Ferromagnetic Exchange Between Coupled Pairs of Electrons

Incomplete shells of 3d electrons in the first transition series of elements are responsible for the ferromagnetism of these elements, but the parallel coupling of the spins of these electrons remains an assumption in the theory of ferromagnetism. It is required that exchange interaction between the 3d electrons of neighbouring atoms should be positive (the sign causing parallel alignment of spins). Mathematically, treatment of ferromagnetic exchange is similar to that of the homopolar chemical bond, in which it is clear that exchange interaction is negative, giving a lower energy for antiparallel spins than for parallel spins. Mathematical difficulties have prevented any adequate demonstration that the reverse is the case in ferromagnetism.