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By employing highly sensitive millikelvin SQUID magnetometry, the magnitudeof the Curie temperature as a function of the Mn concentration x is determinedfor thoroughly characterized Ga1-xMnxN. The interpretation of the results inthe frame of tight binding theory and of Monte Carlo simulations, allows us toassign the spin interaction to ferromagnetic superexchange and to benchmark theaccuracy of state-of-the-art ab initio methods in predicting the magneticcharacteristics of dilute magnetic insulators.

Origin of low-temperature magnetic ordering in Ga1-xMnxN