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From what I understand, for example in the Ising model, we can probe the correlation function via neutron scattering, and the correlation function gives the magnetic susceptibility for the system. Is there a correlation function characteristics of spin waves, or something for us to know that it is there? Looking at the visualization like this enter image description here

I imagine we must have some correlation between the spins. Furthermore, is there a throughout reference on this topic? Thank you!

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  • $\begingroup$ The ferromagnetic spin waves have a dispersion $\omega \propto k^2$, which may be detected by measuring the temperature dependence of the specific heat. $\endgroup$
    – Archisman Panigrahi
    Commented Apr 7 at 19:08
  • $\begingroup$ Thank you for the comment. Can you give a more specific answer? $\endgroup$
    – Kim Dong
    Commented Apr 7 at 20:27

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There are many thorough references on this topic.

A "spin wave" / "magnon" shows up in the spin-spin correlator of the system, which is seen by neutron scattering. Specifically, it measures the correlator $$ \langle S^+(q, \omega)S^-(-q,0)\rangle $$ which in linear spin wave theory [in a nutshell: one equates spin raising (lowering) with the creation (annihilation) of a boson] is proportional to

$$ \langle a^\dagger(q, \omega)a(-q,0)\rangle $$

i.e. the propagator of a free Boson field (that can be calculated analytically). One may then dress these magnons by interactions in the usual perturbative way.

Triple-axis single crystal measurements can measure sharp, dispersive excitations in most conventional magnets. We are inclined to call these 'magnons' because they

  • Correspond to the flip of a neutron spin, i.e. are spin 1,
  • Have a dispersion that generally matches spin-wave theory predictions,
  • Can be tuned by magnetic field in the way spin wave theory predicts, to very good precision.
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