Critical conditions for charged and neutral magnetic bipolaron formation in 1D, 2D and 3D systems

Interaction of two magnetic polarons formed either by single carriers or by excitons is considered in bulk crystals, quantum wells and quantum wires. It is shown that the magnetic bipolaron can be formed if the distance between two polarons is less than some critical value. This critical radius is larger, the lower the temperature and the larger the single polaron radius. Carrier-carrier exchange interaction is shown to be less important for the bipolaron formation than the exchange coupling between carriers and magnetic ions. Charged magnetic bipolarons are expected to be found mostly in semimagnetic quantum wires, while the neutral ones can be observed in any system where the free exciton magnetic polaron can be formed. The critical distance for the neutral magnetic bipolaron formation is much longer than for the charged bipolaron.