The paramagnetic properties of the rare earth ions have been investigated so extensively that a book could be written on the subject, never mind a chapter. This is due in large part to the many studies ofthe EPR spectra of the lanthanides when doped into diamagnetic hosts, and the attendant theoretical development in terms of crystal field theory. Many of the current ideas in magnetism have followed from such studies, especially with regard to relaxation phenomena.Relatively few coordination compounds of the lanthanides have been studied in detail. Superexchange is relatively unimportant, and dipole-dipole interactions therefore tend to dominate the magnetic ordering phenomena; this is enhanced by both the relatively large spin and g-values of many ofthe lanthanides. The compounds which order do so largely at temperatures of 4 K and below as a result. These effects are enhanced by the high coordination number of most rare earth compounds, which works to reduce the strength of any superexchange paths. Also, as a result, there appear to be no lower-dimensional rare earth compounds, at least in the sense described in Chap. 7.It is difficult to generalize about each ion, since the crystal field splitting of any ion, though small, can change from one system to another.The chemistry of the lanthanides has been reviewed [1-3]. The distinguishing features for our purposes are:a) The metal ions are found primarily in the trivalent state. b) High coordination numbers (eight appears to be the commonest) and a variety of geometries are found. Six-coordination and lower are rare. Several typical coordination polyhedra are illustrated in Fig. 9.1. c) Oxygen and nitrogen are the favored donor atoms, but a number of halides have also been studied. d) Spin-orbit coupling is important, the more so energetically than crystal field splittings, and increases with atomic number. This is summarized in Table 9.1. The letter " is once again used as the total angular momentum quantum number.e) The magnetic properties are determined by the 4f electrons, which are wellshielded by the occupied outer shells of 5s and 5p electrons. The 4f electrons are littleinvolved with chemical bonding, which is why superexchange is relatively unimportant. This is well-illustrated in Fig. 9.2, which shows the radial extension of the wave functions [6]. The interactions which dominate the cooperative phenomena with rare earth compounds are dipolar in nature. This is because of the important orbital contributions to the magnetic moment. Thus, since dipole-dipole interactions are long-R. L. Carlin, Magnetochemistry