So upon reading through "Quantum Theory of Magnetism" by Nolting and Ramakanth I saw the derivation of the Stoner excitations as spin flip excitations (in this case for free electrons) in which the excitation continuum looks like this:
which I agree with. Reading in another called "Elementary spin excitations in ultrathin itinerant magnets" by Khalil Zakeri I found the stoner continuum to look like this (picture on the right):
which I do not quite understand (since this seems more like root functions enclosing the continuum area rather than parabolas). Do these graphs talk about different things? Since I thought they both describe the excitation continuum. Would appreciate an explanation or maybe further recourses which go deeper into it.