Heat-Activated Effect of Exchange Coupling Between Two Ferromagnets Separated by an Amorphous Semiconducting Barrier

We try to extend our previous zero-temperature tunneling theory for the exchange coupling between two ferromagnets separated by an amorphous semiconducting barrier to the case of finite temperature. The result exhibits that the tunneling electrons can absorb or emit phonons when they tunnel through the amorphous barrier at finite temperatures so that the interlayer exchange coupling is heat activated. This agrees with the experiments.