  We investigated head-to-head domain walls in nanostrips of epitaxial
$\mathrm{Fe}_4\mathrm{N}(001)$ thin films, displaying a fourfold magnetic
anisotropy. Magnetic force microscopy and micromagnetic simulations show that
the domain walls have specific properties, compared to soft magnetic materials.
In particular, strips aligned along a hard axis of magnetization are wrapped by
partial flux-closure concertina domains below a critical width, while
progressively transforming to zigzag walls for wider strips. Transverse walls
are favored upon initial application of a magnetic field transverse to the
strip, while transformation to a vortex walls is favored upon motion under a
longitudinal magnetic field. In all cases the magnetization texture of such
fourfold anisotropy domain walls exhibits narrow micro-domain walls, which may
give rise to peculiar spin-transfer features.
