Flexoelectricity in twinned ferroelastic thin films generates polarity inside twin walls. The electrical dipoles are typically aligned parallel to twin walls while out-of-plane dipoles are induced elastically by an atomic force microscopy (AFM) tip or by atomic steps in the substrate. Molecular dynamics modeling shows that the out-of-plane dipoles form polar vortex structures next to the domain walls. Flexoelectricity, e.g., by moving AFM tips, produces displacement currents inside these vortices. We estimate that these displacement currents generate magnetic fields with moments in the order of 10⁻⁹ μ_B per atomic layer.

中文翻译：

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铁磁材料中由尖端引起的弯曲电，极性涡旋和磁矩

孪生铁弹性薄膜中的挠性电在孪生壁内部产生极性。电偶极子通常平行于双壁对齐，而平面外偶极子是通过原子力显微镜（AFM）尖端或基板中的原子台阶弹性感应的。分子动力学建模表明，平面外偶极子在畴壁附近形成极性涡旋结构。柔性电，例如，通过移动AFM尖端，在这些涡旋内部产生位移电流。我们估计，这些位移电流产生与在10的阶矩磁场^-9  μ_乙每原子层。