  We consider a three-dimensional micromagnetic model with
Dzyaloshinskii-Moriya interaction in a thin-film regime for boundary vortices.
In this regime, we prove a dimension reduction result: the nonlocal
three-dimensional model reduces to a local two-dimensional Ginzburg-Landau type
model in terms of the averaged magnetization in the thickness of the film. This
reduced model captures the interaction between boundary vortices (so-called
renormalised energy), that we determine by a $\Gamma$-convergence result at the
second order and then we analyse its minimisers. They nucleate two boundary
vortices whose position depends on the Dzyaloshinskii-Moriya interaction.
