  Platinum diselenide (PtSe$_{2}$) is a recently-discovered extrinsic magnet,
with its magnetism attributed to the presence of Pt-vacancies. The host
material to these defects itself displays interesting structural and electronic
properties, some of which stem from an unusually strong interaction between its
layers. To date, it is not clear how the unique intrinsic properties of
PtSe$_2$ will affect its induced magnetism. In this theoretical work, we show
that the defect-induced magnetism in PtSe$_{2}$ thin films is highly sensitive
to: (i) the layer-thickness (ii) defect density, and (iii) substrate choice.
These different factors dramatically modify all magnetic properties, including
the magnitude of local moments, strength of the coupling, and even nature of
the coupling between the moments. We further show that the strong inter-layer
interactions are key to understanding these effects. A better understanding of
the various influences on magnetism, can enable controllable tuning of the
magnetic properties in Pt-based dichalcogenides, which can be used to design
novel devices for magnetoelectric and magneto-optic applications.
