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We combine the anisotropy of magnetic interactions and the point symmetry offinite solids in the study of dipolar clusters as new basic units formultiferroics metamaterials. The hamiltonian of magnetic dipoles with an easyaxis at the vertices of polygons and polyhedra, maps exactly into a hamiltonianwith symmetric and antisymmetric exchange couplings. The last one gives rise toa Dzyaloshinskii-Moriya contribution responsible for the magnetic modes of thesystems and their symmetry groups, which coincide with those of a particle in acrystal field with spin-orbit interaction. We find that the clusters carry spincurrent and that they manifest the magnetoelectric effect. We expect ourresults to pave the way for the rational design of magnetoelectric devices atroom temperature.

Magnetoelectric effect in dipolar clusters