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

TL;DR

This paper derives and implements a spin-polarized XC kernel within TDDFT using the GGA approximation, analyzing its effects on electron energy loss spectra and magnetic excitations.

Contribution

It introduces a quadratic wavevector-dependent XC kernel for spin-polarized TDDFT with GGA, and evaluates its impact on magnetic excitation spectra.

Findings

AGGA kernel has a small impact on EELS despite quadratic q dependence

GGA overestimates exchange spin-splitting, leading to higher magnon energies

Interaction with Stoner continuum suppresses spin-wave intensity

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 \textit{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, {\bf 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.