Band Model for Hall Effect, Magnetization, and Resistivity of Magnetic Metals

The ordinary Hall coefficients for Cu, Ni, Co, and the binary alloys of these elements agree to within a factor of two with predictions based upon the usual band model in which the number of conduction electrons per atom is postulated to be the number, $n_s=0.6\mathrm{}$, of $4s$ electrons required to explain the saturation magnetization in these materials. The factor of two, however, created a dilemma, since both the magnetization data and the Hall data were accurately determined. The Hall results appeared to require that $n_s<0.3\mathrm{}$ whereas the magnetization data requires that $n_s>0.54\mathrm{}$. It will be shown that this dilemma disappears when the $4s$ band is considered divided into two parts in which the electrons with spins parallel to the spontaneous magnetization have much greater mobility than those with spins antiparallel. According to Mott, the antiparallel electrons have low mobility, because they can be scattered into the partially empty $3d$ band, whereas the parallel electrons cannot.