Electronic structure and magnetism inBi2Te3,Bi2Se3, andSb2Te3doped with transition metals (Ti–Zn)

Abstract

A less studied class of magnetic semiconductors based on the tetradymite structure compounds, which include ${\text{Bi}}_{2}{\text{Te}}_{3}$, ${\text{Bi}}_{2}{\text{Se}}_{3}$, and ${\text{Sb}}_{2}{\text{Te}}_{3}$, doped with $3d$ transition-metal $(T)$ elements is investigated using the full-potential linearized muffin-tin orbital method in the local spin-density approximation (LSDA). The small size of the $T$ atoms (Ti\char21{}Zn) relative to the larger Bi/Sb atom site leads to a strong lattice relaxation, which primarily affects the atoms close to the defect in neighboring layers but has less impact within the layer containing the $T$ ion. Even with the relaxation, the size difference leads to quite localized $3d$ states and hence a high-spin state with large magnetic moments. The valence is $3+$ for the first half of the series but reduces closer to $2+$ (Co) or $1+$ (Ni) for the latter half of the series. This reduction is due to hybridization in the transition-metal $3d$ state with the $\text{Se}/\text{Te}\text{ }p$ state of the atom in the layer closest to the $T$ site which reduces the amount of charge transfer between these two atoms. It corresponds to a competition between the stabilization by the exchange energy dominating for the early $T$ ions and the covalent bonding effects for the later ones. For Cu and Zn the trend reverses and the valency is between $2+$ and $3+$ with a small magnetic moment remaining for Cu but a negligible moment for Zn. $\text{LSDA}+U$ calculations for the Fe-Ni atoms slightly change this balance of the two effects and promote higher valency and larger magnetic moment.