We report intrinsic ferromagnetism in monolayer electrides or electrenes, in which excess electrons act as anions. Our first-principles calculations demonstrate that magnetism in such electron-rich two-dimensional (2D) materials originates from the a
nionic electrons rather than partially filled d orbitals, which is fundamentally different from ferromagnetism found in other 2D intrinsic magnetic materials. Taking the honeycomb LaBr$_2$ (La$^{3+}$Br$^{-}_{2}cdot e^{-}$) as an example, our calculations reveal that the excess electron is localized at the center of the hexagon, which leads to strong Stoner-instability of the associated states at the Fermi energy, resulting in spontaneous magnetization and formation of a local moment. The overlap of extended tails of the wave functions of these electrons mediates a long-range ferromagnetic interaction, contributing to a Curie temperature ($T_textrm{c}$) of 235 K and a coercive field ($H_textrm{c}$) of 0.53 T, which can be further enhanced by hole doping. The dual nature, localization and extension, of the electronic states suggests a unique mechanism in such magnetic-element-free electrenes as intrinsic 2D ferromagnets.
We show that when a molecular junction is under an external bias, its properties can not be uniquely determined by the total electron density in the same manner as the density functional theory (DFT) for ground state (GS) properties. In order to corr
ectly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived.By generalizing the Thomas-Fermi-Dirac (TFD) model to non-equilibrium cases, we analytically derived the DMF exchange energy density functional. We implemented the DMF approach into the computational package SIESTA to study non-equilibrium electron transport through molecular junctions. Calculations for a graphene nanoribbon (GNR) junction show that compared with the commonly used textit{ab initio} transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region.
Recent experimental study reveals the optical conductivity of La$_{1-x}$Ca$_x$MnO$_3$ over a wide range of energy and the occurrence of spectral weight transfer as the system transforms from paramagnetic insulating to ferromagnetic metallic phase [Ru
sydi {it et al.}, Phys. Rev. B {bf 78}, 125110 (2008)]. We propose a model and calculation within the Dynamical Mean Field Theory to explain this phenomenon. We find the role of oxygens in mediating the hopping of electrons between manganeses as the key that determines the structures of the optical conductivity. In addition, by parametrizing the hopping integrals through magnetization, our result suggests a possible scenario that explains the occurrence of spectral weight transfer, in which the ferromagnatic ordering increases the rate of electron transfer from O$_{2p}$ orbitals to upper Mn$_{e_g}$ orbitals while simultaneously decreasing the rate of electron transfer from O$_{2p}$ orbitals to lower Mn$_{e_g}$orbitals, as temperature is varied across the ferromagnetic transition. With this scenario, our optical conductivity calculation shows very good quantitative agreement with the experimental data.
