By employing highly sensitive millikelvin SQUID magnetometry, the magnitude
of the Curie temperature as a function of the Mn concentration x is determined
for thoroughly characterized Ga1-xMnxN. The interpretation of the results in
the frame of tight binding theory and of Monte Carlo simulations, allows us to
assign the spin interaction to ferromagnetic superexchange and to benchmark the
accuracy of state-of-the-art ab initio methods in predicting the magnetic
characteristics of dilute magnetic insulators.Comment: 4+ pages, 3 figure