  Altermagnets are compensated magnets belonging to spin symmetry groups that
allow alternating spin polarizations both in the coordinate space of the
crystal and in the momentum space of the electronic structure. In these
materials the anisotropic local crystal environment of the different
sublattices lowers the symmetry of the system so that the opposite-spin
sublattices are connected only by rotations, which results in an unconventional
spin-polarized band structure in the momentum space. This low symmetry of the
crystal structure is expected to be reflected in the anisotropy of the
anomalous Hall effect. In this work, we study the anisotropy of the anomalous
Hall effect in epitaxial thin films of Mn$_5$Si$_3$, an altermagnetic candidate
material. We first demonstrate a change in the relative N\'eel vector
orientation when rotating the external field orientation through systematic
changes in both the anomalous Hall effect and the anisotropic longitudinal
magnetoresistance. We then show that the anomalous Hall effect in this material
is anisotropic with the N\'eel vector orientation relative to the crystal
structure and that this anisotropy requires high crystal quality and unlikely
correlates with the magnetocrystalline anisotropy. Our results provide further
systematic support to the case for considering epitaxial thin films of
Mn$_5$Si$_3$ as an altermagnetic candidate material.

Mesoscale and Nanoscale Physics