Using bilayer films of $\beta$-Ta/Ni$_{0.8}$Fe$_{0.2}$, we fabricate structures consisting of two, three and four crossing ellipses which exhibit shape-induced bi-axial, tri-axial and quadro-axial magnetic anisotropy in the crossing area, respectively. Structures consisting of N crossing ellipses can be stabilized in 2N remanent states by applying (and removing) an external magnetic field. However, we show that with field-free spin-orbit torques induced by flowing currents in individual ellipses, the number of remanent states grows to 2$^\text{N}$. Furthermore, when the current flows between the edges of different ellipses the number of remanent states jumps to 2$^\text{2N}$, including states which exhibit a $\pi$-Neel domain wall in the overlap area. The very large number of accessible remanent magnetic states that are exhibited by the relatively simple magnetic structures paves the way for intriguing spintronics applications including memory devices.

中文翻译：

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具有局部自旋轨道扭矩的指数数量离散剩余态的稳定性

使用 $\beta$-Ta/Ni$_{0.8}$Fe$_{0.2}$ 的双层薄膜，我们制造了由两个、三个和四个交叉椭圆组成的结构，这些椭圆表现出形状诱导的双轴、三轴和四轴磁各向异性在交叉区域，分别。通过施加（和去除）外部磁场，由 N 个交叉椭圆组成的结构可以稳定在 2N 个剩余态。然而，我们表明，在单个椭圆中流动的电流引起的无场自旋轨道扭矩的情况下，剩余态的数量增长到 2$^\text{N}$。此外，当电流在不同椭圆的边缘之间流动时，剩余态的数量跃升至 2$^\text{2N}$，包括在重叠区域表现出 $\pi$-Neel 畴壁的状态。