The criterion of magnetism in semiconductor nanoobjects

The Stoner criterion is known as a useful tool predicting the ferromagnetic state (FM) in metals. This criterion is not applied to nanoobjects, because of their discrete electron spectrum. In our paper we consider a generalization of this criterion, which can be applied to magnetism in semiconductor nanoobjects. To derive it, we compare total energies of the FM and non-magnetic states using many-body perturbation theory. The derived criterion has compact form and may be useful for prediction of ferromagnetism in nanoobjects. To check its precision, we performed first-principle calculations of several semiconductor nanoobjects in the FM and non-magnetic states and compared their results with predicted ones.