Topological Hall effect studied in simple models

Abstract

Recently, a chirality-driven contribution to the anomalous Hall effect has been found that is induced by the Berry phase and does not directly involve spin-orbit coupling. In this paper, we will investigate this effect numerically in a two-dimensional electron gas with a simple magnetic texture model. Both the adiabatic and non-adiabatic regimes are studied, including the effect of disorder. By studying the transition between both regimes the discussion about the correct adiabaticity criterium in the diffusive limit is clarified.

Topological Hall Effect from Strong to Weak Coupling

“…This means that the adiabaticity condition is given by Mτ > 1, which agrees with the conclusion of Ref. 11) based on numerical methods.…”

“…The former region may have relevance to the recent experiment on manganite thin films. We found the adiabaticity condition to be Mτ > 1, in agreement with the literature, 11) and the locality condition to be (q ) 2 < Mτ or q s < 1.…”

“…When the spin-relaxation time τ s (or spin-diffusion length s ) is finite, there appear two more regions (1 for q s < 1, and 2 for q s > 1) in the "weakest-coupling" region, Mτ s < 1 (or τ s < τ ex ). We found that the adiabaticity holds for Mτ > 1 (region 0), 11) and the locality of the effective magnetic field holds for (q ) 2 < Mτ or q s < 1 (regions 0, 1 and 1 ). The expression of THC in each region, written as σ (n) xy for region n, is given by eqs.…”

Large spontaneous Hall effects in chiral topological magnets

“…However, since the discovery of the anomalous Hall effect in 1880 [29], the effect has been seen only in ferromagnets because of the fact that the Berry curvature is usually proportional to the magnetization. On the other hand, the recent theories predict that the Berry curvature could be finite even without magnetization and in zero field, and if it is the case, there should be spin liquids and antiferromagnets that exhibit anomalous Hall effects spontaneously [16][17][18][19][20][21]. These phases in spin liquids and antiferromagnets must represent topologically nontrivial phases.…”

Spin-Hall effect of collimated electrons in zinc-blende semiconductors

“…It also appears in other condensed matter systems, such as in the anomalous Hall effect (AHE) in ferromagnets 9,10 , the AHE in frustrated ferromagnets-e.g. pyrochlore and Kagomé lattices-with chiral spin textures 11,12,13 , and in the so-called topological Hall effect in specially patterned magnetic nanostructures 14,15 . The monopole in general appears through the nontrivial curvature of gauge fields that are associated with an adiabatically evolving quantum system 16,17 .…”