Theory of magnetism in diluted magnetic semiconductor nanocrystals

Abstract

We present a theoretical investigation of magnetism in II-VI diluted magnetic semiconductor nanocrystals (NCs). The energy spectra, magnetizations, and magnetic susceptibilities of singly charged NCs with few substitutional magnetic ${\mathrm{Mn}}^{2+}$ ions are studied as functions of NC size, magnetic dopant distribution, and concentration by using the technique of exact diagonalization. For NCs containing long range interacting Mn ions, the quantum size effects improve the stability of ferromagnetic magnetic polarons. The carrier-mediated spin interactions between magnetic ions result in the enhancement of magnetism. By contrast, the ground states of NCs containing short ranged Mn clusters undergo a series of magnetic phase transitions from antiferromagnetism to ferromagnetism, with decreasing size of NC. An analysis based on a simplified constant interaction model, supported by the numerical calculations of local mean field theory, is presented for the magnetic NCs with many magnetic ions over a wide range of Mn concentration and NC size. Accordingly, we derive the condition for the formation of magnetic polaron and predict the observable signatures of the magnetic phases in magnetization measurements.