||Ferromagnetism of metallic systems, especially those including transition metals, has been a controversial subject of modern science for a long time. This controversy stems from the apparent dual character of the rf-electrons responsible for magnetism in transition metals, i.e., they are itinerant electrons described by band theory in their ground state, while at finite temperatures they show various properties that have long been attributed to a system consisting of local magnetic moments. The most familiar example of these properties is the Curie-Weiss law of magnetic susceptibility obeyed by almost all ferromagnets above their Curie temperatures.
At first the problem seemed to be centered around whether the (/-electrons themselves are localized or itinerant. This question was settled in the 1950s and early 1960s by various experimental investigations, in particular by observations of d-electron Fermi surfaces in ferromagnetic transition metals. These observations are generally consistent with the results of band calculations.
Theoretical investigations since then have concentrated on explaining this dual character of d-electron systems, taking account of the effects of electron-electron correlations in the itinerant electron model. The problem in physical terms is to study the spin density fluctuations, which are neglected in the mean-field or one-electron theory, and their influence on the physical properties.
There have been two main streams in the research in this direction. One has been to study the local moments in metals or the possibility for the itinerant electrons to exhibit spin density fluctuations that are described at least approximately as a set of local magnetic moments. This approach attained remarkable success in the 1960s from a qualitative point of view and has been extended further since then.
The other stream of research has been to improve the mean-field theory by taking into account the spatially extended spin density fluctuations in contrast with the local moment picture. This line of approach, represented by the random-phase approximation, was, however, not successful until the early 1970s when a self-consistent theory of coupled modes of extended spin fluctuations was advanced and the difficulties of the random-phase approximation were removed. This improved theory was remarkably successful when applied to weakly ferromagnetic metals where the long-wavelength components of spin fluctuations are the predominant thermal excitations.