with the same circulations (CCW, CCW) in nanodisk Pair B.
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[1] 董丹娜, 蔡理, 李成, 刘保军, 李闯, 刘嘉豪 2018 物理学报 67 228502
Google Scholar
Dong D N, Cai L, Li C, Liu B J, Li C, Liu J H 2018 Acta Phys. Sin. 67 228502
Google Scholar
[2] Legrand W, Maccariello D, Ajejas F, Collin S, Vecchiola A, Bouzehouane K, Reyren N, Cros V, Fert A 2020 Nat. Mater. 19 34
Google Scholar
[3] Wang R F, Nisoli C, Freitas R S, Li J, McConville W, Cooley B J, Lund M S, Samarth N, Leighton C, Crespi V H, Schiffer P 2006 Nature 439 303
Google Scholar
[4] Nakano K, Chiba D, Ohshima N, Kasai S, Sato T, Nakatani Y, Sekiguchi K, Kobayashi K, Ono T 2011 Appl. Phys. Lett. 99 262505
Google Scholar
[5] Nakano K, Tanabe K, Hiramatsu R, Chiba D, Ohshima N, Kasai S, Sato T, Nakatani Y, Sekiguchi K, Kobayashi K, Ono T 2013 Appl. Phys. Lett. 102 072405
Google Scholar
[6] Möller M, Gaida J H, Schäfer S, Ropers C 2020 Commun. Phys. 3 36
Google Scholar
[7] Noske M, Gangwar A, Stoll H, Kammerer M, Sproll M, Dieterle G, Weigand M, Fähnle M, Woltersdorf G, Back C H, Schütz G 2014 Phys. Rev. B 90 104415
Google Scholar
[8] Ma X P, Cai M X, Li P, Shim J H, Piao H G, Kim D H 2020 J. Magn. Magn. Matter 502 166481
Google Scholar
[9] Ma X P, Shim J H, Piao H G, Kim D H, Kim D E 2019 Jpn. J. Appl. Phys. 58 100909
Google Scholar
[10] Jin W, He H, Chen Y, Liu Y 2009 J. Appl. Phys. 105 013906
Google Scholar
[11] Chou K W, Puzic A, Stoll H, Dolgos D, Schütz G 2007 Appl. Phys. Lett. 90 202505
Google Scholar
[12] Rückriem R, Schrefl T, Albrecht M 2014 Appl. Phys. Lett. 104 052414
Google Scholar
[13] Mesler B L, Buchanan K S, Im M Y, Fischer P 2012 J. Appl. Phys. 111 07D311
Google Scholar
[14] Han H S, Lee S, Jung D H, Kang M, Lee K S 2020 Appl. Phys. Lett. 117 042401
Google Scholar
[15] Cambel V, Karapetrov G 2011 Phys. Rev. B 84 014424
Google Scholar
[16] Shimon G, Adeyeye A O, Ross C A 2013 Phys. Rev. B 87 214422
Google Scholar
[17] Agramunt-Puig S, Del-Valle N, Navau C, Sanchez A 2014 Appl. Phys. Lett. 104 012407
Google Scholar
[18] Yakata S, Miyata M, Nonoguchi S, Wada H, Kimura T 2010 Appl. Phys. Lett. 97 222503
Google Scholar
[19] Uhlíř V, Urbánek M, Hladík L, Spousta J, Im M Y, Fischer P, Eibagi N, Kan J J, Fullerton E E, Šikola T 2013 Nat. Nanotechnol. 8 341
Google Scholar
[20] Huang C H, Wu K M, Wu J C, Horng L 2013 J. Appl. Phys. 113 103905
Google Scholar
[21] Gaididei Y, Sheka D D, Mertens F G 2008 Appl. Phys. Lett. 92 012503
Google Scholar
[22] Li J, Wang Y, Zhao Z, Cao J, Zhu F, Tai R 2020 IEEE Trans. Magn. 56 4300306
[23] Kimura T, Otani Y, Masaki H, Ishida T, Antos R, Shibata J 2007 Appl. Phys. Lett. 90 132501
Google Scholar
[24] Sugimoto S, Fukuma Y, Kasai S, Kimura T, Barman A, Otani Y 2011 Phys. Rev. Lett. 106 197203
Google Scholar
[25] Konoto M, Yamada T, Koike K, Akoh H, Arima T, Tokura Y 2008 J. Appl. Phys. 103 023904
Google Scholar
[26] Vansteenkiste A, Leliaert J, Dvornik M, Helsen M, Garcia-Sanchez F, Waeyenberge B V 2014 AIP Adv. 4 107133
Google Scholar
[27] Van Waeyenberge B, Puzic A, Stoll H, Chou K W, Tyliszczak T, Hertel R, Fähnle M, Brückl H, Rott K, Reiss G, Neudecker I, Weiss D, Back C H, Schütz G 2006 Nature 444 461
Google Scholar
[28] Vavassori P, Bovolenta R, Metlusho V, Ilic B 2006 J. Appl. Phys. 99 053902
Google Scholar
[29] Saitoh E, Kawabata M, Harii K, Miyajima H, Yamaoka T 2004 J. Appl. Phys. 95 1986
Google Scholar
[30] Liu Y, Hou Z, Gliga S, Hertel R 2009 Phys. Rev. B 79 104435
Google Scholar
[31] Yu Y S, Jung H, Lee K S, Fischer P, Kim S K 2011 Appl. Phys. Lett. 98 052507
Google Scholar
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