2) In class we discussed how non-interacting spins align with an external magnetic field. For quantum...
2) In class we discussed how non-interacting spins align with an external magnetic field. For quantum spins in three dimensions the magnetization can be written HeffB М 3 пиеg B, (а), а — Heff = g)where kвт 2J+1 coth (acotha 2J+1 :a) is the Brillouin function В (а) 2J 2J JU+1)+S(S+1)+L (L+ 1) and g 1 is the Lande g-factor 2J+1) Here will specialize to the case J1/2 (L=0, S=1/2). a) Calculate the Lande g-factor for this case b) Starting from the general expression above for B,(a), show that B1/2 (a) = tanha c) Plot M/nuef vs H from 0 to 10 Tesla, for temperatures of 2K, 5K, and 10K. For each temperature, over what magnetic field range is M xH?