Theory of Transport in Skyrmion Systems: Topological Hall Effect

Skyrmion materials have attracted substantial recent interest, particularly for the effect of magnetic textures on the motion of itinerant electrons. Measurements of the Hall resistivity have usually been analyzed using a sum of the regular Hall effect and the anomalous Hall effect, and interpreting the remaining signal as a topological Hall effect. The topological Hall resistivity is then described using a simple model where the real-space Berry curvature of itinerant electrons is described as a uniform magnetic field with magnitude proportional to skyrmion density. In this talk, we will present a theory of electronic transport in systems with spin-orbit coupled itinerant electrons coupled to chiral magnetic textures, where we analyze Berry curvature effects in real- and momentum-space in both the semi-classical and quantum regimes.