The Properties of Defects in Magnetic Insulators

The introduction of a low concentration of defects into a magnetic insulator modifies the spectrum of the magnetic excitations. In general the spectrum consists of a set of impurity modes associated with the defect and its immediate neighbors. Impurity modes that occur outside the band of host excitations are localized in the neighborhood of the defect and at the same time perturb the host band, while modes lying within the band lead to resonant behavior of the excitations of the host. In recent years, optical, neutron scattering, and nuclear magnetic resonance techniques have been used to study mixed crystals of antiferromagnetic transition metal fluorides. Many of the features may be understood by using the molecular field or Ising model for the excitations. An improvement on this form of the theory is to use a cluster model to describe the excitations near to the defect. Some features may however be described only when the excitations of the host are treated adequately; this requires the use of Green's function theories that have been developed for antiferromagnets containing defects. A detailed comparison is presented of the predictions of the various theories with the experimental results. Although the theory is fairly satisfactory for a low concentration of defects and low temperatures, considerable complexities arise in extending it to higher temperatures and large concentrations.