Stabilization of Skyrmion States by a Gradient of Curvature in Ferromagnetic Shells

Skyrmions represent a class of chiral magnetic textures with unique properties relevant for spintronic and spin-orbitronic applications [1]. Geometrical curvature can be used as an efficient mean to tailor chiral and anisotropic responses of thin ferromagnetic shells [2-4]. This was recently confirmed by quantifying the strength of the Dzyaloshinskii-Moriya interaction (DMI) in curved nanostripes [5]. Furthermore, there are numerous predictions of the stabilization of curvature-driven of small-radius skyrmions in spherical shells [6] and an appearance of skyrmion lattices as the ground state in intrinsically chiral curvilinear thin films [7].

Here, we demonstrate a new pathway of stabilizing Neel skyrmion and skyrmionium states relying on the gradient of curvature using a magnetic thin film hosting a circular nanoindentation [8]. These skyrmion states can be formed in a material even without an intrinsic DMI. We propose a physical picture of this effect, which is related to the pinning of a chiral magnetic domain wall at the bend of a nanoindentation. Geometry of the film is described by two principal curvatures k1(r), describing film geometry in radial direction, and k2(r) inversely proportional to the distance from origin. In this respect, the spatial inhomogeneity of the curvature-induced DMI governing by k1(r) is responsible for the stabilization of the skyrmion state. The lateral dimensions of the stabilized chiral magnetic textures are varied in a broad range by engineering the size of the nanoindentation. We describe the stability condition of skyrmion states. Furthermore, on the fundamental side, we put forth a general analytical framework allowing us to map a complex problem of the description of a magnetic texture at a surface of revolution to a standard planar problem with modified constants of DMI and magnetic anisotropy. In this respect, our model predicts a new mechanism of pinning of magnetic domain walls in planar ferromagnetic films with intrinsic DMI on inhomogeneities of the DMI.

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