Magnetism in reduced dimensions

We propose a short overview of a few selected issues of magnetism in reduced dimensions, which are the most relevant to set the background for more specialized contributions to the present Special Issue. Magnetic anisotropy in reduced dimensions is discussed first, on a theoretical basis, then with experimental reports and views from surface to single-atom anisotropy. Then, conventional magnetization states are reviewed, including macrospins, single domains, multidomains, and domain walls in stripes. Dipolar coupling is examined for lateral interactions in arrays, and for interlayer interactions in films and dots. Finally thermally-assisted magnetization reversal and superparamagnetism are presented. For each topic we have sought a balance between well established knowledge and recent developments. To cite this article: O. Fruchart, A. Thiaville, C. R. Physique 6 (2005).