Electronic structure and magnetic properties of transition-metal doped Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$, and Sb$_{2}$Te$_{3}$ for diluted magnetic semiconductors

The semiconducting tetradymite-structure materials Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$, and Sb$_{2}$Te$_{3}$ serve as the basis for high-performance room-temperature thermoelectric devices. Recently, it was found that these materials act as diluted magnetic semiconductors (DMS) with T$_{c} \sim$ 10 K using a few percent doping of transition metal atoms ($T$ = Ti, V, Cr, Mn, Fe). Electronic structure calculations have been performed using the full-potential linear muffin-tin orbital (FP-LMTO) method to understand these materials magnetic properties. The $T$ atoms substitute at the much larger Bi/Sb sites which leads to isolated atomic-like states with very little crystal-field splitting and approximately 3+ valence. This leads to a high spin state with the magnetic moments essentially following Hund's rule. The position of the $T$ 3$d$ states in the band gap will be investigated by analysis of the density of states (DOS). The effects of lattice relaxation and the magnetic interaction of $T$ atoms in the unit cell will also be investigated.