Ab initio transport theory for digital ferromagnetic heterostructures.

We present a theoretical density functional study of the electronic, magnetic, and transport properties of digital ferromagnetic heterostructures, obtained by d doping GaAs with Mn. In the absence of intrinsic donors these systems have a half metallic density of states, with an exchange interaction much stronger than that of a random alloy with the same Mn concentration. Our ab initio ballistic transport calculations show that the carriers at the Fermi energy are strongly confined within a few monolayers around the MnAs plane. This strong confinement is responsible for the large exchange coupling and the twodimensional half metallic behavior. Diluted magnetic semiconductors (DMS) based on III-V materials [1,2] are receiving great attention for the intriguing interplay between magnetic and electronic properties [3] and for the large potential for future electronic devices [4]. Ga12xMnxAs, which is structurally compatible with most epitaxially grown III-V’s, is the prototype of these materials. Here the Mn ions substitute randomly for the Ga ions, providing both localized S 52 spins and free carriers (holes). The antiferromagnetic exchange coupling between the hole spin and the Mn spin is responsible for the long range ferromagnetic interaction, which can be described in a first approximation by the Zener model [5]. One important result of the model is that the Curie temperature is a linear function of the Mn concentration. Although the inclusion in the model of correlation effects [6] modifies this linear dependence, there is general agreement that an increase in the Mn concentration enhances the Curie temperature of the system. Unfortunately, the solubility limit of Mn in GaAs is rather small, since MnAs naturally occurs in a hexagonal phase with [6]-coordinated Mn [7]. However large Mn concentration, up to 50% can be obtained in zinc blende MnAs submonolayers embedded into GaAs to form a MnAsGaAs superlattice [8]. These structures, called digital ferromagnetic heterostructures (DFH) have remarkable properties. First, the Curie temperature decays for increasing GaAs interlayer thickness, and saturates for thicknesses larger than 50 GaAs ML. The value of Tc at saturation depends on the Mn concentration [8]. A saturation is unexpected according to the Zener model for three-dimensional systems, since the total Mn concentration in the sample decreases with the increase of the GaAs thickness. This separation dependence suggests that DFH’s behave like planar systems, although to date there is no direct proof that the free carriers responsible for the magnetic interaction are confined in the MnAs layers. Second, Hall measurements in the direction parallel to the MnAs planes show an anomalous Hall effect for undoped samples, which disappears upon Be doping [9,10]. Large Shubnikov de Haas oscillations are found in doped samples, although surprisingly the charge densities extracted from the Hall coefficient and from the Shubnikov de Haas oscillations are different. This suggests that two different carrier types could be present in the system. In this Letter we investigate theoretically the magnetic and transport properties of undoped DFH. In particular, we address the following questions: (i) What is the real dimensionality of the system? (ii) Are the carriers spin polarized? (iii) What is the carrier distribution in the system? We perform density functional theory [11] calculations within the local spin density approximation using the Ceperley-Alder [12] form of the exchange-correlation potential. We use scalar relativistic Troullier-Martins pseudopotentials [13] with nonlinear core corrections and Kleinman-Bylander factorization. We choose the SIESTA implementation [14] because it uses a localized orbital basis set obtained from the numerical solution of the free atom pseudopotential, and a confining spherical potential of radius rc. The cutoff radius rc fixes the radial extension of the wave functions, which therefore are localized in space. This allows us to investigate systems with a large number of atoms. Further details of the method and its optimization have already been presented [15]. Each DFH superlattice is constructed by considering N GaAs cubic