In this work, we investigate intrinsic magnetic properties of monolayer electrides LaBr2 and La2Br5, 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 LaBr2 by Mermin-Wagner theorem, while intersite anisotropy in La2Br5 stabilises weakly coupled ferromagnetic chains along the monoclinic b axis. Our study shows that electride materials combining peculiar features of both localised and delocalised atomic states constitute a unique class of strongly correlated materials.Introduction. Electrides are a unique class of ionic materials, where the electron density is neither localised at any atomic orbital, nor fully delocalised like in metals. Instead, their electrons occupy interstitial regions formed by cavities in the crystal structure, where they act as anions [1, 2]. Materials with anionic electrons offer versatile functionalities, such as high electrical conductivity [3], ultra-low work functions [4], and non-linear optical responses [5], ranging their applications as electron emitters [6], battery anodes [7], and agent catalysts [8].Their physical properties are in large part determined by topology of the voids confining anionic electrons. In 2003, Matsuishi et al [9] demonstrated the first inorganic material [Ca 24 Al 28 O 64 ] +4 ·4e − stable at room temperature, which shows the high density of anionic electrons trapped in the crystallographic cages, forming a quasizero-dimensional electride with high electronic conductivity due to tunnelling through the cages [10, 11]. Recently, a novel layered electride [Ca 2 N] + ·e − has been reported, where owing to a highly delocalised nature the quasi-two-dimensional anionic electrons confined in the interlayer regions display an extreme electron mobility and long mean scattering time [12, 13]. Later on, strong localisation of anionic electrons has been observed in a layered transition-metal hypocarbide [Y 2 C] 2+ ·2e − with the quasi-two-dimensional anionic electrons in the interlayer spaces [14, 15]. Finally, it was shown that Ca 2 N can be exfoliated into two-dimensional...