Thermodynamic transport theory of spin waves in ferromagnetic insulators

We use the Boltzmann transport theory in the relaxation time approximation to describe the thermal transport of spin waves in a ferromagnet. By treating spin waves as magnon excitations we are able to compute analytically and numerically the coefficients of the constitutive thermo-magnetic transport equations. As a main result, we find that the absolute thermo-magnetic power coefficient $\epsilon_M$, relating the gradient of the potential of the magnetization current and the gradient of the temperature, in the limit of low temperature and low field, is a constant $\epsilon_M = -0.6419 \, k_B/\mu_B$. The theory correctly describes the low-temperature and magnetic-field dependencies of spin Seebeck experiments. Furthermore, the theory predicts that in the limit of very low temperatures the spin Peltier coefficient $\Pi_M$, relating the heat and the magnetization currents, tends to a finite value which depends on the amplitude of the magnetic field. This indicates the possibility to exploit the spin Peltier effect as an efficient cooling mechanism in cryogenics.