# Bethe-Slater curve

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.[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]

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

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