Peltier heat of a small polaron in a magnetic semiconductor

For the first time the heat transported with a small polaron in both antiferromagnetic and ferromagnetic semiconductors is calculated. This heat, the Peltier heat, π, is obtained from the change of the entropy of the total system upon introduction of a charge carrier. We explicitly consider both the intrasite and intersite exchange interactions between a small polaron and the interacting spins of a spin-1/2 magnet. There are two competing magnetic contributions to the Peltier heat. First, adding the carrier increases the spin entropy of the system. This provides a positive contribution to π. Second, the exchange between the carrier and the sites about it enhances the exchange binding between these sites. This reduces the energetically allowable spin configurations and provides a negative contribution to π. At extremely high temperatures when kT exceeds the intrasite exchange energy, the first effect dominates. Then π is simply augmented by kT ln 2. However, well below the magnetic transition temperature the second effect dominates. In the experimentally accessible range between these limits both effects are comparable and sizable. The net magnetic contribution to the Peltier heat rises with temperature. Thus, a carrier's interactions with its magnetic environment produces a significant and distinctive contribution to its Peltier heat