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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: enter image description here

enter image description here

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): enter image description here 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.

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I think Fig.1(b) from Zakeri is consistent with Fig.8.6(b) from Nolting and Ramakanth. Note that as we see in Fig.1(a), in this case, the ferromagnetism is at its maximum. Therefore the minimum of Stoner continuum is finite ($\omega_{min}=\delta$).