  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.
