Exchange Interaction

Abstract

We atttempt at gaining a detailed understanding of the microscopic interaction which is responsible, below a critical temperature (T _C or T _N), for the spontaneous collective ordering of the permanent magnetic moments, that exist in ferro-, ferri- and antiferromagnetic materials. For this, we discuss first two phenomenological theories, namely, the concept of the exchange field and the Weiss’ theory of ferromagnets. For collective magnetism, the so-called exchange interaction is responsible, which, even though is of pure electrostatic origin, can be understood only quantum mechanically. The direct exchange interaction is qualitatively explained according to the Heitler–London procedure and with the help of the Dirac’s vector model. This interaction is determined by the overlap integrals of the wavefunctions of the participating magnetic ions and is therefore of very short range. That is why, more often than the direct, an indirect exchange interaction is realized. We discuss the three most important coupling mechanisms, the RKKY – interaction for metals, the super-exchange for insulators and the so-called double exchange which is operative in some “bad” conductors. All these theories finally lead to the same operator form for the model Hamiltonian (Heisenberg model).