Resonant optical topological Hall conductivity from skyrmions

We study the high frequency Hall conductivity in a two-dimensional (2D) model of conduction electrons coupled to background magnetic skyrmion texture via an effective Hund's coupling term. For ordered crystal, Kubo formula calculation using basis crystal Chern bands reveals resonant response at set by coupling: $\hbar\omega_{\text{res}} \approx J_H$. A complementary real-space for isolated box similar response. linear relation between area under curve and density is discovered numerically further elucidated gradient expansion which valid smooth textures local approximation based on spin-trimer calculation. point out issue distinguishing this contribution from feature arising spin-orbit interactions, as demonstrated Rashba collinear ferromagnet, analogous difficulty unambiguously separating d.c. topological effect anomalous effect. The proposed provide potentially useful optical signature skyrmions probes such scanning magneto-optical Kerr microscopy.