A magnet has two poles, as any child can tell you. However, the familiar dipole configuration is not the only one that a magnet can have. The configuration of any magnet is the result of several competing energies: the exchange energy of interaction among the atomic moments, the magnetostatic energy of the magnetic field itself, and the magnetocrystalline anisotropy energy. The relative importance of each of the three energies depends on the size, shape, and material properties of the magnet.
The exchange interaction is what causes magnetic ordering in the first place. The most common representation of exchange energy is the Heisenberg interaction of , a sum of interactions with strength Jij between neighboring moments S on sites i and j. The minus sign ensures that when Jij > 0, the lowest exchange energy is found...
