# Bethe–Slater curve

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Bethe–Slater curve: elements above the horizontal axis are ferromagnetic, and those below are antiferromagnetic

The Bethe–Slater curve is a graphical representation of exchange energy for transition metals as a function of the ratio of the interatomic distance a to the radius r of the 3d electron shell.[1]

The curve illustrates why certain metals are ferromagnetic and other antiferromagnetic.

For a pair of atoms, the exchange interaction wij (responsible for the energy E) is calculated as:[2]

${\displaystyle w_{ij}=-2J_{ex}S_{i}\cdot S_{j}}$

where: J = exchange integral; S = electron spins; i and j = indices of the two atoms.