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

Abstract

We present a study of transport in multiple-band noninteracting Fermi metallic systems based on the Keldysh formalism and the self-consistent T-matrix approximation ͑TMA͒ taking into account the effects of Berry curvature due to spin-orbit coupling. We apply this formalism to a Rashba two-dimensional electron-gas ferromagnet and calculate the anomalous Hall effect ͑AHE͒ and anisotropic magnetoresistance ͑AMR͒. The numerical calculations of the AHE 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 xy ϳ xx , with varying around 1.6, this is found not to be true in general as xy can go through a change in sign as a function of disorder strength in some cases. Furthermore, the disordered region consistent with the TMA is relatively narrow and a theory with a wider range of applicability in strong disorder limit 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 nonequilibrium distribution function. These calculations confirm recent findings on the unreliability of common approximations to the Boltzmann equation.

Role of band-index-dependent transport relaxation times in anomalous Hall effect

“…For the 2D massive Dirac model, the equivalence between the Kubo-Streda and SBE approaches under the non-crossing approximation has been shown [3]. However, for the 2D spin-polarized Rashba model, although the equivalence between KuboStreda and Keldysh formalisms has been explicitly shown [17], existing SBE calculations [10,13] do not produce fully same results for side-jump and skew scattering as quantum-mechanical transport theories [4,16,17]. Sinitsyn et al [10] analyzed the coordinate-shift effects in the limit of smooth disorder potential, showing that the contribution of coordinate-shift has the same sign as the intrinsic one for sufficiently large Fermi energy.…”

“…The importance of the inter-band coherence effects in the topologically non-trivial band structures [2] has been highlighted theoretically [3,4]. Some simple but topologically non-trivial band models, such as the two-dimensional (2D) massive Dirac model [3,5,6] and 2D spin-polarized Rashba model [4,[7][8][9][10][11][12][13][14][15][16][17], have been studied for analytical account of both the intrinsic and extrinsic mechanisms for AHE. While the intrinsic mechanism stems solely from the nontrivial band structure, the extrinsic mechanism relies on the existence of disorder and is the sum of two contributions known as skew scattering and side-jump.…”

Magnetic-proximity-induced magnetoresistance on topological insulators

“…In the absence of a general theory, several studies addressed the AMR in a simple model system, viz., the two-dimensional (2D) electron gas with Rashba and Dresselhaus SOCs. The applied methods were the Boltzmann equation [3,4] and the linear-response Kubo formalism [5,6].…”

Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. I. Kinetic equation and anomalous Hall and spin-Hall effects

“…Within the anomalous Hall effect first described in Ref. 13 the spin polarization takes over the role of a magnetic field and creates a current contribution [14][15][16] . This effect occurs when timesymmetry is broken 17 and is related to the inverse spin Hall effect 18 .…”