The Hall effect, the transverse response of current by external or internal magnetic field, has been widely used as one of the material characteristics for itinerant systems, since the discovery by Edwin Hall in 1879. The precise underlying mechanism, however, has been only possible in recent years in terms of topology in the momentum or the real spaces. In this talk, I will briefly review the current understanding of the Hall effects based on Berry curvature, with an emphasis on the anomalous Hall effect in itinerant magnets, and will introduce our recent works on a ferromagnet Fe₃GeTe₂ [1] and a frustrated antiferromagnet PdCrO₂ [2,3].

[1] K. Kim, J. Seo et al. Nat. Mater. 17, 794-799 (2018). 

[2] J. M. Ok et al. Phys. Rev. Lett. 111, 176405 (2013).

[3] J. M. Ok, H. S. Jeon et al. unpublished