Adiabatic generalized gradient approximation kernel in time-dependent density functional theory

Abstract

A complete understanding of a material requires both knowledge of the excited states as well as of the ground state. In particular, the low energy excitations are of utmost importance while studying the electronic, magnetic, dynamical, and thermodynamical properties of the material. Time-Dependent Density Functional Theory (TDDFT), within the linear regime, is a successful ab-initio method to access the electronic charge and spin excitations. However, it requires an approximation to the exchange-correlation (XC) kernel which encapsulates the effect of electron-electron interactions in the many-body system. In this work we derive and implement the spin-polarized XC kernel for semi-local approximations such as the adiabatic Generalized Gradient Approximation (AGGA). This kernel has a quadratic dependence on the wavevector, q, of the perturbation, however the impact of this on the electron energy loss spectra (EELS) is small. Although the GGA functional is good in predicting structural properties, it generality overestimates the exchange spin-splitting. This leads to higher magnon energies, as compared to both ALDA and experiment. In addition, interaction with the Stoner spin-flip continuum is enhanced by AGGA, which strongly suppresses the intensity of spin-waves. arXiv:1808.00215v1 [cond-mat.mtrl-sci] 1 Aug 2018

Dynamic transverse magnetic susceptibility in the projector augmented-wave method: Application to Fe, Ni, and Co

“…This is in contrast to the → N direction, in which the magnon mode remains well defined throughout the entire first BZ with a single plateau around 150 meV and a total bandwidth of 337 meV. The observed jumps in magnon dispersion as well as the disappearance of the magnon mode in the → H direction agree well with previous theoretical results [16,18,24,26,27,33]. The magnon frequency jumps arise because the magnon mode crosses stripe-like features in the Kohn-Sham spectrum corresponding to well-defined Stoner excitations residing below the main Stoner continuum.…”

“…Through a systematic convergence analysis, we pinpoint contributions to the gap error from different computational parameters and show that the problem can be effectively overcome by applying a gap error correction procedure. This conclusion validates the common practice in the literature [24][25][26][27]. Furthermore, we discuss the convergence of magnon modes inside the Stoner continuum, the transverse magnetic continuum of single-particle excitations.…”

“…The crystal structures of the transition metals investigated are described using ASE [40] with experimental lattice constants a = 2.867 Å for bcc-Fe, a = 3.524 Å for fcc-Ni, a = 3.539 Å for fcc-Co and a = 2.507 Å for hcp-Co taken from [24,27] and the references therein. We investigate only reduced wave vectors q commensurate with the Monkhorst-Pack grid of the ground state calculation.…”

“…Regarding the latter, one needs to use an exchange-correlation kernel that in the static limit gives the same ground state spin densities as the ground state DFT calculation, on the basis of which the Kohn-Sham susceptibility is computed. Otherwise, (δW μ s (r, t )) cannot be considered a perturbative quantity, so that the linear response relation (27) and consequently also the Dyson equation ( 28) no longer holds. As an example, using an ALDA kernel on top of a GGA ground state calculation will result in a gap error, which is why we are restricted to the use of LDA for the ground state at present.…”

“…11(c) the extracted dispersion in magnon peak positions along the → N direction is compared with experimental as well as ab initio references. Singh [27], Rousseau [26], Buczek [24], and coworkers use different implementations of the LR-TDDFT methodology in the ALDA, removing the gap error by applying a constant frequency shift, adding a corrective contribution to χ +− KS and forcing the smallest q = 0 energy eigenvalue of χ +− to zero, respectively. Müller and coworkers [17] apply MBPT in the LDA, but with an ad hoc adjustment of the exchange splitting to remove the gap error.…”