Atomic-orbital-free intrinsic ferromagnetism in electrenes

Atomic orbitals play fundamental roles in the modern theory of magnetism, not only providing local moments via their partial occupation, but also offering exchange interactions through their direct or indirect hybridization. Here, we report atomic-orbital-free intrinsic ferromagnetism in monolayer electrides or electrenes, in which excess electrons act as anions. Taking the honeycomb LaBr2(La3+Br2-.e(-)) as an example, our first-principles calculations, in combination with a low-energy effective model in the basis of the Wannier function and Anderson's superexchange theory, reveal that the excess electron is localized at the center of the hexagon, which leads to the spontaneous formation of a local moment due to the strong Stoner instability of the associated state near the Fermi level (E-f). The large off-site Coulomb interaction and extended tails of both wave and Wannier functions indicate a significant spatial extension of the anionic electron state in LaBr2. The overlap of the long tails mediates an extended ferromagnetic direct exchange to second-nearest neighbors (up to 7-8 angstrom), in sharp contrast to the conventional direct exchange which is short ranged due to the overlap of atomic orbitals with limited spatial extension. The dual nature, localization and extension, of the anionic electron state results in a unique magnetic mechanism in such atomic-orbital-free intrinsic two-dimensional ferromagnets.