Anisotropic fractal magnetic domain pattern in bulk Mn$_{1.4}$PtSn

The tetragonal compound Mn$_{1.4}$PtSn with the $D_{2d}$ symmetry recently attracted attention as the first known material that hosts magnetic antiskyrmions, which differ from the so far known skyrmions by their internal structure. The latter have been found in a number of magnets with the chiral crystal structure. In previous works, the existence of antiskyrmions in Mn$_{1.4}$PtSn was unambiguously demonstrated in real space by means of Lorentz transmission electron microscopy on thin-plate samples ($sim$100~nm thick). In the present study, we used small-angle neutron scattering and magnetic force microscopy to perform reciprocal- and real-space imaging of the magnetic texture of bulk Mn$_{1.4}$PtSn single-crystals at different temperatures and in applied magnetic field. We found that the magnetic texture in the bulk differs significantly from that of thin-plate samples. Instead of spin helices or an antiskyrmion lattice, we observe an anisotropic fractal magnetic pattern of closure domains in zero field above the spin-reorientation transition temperature, which transforms into a set of bubble domains in high field. Below the spin-reorientation transition temperature the strong in-plane anisotropy as well as the fractal self-affinity in zero field is gradually lost, while the formation of bubble domains in high field remains robust. The results of our study highlight the importance of dipole-dipole interactions in thin-plate samples for the stabilization of antiskyrmions and identify criteria which should guide the search for potential (anti)skyrmion host materials. Moreover, they provide consistent interpretations of the previously reported magnetotransport anomalies of the bulk crystals.