Effect of magnon-phonon thermal relaxation on heat transport by magnons

Abstract

The experimental evidence for heat transport by magnons in magnetic insulators is reviewed. It is noted that in a thermally isolated system, the magnon temperature comes to equilibrium with the phonon temperature with a finite relaxation time ${\ensuremath{\tau}}_{\mathrm{mp}}$. Since a conventional thermal-conductivity experiment is inherently a nonequilibrium situation, the steady-state magnon temperature gradient will differ from that of the phonons. A calculation is presented to show how the experimentally measured conductivity depends on ${\ensuremath{\tau}}_{\mathrm{mp}}$, as well as on the intrinsic magnon and phonon conductivities ${K}_{m}$ and ${K}_{p}$. In the limit of very long relaxation times, only ${K}_{p}$ is experimentally observed, regardless of the magnitude of ${K}_{m}$. The calculation is illustrated for the ferrimagnet YIG and the antiferromagnet Mn${\mathrm{F}}_{2}$, using magnon-phonon relaxation times measured by magnetic-resonance experiments. It is shown that ${\ensuremath{\tau}}_{\mathrm{mp}}$ for YIG is short enough to allow magnon heat transport to be observed, which is in agreement with experimental results. It is also shown that the long relaxation time for Mn${\mathrm{F}}_{2}$ may be responsible for the absence of magnon conductivity in this material. This general explanation may also apply to many other magnetic systems.