# Question: conduction electron ferromagnetism we approximate the effect of exchange interactions...

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**Conduction electron ferromagnetism**

We approximate the effect of exchange interactions among the conduction electrons if we assume that electrons with parallel spins interact with one another with energy , and is positive, while electrons with antiparallel spins do not interact with each other.

1) Show that the total energy of the spin-up band is given by , where is the total number of electrons. Find a similar expresion for . Hint: consider that the number of pairs of electrons with parallel spin-up and spin-downs is and respectively.

2) Minimize the total energy density , then solve for . Show the magnetization is , where is the total electron density, so that the exchange interaction enhances the susceptibility.

3) Finally, show that with , the total energy is unstable at when .