Transition Temperature of a Magnetic Semiconductor with Angular Momentumj

We employ dynamical mean-field theory to identify the materials properties that optimize $T_c$ for a generalized double-exchange model. We reach the surprising conclusion that $T_c$ achieves a maximum when the band angular momentum $j$ equals $3/2$ and when the masses in the $m_j=\pm 1/2$ and $\pm 3/2$ subbands are equal. However, we also find that $T_c$ is significantly reduced as the ratio of the masses decreases from one. Consequently, the search for dilute-magnetic semiconductor materials with high $T_c$ should proceed on two fronts. In semiconductors with $p$ bands, such as the currently studied Mn-doped Ge and GaAs semiconductors, $T_c$ may be optimized by tuning the band masses through strain engineering or artificial nanostructures. On the other hand, semiconductors with $s$ or $d$ bands with nearly equal effective masses might prove to have higher $T_c$’s than $p$-band materials with disparate effective masses.