We exhaustively construct instanton solutions and elucidate their properties in one-dimensional antiferromagnetic chiral magnets based on the $O\left(3\right)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips called merons) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.

中文翻译：

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手性磁铁的瞬间

我们详尽地构造了瞬时子解，并根据其在一维反铁磁手性磁体中阐明了它们的性质。 $Ø（3）$具有Dzyaloshinskii-Moriya（DM）相互作用的自旋链的非线性sigma模型描述。通过引入易轴电位和交错磁场，我们获得了一个相图，该相图由在易轴主导情况下具有两个点（或一个点）的基态相位，在球体的固定纬度下的螺旋调制组成，以及一个允许在任意纬度进行螺旋调制的三临界点。我们发现，在这些阶段中，瞬间子（或二维欧几里得空间中的天空粒子）以不同的方式出现为复合孤子：在易轴主导情况下的时域壁或壁-对壁对（bions），位错（或称为相移）分数阶瞬时数在螺旋状态的瓜子），和孤立的瞬时子和热量在三临界点处位于螺旋调制的顶部。我们还表明，具有DM交互作用和易平面电位的模型可以映射到没有它们的模型中，从而为研究具有DM交互作用的模型提供了有用的工具。