Effects of Compensation on the Galvanomagnetic Properties of Nonmagnetic and Ferromagnetic Metals

Measurements of the galvanomagnetic properties of nickel in the high-field region are described. For a general field direction the magnetoresistance saturates and the Hall coefficient is linear with the field and corresponds within experimental error to one electron per atom. This behavior is at variance with the systematic rules for the observed galvanomagnetic properties of nonmagnetic metals, from which one expects nickel to behave like a compensated metal, having a quadratic magnetoresistance and a vanishingly small Hall coefficient at sufficiently high fields. The theoretical explanation of these rules has been known qualitatively for some time, but is here developed rigorously and shown to account for the available experimental data for nonmagnetic metals in the high-field region. The theory is extended to ferromagnetic metals by considering the effect of removing the spin degeneracy of the energy bands. It is shown that the behavior of nickel can then be explained in terms of a simple model in which one spin-up (higher energy) sheet of the Fermi surface in a single spin zone of the $d$ band has an electron character. The observed approach to compensated behavior of iron is consistent with the theory, and indicates that an alternative explanation of the behavior of nickel in terms of a low mobility in the $d$ bands is unlikely to be true.