Magnon Hall effect

Hall effect is an ancient but highly potential subfield in condensed matter physics, and its origin can be traced back hundreds of years. In 1879, Hall made a momentous discovery that when a current-carrying conductor is placed in a magnetic field, the Lorentz force pushes its electrons to one side of the conductor. This intriguing phenomenon was dubbed Hall effect. Since then, a series of novel Hall effects have been discovered, including anomalous Hall effect, quantum Hall effect, spin Hall effect, topological Hall effect, and planar Hall effec. Notably, Hall effects play an important role in realizing the information transport, since it can realize the mutual conversion of current in different directions. In bosonic systems such as magnons, a series of magnon Hall effects have been found, jointly driving the development of the magnon-based spintronics. In this perspective, we review the researches of the Hall effect in magnonic system in recent years, and briefly introduce its modern semi-classical theories, including virtual electromagnetic field theory and scattering theory. Furthermore, we introduce the different magnon Hall effects and clarify the physics behind them. Finally, the prospect of magnon Hall effect is discussed.