  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.
