We investigate the effect of curvature on the energy and stability of domain wall configurations in curved cylindrical nanotubes and nanowires. We use micromagnetic simulations to calculate the phase diagram for the transverse wall (TW) and vortex wall (VW) states in tubes, finding the lower energy configuration and the metastability region where both types of walls can exist. The introduction of curvature shifts the range for which the TW is the ground state domain wall to higher diameters and increases the range of metastability. We interpret this behavior to be primarily due to the curvature-induced effective Dzyaloshinskii–Moriya term in the exchange energy. Furthermore, we demonstrate qualitatively the same behavior in solid cylindrical nanowires. Comparing both tubes and wires, we observe how while in tubes curvature tends to suppress the transformation from the TW to VW, in wires it promotes the transformation of the VW containing the Bloch point into the TW. These findings have important implications in the fundamental understanding of domain walls in 3D geometries and the design of future domain wall devices.

中文翻译：

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弯曲圆柱形纳米管和纳米线中磁畴壁的微磁建模

我们研究曲率对弯曲圆柱形纳米管和纳米线中畴壁结构的能量和稳定性的影响。我们使用微磁模拟来计算管中横向壁 (TW) 和涡旋壁 (VW) 状态的相图，找到两种类型壁都可以存在的较低能量配置和亚稳态区域。曲率的引入将 TW 作为基态畴壁的范围转移到更高的直径，并增加了亚稳态范围。我们将这种行为解释为主要是由于交换能量中曲率引起的有效 Dzyaloshinskii-Moriya 项。此外，我们在实心圆柱形纳米线中定性地证明了相同的行为。比较管子和电线，我们观察到，虽然在管道中曲率倾向于抑制从 TW 到 VW 的转换，但在电线中它促进了包含布洛赫点的 VW 到 TW 的转换。这些发现对 3D 几何结构中畴壁的基本理解和未来畴壁器件的设计具有重要意义。