Ab initio calculations of the magnetic properties of Mn impurities on GaAs (110) surfaces

We present a computational study of individual and pairs of substitutional Mn impurities on the (110) surface of GaAs samples based on density functional theory. We focus on the anisotropy properties of these magnetic centers and their dependence on on-site correlations, spin-orbit interaction, and surface-induced symmetry-breaking effects. For a Mn impurity on the surface, the associated acceptor-hole wave function tends to be more localized around the Mn than for an impurity in bulk GaAs. The magnetic anisotropy energy for isolated Mn impurities is of the order of 1 meV, and can be related to the anisotropy of the orbital magnetic moment of the Mn acceptor hole. Typically Mn pairs have their spin magnetic moments parallel aligned, with an exchange energy that strongly depends on the pair orientation on the surface. The spin magnetic moment and exchange energies for these magnetic entities are not significantly modified by the spin-orbit interaction, but are more sensitive to on-site correlations. Correlations in general reduce the magnetic anisotropy for most of the ferromagnetic Mn pairs.

Figure 1

A relaxed GaAs (110) surface with a Mn impurity. The arrows indicate different crystallographic axes of the surface supercell defined for this work.

Figure 2

The density of Mn $d$ states calculated with $U=0$ (blue, dark line) and $U=4$ eV (red, gray line), respectively. The inset shows the DOS near the Fermi level.

Figure 3

(Top) The density of As $p$ states of pure GaAs surface. (Bottom) The $p$ partial DOS of the same As atom when a nearby Ga atom is substituted by a Mn atom. The vertical dashed line in both panels represents the Fermi energy. The two vertical red lines delimit the energy-gap region for pure GaAs, which is clearly identifiable in the top panel. To compare the two cases, we have aligned the edge of the two conduction bands.

Figure 4

The eigenvalues of the eigenstates in the surroundings of the GaAs energy gap. The red (diamond marker) is for pure GaAs. The dashed blue (square marker) and green (circular marker) curves are for the cases when a surface Mn impurity is present with blue corresponding to $U=0$ and green corresponding to $U=4$ eV. Note the appearance of the hole acceptor state in the gap, a few hundred meV above the GaAs valence-band edge. The acceptor state energy is moderately affected by the presence of Hubbard $U$ correlations, a sign that this state is in part hybridized with $d$ states.

Figure 5

Difference in the As $p$ density states for two directions of the magnetization, $\langle 001\rangle$ and $\langle 010\rangle$, in the presence of SOI and for $U=4$ eV.

Figure 6

Density of $d$ states for different orientations of a pair of Mn on (110) surface of GaAs. See Fig. 1 for different orientations of the pair relative to the crystallographic axes. The inset shows the DOS near the Fermi level.

Figure 7

Dependence of the exchange energy constant $J$ on the orientation and Mn separation for a pair of Mn impurities on the (110) surface of GaAs.

Figure 8

Surface anisotropy for a pair of Mn impurity on (110) surface of GaAs.