Critical sample aspect ratio and magnetic field dependence for antiskyrmion formation in Mn1.4PtSn single crystals

${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ is the first material in which antiskyrmions have been observed in ultrathin single-crystalline specimens. While bulk crystals exhibit fractal patterns of purely ferromagnetic domain ordering at room temperature, ultrathin ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ lamellae clearly show antiskyrmion lattices with lattice spacings up to several $\ensuremath{\mu}\mathrm{m}$. In the paper presented here, we systematically investigate the thickness region from 400 nm to 10 $\ensuremath{\mu}\mathrm{m}$ using $100\ifmmode\times\else\texttimes\fi{}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$ wide ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ plates, and identify the critical thickness-to-width aspect ratio ${\ensuremath{\alpha}}_{0}=0.044$ for the ferromagnetic fractal domain to the noncollinear texture phase transition. Additionally, we also explore these noncollinear magnetic textures below the critical aspect ratio ${\ensuremath{\alpha}}_{0}$ above and below the spin-reorientation transition temperature ${T}_{\mathrm{SR}}$ 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.