First-principles calculations on the origin of ferromagnetism in transition-metal doped Ge

Many researchers have shown an interest in Ge-based dilute magnetic semiconductors (DMSs) due to potential advantages for semiconductor spintronics applications. There has been great discussion about mechanisms of experimentally observed ferromagnetism in (Ge,Fe) and (Ge,Mn). We investigate the electronic structures, structural stabilities, magnetic exchange coupling constants, and Curie temperature of Ge-based DMSs, and clarify origins of the ferromagnetism, on the basis of density functional theory calculations. In both the (Ge,Fe) and (Ge,Mn) cases, the inhomogeneous distribution of the magnetic impurities plays an important role to determine the magnetic states; however, physical mechanisms of the ferromagnetism in these two materials are completely different. By the spinodal nanodecomposition, the Fe impurities in Ge gather together with keeping the diamond structure, so that the number of the first-nearest-neighbor Fe pairs with strong ferromagnetic interaction increases. Therefore, the Curie temperature drastically increases with the progress of the annealing. Our cluster expansion method clearly reveals that the other ordered compounds with different crystal structures such as Ge3Mn5 and Ge8Mn11 are easily generated in the (Ge,Mn) system. The estimated Curie temperature of Ge3Mn5 is in agreement with the observed Curie temperature in experiments. It should be considered that the precipitation of the ferromagnetic Ge3Mn5 clusters is an origin of high Curie temperature in (Ge,Mn).