We examine the ultrafast demagnetization process of iron-based materials, namely, ${\mathrm{Fe}}_{6}$ clusters and bulk bcc Fe, with time-dependent spin-density functional theory (TDSDFT). The magnetization continuity equation is reformulated and the torque due to the spin-current divergence is written in terms of an effective time-dependent kinetic magnetic field, an object already introduced in the literature. Its time evolution, as extracted from the TDSDFT simulations, is identified as one of the main sources of the local out-of-equilibrium spin dynamics and it plays a major role in the demagnetization process in combination with the spin orbit interaction. Such demagnetization is particularly strong in hot spots where the kinetic torque is maximized. Finally, we find the rate of demagnetization in ${\mathrm{Fe}}_{6}$ to be strongly dependent on the direction of polarization of the exciting electric field and this can be linked to the out-of-equilibrium distribution of the kinetic field in two comparative cases.