Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2003-02-27
Phys. Rev. Lett. {\bf 91}, 057202 (2003)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4 pages, 1 eps figure, final version
Scientific paper
10.1103/PhysRevLett.91.057202
We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity $\sigma_{xy}^{AH}$. We show that $\sigma_{xy}^{AH}$ is proportional to the first derivative of the density of states $\varrho(\epsilon)$ and thus can be expected to change sign as a function of impurity band filling. We also show that $\sigma_{xy}^{AH}$ depends on temperature as the longitudinal conductivity $\sigma_{xx}$ within logarithmic accuracy.
Balents Leon
Burkov Andriy
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