Effects of Crystallographic and Shape Anisotropies on Dopant-Carrier Exchange Interactions in Magnetic Semiconductor Quantum Dots

The roles of nanocrystal shape and crystalline anisotropy on carrier-mediated magnetism in diluted magnetic semiconductor nanocrystals have been examined in this work. A combination of density functional theory and analytical perturbation theory are used to investigate the electronic structures of Mn 2+ -doped nanocrystals of varied shapes and sizes. Density functional calculations are used to compute the magnetic exchange energies and to analyze the band edge splitting in these materials. To understand the observed anisotropic magnetism, we have derived a perturbative relationship between the magnetic exchange and nanocrystal anisotropy to illustrate the effect in an analytical and quantum mechanical expression. The first-principles calculations and the analytical predictions are in excellent agreement, and the anisotropic driving terms in the magnetic exchange are very well explained by the final perturbation equation.