Dzyaloshinskii-Moriya anisotropy in nanomagnets with in-plane magnetization

We report on a source of in-plane anisotropy in nanomagnets due to the presence of Dzyaloshinskii-Moriya interaction (DMI). This anisotropy depends on the shape of the magnet, and is orthogonal to the demagnetization shape anisotropy. This effect originates from the DMI energy reduction due to an out-of-plane tilt of the spins at edges oriented perpendicular to the magnetization. Our numerical and analytical investigations demonstrate that this energy reduction can compensate the demagnetization shape anisotropy energy in magnets of elongated shape, provided that their volumes are small enough and thus that their magnetization is quasiuniform. Our model agrees quantitatively with magnetic force microscopy observations on preliminary sub-100-nm structures.