  We study the classical antiferromagnetic Heisenberg model on the triangular
lattice with Dzyaloshinskii-Moriya interactions in a magnetic field. We focus
in particular in the emergence of a composite spin crystal phase, dubbed
antiferromagnetic skyrmion lattice, that was recently observed in [Phys. Rev. B
92, 214439 (2015)] for intermediate fields. This complex phase can be made up
from three inter-penetrated skyrmion lattices, one for each sub-lattice of the
original triangular one. Following these recent numerical results, in this
paper we explicitly construct the low-energy effective action that reproduces
the correct phenomenology and could serve as a starting point to study the
coupling to charge carriers, lattice vibrations, structural disorder and
transport phenomena.
