  Mn1.4PtSn is the first material in which antiskyrmions have been observed in
ultra-thin single crystalline specimens. While bulk crystals exhibit fractal
patterns of purely ferromagnetic domain ordering at room temperature,
ultra-thin Mn1.4PtSn lamellae clearly show antiskyrmion lattices with lattice
spacings up to several $\mu$m. In the work presented here, we systematically
investigate the thickness region from 400 nm to 10 $\mu$m using 100 $\times$
100 $\mu$m$^2$ -wide Mn1.4PtSn plates, and identify the critical
thickness-to-width aspect ratio $\alpha_0 = 0.044$ for the ferromagnetic
fractal domain to the non-collinear texture phase transition. Additionally, we
also explore these non-collinear magnetic textures below the critical aspect
ratio $\alpha_0$ above and below the spin-reorientation transition temperature
$T_{SR}$ while applying variable external magnetic fields. What we find is a
strong hysteresis for the occurrence of an antiskyrmion lattice, since the
antiskyrmions preferentially nucleate by pinching them off from helical stripes
in the transition to the field polarized state.
