Nonlinear Anomalous Hall Effect and Negative Magnetoresistance in a System with Random Rashba Field

We predict two spin-dependent transport phenomena in two-dimensional electron systems, which are induced by a spatially fluctuating Rashba spin-orbit interaction. When the electron gas is magnetized, the random Rashba interaction leads to the anomalous Hall effect. An example of such a system is a narrow-gap magnetic semiconductor-based symmetric quantum well. We show that the anomalous Hall conductivity reveals a strongly nonlinear dependence on the magnetization, decreasing exponentially at large spin density. We also show that electron scattering from a fluctuating Rashba field in a two-dimensional nonmagnetic electron system leads to a negative magnetoresistance arising solely due to spin-dependent effects.

Figure 1

Spin-split Fermi surface. $1/R$ is the possible range of momentum change, $|\mathbf{q}|=|{\mathbf{k}}^{\prime }-\mathbf{k}|$ in the spin-flip scattering process between two Fermi surfaces. The dashed circle corresponds to the Fermi momentum $k_F$. In the limit of small Fermi surface splitting, $\Delta K=2Mm/k_F$ for $B=0$ (spin orientation is taken with respect to the $z$ axis), or $|\Delta K|=2\beta Bm/k_F$ for $M=0$ (spin orientation is taken with respect to the $x$ axis).

Figure 2

Feynman graph for the anomalous Hall current. Matrix elements in the vertices are determined by Eqs. (3, 4, 5).

Figure 3

Anomalous Hall conductivity as a function of spin splitting parameter $M$ for indicated values of $R$. Other parameters are defined in the text.