= Inelastic neutron scattering
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<Inelastic neutron scattering> resolves $E_i-E_f\ne0$. Through <conservation of energy>, a peak at positive $\hbar\omega$ identifies an allowed excitation <energy>; through <momentum conservation>, its location in $\mathbf Q$ constrains the spatial variation of that excitation. A <phonon> is a quantum of lattice vibration; a <magnon> is a quantum of a <spin wave>. Their different couplings make <energy> transfer alone insufficient to identify which was created.
<Bertram Neville Brockhouse>'s <aluminium> experiment rotated a large single <crystal>, scanning analyzer angle for neutron groups. His <vanadium> comparison exposed the elastic resolution. Later <magnetite> measurements used a <magnetic field> intensity test to identify <magnons>.<Slow Neutron Spectroscopy and the Grand Atlas of the Physical World by Bertram Neville Brockhouse>[1994 lecture, pp. 115–121, Figs. 3–6]{ref}
Successive orientations sample different <wave vectors>; analyzer settings distinguish outgoing <energies>. This supplies points on a <dispersion relation>, rather than only an angular diffraction pattern. Finite resolution can merge neighboring excitations; background, multiple scattering and processes involving several <phonons> can complicate interpretation. A lattice model is a testable explanation of selected features, not a guarantee that every spectral peak has the same origin.
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