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Unformatted text preview: x ) N ↓ N e = 1 2 (1x ) (2) where N ↑ ( ↓ ) is the total number of upspins (downspins) and N e is the total number of electrons. Minimize the total energy of the system with respect to x . Plot the polarization of the system x as a function of N ( ± F ) U . Exercise 13.3 ParticleHole Excitations in Itinerant Ferromagnets In section 7.3 of the lecture notes the lowenergy spectrum of (magnons) spinwaves in itinerant ferromagnets was derived. It is crucial for the existence of welldeﬁned magnons that elementary particlehole excitations are gapped. Try to explain (without detailed calculations) why there is such a gap and why it is important for the observability of magnons! Oﬃce hour: Monday, May 30th, 2011  9:00 to 11:00 am HIT K 12.1 Jonathan Buhmann...
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 Spring '11
 Sigrist

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