Spin chirality and hall-like transport phenomena of spin excitations

Experimental and theoretical aspects of Hall-type transport of spins in magnetic insulators are reviewed. A general formalism for linear response theory of thermal Hall transport in the spin model is developed, which is general enough to be applicable to both the magnon and the paramagnetic, spin-liquid regimes. The expression of the energy current operator in the spin language is shown to be closely related to the spin chirality operator. Recent experiments on magnon-mediated thermal Hall transport in the two-dimensional kagome, and three-dimensional pyrochlore ferromagnetic insulators are reviewed in light of the multi-band magnon theory of Hall transport, and compared to the more mysterious thermal Hall transport found in the putative quantum spin ice material. As realizations of spinchirality driven magnon transport in the real space, we review the general theory of emergent gauge fields governing the magnon dynamics in the textured magnet, and discuss its application to the magnon-Skyrmion scattering problem. Topological magnon Hall effect driven by the Skyrmion texture is discussed.