Research progress in the magnetic domain wall topology

Zhang Ying; Li Zhuo-Lin; Shen Bao-Gen

doi:10.7498/aps.73.20231612

Abstract

Topological magnetic skyrmions, as information units, possess distinct advantages such as high reliability, enhanced integration, and low energy consumption. These novel topological characteristics offer critical material and technological support for the rapid development of information technology, 5G communication, and big data. However, the application of magnetic skyrmions in practical devices is severely impeded by certain limitations, including their stability dependence on magnetic field and the deflection caused by the skyrmion Hall effect under electric current. Consequently, exploring new topological magnetic domain structures and material systems suitable for application becomes a pivotal area of research. This paper primarily focuses on experimental studies utilizing high-resolution Lorentz transmission electron microscopy for in situ real-space observation and manipulation of topological merons and skyrmions inside the magnetic domain wall, confirming the theoretical prediction of magnetic domain wall skyrmions in 2013. We has firstly achieved topological meron chains inside the domain walls by using the spin reorientation transition in two-dimensional van der Waals Fe_5–xGeTe₂ magnets, and systematically studied the dynamic behavior of domain wall topological magnetic domain structures under external electric and magnetic fields, filling the blanks in this research area. The important and special roles of magnetic domain walls are revealed at the same time. Then the GdFeCo amorphous ferrimagnetic thin film was designed and prepared based on the summarized mechanism with the domain wall meron pairs successfully reproduced. Moreover, the reversible topological transformation from domain wall meron pair to domain wall skyrmions has also been realized without external magnetic field during spin reorientation transformation as temperature changing. The results of micromagnetic simulation and electric experiments on the topological domains in domain walls would provided a strong basis and support for the future research.

Keywords:

magnetic domain wall meron /
magnetic domain wall skyrmion /
spin reorientation transition /
Lorentz transmission electron microscopy /
two-dimensional magnet

Authors and contacts

State Key Laboratory of Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Zhang Ying, zhangy@iphy.ac.cn

Funds: Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences, China (Grant No. XDB33030100), the Science Centre of the National Science Foundation of China (Grant No. 52088101), the National Natural Science Foundation of China (Grant Nos. 52271195, 52130103), and the Project for Young Scientists in Basic Research of the Chinese Academy of Sciences, China (Grant No. YSBR-084).

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Cited By

图 1 常见的拓扑磁畴结构自旋分布图　(a)布洛赫型斯格明子^[3]; (b) Néel型斯格明子^[3]; (c)反斯格明子^[3]; (d)双斯格明子^[10]; (e)麦韧^[11]

Figure 1. Schematics of typical topological domain structures: (a) Bloch-type skyrmions^[3]; (b) Néel-type skyrmions^[3]; (c) anti-skyrmions^[3]; (d) biskyrmions^[10]; (e) meron^[11].

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图 2 (a)拓扑霍尔效应示意图^[1,27]; (b)实验结果^[26]

Figure 2. (a) Schematics of topological Hall effect^[1,27]; (b) experiment results^[26].

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图 3 二维磁体Fe_5–xGeTe₂畴壁中的麦韧链^[11]　(a) Fe_5–xGeTe₂的晶体结构示意图, Fe(1)和Ge位置被部分占据(用色差表示); (b), (e) 180 K下两条畴壁对中选定区域的TIE解析面内磁化分布(箭头和颜色分别表示平面内磁化的方向和强度); (c) 250 K面内 180°畴壁的L-TEM图像衬度(标尺为1 μm); (d)麦韧对在温度降低过程中的衬度演化; (f) 180°畴壁的三维内部磁矩排布示意图; (g), (h)两种手性(顺时针和逆时针)的麦韧结构

Figure 3. Meron chains inside domain walls in 2D ferromagnets Fe_5–xGeTe₂^[11]: (a) Crystal structures of Fe_5–xGeTe₂, and the positions of Fe(1) and Ge is partially occupied (labelled by color difference); (b), (e) the in-plane magnetization resolved by TIE in the selected regions of two domain walls at 180 K (arrow and color represents direction and amplitude of in-plane magnetization respectively); (c) the L-TEM contrast of in-plane 180° domain walls at 250 K (the scale is 1 μm); (d) evolution of meron pair contrast during cooling process; (f) 3D distribution of magnetization inside 180° domain walls; (g), (h) merons with two different chirality (clockwise and anti-clockwise).

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图 4 Fe_5–xGeTe₂中畴壁麦韧链生成的物理机制^[11]　(a)磁化率χ在磁场沿两个方向(H//c和H//ab)时的温度依赖曲线; (b)不同温度下磁场沿垂直方向和面内方向(H//c和H//ab)的M-H曲线; (c)自旋重取向区间存在的平行和垂直于c轴的磁畴结构; (d), (e)温度高于100 K (d)和低于100 K (e)时, [110]晶带轴的选区电子衍射图

Figure 4. Origin of domain wall meron chains in Fe_5–xGeTe₂^[11]: (a) Temperature dependence of magnetic susceptibility χ as the magnetic field along two directions (H//c and H//ab); (b) M-H curve as magnetic fields along out-of-plane and in-plane direction (H//c and H//ab) at different temperature; (c) directions of domains parallel and perpendicular to c axis during SRT; (d), (e) SAED patterns of [110] ribbon axis at temperature above 100 K (d) and below 100 K (e).

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图 5 麦韧链的动力学行为^[11]　(a)样品施加电压的电路结构示意图; (b), (c)麦韧链在电压作用后的位置变化; (d)沿c轴倾斜样品引入磁场的示意图; (e), (f)固定垂直磁场为0.02 T下, 畴壁麦韧链在样品倾斜角度为4°和–12° 的位置分布; (g)畴壁麦韧链间距随倾斜角的变化(标尺为500 nm)

Figure 5. Dynamic behavior of meron chains^[11]: (a) Schematics of circuit when applying; (b), (c) position change of meron chains after applying voltage; (d) schematics of introduced magnetic field with sample tilted along c-axis; (e), (f) distribution of domain wall meron chain positions at the sample tilted angle of 4° and –12° with fixed perpendicular field of 0.02 T; (g) interval between domain wall meron chains with the variation of tilted angle (The scale bar is 500 nm).

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图 6 随温度变化畴壁麦韧对与畴壁斯格明子之间转化^[46]　(a)—(e) 不同温度时, 样品Gd_15+x(Fe₉₄Co₆)_85–x (x = 0.2)在L-TEM下的磁畴壁衬度; (f), (g) 243 K畴壁两侧和内部磁矩强度输运方程解析结果; (h) 图(a)—(e)中黄框部分放大; (i), (j) 300 K畴壁两侧和内部磁矩强度输运方程解析结果(标尺为2 μm)

Figure 6. Meron pair contrast change with temperature^[46]: (a)–(e) Evolution of domain wall L-TEM contrast with temperature in Gd_15+x(Fe₉₄Co₆)_85–x (x = 0.2); (f), (g) TIE results inside and outside domain walls at 243 K; (h) enlarged part of yellow box in panels (a)–(e); (i), (j) TIE results inside and outside domain walls at 300 K (The scale bar is 2 μm).

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图 7 磁性参数变化决定的磁畴壁拓扑结构演变及微磁学模拟结果^[46]　(a) Gd_15+x(Fe₉₆Co₆)_85–x (x = 0.2)样品不同温度下的单轴各向异性常数K_u和饱和磁化强度M_s实验数据; (b)不同K_u和M_s下麦韧对拓扑数演化结果相图及实验中自旋重取向转变温区所在区域; (c), (h) L-TEM衬度模拟结果; (d)—(g) 270—300 K麦韧对到斯格明子的模拟畴壁演化, 面外磁化由红色(+m_z)和蓝色(–m_z)表示, 面内磁化由白色区域和黑色箭头表示; (i)—(k)对应的自旋结构示意图立体投影

Figure 7. Micromagnetic simulation results of domain wall topological transition^[46]: (a) Experimental data of anisotropy constant K_u and saturation magnetization M_s at different temperature in Gd_15+x(Fe₉₆Co₆)_85–x (x = 0.2); (b) the phase diagram of topological transition starting from meron pair at different K_u and M_s value and the SRT regions observed in experiment; (c), (h) simulation results of corresponding L-TEM contrast; (d)–(g) evolution from meron pairs to skyrmions by simulation at 270–300 K, the out-of-plane magnetization is indicated by red (+m_z) and blue (–m_z), the in-plane magnetization is indicated by white region and black arrows; (i)–(k) 3D schematics of corresponding spin structures.

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图 8 不同F_q值下畴壁拓扑结构演化的微磁学模拟结果^[46]

Figure 8. Simulated topological domain evolution in domain wall for different value of F_q^[46].

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图 9 畴壁麦韧链结构及生成机理示意图^[46]

Figure 9. Schematics of domain meron pair and its forming mechanism^[46].

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图 10 微磁学模拟下电流驱动下畴壁斯格明子随时间的位移^[46]

Figure 10. Simulated drift of domain wall skyrmions with time under applied current^[46].

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图 11 电流调控实验结果^[46]　(a)原位电流实验示意图; (b)畴壁斯格明子在32 mA直流下不同时间点的位置变化(标尺为500 nm)

Figure 11. Experimental results under electric stimulus^[46]: (a) Schematics of in-situ current experiments; (b) position change of domain wall skyrmions at different time under 32 mA DC (The scale bar is 500 nm).

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