= Itinerant spin-flip particle-hole continuum
Spin reversal in exchange-split bands creates an electron-hole excitation with energy $\epsilon_{k+q}-\epsilon_k+2M$ for a majority-to-minority flip in the simple uniform model with $M>0$. Its allowed continuum depends on occupied initial and empty final states. At $q=0$ all such allowed transitions have exchange energy $2M$; finite momentum changes the thresholds. A collective <ferromagnetic magnon> can remain gapless below this continuum when spin rotation is exact. The continuum is not the same excitation as a longitudinal amplitude mode.
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