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

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 assess 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 semilocal approximation, the so-called adiabatic generalized gradient approximation (AGGA). This kernel has a quadratic dependence on the wave vector q of the perturbation, however the impact of this on the electron energy loss spectra (EELS) is small. We show that the AGGA generally worsens the spin-excitation spectra by overestimating the magnon energies and suppressing the intensity of spin waves.