Thermal Hall conductivity of magnons described by a noninteracting boson Hamiltonian is derived by the linear response theory. The thermal Hall conductivity is expressed by the Berry curvature in momentum space, which also has the prevailing form for bosonic systems. This theory covers various spin waves, such as spin waves in antiferromagnets and magnetostatic spin waves. As an example, we calculate the thermal Hall conductivity by the magnetostatic spin wave in yttrium iron garnet and reveal its dependence on a magnetic field and temperature.

• Received 18 June 2013
• Revised 8 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.054420