Abstract The purpose of the research is the construction of the analytical model for description of a number of topological objects in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction (DMI) including vortices, antivortices, skyrmions, antiskyrmions, skyrmioniums and their bound states, which are the exact dynamic solutions of the nonlinear Landau-Lifshitz equations. “Relativistic contraction” of skyrmion-like topological object size in the direction of motion is demonstrated for “subcritical” case when its velocity is less than spin wave velocity in antiferromagnet. Lorentz-like “supercritical” transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet. In particular, the results of the analytical model are applied for an antiferromagnet in the form of cylindrical nanoshell; in this case, there are more than one solution of the nonlinear Landau-Lifshitz equations for the same boundary and initial conditions. It means that vortices, skyrmions, skyrmioniums and their bound states represent the ground state and the excited states in an antiferromagnetic cylindrical nanoshell. The particular cases of the exact static solutions of the nonlinear Landau-Lifshitz equations include the well-known one-dimensional solutions such as Bloch domain, Neel domain wall, Shirobokov domain structure, antiferromagnetic vortices, two-dimensional Belavin-Polyakov soliton, three-dimensional Hodenkov soliton and target type soliton. The results of this paper can be used for further development of theory of the antiferromagnetic soliton and skyrmion physics. Besides, the exact dynamic solutions of the nonlinear Landau-Lifshitz equations can serve as the reference solutions for testing the results of micromagnetic simulations.

中文翻译：

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具有 DMI 的反铁磁体中类 Skyrmion 结构的 3D 分析模型

摘要 本研究的目的是构建用于描述具有单轴磁各向异性和 Dzyaloshinskii-Moriya 相互作用 (DMI) 的二亚晶格反铁磁体中的许多拓扑物体的分析模型，包括涡旋、反涡旋、斯格明子、反斯格明子、斯格明子和它们的束缚态，是非线性 Landau-Lifshitz 方程的精确动态解。在“亚临界”情况下，当其速度小于反铁磁​​体中的自旋波速度时，证明了类似斯格明子的拓扑物体尺寸在运动方向上的“相对论收缩”。对于在反铁磁体中以大于自旋波速度的速度运动的类似斯格明子的磁性结构，发现了类似洛伦兹的“超临界”变换。特别是，分析模型的结果适用于圆柱形纳米壳形式的反铁磁体；在这种情况下，对于相同的边界和初始条件，非线性 Landau-Lifshitz 方程有多个解。这意味着涡旋、斯格明子、斯格明子及其束缚态代表了反铁磁圆柱形纳米壳中的基态和激发态。非线性 Landau-Lifshitz 方程的精确静态解的特殊情况包括众所周知的一维解，例如 Bloch 域、Neel 畴壁、Shirobokov 畴结构、反铁磁涡旋、二维 Belaviin-Polyakov 孤子、三维霍登科夫孤子和目标型孤子。本文的研究结果可用于反铁磁孤子和斯格明子物理理论的进一步发展。此外，非线性Landau-Lifshitz方程的精确动力学解可以作为检验微磁模拟结果的参考解。