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.