  We construct three-orbital tight-binding models describing single-component
molecular conductors [Pt(dmdt)$_2$] and [Ni(dmdt)$_2$] using first-principles
calculations. We show that [Ni(dmdt)$_2$] is a Dirac nodal line system with
highly one-dimensional edge states at the (001) edge, similar to
[Pt(dmdt)$_2$], as demonstrated in prior studies. To investigate possible edge
magnetism, we calculate longitudinal and transverse spin susceptibilities using
real-space-dependent random-phase approximation (RPA) in three-orbital Hubbard
models in the presence of spin--orbit coupling. We find that the edge
spin-density wave (SDW) is induced by the Coulomb repulsion and incommensurate
nestings of the Fermi arcs. We also find that the magnetic structure of the
edge SDW can be changed via extremely small carrier doping, which is
controllable in molecular conductors.
