Anomalous Hall Current Research Articles

Effect of scattering on intrinsic anomalous Hall effect investigated by Lorenz ratio

We have investigated the effect of scattering on intrinsic anomalous Hall effect (AHE) for typical itinerant ferromagnets of Fe, Co, Ni, and their impurity-doped specimens in terms of the Hall Lorenz ratio ${L}_{xy}={\ensuremath{\kappa}}_{xy}/{\ensuremath{\sigma}}_{xy}T$, the ratio of thermal $({\ensuremath{\kappa}}_{xy})$ to electrical $({\ensuremath{\sigma}}_{xy})$ Hall conductivities divided by temperature $(T)$. We show that Lorenz ratio for the intrinsic anomalous Hall current (AHC) $(L_{xy}{}^{\text{A}})$ is almost constant and coincides with ${L}_{0}=2.44\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{W}\text{ }\ensuremath{\Omega}/{\text{K}}^{2}$ (Wiedemann-Franz law) in the clean region (e.g., ${\ensuremath{\rho}}_{xx}=1--3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\ensuremath{\Omega}\text{ }\text{cm}$), indicating the scattering-free nature of intrinsic AHE. On the other hand, the Lorenz ratio for the AHC begins to decrease from ${L}_{xy}={L}_{0}$ with increasing ${\ensuremath{\rho}}_{xx}$ above $3--6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\ensuremath{\Omega}\text{ }\text{cm}$, which indicates the crossover from the scattering-free to scattering-dependent nature of AHE. The scattering rate $(\ensuremath{\hbar}/\ensuremath{\tau})$ corresponding to the crossover resistivity is comparable with the gap magnitude formed at the band anticrossing point caused by the spin-orbit interaction.

An Extended Extrinsic Mechanism for Anomalous Hall Effect

The extrinsic mechanism for anomalous Hall effect in ferromagnets is extended to include the contributions both from spin-orbit-dependent impurity scattering and from the spin-orbit coupling induced by external electric fields. The results obtained suggest that, within the framework of the extrinsic mechanisms, the anomalous Hall current in a ferromagnet may also contain a substantial amount of dissipationless contribution independent of impurity scattering. After the contribution from the spin-orbit coupling induced by external electric fields is included, the total anomalous Hall conductivity is about two times larger than that due to spin-orbit dependent impurity scatterings.

Extrinsic anomalous Hall effect in charge and heat transport in pure iron,Fe0.997Si0.003, andFe0.97Co0.03

We have investigated thermal and electrical Hall conductivities for nominally pure and impurity-doped iron to examine the skew-scattering-induced anomalous Hall effect in the low-temperature clean-limit regime. In Fe, ${\text{Fe}}_{0.997}{\text{Si}}_{0.003}$, and ${\text{Fe}}_{0.97}{\text{Co}}_{0.03}$, we have observed the steep change in the electrical and thermal Hall conductivities below 100 K. The abrupt change in the Lorenz numbers for the anomalous Hall component $({L}_{xy}^{A})$ that includes even the sign change signaling the opposite flow of charge and heat currents is also observed around the crossover temperature of Hall conductivity. These observations indicate the emergence of the dissipative anomalous Hall current induced by the skew scattering below 100 K.

Magnetotransport in the insulating regime of Mn-doped GaAs

We consider transport in the insulating regime of GaMnAs. We calculate the resistance, magnetoresistance, and Hall effect, assuming that the Fermi energy is in the region of localized states above the valence-band mobility edge. Both hopping and activated band transport contributions are included. The anomalous Hall current from band states is very different from the hopping Hall current and has extrinsic (skew) and intrinsic (Luttinger) contributions. Comparison with experiment allows us to assess the degree to which band and hopping contribution determine each of the three transport coefficients in a particular temperature range. There are strong indications that the insulating state transport in GaMnAs is controlled primarily by extended state, band edge, transport rather than by variable range hopping, as reported in the literature.

Electric field control photo-induced Hall currents in semiconductors

We generate spin-polarized carrier populations in GaAs and low temperature-grown GaAs (LT-GaAs) by circularly polarized optical beams and pull them by external electric fields to create spin-polarized currents. In the presence of the optically generated spin currents, anomalous Hall currents with an enhancement with increasing doping are observed and found to be almost steady in moderate electric fields up to ∼120 mV μm −1, indicating that photo-induced spin orientation of electrons is preserved in these systems. However, a field ∼300 mV μm −1 completely destroys the electron spin polarization due to an increase of the D’yakonov–Perel’ spin precession frequency of the hot electrons. This suggests that high field carrier transport conditions might not be suitable for spin-based technology with GaAs and LT-GaAs. It is also demonstrated that the presence of the excess arsenic sites in LT-GaAs might not affect the spin relaxation by Bir–Aronov–Pikus mechanism owing to a large number of electrons in n-doped materials.

Lorenz Number Determination of the Dissipationless Nature of the Anomalous Hall Effect in Itinerant Ferromagnets

We have measured the thermal Hall conductivity for ferromagnetic Ni and Ni0.97Cu0.03. In the low temperature region ( less, similar 100 K), we show for the first time that the Wiedemann-Franz law is satisfied even for the anomalous Hall current. While the Hall Lorenz number for the normal part decreases rapidly with temperature, that for the anomalous part shows much less deviation from the free-electron Lorenz number. This evidences the dissipationless nature of the anomalous Hall effect.

Anomalous Hall effect in two-dimensional systems with magnetization: The roles of electron-impurity and electron-phonon scatterings

We present a kinetic equation approach to investigate the anomalous Hall effect in two-dimensional systems with magnetization considering both electron-impurity and electron-phonon scatterings. In our study, the spin-orbit interaction due to the external driving electric field as well as the extrinsic spin-orbit couplings induced by electron-impurity and electron-phonon scatterings are taken into account, while the intrinsic Rashba and Dresselhaus spin-orbit couplings are ignored. We derive the side-jump contributions to anomalous Hall current in terms of the distribution function and obtain the skew-scattering contribution by considering electron-impurity (and electron-phonon) scattering up to the second Born approximation. By performing a numerical calculation for InSb-based quantum wells, the temperature dependencies of the various components of anomalous Hall current are examined. We also discuss the roles of electron-impurity and electron-phonon scatterings in contributing to the total anomalous Hall current.

Anomalous Hall effect in Rashba two-dimensional electron systems based on narrow-band semiconductors: Side-jump and skew scattering mechanisms

We employ a helicity-basis kinetic equation approach to investigate the anomalous Hall effect in two-dimensional narrow-band semiconductors considering both Rashba and extrinsic spin-orbit (SO) couplings, as well as a SO coupling directly induced by an external driving electric field. Taking account of long-range electron-impurity scattering up to the second Born approximation, we find that the various components of the anomalous Hall current fit into two classes: (a) side-jump and (b) skew scattering anomalous Hall currents. The side-jump anomalous Hall current involves contributions not only from the extrinsic SO coupling but also from the SO coupling due to the driving electric field. It also contains a component which arises from the Rashba SO coupling and relates to the off-diagonal elements of the helicity-basis distribution function. The skew scattering anomalous Hall effect arises from the anisotropy of the diagonal elements of the distribution function and it is a result of both the Rashba and extrinsic SO interactions. Further, we perform a numerical calculation to study the anomalous Hall effect in a typical $\mathrm{InSb}∕\mathrm{AlInSb}$ quantum well. The dependencies of the side-jump and skew scattering anomalous Hall conductivities on magnetization and on the Rashba SO coupling constant are examined.

Anomalous Hall Heat Current and Nernst Effect in theCuCr2Se4−xBrxFerromagnet

In a ferromagnet, an anomalous Hall heat current, given by the off-diagonal Peltier term alpha(xy), accompanies the anomalous Hall current. By combining Nernst, thermopower, and Hall experiments, we have measured how alpha(xy) varies with hole density and lifetime tau in CuCr2Se4-xBrx. At low temperatures T, we find that alpha(xy) is independent of tau, consistent with anomalous-velocity theories. Its magnitude is fixed by a microscopic geometric area A approximately 34 A(2). Our results are incompatible with some models of the Nernst effect in ferromagnets.

Hall effect in a magnetic field parallel to interfaces of a III-V semiconductor quantum well

We have discovered that the spin-orbit coupling of electrons confined in a III-V semiconductor quantum well gives rise to an anomalous Hall current when both magnetic field and electric field are applied parallel to interfaces of the well. This Hall current is always perpendicular to the electric field, and depends strongly on the orientations of the electric and magnetic fields with respect to crystal axes. The Hall current is larger in samples with lower electron mobility. Our theory predicts that this effect can be observed in asymmetric quantum wells grown along the [011] direction, but not in [001]- and [111]-oriented quantum wells.

Theory of magnetooptical effects in ferromagnetic nickel

A theory is developed for magnetooptical effects in ferromagnetic nickel with allowance for the topology of the Fermi surface at low temperatures, when the carriers are scattered on ionized impurity centers. The contribution to the frequency conductivity tensor $$\tilde \sigma _{yx} (K,\omega )$$ due to the anisotropy of the Fermi surfaces of nickel is found and it is shown that this contribution in the first approximation of perturbation theory reduces to a decrease of the tensor $$\tilde \sigma _{yx} (K,\omega )$$ . An estimate is made of the influence of the density of states of nickel on the anomalous frequency-dependent Hall current and a study is also made of the case of low and high frequencies, when, respectively,ω 2 τ 2 « 1 andω 2 τ 2 » 1.

Anomalous hall effect in semiconductors

The anomalous Hall effect due to the orbital magnetism has been investigated in a weakly doped semiconductor in the presence of a magnetic field. For a collisionless electron gas, we have calculated the conductivity tensor and (besides the usual Hall effect) we have obtained an anomalous current proportional to E × M We find that for ω = 0 no particular affect arises; for finite frequencies, we give the first non trivial term of the anomalous Hall current. We also discuss the influence of the collisions and the conditions for observing the predicted effects experimentally.