  We show the possibility of long-range ferrimagnetic ordering with a
saturation magnetisation of the order of 1 Bohr magneton per spin for
arbitrarily low concentration of magnetic impurities in semiconductors,
provided that the impurities form a superstructure satisfying the conditions of
the Lieb-Mattis theorem. Explicit examples of such superstructures are given
for the wurtzite lattice, and the temperature of ferrimagnetic transition is
estimated from a high-temperature expansion. Exact diagonalization studies show
that small fragments of the structure exhibit enhanced magnetic response and
isotropic superparamagnetism at low temperatures. A quantum transition in a
high magnetic field is considered and similar superstructures in cubic
semiconductors are discussed as well.
