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Unformatted text preview: x ) N ↓ N e = 1 2 (1-x ) (2) where N ↑ ( ↓ ) is the total number of up-spins (down-spins) 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 Particle-Hole Excitations in Itinerant Ferromagnets In section 7.3 of the lecture notes the low-energy spectrum of (magnons) spin-waves in itinerant ferromagnets was derived. It is crucial for the existence of well-deﬁned magnons that elementary particle-hole 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