Ab initio electronic structure, optical, and magneto-optical properties of MnGaAs digital ferromagnetic heterostructures

We report on a theoretical study of the electronic, optical, and magneto-optical properties of digital ferromagnetic heterostructures based on Mn $\delta$-doped GaAs. We consider different structures corresponding to Mn contents within the range 12%–50% and we study how the system changes as a function of the doping concentration. Our first-principles approach includes the spin-orbit interaction in a fully relativistic pseudopotential scheme and the local-field effect in the description of the optical absorption. We show that Mn $\delta$-doped GaAs shares many properties with the uniformly doped $\mathrm{Ga}{}_{1-x}\mathrm{Mn}{}_x\mathrm{As}$ system, i.e., half-metallicity, similar absorption spectra, and moderate Kerr rotation angles in the visible spectral region.

Figure 1

Atomic structure (unit cells) of some of the studied $\delta$-doped materials. Yellow spheres are As atoms, the violet ones represent Ga, and the cyan color is used for Mn. The corresponding Mn-doping concentrations are $12.5\%$ (rightmost structure, an 8-layer supercell with 7 GaAs layers separating MnAs ones); $16.7\%$ (6-layer supercell with 5 GaAs layers); $25\%$ (leftmost, 4-layer supercell with 3 GaAs layers); $50\%$ (2-layer supercell, not shown).

Figure 2

Spin-resolved density of states of the four studied Mn-doped GaAs heterostructures, compared with that of bulk GaAs (black dashed line). Panels (a) to (d) correspond to decreasing Mn concentrations, from $50\%$ to $12.5\%$. Spin-up and spin-down components are computed by projecting the spinorial wave functions onto the $S_z$-spin eigenstates. The inset of each figure shows a zoom in the vertical scale of the density of states in the minority-spin channel close to the Fermi level.

Figure 3

Kohn-Sham band structure and total DOS for the $25\%$ doping case [panel (b) of Fig. 2]. The red line is drawn at the Fermi energy.

Figure 4

Kohn-Sham band structure and total DOS for the $50\%$ doping case [panel (a) of Fig. 2]. The red line is drawn at the Fermi energy.

Figure 5

Projected density of states of the studied MnGaAs heterostructures. The projections on As $p$ orbitals [panels (a1)–(a3)], Mn $d$ orbitals [panels (b1)–(b3)], and Ga $p$ orbitals [panels (c1)–(c3)] are shown for the structures with 3 (blue), 5 (green), and 7 (red) GaAs layers between the Mn layers, respectively. The projection on As and Ga species is atom resolved. Atoms are selected according to their distance from the Mn layer, as 1st nearest neighbor (thick continuous line), 2nd (thick dashed line), 3rd (dotted line), and 4th (thin dashed line). The case of bulk GaAs is also shown for comparison (thin continuous black line).

Figure 6

Schematic electronic diagram for the As-Mn binding represented as two resonant configurations. Each Mn orbital has four first-nearest-neighbor As atoms. In a first approximation, a hole is shared between the four Mn-As $s{p}^3$ bond orbitals and the Mn $d$ orbitals. In practice the hole delocalizes also on the other $s{p}^3$ orbitals of the doped GaAs and is responsible of the ferromagnetic interaction between different Mn layers.

Figure 7

Computed UV-VIS absorption spectra for light polarization parallel to the Mn layers. Panel (a) shows the bulk GaAs case as reference, and Mn $\delta$-doped heterostructures with $12.5\%,16.7\%$, and $25\%$ Mn concentration are shown in panels (b), (c), and (d), respectively. The dashed lines and continuous lines represent the IP-RPA and RPA results, respectively. Theoretical spectra are compared with experimental data for bulk GaAs (circles in panel (a), from Ref. [27]) and for a uniformly Mn-doped GaAs sample at low doping concentrations (dots in panel (b), from Ref. [25]). We also compare with the FLAPW ab initio results of Ref. [10], computed for a uniformly doped system with a concentration of $6.25\%$ (dot-dashed line).

Figure 8

Computed UV-VIS absorption spectra of bulk GaAs [panel (a)] and Mn $\delta$-doped heterostructures with $12.5\%$ [panel (b)], $16.7\%$ [panel (c)], and $25\%$ [panel (d)] Mn doping, for light polarization perpendicular to the Mn layers (grazing incidence). As in Fig. 7, the dashed lines and continuous lines represent IP-RPA and RPA results, respectively.

Figure 9

Kerr parameters computed at the IP-RPA level for three Mn $\delta$-doped GaAs heterostructures. Central panels show the spectrum of the $12.5\%$ Mn DFH (red line); the results for the $16.7\%$ and $25\%$ Mn concentrations are shown in bottom panels (green and dashed blue lines, respectively). In the top panel, we show, for comparison, several experimental data for uniformly doped samples: black dots are for a $6\%$ Mn sample considered in Ref. [35], the red dots are for a $3\%$ Mn case (Ref. [28]), and violet dots refer to a $2\%$ Mn sample (Ref. [29]). Finally blue empty dots in right top panel are experimental data for the reflection MCD in a uniformly doped sample with $3\%$ Mn from Ref. [28]. In bottom panels, we report as dashed lines the results of FLAPW (LDA + stretched bands) calculations for a uniformly doped system, from Ref. [10].

Figure 10

Real and imaginary part of the diagonal and off-diagonal components of $\epsilon$ for the Mn $\delta$-doped GaAs heterostructure corresponding to a $12.5\%$ doping (Ref. [28]).

Figure 11

Faraday parameters/transmission MCD computed at the IP-RPA level for three Mn $\delta$-doped GaAs heterostructures, corresponding to $12.5\%,16.7\%$, and $25\%$ Mn concentrations. Black empty dots are experimental data for uniformly doped samples with $1\%$ Mn, from Ref. [36].