Localised Magnetism in 2D Electrides

Electride materials offer diverse functionalities owing to their high electron mobility and low work function. Of particular importance are magnetic electrides where the anionic electrons confined in interstitial regions can exhibit both itinerant and localised magnetism and whose experimental realisation and theoretical understanding are still in their infancy. By considering two monolayer electrides LaBr2 and La2Br5, we show that a Mott insulating state can be realised in electrides with localised magnetic moments formed by anionic electrons. Having demonstrated that conventional first-principles approaches are incapable of treating such non-atomic magnetic orbitals, 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, 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 kinetic superexchange. On the basis of 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. Our study showcases that electride materials combining peculiar features of both localised and delocalised atomic states constitute a unique class of strongly correlated materials.