Low-temperature Peltier heat of an itinerant electron in a ferromagnetic semiconductor.

Abstract

The Peltier heat of a wide-band itinerant carrier in a ferromagnetic semiconductor has been calculated for temperatures below the Curie temperature. In this regime we treat the spin fluctuations within the spin-wave approximation. The coupling of the charge carrier to the local moments is via local intra-atomic (e.g., s-f or s-d) exchange. Taking the strength of the intra-atomic exchange interaction to be small compared with the carrier's electronic bandwidth, we treat the interaction between the carrier and the local moments perturbatively through second order. We use the perturbed energy to compute the free energy of the coupled electron-magnon system. From the carrier-induced change of the system's free energy we directly obtain the carrier's Peltier heat. The Peltier heat contains two terms of opposite sign which both increase in magnitude with increasing temperature. These two terms arise from the first- and second-order contributions to the energy of the coupled system. Except at very low temperatures, the first-order contribution dominates. Then the electron-magnon interaction provides a negative contribution to the Peltier heat of a ferromagnetic semiconductor. The magnitude of this contribution varies as ${T}^{3/2}$.