  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
spiralling type. Here we establish a novel approach to generate a linear
magnetoelectric coupling in insulators with a conventional, ferromagnetic
ground state. We show that nanoscale curved geometries 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 activate a
magnetoelectric monopole in the recently synthesised two-dimensional magnets.
We also demonstrate that in zig-zag shaped ferromagnetic wires in planar
architectures, a magnetic toroidal moment triggers a direct linear
magnetoelectric coupling.
