We present a theory of interstitial Mn in Mn-doped ferromagnetic semiconductors. Using densityfunctional theory, we show that under the non-equilibrium 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.Ferromagnetism in dilute magnetic semiconductors is generally believed to be mediated by carriers-electrons or holes-originating from the magnetic dopants themselves. For example, an isolated Mn impurity in GaAs can substitute for Ga and contribute one hole, which is weakly bound to its acceptor core [1]. GaAs samples with Mn dopant concentrations in the range 1-2% are ferromagnetic insulators, while samples in the range 3-6% are ferromagnetic metals [2]. In the metallic phase the nominal hole concentration, p, is in principle equal to the number of Mn atoms per unit volume. Measured hole concentrations are much smaller, by factors ranging from ∼3 for MnGaAs [2] to ∼10 or more for MnGe [3]. In most theories of ferromagnetism in dilute magnetic semiconductors, reduced hole concentrations suppress the Curie temperature [4,5,6]. The reverse scenario-raising the Curie temperature by increasing the hole concentrationis therefore of great current interest. For current theoretical reviews see Refs. [5,6].Recent experiments show a strong correlation between Curie temperature, carrier concentration, and the fraction of Mn found at interstitial sites [7]. In this paper we address several questions not yet settled by experiment. (1) By what mechanism are interstitials formed, given that their calculated formation energies are considerably higher than substitutionals? (2) What determines the relative abundance of interstitials and substitutionals? (3) Under what (doping) conditions do interstitials act as compensators? (4) What role does compensation play in the ferromagnetism?To answer these questions, we use density-functional theory (DFT) to establish the following: (i) During the MnGaAs growth, Mn adatoms follow a very simple lowenergy pathway to directly form interstitial Mn near the surface. (ii) The deposition of additional As converts some of these interstitials to substitutional sites. (iii) The remaining interstitial Mn atoms act as donors, each compensating two substitutional acceptors. Finally, we show that within an impurity-band model, ferromagnetism below the metal-insulator transition is most favorable-in the sense of the highest Curie temperature-for 0.5 holes per substitutional Mn.For MnGaAs grown by MBE, recent channeling Rutherford backscattering experiments show that as much as ∼15% of the total Mn may be interstitial [7]. An open theoretical question is how interstitial Mn might be formed, under what conditions, and in what concentration. ...
