Low-temperature magnon thermal conductivity of ferromagnetic insulators with impurities

The spin-wave thermal conductivity at low temperatures has been calculated for ferromagnetic insulators containing magnetic defects. The temperature range is such that we neglect those magnon scattering processes which can redistribute the magnon distribution, such as the magnon-magnon interactions. The effect of the external magnetic field has also been studied, and we observe that within the validity of the energy relation $E\left(\overrightarrow{k}\right)={\alpha k}^2$, the magnon conductivity has a $T^2$ dependence.