Magnetoelectricity induced by rippling of magnetic nanomembranes and wires

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.