Stabilization of exponential number of discrete remanent states with localized spin-orbit torques

Using bilayer films of β-Ta/Ni0.8Fe0.2, 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 N. Furthermore, when the current flows between the edges of different ellipses, the number of remanent states jumps to 2 2 N, including states that exhibit a π-Néel 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.