Ferromagnetic Hall Effect with Electron-Phonon Interactions

A theoretical analysis, based on Kubo's formalism of current correlation functions, is made for the ferromagnetic Hall effect in the case of transport limited by electron-phonon scattering. The antisymmetric, off-diagonal conductivity is, to first order in the magnetization, found to be of order zero in the electron-phonon interaction (assumed to be weak) and, to this order, is equivalent to Karplus and Luttinger's results. Several corrections are analyzed and found to be of higher order in the scattering potential. The analysis is carried through for monocrystalline iron by using Wood's dispersion curves. It is found that Rₛ=+0.55×10^-12 {Ω} cm/G at T=293^∘K, which has the correct sign and is smaller, by a factor of roughly 1/3, than Dheer's experimental values for iron whiskers. Our temperature dependence of Rₛ is almost entirely as ρₓₓ², which fails to explain the temperature dependence of Rₛ below 75^∘{}K in iron whiskers.