  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.
