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Gallium nitride doped with small concentration of manganese (GaxMn1-xN) is one of the most diluted magnetic semiconductors which used for the spintronic applications. In this work, the Ga31Mn1N32 in the zinc-blende (ZB) and rocksalt (RS) structures were investigated. We employed the ab-initio density functional theory (DFT) within the generalized gradient approximation (GGA) to study electronic and magnetic properties, such as the band structure, the density of state and the magnetic moment. The structural phase transitions under pressure up to 60 GPa were also studied. We found that the Ga31Mn1N32 in ZB phase is stable at ambient pressure, and change to the RS phase about 42 GPa. Finally, our calculations are in consistent with other experimental and theoretical literature.