Low-temperature thermal conductivity of ferrimagnetic insulators

The low-temperature thermal conductivity of ferrimagnetic systems is calculated by using the thermal conductivity integral relating it to the phonon relaxation time. Different processes which contribute to the phonon relaxation, such as mass defect, external boundary and spin-wave scattering, are taken into account. The spin-wave contribution is calculated by using Boltzmann's equation for the relaxation time and by using the matrix elements of the phonon-magnon interaction term calculated earlier. The calculation is restricted to interactions involving `acoustic' modes of phonons and magnons, and the relaxation frequency is found to be proportional to the third power of the phonon wave vector. The theory is compared with experimental results on ferrites (e.g. MnFe 2 O 4 ) and on magnetic garnets (e.g. Y 3 Fe 2 Fe 3 O 12 ). The agreement in the case of the ferrite is good between 5 °K to 15 °K and is only satisfactory for the garnet. However, the agreement in the region where magnon scattering of phonons is important strongly supports the mechanism considered here. The agreement near 5 °K might improve by considering the magnon contribution to heat current which may not be entirely negligible.