A very general theoretical discussion of the values of sp d exchange constants is given starting from symmetry properties of diluted magnetic semiconductors. Complex structure of the valence band is fully taken into account with interacting heavy and light holes as well as spin-orbit split-off states kept in the consideration. The form of the Hamiltonian is derived and shown to be, in a general case, anisotropic. A series of approximations is made that reduces the Hamiltionian to a simple form introduced in Chap. 1. Specific cases of two-dimensional quantum wells and zero-dimensional spherical quantum dots are considered. Finally, the role of sp d interaction in spin relaxation processes is discussed.
IntroductionIn semiconductor nano-heterostructures the potential energy, that a charge carrier experiences, changes on the length scale that is comparable to the characteristic wavelength of the carriers. In such a case, the quantum-size effects play a dominant role. The quantum confinement significantly affects the exchange interaction between carriers and localized spins of the magnetic ions. The effective exchange Hamiltonian becomes anisotropic because the presence of interfaces reduces the symmetry. In narrow structures with high potential barriers, the quantum confinement changes the ground state energy of the carriers to such an extent that the changes of the ground energy can be comparable to the band gap energy of a bulk