Magnetoelectric crystals have the interesting property that they allow electric fields to induce magnetic polarizations, and vice versa, magnetic fields to generate ferroelectric polarizations. Having such a magnetoelectric coupling usually requires complex types of magnetic textures, e.g., of spiraling type. Here, we establish a previously unknown approach to generate linear magnetoelectric coupling in ferromagnetic insulators with intrinsic Dzyaloshinskii-Moriya interaction (DMI). We show that the effect of nanoscale curved geometries combined with the intrinsic DMI of the magnetic shell lead to a reorganization of the magnetic texture that spontaneously breaks inversion symmetry and thereby induces macroscopic magnetoelectric multipoles. Specifically, we prove that structural deformation in the form of controlled ripples activates a magnetoelectric monopole in the recently synthesized two-dimensional magnets. We also demonstrate that in zigzag-shaped ferromagnetic wires in planar architectures, a magnetic toroidal moment triggers direct linear magnetoelectric coupling.
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