First-principles calculations of the magnetic properties of (Cd,Mn)Te nanocrystals

Abstract

We investigate the electronic and magnetic properties of Mn-doped CdTe nanocrystals (NCs) with $\ensuremath{\sim}2\text{ }\text{nm}$ in diameter which can be experimentally synthesized with Mn atoms inside. Using the density-functional theory, we consider two doping cases: NCs containing one or two Mn impurities. Although the $\text{Mn}\text{ }d$ peaks carry five up electrons in the dot, the local magnetic moment on the Mn site is $4.65{\ensuremath{\mu}}_{B}$. It is smaller than $5{\ensuremath{\mu}}_{B}$ because of the $sp\text{\ensuremath{-}}d$ hybridization between the localized $3d$ electrons of the Mn atoms and the $s$- and $p$-type valence states of the host compound. The $sp\text{\ensuremath{-}}d$ hybridization induces small magnetic moments on the Mn-nearest-neighbor Te sites, antiparallel to the Mn moment affecting the $p$-type valence states of the undoped dot, as usual for a kinetic-mediated exchange magnetic coupling. Furthermore, we calculate the parameters standing for the $sp\text{\ensuremath{-}}d$ exchange interactions. Conduction ${N}_{0}\ensuremath{\alpha}$ and valence ${N}_{0}\ensuremath{\beta}$ are close to the experimental bulk values when the Mn impurities occupy bulklike NCs' central positions, and they tend to zero close to the surface. This behavior is further explained by an analysis of valence-band-edge states showing that symmetry breaking splits the states and in consequence reduces the exchange. For two Mn atoms in several positions, the valence edge states show a further departure from an interpretation based in a perturbative treatment. We also calculate the $d\text{\ensuremath{-}}d$ exchange interactions $|{J}^{dd}|$ between Mn spins. The largest $|{J}^{dd}|$ value is also for Mn atoms on bulklike central sites; in comparison with the experimental $d\text{\ensuremath{-}}d$ exchange constant in bulk ${\text{Cd}}_{0.95}{\text{Mn}}_{0.05}\text{Te}$, it is four times smaller.