Topological hall transport: Materials, mechanisms and potential applications

Topological Hall effect (THE) and its inverse effect (skyrmion Hall effect) generally occurs in magnetic materials with topological properties, as a consequence of nonuniform and noncollinear magnetization as well as special chirality. Its mechanism and properties are different from those of conventional anomalous Hall effect induced by uniform magnetization. Following the seminal theoretical model of THE, the experimental research of THE has achieved the significant progress in the development of magnetic topological state (magnetic vortex, meron, skyrmion) and spintronics in the past decade. In this topical review, we focus on the recent experimental progress in the observation of THE and various theoretical understandings. The first part introduces the phenomenological description of THE commonly observed in experiments. Next, we present a survey of different materials hosting THE and summarize the relevant theories of THE as well as the approach of tuning THE. Finally, we will conclude our review by summarizing the present status and the perspective of the field.