The origin of the interaction which lines up the spins in a magnetic system is the exchange interaction. When spin magnetic moments of adjacent atoms and make an angle , the exchange energy, , between the two moments can be expressed as
Although the exchange interaction produces strong interactions between neighbouring magnetic atoms it can also be mediated by various mechanisms, producing long range effects. As the exchange energy for neighbouring atoms is dependent only upon the angle between them it does not give rise to anisotropy.
In multilayers where magnetic layers are separated by a non-magnetic layer, there can be an exchange coupling between the two magnetic layers mediated by, for example, the RKKY interaction (see Section 5.4). The exchange coupling is composed of two terms: an isotropic exchange coupling and an anisotropic Dzialoshinski-Moriya exchange coupling.
The total exchange interaction energy is given by
The anisotropic exchange energy is given by
Dr John Bland, 15/03/2003