Stabilization and current-induced motion of antiskyrmion in the presence of anisotropic Dzyaloshinskii-Moriya interaction

Siying Huang, Chao Zhou, Gong Chen, Hongyi Shen, Andreas K. Schmid, Kai Liu, and Yizheng Wu

Phys. Rev. B 96, 144412 – Published 9 October 2017

Abstract

Topological defects in magnetism have attracted great attention due to fundamental research interests and potential novel spintronics applications. Rich examples of topological defects can be found in nanoscale nonuniform spin textures, such as monopoles, domain walls, vortices, and skyrmions. Recently, skyrmions stabilized by the Dzyaloshinskii-Moriya interaction have been studied extensively. However, the stabilization of antiskyrmions is less straightforward. Here, using numerical simulations we demonstrate that antiskyrmions can be a stable spin configuration in the presence of anisotropic Dzyaloshinskii-Moriya interaction. We find current-driven antiskyrmion motion that has a transverse component, namely, the antiskyrmion Hall effect. The antiskyrmion gyroconstant is opposite to that for skyrmion, which allows the current-driven propagation of coupled skyrmion-antiskyrmion pairs without an apparent skyrmion Hall effect. The antiskyrmion Hall angle strongly depends on the current direction, and a zero antiskyrmion Hall angle can be achieved at a critic current direction. These results open up possibilities to tailor the spin topology in nanoscale magnetism, which may be useful in the emerging field of skyrmionics.

Received 31 May 2017
Revised 1 September 2017

DOI:https://doi.org/10.1103/PhysRevB.96.144412

Physics Subject Headings (PhySH)

Skyrmions Spin texture

Ferromagnets Nanowires

Landau-Lifschitz-Gilbert equation Micromagnetic modeling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Siying Huang¹, Chao Zhou¹, Gong Chen^2,*, Hongyi Shen¹, Andreas K. Schmid³, Kai Liu², and Yizheng Wu^1,4,†

¹Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
²Department of Physics, University of California, Davis, California 95616, USA
³NCEM, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China

^*gchenncem@gmail.com
^†wuyizheng@fudan.edu.cn

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Vol. 96, Iss. 14 — 1 October 2017

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Images

Figure 1
Skyrmion and antiskyrmion configurations corresponding to isotropic and anisotropic DMI, respectively. (a, b) Schematic diagrams of isotropic and anisotropic DMI. Red balls indicate atomic spins at the interface while blue arrows indicate the Dzyaloshinskii-Moriya vectors. (c, d) Arrows-array representation of skyrmion and antiskyrmion spin configurations. (e, f) Construction recipes for skyrmion and antiskyrmion in order parameter space. Note that panels (c) and (d) can be derived from panels (e) and (f) through stereographic projection. In panels (c–f), different colors of the arrows correspond to different angles between the spins and normal direction of the interface.
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Figure 2
Isolated antiskyrmion in a nanodisk (diameter 80 nm) in the presence of anisotropic DMI with $D_{x} = - D_{y}$ . (a) Total micromagnetic energy (including the DMI, exchange, dipolar, and anisotropy energies) for different states of the nanodisk as a function of $D_{x}$ along the line of $D_{x} = - D_{y}$ in $(D_{x}, D_{y})$ space. Dashed lines indicate that the corresponding states are unstable in the simulations and tend to relax to more stable states. $D^{'}$ and $D^{''}$ indicate points where two different states are energetically degenerate. Insets show examples of relaxed magnetization distributions of the nanodisk for several points in the graph. (b) Magnetization distribution for an antiskyrmion ground state with $D_{x} = - D_{y} = 4 mJ m^{- 2}$ . Red, white, and blue colors indicate out-of-plane magnetization distribution as shown in the color bar, as used throughout the paper. Black arrows highlight the in-plane orientation of spins.
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Figure 3
Phase diagram of skyrmion and antiskyrmion states in $(D_{x}, D_{y})$ space. (a) Phase diagram for a 80-nm-wide, 0.4-nm-thick cobalt nanodisk on a substrate inducing DMI in zero field. Regions colored cyan, yellow, and green correspond to quasiuniform, skyrmion/antiskyrmion, and multidomain states, respectively. White dots show the phase boundary obtained from the simulations. The blue dashed loops outline regions labeled II where skyrmion and antiskyrmions are the most stable states. In regions labeled I (III) the energy of multidomain (quasiuniform) states is lower than that of skyrmion/antiskyrmion states. (b–i) Representative magnetization distribution graphs for $(D_{x}, D_{y})$ values listed under each graph (in units of $mJ m^{- 2}$ ), where blue dots in (a) mark the corresponding phase diagram coordinates. The relationship between different colors and in-plane magnetization directions is shown in the color wheel, and in-plane spin orientations are highlighted by white arrows.
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Figure 4
Current-induced motion of skyrmions and antiskyrmions on nanotracks. (a) Current-driven motion of skyrmions and antiskyrmions on nanotracks for different current densities. White dashed lines indicate trajectories and black arrows show the in-plane spin orientations in the perimeters of the skyrmion/antiskyrmion. (b) The simulated skyrmion and antiskyrmion velocity as a function of current density. The velocities of skyrmions and antiskyrmions are almost equal at all current densities.
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Figure 5
Anisotropic antiskyrmion Hall effect. (a) Skyrmion motion trajectory with current along the $x$ axis. (b–d) Antiskyrmion motion trajectories with the current direction at $θ = 0^{\circ}, - 90^{\circ}$ , and $- 34 . 5^{\circ}$ to the $x$ axis, respectively. White dashed lines in panels a–d represent the trajectories. (e) Skyrmion and antiskyrmion Hall angle $Φ$ as a function of DMI constant. (f) Antiskyrmion Hall angle $Φ$ as a function of current direction θ, where the solid line is a linear fit. In these simulations the size of the nanotrack is $300 \times 300 \times 0.4 n m^{3}$ , and the applied current density is $10 MA c m^{- 2}$ .
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Figure 6
Current-induced motion of ferromagnetically coupled antiskyrmion-skyrmion pairs. (a) Illustration of a antiskyrmion-skyrmion pair in a bilayer system. (b) decomposition distance ΔX as a function of the interface coupling strength σ. The red line is a guide to eye. The blue shadowed line represents the critical value of σ above which the antiskyrmion-skyrmion pair remains coupled. (c) Current-induced motion of an antiskyrmion-skyrmion pair which is not sufficiently coupled, at coupling strength $σ = 0.01 mJ m^{- 2}$ . (d) Current-induced motion of antiskyrmion-skyrmion pair that remains coupled, at sufficient coupling strength $σ = 0.08 mJ m^{- 2}$ . Dashed lines in panels (c) and (d) represent the trajectories. Size of the coupled bilayer nanotrack is $200 \times 80 \times 1.2 n m^{3}$ , current density is $5 MA c m^{- 2}$ , and $D_{x} = 3 mJ m^{- 2}$ .
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