  We study the effects of an in-plane Dzyaloshinskii-Moriya interaction under
an external magnetic field in the highly frustrated kagome antiferromagnet. We
focus on the low-temperature phase diagram, which we obtain through extensive
Monte-Carlo simulations. We show that, given the geometric frustration of the
lattice, highly non trivial phases emerge. At low fields, lowering the
temperature from a cooperative paramagnet phase, the kagome elementary
plaquettes form non-coplanar arrangements with non-zero chirality, retaining a
partial degeneracy. As the field increases, there is a transition from this
"locally chiral phase" to an interpenetrated spiral phase with broken
$\mathcal{Z}_{3}$ symmetry. Furthermore, we identify a quasi-skyrmion phase in
a large portion of the magnetic phase diagram, which we characterize with a
topological order parameter, the scalar chirality by triangular sublattice.
This pseudo-skyrmion phase (pSkX) consists of a crystal arrangement of three
interpenetrated non-Bravais lattices of skyrmion-like textures, but with a
non-(fully)-polarized core. The edges of these pseudo-skyrmions remain
polarized with the field, as the cores are progressively canted. Results show
that this pseudo-skyrmion phase is stable up to the lowest simulated
temperatures, and for a broad range of magnetic fields.
