  Intermetallic Pd-doped (Fe,Ni)$_3$P, that crystalizes in a
non-centrosymmetric tetragonal structure with $S_4$ symmetry, has recently been
discovered to host magnetic antiskyrmions, antivortex-like topological spin
textures. In this material, uniaxial magnetic anisotropy and dipolar
interactions play a significant role, giving rise to finely branched magnetic
domain patterns near the surface of bulk crystals, as revealed by a previous
magnetic force microscopy (MFM) measurement. However, small-angle neutron
scattering (SANS) is a more suitable method for characterizing bulk properties
and fractal structures at the mesoscopic length scale. In this study, using
SANS and MFM, we quantitatively investigate the magnetic domain structure in
bulk single crystals of (Fe$_{0.63}$Ni$_{0.30}$Pd$_{0.07}$)$_3$P. The SANS
results demonstrate that the magnetic domain structure exhibits anisotropic
fractal character on the length scale down to the width of the magnetic domain
walls. The fractal features are gradually lost in magnetic fields, and
different field dependences are observed at 300 K and 2 K due to a
temperature-dependent anisotropy. This study quantifies the fractality of the
highly anisotropic magnetic domain structures in an antiskyrmion material, and
highlights the versatility of SANS for the study of fractal structures in
magnetic systems.
