Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets

TL;DR

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Contribution

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Abstract

The mechanism of the anomalous Hall transport phenomena, if it is of the intrinsic or extrinsic origin, has been controversial. We present a unified theory of them for ferromagnetic metals with dilute impurities at the zero temperature, in terms of a quantum transport theory with the self-consistent T-matrix approximation. With the Fermi energy E_F and the spin-orbit interaction energy E_{SO} being fixed (E_F > E_{SO}), three regimes are found as a function of the scattering rate \hbar/\tau. (i) In the superclean case \hbar/\tau < u_{imp} E_{SO}D, the skew scattering from the vertex correction dominates the anomalous Hall conductivity \sigma_{xy}, where u_{imp} is the impurity potential strength and D is the density of states. With increasing \hbar/\tau, this extrinsic skew-scattering contribution rapidly decays. (ii) In the moderately dirty regime u_{imp}E_{SO}D < \hbar/\tau < E_{SO}, \sigma_{xy} is dominated by the intrinsic dissipationless Berry-phase contribution, which is resonantly enhanced to the order of e^2/\hbar when an accidental degeneracy of band dispersions around the Fermi level is lifted by the spin-orbit interaction. (iii) Further increasing \hbar/\tau, a \sigma_{xy}\propto\sigma_{xx}^{1.6} scaling appears, which has been verified by recent experiments. The themal and thermoelectric Hall conductivities are also discussed.