Hybrid skew scattering regime of the anomalous Hall effect in Rashba systems: unifying Keldysh, Boltzmann, and Kubo formalisms

We present the analytical description of the anomalous Hall effect (AHE) in a 2DEG ferromagnet within the Keldysh formalism. These results unify all three linear response approaches to anomalous Hall transport and close a long standing debate. We are able to identify a new extrinsic AHE regime dominated by a hybrid skew scattering mechanism. This new contribution is inversely proportional to the impurity concentration, resembling the normal skew scattering, {\em but} independent of the impurity-strength, resembling the side-jump mechanism. Within the Kubo formalism this regime is captured by higher order diagrams which, although weak, dominate when both subbands are occupied; this regime can be detected by variable remote doping experiments that we describe.Comment: 5 pages, 2 figure

Tailoring Chirp in Spin-Lasers

The usefulness of semiconductor lasers is often limited by the undesired frequency modulation, or chirp, a direct consequence of the intensity modulation and carrier dependence of the refractive index in the gain medium. In spin-lasers, realized by injecting, optically or electrically, spin-polarized carriers, we elucidate paths to tailoring chirp. We provide a generalized expression for chirp in spin-lasers and introduce modulation schemes that could simultaneously eliminate chirp and enhance the bandwidth, as compared to the conventional (spin-unpolarized) lasers.Comment: 4 pages, 3 figure

Integral and fractional Quantum Hall Ising ferromagnets

We compare quantum Hall systems at filling factor 2 to those at filling factors 2/3 and 2/5, corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P=1) and paramagnetic (P=0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At filling factor 2, we find spin domains at half-polarization (P=1/2), while antiferromagnetic order seems most favorable in the CF systems. The transition between P=0 and 1, as seen when e.g. the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompresible half-polarized state is found in some models

Anisotropic magnetoresistance of spin-orbit coupled carriers scattered from polarized magnetic impurities

Anisotropic magnetoresistance (AMR) is a relativistic magnetotransport phenomenon arising from combined effects of spin-orbit coupling and broken symmetry of a ferromagnetically ordered state of the system. In this work we focus on one realization of the AMR in which spin-orbit coupling enters via specific spin-textures on the carrier Fermi surfaces and ferromagnetism via elastic scattering of carriers from polarized magnetic impurities. We report detailed heuristic examination, using model spin-orbit coupled systems, of the emergence of positive AMR (maximum resistivity for magnetization along current), negative AMR (minimum resistivity for magnetization along current), and of the crystalline AMR (resistivity depends on the absolute orientation of the magnetization and current vectors with respect to the crystal axes) components. We emphasize potential qualitative differences between pure magnetic and combined electro-magnetic impurity potentials, between short-range and long-range impurities, and between spin-1/2 and higher spin-state carriers. Conclusions based on our heuristic analysis are supported by exact solutions to the integral form of the Boltzmann transport equation in archetypical two-dimensional electron systems with Rashba and Dresselhaus spin-orbit interactions and in the three-dimensional spherical Kohn-Littinger model. We include comments on the relation of our microscopic calculations to standard phenomenology of the full angular dependence of the AMR, and on the relevance of our study to realistic, two-dimensional conduction-band carrier systems and to anisotropic transport in the valence band of diluted magnetic semiconductors.Comment: 15 pages, Kohn-Littinger model adde

Semiclassical framework for the calculation of transport anisotropies

We present a procedure for finding the exact solution to the linear-response Boltzmann equation for two-dimensional anisotropic systems and demonstrate it on examples of non-crystalline anisotropic magnetoresistance in a system with spin-orbit interaction. We show that two decoupled integral equations must be solved in order to find the non-equilibrium distribution function up to linear order in the applied electric field. The examples are all based on the Rashba system with charged magnetic scatterers, a system where the non-equilibrium distribution function and anisotropic magnetoresistance can be evaluated analytically. Exact results are compared to earlier widely-used approximative approaches. We find circumstances under which approximative approaches may become unreliable even on a qualitative level.Comment: submitted to PR

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

We present a study of transport in multiple-band non-interacting Fermi metallic systems based on the Keldysh formalism, taking into account the effects of Berry curvature due to spin-orbit coupling. We apply this formalism to a Rashba 2DEG ferromagnet and calculate the anomalous Hall effect (AHE) and anisotropic magnetoresistance (AMR). The numerical calculations reproduce analytical results in the metallic regime revealing the crossover between the skew scattering mechanism dominating in the clean systems and intrinsic mechanism dominating in the moderately dirty systems. As we increase the disorder further, the AHE starts to diminish due to the spectral broadening of the quasiparticles. Although for certain parameters this reduction of the AHE can be approximated as $\sigma_{xy}\thicksim\sigma_{xx}^{\varphi}$ with $\varphi$ varying around 1.6, this is found not to be true in general as $\sigma_{xy}$ can go through a change in sign as a function of disorder strength in some cases. The reduction region in which the quasiparticle approximation is meaningful is relatively narrow; therefore, a theory with a wider range of applicability is called for. By considering the higher order skew scattering processes, we resolve some discrepancies between the AHE results obtained by using the Keldysh, Kubo and Boltzmann approaches. We also show that similar higher order processes are important for the AMR when the nonvertex and vertex parts cancel each other. We calculate the AMR in anisotropic systems properly taking into account the anisotropy of the non-equilibrium distribution function. These calculations confirm recent findings on the unreliability of common approximations to the Boltzmann equation.Comment: 21 pages, 14 figure