Figure 1.

Geometry and choice of coordinate axes for the nanoring used in the DMI calculations. The inner and outer radii are $R_1$ and $R_2$, respectively, and the thickness is L (with $L\ll R_2$). The applied magnetic field $B_0$ is in the plane of the ring along the z direction and the DMI axial vector was chosen to be in the $xz$ plane (see text).