Hall Effect in Ferromagnetics

Abstract

Both the unusually large magnitude and strong temperature dependence of the extraordinary Hall effect in ferromagnetic materials can be understood as effects of the spin-orbit interaction of polarized conduction electrons. It is shown that the interband matrix elements of the applied electric potential energy combine with the spin-orbit perturbation to give a current perpendicular to both the field and the magnetization. Since the net effect of the spin-orbit interaction is proportional to the extent to which the electron spins are aligned, this current is proportional to the magnetization. The magnitude of the Hall constant is equal to the square of the ordinary resistivity multiplied by functions that are not very sensitive to temperature and impurity content. The experimental results behave in such a way also.

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

“…where we always have in mind the prescription (18). Using this notation, one can further rewrite Eq.…”

“…(18). This is nothing but the standard EOM for the momentum of the electron wave packet shown in Eq.…”

“…∆Ω (1) xµ is a irrelevant term 8 which vanishes with the help of prescription introduced in Eq. (18). For a later convenience, let us introduce the following abbreviated vector notation for z n k (t), t :…”

“…(73) is given in Appendix C. We then apply the prescription (18), replacing k in the integrant by its mean valuek. The contribution to the spin Hall current by an electron occupying the j-th pseudospin state atk is, therfore,…”

“…[17] is nothing but a manifestation of Berry phase. Its relevance to band structure had also been recognized in limited situations, such as anomalous Hall effect (AHE), [18,20] as well as in the study of quantized Hall conductance. [21] The role of Berry phase in ferroelectrics has also been of much theoretical interest.…”