Spin waves in one-dimensional magnetic systems

Abstract

A magnetic material consists of a large number of coupled magnetic dipoles. Where does this coupling come from and how do differently coupled systems behave? Performing a Heitler-London calculation shows that the Coulomb interaction and the Pauli exclusion principle result in a split of energy levels which in turn causes the coupling. Which energy level is lowest will determine the type of magnetisation; ferromagnetic or antiferromagnetic. Combining exact analysis of the Ising model with mean field theory one finds that phase transitions occur in ferromagnetic systems as a function of temperature, one-dimensional systems excluded. At low temperatures a thermal fluctuation will result in a spin wave in the magnetic material. By viewing the spin wave as a perturbation of the ground state the Bloch equations are linearised and solved for one-dimensional systems. The final products are the dispersion relations that describe the motion of spin waves in differently coupled systems.