Self-Compensation in Manganese-Doped Ferromagnetic Semiconductors

We present a theory of interstitial Mn in Mn-doped ferromagnetic semiconductors. Using density-functional theory, we show that under the nonequilibrium conditions of growth, interstitial Mn is easily formed near the surface by a simple low-energy adsorption pathway. In GaAs, isolated interstitial Mn is an electron donor, each compensating two substitutional Mn acceptors. Within an impurity-band model, partial compensation promotes ferromagnetic order below the metal-insulator transition, with the highest Curie temperature occurring for 0.5 holes per substitutional Mn.

Figure 1

Potential-energy surface for Mn adsorption on GaAs(001), plotted in a plane normal to the surface and containing the As surface dimer. The minimum energy adsorption site is the subsurface interstitial site labeled $i$; the corresponding surface geometry is shown (light gray for As, dark gray for Ga, yellow for Mn). Typical adsorption pathways funnel Mn adatoms to this interstitial site (heavy curves) or to a cave site, $c$ (light curves). Inset: Binding energy of a Mn adatom centered on the As dimer; for comparison, results are also shown for a Ga adatom. When additional As is deposited, the metastable Mn site, $s$, becomes more favorable and leads to partial incorporation of substitutional Mn.

Figure 2

Formation energies of isolated Mn impurities in GaAs, for different charge states as a function of the Fermi level. Inset: Transition levels (crossing points of the formation energies) between stable charge states of substitutional and interstitial Mn impurities.

Figure 3

Dependence of Curie temperature on hole concentration for $1.5\%$ Mn, in two different insulating regimes. (a) Mott-Hubbard insulator, $U>W$. (b) Anderson localization, with the arbitrary choice $U=0.65W$. Upper and lower Hubbard bands are shown.