Spatial Structure of Mn-Mn Acceptor Pairs in GaAs

The local density of states of Mn-Mn pairs in GaAs is mapped with cross-sectional scanning tunneling microscopy and compared with theoretical calculations based on envelope-function and tight-binding models. These measurements and calculations show that the crosslike shape of the Mn-acceptor wave function in GaAs persists even at very short Mn-Mn spatial separations. The resilience of the Mn-acceptor wave function to high doping levels suggests that ferromagnetism in GaMnAs is strongly influenced by impurity-band formation. The envelope-function and tight-binding models predict similarly anisotropic overlaps of the Mn wave functions for Mn-Mn pairs. This anisotropy implies differing Curie temperatures for Mn $\delta$-doped layers grown on differently oriented substrates.

Figure 1

$X$-STM constant-current images of Mn $\delta$-doped GaAs with intentional Mn concentrations of $3\times {10}^{13}{\mathrm{cm}}^{-2}$: (a) $51\times 29{\mathrm{nm}}^2$; (b) $43\times 20{\mathrm{nm}}^2$; (c) $12\times 10{\mathrm{nm}}^2$; (d) $13\times 10{\mathrm{nm}}^2$. Images were acquired at a sample bias of $U_s=+1.5\mathrm{V}$ on a cleaved (110) surface. Note appearance of continuous background DOS around the layer in (b).

Figure 2

Topography of Mn-Mn pairs: (a) $12\times 12{\mathrm{nm}}^2$, $X$-STM image of two ionized Mn separated by 1.4 nm ($U_s=-0.6\mathrm{V}$); (b) schematic of the (110) surface showing the location of subsurface Mn; (c) same area as (a), imaged with $U_s=+1.1\mathrm{V}$ so the Mn are neutral; (d) $6\times 6{\mathrm{nm}}^2$, $X$-STM image of two Mn separated by 0.8 nm ($U_s=+1.55\mathrm{V}$); (e), (f) calculation with TBM of (c), (d), with parallel spins.

Figure 3

Calculated absolute differences between interacting and superimposed Mn-acceptor states $|{\psi }_{\mathrm{int}}{|}^2-|{\psi }_{\sup }{|}^2$: (left set) difference for ${\mathrm{Mn}}_0-{\mathrm{Mn}}_1$ pair; (right set) difference for ${\mathrm{Mn}}_0-{\mathrm{Mn}}_2$ pair. Relative spin orientations of Mn atoms are indicated by the arrows. Each plot is $6\times 6{\mathrm{nm}}^2$ and normalized to the maximum difference in the plot. $\Delta$ is the root mean square difference between the pair topography and a noninteracting baseline, as defined in the text.

Figure 4

Separation-dependent overlap of noninteracting Mn acceptors calculated for separations along three crystallographic directions using the envelope-function model (EFM) and the tight-binding model (TBM).

Figure 5

Directional dependence of the Mn wave function overlap for Mn-Mn separations $D$ calculated using the EFM. The curves are normalized to the maximum value $N$ given in Table .