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I am reading about electronic structure. The book uses the homogeneous electron gas as a model. The book uses the terms ‘polarised’, ‘unpolarised’ and ‘partially polarised’ in relation to electron spin, but these terms have not been defined. What do they mean in this context, and how can I determine if I am working with a system that is polarised, partially polarised or unpolarised?

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The context is not clear, but these terms were once introduced to me when I learned about the prediction of ferromagnetism in the Hartree-Fock approximation of a Fermi gas. See for example chapter 32 of Ashcroft and Mermin.

An electron gas is polarised when the exchange energy is sufficiently large such that all spins align, resulting in a nonzero net magnetization. In contrast, the electron gas in completely unpolarised if there is an equal amount of spin up electron and spin down electrons, such that the net magnetization vanishes. The partially polarised case will be the intermediate case.

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