Stabilization of half metallicity in Mn-doped silicon upon Ge alloying

We propose ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}$ alloys as suitable candidates for spintronic applications. Remarkably, our first-principles investigation explains, within the local spin density approximation, the microscopic mechanism that stabilizes the half metallicity in Si matrices under Ge alloying and shows that it can spontaneously occur: in fact, half metallicity is determined by $p\text{−}d$ hybridization in the presence of Ge atoms surrounding Mn impurities, and this particular environment is energetically favored over other possible local composition fluctuations, such as excess of Si atoms around Mn. A detailed discussion of the trends of defect formation energy and of magnetization as a function of alloy composition and configuration completes the present work.

Figure 1

(a) Formation energy difference $\left(\Delta H_f\right)$, (b) total magnetic moment $\left({\mu }_{\mathit{tot}}\right)$, and (c) absolute magnetic moments $\left({\mu }_{\mathit{abs}}\right)$ as a function of concentration $x$ in Mn-doped ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}$ alloys for VC systems (solid circles). For comparison, values for the RA systems are also shown (open symbols): squares if NN of Mn are Si, circles if they are Ge. Dotted and dashed lines are a guide to the eye connecting configurations with similar local environments.

Figure 2

Magnetic moment $\mu$ $\left({\mu }_B\right)$ on the atomic sites occupying different neighboring shells as a function of the distance from the Mn impurity placed at the origin of the cell. The different curves are relative to different ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-}$ $x$ concentrations.

Figure 3

Density of states for the $x=0.5$ concentration: (a), (b) Total density of states for $R_4$ and $R_3$ systems, respectively. Density of states projected on (c) Mn in $R_4$, (d) Mn in $R_3$, (e) Ge NN in $R_4$, and (f) Si NN in $R_3$. Positive and negative values are relative to the majority- and minority-spin states, respectively.

Figure 4

Projected density of states on the Mn site resolved into states with $t_{2g}$- and $e_g$-like symmetries for the ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}$ alloy with $x=0.25$ and $x=1.0$ [panels (a) and (b), respectively]. The inset shows the total magnetic moment behavior as a function of the Mn-Si distance in structures having Mn surrounded by four Si atoms.