Lieb-Mattis ferrimagnetism in diluted magnetic semiconductors

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.