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I am taking a course on solid state physics. The class is mostly based on Ashcroft-Mermin's "Solid State Physics". Yesterday I sat for an exam and there was a question I couldn't answer: "Which interaction is the responsible for long-range magnetism?"

After the exam, we were discussing about it with the the rest of the classmates. Some said it was spin-spin interaction, but that doesn't make any sense to me, I don't even know what that would mean. Some others said it was wrong to say dipole-dipole... but no one was certain.

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Exchange interaction, which is a fancy way of saying spin-spin interaction. However, conditions have to be right (below Curie temperature) otherwise entropy washes the order out.

Two electrons have a total wavefunction $\psi(x_1,x_2, s_1, s_2)$ that is antisymmetric (changes sign) when we interchange $x_1,x_2$ and $s_1, s_2$ (Pauli exclusion principle). You can generalize to any number of identical fermions).

The Coulomb repulsion between two electrons is lower when they are in a spin-aligned state, because by the Pauli exclusion principle, they can't be in the same position, so their combined wavefunction $\psi(x_1,x_2)$ goes to zero when $x_1 \approx x_2$. In other words, they have less probability to be in a position where the electrical potential energy is highest. This state has lower energy. (Convince yourself that $\psi(x_1, x_2, \uparrow, \uparrow) = 0$ if $x_1 = x_2$)

Of course, if their spins are anti-aligned, then they can be close together, so that wavefunction has has a greater probability for them to be in a position where the electrical potential energy is highest. This state has higher energy.

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  • $\begingroup$ Hi: I'd already read that wikipedia entry and I get confused with last paragraph under "Exchange Interactions between localized electron magnetic moments">>"Effects of exchange", it says: "Normally, exchange interactions are very short-ranged, confined to electrons in orbitals on the same atom (intra-atomic exchange) or nearest neighbor atoms (direct exchange) but longer-ranged interactions can occur via intermediary atoms and this is termed Superexchange." When talking about exchange you mean no direct but also indirect and super exchange? $\endgroup$
    – myradio
    Dec 4 '13 at 21:00
  • $\begingroup$ Well, the exchange interaction is the cause of the over-all effect. $\endgroup$ Dec 4 '13 at 21:34

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