Orbital pathways for Mn2+-carriersp−dexchange in diluted magnetic semiconductor quantum dots

Abstract

Manganese-carrier magnetic exchange interactions in strongly quantum-confined Mn${}^{2+}$-doped CdSe quantum dots (QDs) having ${d}_{\mathrm{QD}}$ $=$ 1.52, 2.08, and 2.54 nm have been investigated using a combination of density functional theory (DFT) and perturbation theory calculations. Established perturbation expressions have been tested by comparing the exchange energies predicted from these expressions (using DFT results as input parameters) with those calculated directly by DFT. These comparisons allow the dominant orbital pathways responsible for Mn${}^{2+}$-carrier exchange to be identified and analyzed. The Mn${}^{2+}$-valence-band(VB)-hole exchange interaction is described well using the long-accepted antiferromagnetic (AFM) $p$-$d$ kinetic exchange pathway. The Mn${}^{2+}$-conduction-band(CB)-electron interaction is described well using the recently proposed ferromagnetic (FM) kinetic s-s exchange pathway. AFM kinetic s-d exchange interactions previously proposed to become dominant in quantum-confined diluted magnetic semiconductors (DMSs) have been evaluated quantitatively by both DFT and perturbation theory and are found to be weak compared to the FM s-s interaction, even in these strongly confined QDs. The magnitudes of the mean-field exchange parameters are found to be nearly independent of quantum confinement over this range of QD diameters, and the dominant orbital pathways are not fundamentally altered by quantum confinement.