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 thermomagnetic transport equations. As a main result, we find that the absolute thermomagnetic 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.