Ferromagnetic Hall Effect with Electron-Phonon Interactions

Abstract

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 electronphonon 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 R s = +0.55 X10 -12 £} cm/G at r=293°K, which has the correct sign and is smaller, by a factor of roughly J, than Dheer's experimental values for iron whiskers. Our temperature dependence of R s is almost entirely as p xx 2 , which fails to explain the temperature dependence of R s below 75°K in iron whiskers.

First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe

“…Although the effect has been recognized for more than a century [2], it is still somewhat poorly understood, a circumstance reflected by the controversial and sometimes confusing literature on the subject. Previous theoretical work has failed to explain the magnitude of the observed effect even in well understood materials like Fe [4].…”

“…[The only previous evaluation of the AHC of which we are aware [4] found that xy 20:9 cm ÿ1 for Fe.] The remaining discrepancy between theory and experiment is likely due to shortcomings of the GGA, neglect of scattering effects, and experimental uncertainties.…”

Scaling of the anomalous Hall current in Fe100−x(SiO2)Xu1, Zhang2, Wang3 et al. 2011Phys. Rev. B

“…However, it has not been possible to compare the theories and experiments quantitatively because it is very difficult to model the scattering potentials in real materials. 5,6 Only recently, the intrinsic mechanism proposed by Karplus and Luttinger was re-examined. [6][7][8][9][10] It was found that the anomalous Hall conductivity can indeed be caused by the Berry curvatures in momentum space, [6][7][8][9][10] where the Berry curvature is defined by n (k) = −Im ∇ k u nk | × |∇ k u nk , where u nk is the Bloch wave function in the nth band.…”

Overlooked contribution to the Hall effect in ferromagnetic metals

“…Later, it was proposed that in addition to skew scattering a 'side-jump' occurs [5] when a magnetic carrier scatters off an impurity, which will also give a contribution to the anomalous Hall effect. While there has not been general agreement on whether skew scattering or side jump are dominant in various cases, and on whether impurity scattering or phonon scattering dominates, there seems to be a consensus that the anomalous Hall effect only arises from scattering by potentials that break the lattice periodicity [8][9][10][11][12]2]. Furthermore it is also generally assumed that the effect is proportional to the magnetization of the system as given by Eq.…”