  In this work, we investigate intrinsic magnetic properties of monolayer
electrides LaBr$_{2}$ and La$_{2}$Br$_{5}$, where excess electrons do not
reside at any atomic orbital and act as anions located at interstitial regions.
Having demonstrated that conventional first-principles approaches are incapable
of treating such non-atomic magnetic orbitals largely underestimating
insulating band gaps, we construct effective electronic models in the basis of
Wannier functions associated with the anionic states to unveil the microscopic
mechanism underlying magnetism in these systems. Being confined at
zero-dimensional cavities in the crystal structure, the anionic electrons will
be shown to reveal an exotic duality of strong localisation like in $d$- and
$f$-electron systems and large spatial extension inherent to delocalised atomic
orbitals. While the former tends to stabilise a Mott-insulating state with
localised magnetic moments, the latter results in direct exchange between
neighbouring anionic electrons that dominates over antiferromagnetic
superexchange interactions. On the basis of the derived spin models, we argue
that any long-range magnetic order is prohibited in LaBr$_{2}$ by Mermin-Wagner
theorem, while intersite anisotropy stabilises weakly coupled ferromagnetic
chains along the monoclinic $\mathbf{b}$ axis in La$_{2}$Br$_{5}$. Our study
shows that electride materials combining peculiar features of both localised
and delocalised atomic states constitute a unique class of strongly correlated
materials.
