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Register a new userDensity functional theory study of vacancy induced magnetism in Li$_{3}$N
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The effect of lithium vacancies in the hexagonal structure of $alpha-$Li$_3$N, is studied within the framework of density functional theory. Vacancies ($square$) substituting for lithium in $alpha-$Li$_2$(Li$_{1-x}square_x$)N are treated within the coherent potential approximation as alloy components. According to our results long range N($p$)-ferromagnetism ($sim 1$ $mu_B$) sets in for vacancy substitution within the [Li$_2$N] layers ($x ge 0.7$) with no significant change in unit cell dimensions. By total energies differences we established that in-plane exchange couplings are dominant. Vacancies substituting inter-plane Li, leads to a considerable structural collapse ($c/a approx 0.7$) and no magnetic moment formation.
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Density functional theory (DFT) calculations are used to investigate the electronic and magnetic structures of a two-dimensional (2D) monolayer Li$_{2}$N. It is shown that bulk Li$_{3}$N is a non-magnetic semiconductor. The non-spinpolarized DFT calculations show that $p$ electrons of N in 2D Li$_{2}$N form a narrow band at the Fermi energy $E_{rm{F}}$ due to a low coordination number, and the density of states at the Fermi energy ($g(E_{rm{F}}$)) is increased as compared with bulk Li$_{3}$N. The large $g(E_{rm{F}}$) shows instability towards magnetism in Stoners mean field model. The spin-polarized calculations reveal that 2D Li$_{2}$N is magnetic without intrinsic or impurity defects. The magnetic moment of 1.0,$mu_{rm{B}}$ in 2D Li$_{2}$N is mainly contributed by the $p_{z}$ electrons of N, and the band structure shows half-metallic behavior. {Dynamic instability in planar Li$_{2}$N monolayer is observed, but a buckled Li$_{2}$N monolayer is found to be dynamically stable.} The ferromagnetic (FM) and antiferromagnetic (AFM) coupling between the N atoms is also investigated to access the exchange field strength. {We found that planar (buckled) 2D Li$_{2}$N is a ferromagnetic material with Curie temperature $T_{c}$ of 161 (572) K.}
textit{Ab-initio} calculations based on density functional theory with local spin density approximation are used to study defects-driven magnetism in bulk $alpha$-Li$ _{3}$N. Our calculations show that bulk Li$ _{3} $N is a non-magnetic semiconductor. Two types of Li vacancies (Li-I and Li-II) are considered, and Li-vacancies (either Li-I or Li-II type) can induce magnetism in Li$ _{3}$N with a total magnetic moment of 1.0 $mu_{rm B}$ which arises mainly due to partially occupied N-$p$-orbitals around the Li vacancies. The defect formation energies dictate that Li-II vacancy, which is in the Li$ _{2}$N plane, is thermodynamically more stable as compared with Li-I vacancy. The electronic structures of Li-vacancies show half-metallic behavior. On the other hand N-vacancy does not induce magnetism and has a larger formation energy than Li-vacancies. N vacancy derived bands at the Fermi energy are mainly contributed by the Li atoms. Carbon is also doped at Li-I and Li-II sites, and it is expected that doping C at Li-I site is thermodynamically more stable as compared with Li-II site. Carbon can induce metallicity with zero magnetic moment when doped at Li-I site, whereas magnetism is observed when Li-II site is occupied by the C impurity atom and C-driven magnetism is spread over the N atoms as well. Carbon can also induce half-metallic magnetism when doped at N site in Li$ _{3}$N, and has a smaller defect formation energy as compared with Li-II site doping. The ferromagnetic (FM) and antiferromagnetic (AFM) coupling between the C atoms is also investigated, and we conclude that FM state is more stable than the AFM state.
The magnetic properties of the intermetallic compound FeAl are investigated using exact exchange density functional theory. This is implemented within a state of the art all-electron full potential method. We find that FeAl is magnetic with a moment of 0.70 $mu_B$, close to the LSDA result of 0.69 $mu_B$. A comparison with the non-magnetic density of states with experimental negative binding energy result shows a much better agreement than any previous calculations. We attribute this to the fine details of the exchange field, in particular its asymmetry, which is captured very well with the orbital dependent exchange potential.
Modeling layered intercalation compounds from first principles poses a problem, as many of their properties are determined by a subtle balance between van der Waals interactions and chemical or Madelung terms, and a good description of van der Waals interactions is often lacking. Using van der Waals density functionals we study the structures, phonons and energetics of the archetype layered intercalation compound Li-graphite. Intercalation of Li in graphite leads to stable systems with calculated intercalation energies of $-0.2$ to $-0.3$~eV/Li atom, (referred to bulk graphite and Li metal). The fully loaded stage 1 and stage 2 compounds LiC$_6$ and Li$_{1/2}$C$_6$ are stable, corresponding to two-dimensional $sqrt3timessqrt3$ lattices of Li atoms intercalated between two graphene planes. Stage $N>2$ structures are unstable compared to dilute stage 2 compounds with the same concentration. At elevated temperatures dilute stage 2 compounds easily become disordered, but the structure of Li$_{3/16}$C$_6$ is relatively stable, corresponding to a $sqrt7timessqrt7$ in-plane packing of Li atoms. First-principles calculations, along with a Bethe-Peierls model of finite temperature effects, allow for a microscopic description of the observed voltage profiles.
The study of zinc oxide, within the homogeneous electron gas approximation, results in overhybridization of zinc $3d$ shell with oxygen $2p$ shell, a problem shown for most transition metal chalcogenides. This problem can be partially overcome by using LDA+$U$ (or, GGA+$U$) methodology. However, in contrast to the zinc $3d$ orbital, Hubbard type correction is typically excluded for the oxygen $2p$ orbital. In this work, we provide results of electronic structure calculations of an oxygen vacancy in ZnO supercell from ab initio perspective, with two Hubbard type corrections, $U_{mathrm{Zn}-3d}$ and $U_{mathrm{O}-2p}$. The results of our numerical simulations clearly reveal that the account of $U_{mathrm{O}-2p}$ has a significant impact on the properties of bulk ZnO, in particular the relaxed lattice constants, effective mass of charge carriers as well as the bandgap. For a set of validated values of $U_{mathrm{Zn}-3d}$ and $U_{mathrm{O}-2p}$ we demonstrate the appearance of a localized state associated with the oxygen vacancy positioned in the bandgap of the ZnO supercell. Our numerical findings suggest that the defect state is characterized by the highest overlap with the conduction band states as obtained in the calculations with no Hubbard-type correction included. We argue that the electronic density of the defect state is primarily determined by Zn atoms closest to the vacancy.
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