"Quasi two-dimensional" spin distributions in II-VI magnetic   semiconductor heterostructures: Clustering and dimensionality
  Spin clustering in diluted magnetic semiconductors (DMS) arises from antiferromagnetic exchange between neighboring magnetic cations and is a strong function of reduced dimensionality. Epitaxially-grown single monolayers and abrupt interfaces of DMS are, however, never perfectly two-dimensional (2D) due to the unavoidable inter-monolayer mixing of atoms during growth. Thus the magnetization of DMS heterostructures, which is strongly modified by spin clustering, is intermediate between that of 2D and 3D spin distributions. We present an exact calculation of spin clustering applicable to arbitrary distributions of magnetic spins in the growth direction. The results reveal a surprising insensitivity of the magnetization to the form of the intermixing profile, and identify important limits on the maximum possible magnetization. High-field optical studies of heterostructures containing "quasi-2D" spin distributions are compared with calculation. 
S. A. Crooker, N. Samarth, D. D. Awschalom