Reentrant ferromagnetism in a class of diluted magnetic semiconductors

Considering a general situation where a semiconductor is doped by magnetic impurities leading to a carrier-induced ferromagnetic exchange coupling between the impurity moments, we show theoretically the possible generic existence of three ferromagnetic transition temperatures T-1 > T-2 > T-3, with two distinct ferromagnetic regimes existing for T-1 > T > T-2 and T < T-3. Such an intriguing reentrant ferromagnetism, with a paramagnetic phase (T-2 > T > T-3) between two ferromagnetic phases, arises from a subtle competition between indirect exchange induced by thermally activated carriers in an otherwise empty conduction band versus the exchange coupling existing in the impurity band due to the bound carriers themselves. We comment on the possibility of observing such a reentrance phenomenon in diluted magnetic semiconductors and magnetic oxides.