From ultrasoft pseudopotentials to the projector augmented-wave method
TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.
Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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TL;DR: In this paper, it was shown that spin polarization due to spin-orbit coupling requires broken inversion symmetry, rather than global space-group asymmetry, and that a hitherto overlooked form of spin polarization should also exist in centrosymmetric structures.
Abstract: Spin polarization due to spin–orbit coupling requires broken inversion symmetry. Now, calculations show that the effect arises from local site-asymmetry rather than global space-group asymmetry, and that a hitherto overlooked form of spin polarization should also exist in centrosymmetric structures.
400 citations
TL;DR: In this paper, the authors used density functional theory (DFT) and generalized gradient approximation (GGA) to find an antiferromagnetic ground state at the experimental volume, which is 388 meV/(Fe atom) below the ferromagnetic solution.
Abstract: Rhombohedral $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ has been studied by using density-functional theory (DFT) and the generalized gradient approximation (GGA). For the chosen supercell all possible magnetic configurations have been taken into account. We find an antiferromagnetic ground state at the experimental volume. This state is 388 meV/(Fe atom) below the ferromagnetic solution. For the magnetic moments of the iron atoms we obtain $3.4{\ensuremath{\mu}}_{\mathrm{B}},$ which is about $1.5{\ensuremath{\mu}}_{\mathrm{B}}$ below the experimentally observed value. The insulating nature of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ is reproduced, with a band gap of 0.32 eV, compared to an experimental value of about 2.0 eV. Analysis of the density of states confirms the strong hybridization between Fe $3d$ and O $2p$ states in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}.$ When we consider lower volumes, we observe a transition to a metallic, ferromagnetic low-spin phase, together with a structural transition at a pressure of 14 GPa, which is not seen in experiment. In order to take into account the strong on-site Coulomb interaction U present in ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ we also performed $\mathrm{D}\mathrm{F}\mathrm{T}+U$ calculations. We find that with increasing U the size of the band gap and the magnetic moments increase, while other quantities such as equilibrium volume and Fe-Fe distances do not show a monotonic behavior. The transition observed in the GGA calculations is shifted to higher pressures and eventually vanishes for high values of U. Best overall agreement, also with respect to experimental photoemission and inverse photoemission spectra of hematite, is achieved for $U=4\mathrm{eV}.$ The strength of the on-site interactions is sufficient to change the character of the gap from $d\ensuremath{-}d$ to $\mathrm{O}\ensuremath{-}p\ensuremath{-}\mathrm{Fe}\ensuremath{-}d.$
400 citations
TL;DR: SeeK-path as discussed by the authors is a free online service to compute and visualize the first Brillouin zone, labeled k -points and suggested band paths for any crystal structure, that made available at http://www.materialscloud.org/tools/seekpath/.
399 citations
TL;DR: In this article, periodic spin-polarized density functional theory (DFT) predictions of hydrogen adsorption, absorption, dissolution, and diffusion energetics on and in ferromagnetic (FM) body-centered cubic (bcc) iron are reported.
Abstract: We report periodic spin-polarized density functional theory (DFT) predictions of hydrogen adsorption, absorption, dissolution, and diffusion energetics on and in ferromagnetic (FM) body-centered cubic (bcc) iron. We find that H prefers to stay on the Fe surface instead of subsurfaces or in bulk. Hydrogen dissolution in bulk Fe is predicted to be endothermic, with hydrogen occupying tetrahedral (t) sites over a wide range of concentrations. This is consistent with the known low solubility of H in pure Fe. In the initial absorption step, we predict that H occupies the deep subsurface t-site for Fe(110) and the shallow subsurface t-site for Fe(100). Diffusion of H into Fe subsurfaces is predicted to have a much lower barrier for Fe(100) than Fe(110). For H diffusion in bulk Fe, we find that H diffuses through bcc Fe not via a straight line trajectory, but rather hops from one t-site to a neighboring t-site by a curved path. Moreover, we exclude a previously suggested path via the octahedral site, due to its higher barrier and the rank of the saddle point. Quantum effects on H diffusion through bulk Fe are discussed.
399 citations
TL;DR: In this article, the electronic and magnetic properties of Mn-doped monolayer MoS were investigated using a combination of first-principles density functional theory (DFT) calculations and Monte Carlo simulations.
Abstract: We investigate the electronic and magnetic properties of Mn-doped monolayer MoS${}_{2}$ using a combination of first-principles density functional theory (DFT) calculations and Monte Carlo simulations. Mn dopants that are substitutionally inserted at Mo sites are shown to couple ferromagnetically via a double-exchange mechanism. This interaction is relatively short ranged, making percolation a key factor in controlling long-range magnetic order. The DFT results are parameterized using an empirical model to facilitate Monte Carlo studies of concentration- and temperature-dependent ordering in these systems, through which we obtain Curie temperatures in excess of room temperature for Mn doping in the range of 10--15$%$. Our studies demonstrate the potential for engineering a new class of atomically thin dilute magnetic semiconductors based on Mn-doped MoS${}_{2}$ monolayers.
399 citations
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Book•
31 Dec 1993
TL;DR: The linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged.
Abstract: With its extreme accuracy and reasonable computational efficiency, the linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. This volume presents a thorough and self-conta
1,150 citations