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As I understand it, in a ferromagnetic material unpaired electrons on the atomic sites interact (exchange interaction) with nearest neighbours, aligning the moments and producing the magnetisation that we can measure. However, ferromagnets also have additional conduction electrons. My question is, do these conduction electrons contribute at all to the spontaneous magnetisation we see? Or is it purely an atomic electron phenomenon?

Thanks

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The contribution of the $4sp$ bands to the total moment in iron, nickel and cobalt is quite negligible compared to that of the $3d$ electrons. It is also oscillating as a function of the electron wave vector. Several experiments show that there are effects: hyperfine effects (Mössbauer), NMR (Knight shift) and spin-dependent STM show that $s$ orbitals are spin-polarized. The conductivity of the transition metals is lower than eg copper because of scattering processes involving $3d$ orbitals. This also involves spin: there are anomalies in the resistivity near the Curie temperature.

Then there are of course theoretical models of the electronic structure. But those models have their limitations, and assigning spin to different orbitals is somewhat arbitrary.

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