Bethe–Slater curve

File:Bethe-Slater curve by Zureks.svg

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

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.

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

For a pair of atoms, the exchange interaction w_ij (responsible for the energy E) is calculated as:

$w_{ij}= - 2 \cdot J \cdot S_i \cdot S_j$

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