First-principles study of the effects on ferromagnetic coupling in Mn/GaAs digital ferromagnetic heterostructure by free holes Injection and Be co-dopant

We use density functional theory to study the effect of free holes injection and Be co-dopant on the ferromagnetic coupling in Mn/GaAs digital ferromagnetic heterostructure (DFH). The injection of free holes is simulated by assigning a range of concentrations of missing electrons in unit cell. The $\delta$-layer doping of Mn atoms in GaAs introduces three spin-polarized hole bands which are the consequence of hybridization between the $d$-states of the Mn atoms and the $p$-states of the nearest neighboring As atoms. The distribution of hole charge density shows that these spin-polarized holes are confined to the vicinity of the Mn $\delta$-layer. After the injection of free holes, the Fermi energy E$_{F}$ is lowered, then the number of spin-polarized holes in the layer of MnAs is increased monotonously. We characterize the ferromagnetic coupling by the total energy difference between the ferromagnetic and the antiferromagnetic phases , E$_{FA}$, per one pair of Mn atoms. The results of E$_{FA}$, E$_{F}$, and the projected spin-polarized holes at Mn and the nearest neighboring As atoms are shown as a function of concentration of the injected free holes. We demonstrate the enhancement of the ferromagnetic coupling, which is in agreement with the experimental results of Nazmul et al.$^{[1]}$. In contract, after the Be co-dopant in Mn/GaAs-DFH, the ferromagnetic coupling is deteriorated. We will give the explanation. [1] A. M. Nazmul et at. Phys. Rev. B67, 241308(R) (2003).