The fluctuations of the magnetic order parameter, or longitudinal spin excitations, are investigated theoretically in the ferromagnetic Fe and Ni as well as in the antiferromagnetic phase of the pnictide superconductor FeSe. The charge and spin dynamics of these systems is described by evaluating the generalized charge and spin density response function calculated from first-principles linear response time dependent density functional theory within adiabatic local spin density approximation. We observe that the formally non-interacting Kohn-Sham system features strong coupling between the magnetization and charge dynamics in the longitudinal channel and that the coupling is effectively removed upon the inclusion of the Coulomb interaction in the charge channel and the resulting appearance of plasmons. The longitudinal spin fluctuations acquire a collective character without the emergence of the Goldstone boson, similar to the case of paramagnon excitations in non-magnetic metals like Pd. In ferromagnetic Fe and Ni the longitudinal spin dynamics is governed by interactions between low-energy intraband electron-hole pairs while in quasi two dimensional antiferromagnet FeSe it is dominated by the interband transitions with energies of the order of exchange splitting. In the later material, the collective longitudinal magnetization fluctuations feature well defined energies and long life times for small momenta and appear below the particle-hole continuum. The modes become strongly Landau-damped for growing wave-vectors. We relate our theoretical findings to existing experimental spin-polarized electron energy loss spectroscopy results. In bulk bcc Fe, the longitudinal magnetic modes appear above the typical energies of transverse spin-waves, have energies comparable with the Stoner spin-flip excitation continuum, and are order of magnitude less energetic than the charge dynamics.
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