We present a theory for vacancy or non magnetic impurity induced ferromagnetism. The model depends only on very few free parameters. The theoretical approach is based on a correlated model for anions (oxygen orbitals) with on-site potentials on the neighbouring oxygen sites of the defect (vacancy or non magnetic impurity). First, for a fixed value of the correlation parameter it is shown that beyond a critical value of the on-site potential strength a magnetic moment appears on the oxygen sites neighbouring the non magnetic defect. By using techniques (Green's function approach for the exchange couplings and Self Consistent-Local RPA) which allow us to treat the randomness exactly, we are able to calculate the magnetic couplings between the total induced moment around the vacancies/non magnetic impurity, the Curie temperature and the dynamical properties (magnetic excitation spectrum) as a function of the strength of the disorder, doping, density of defects and strength of the correlation parameter. For physically reasonable parameters, our theory predicts Curie temperature well above room temperature for relatively small concentration of defects (few percent).Some of our results are discussed in relation to questions of stability and reproducibility raised in some recent experiments. Finally, we predict ferromagnetism with high Curie temperature in a new class of materials as Zr_1-x K_xO₂, Hf_1-xNa_xO₂ and Ti_1-xK_xO₂ for example. Some of our predictions were recently confirmed by first principle calculations.

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