  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. Here, we challenge this well-established
paradigm, and propose to explore a Heisenberg-exchange-free magnetic world.
There, 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. The isolated
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.
