[en] Isotropic Heisenberg exchange naturally appears as the main interaction in magnetism, usually favouring long-range spin-ordered phases. The anisotropic Dzyaloshinskii–Moriya interaction arises from relativistic corrections and is a priori much weaker, even though it may sufficiently compete with the isotropic one to yield new spin textures. In this work, we challenge this well-established paradigm, and propose to explore a Heisenberg-exchange-free magnetic world. In this case, the Dzyaloshinskii–Moriya interaction induces magnetic frustration in two dimensions, from which the competition with an external magnetic field results in a new mechanism producing skyrmions of nanoscale size. A single nanoskyrmion can already be stabilized in a few-atom cluster, and may then be used as LEGO^® block to build a large magnetic mosaic. The realization of such topological spin nanotextures in sp- and p -electron compounds or in ultracold atomic gases would open a new route toward robust and compact magnetic memories. (letter)