Unusual Directional Dependence of Exchange Energies in GaAs Diluted with Mn: Is the RKKY Description Relevant?

Ferromagnetism in Mn-doped GaAs, the prototypical dilute magnetic semiconductor (DMS), has so far been attributed to hole mediated RKKY-type interactions. First-principles calculations reveal a strong direction dependence of the ferromagnetic (FM) stabilization energy for Mn pairs, a dependence that cannot be explained within RKKY. In the limit of a hostlike hole engineered here where the RKKY model is applicable, the exchange energies are strongly reduced, suggesting that this limit cannot explain the observed ferromagnetism. The dominant contribution stabilizing the FM state is found to be maximal for $⟨110⟩$-oriented Mn pairs and minimal for $⟨100⟩$-oriented Mn pairs, providing an alternate explanation for magnetism in such materials in terms of energy lowering due to $p$-$d$ hopping interactions, and offering a new design degree of freedom to enhance FM.

Figure 1

The broadened up ($+$), down ($-$) spin TM $d$ PDOS in spheres of radius $1.2\AA$ with $t_2$, $e$ symmetry for different TMs.

Figure 2

Schematic energy levels for two interacting TM with their spins FM [(a),(c)] and AFM [(b),(d)] aligned and highest occupied level fully [(a),(b)], partially [(c),(d)] filled.

Figure 3

Distance/orientation dependence of $E_{\mathrm{F}\mathrm{M}}/E_{\mathrm{A}\mathrm{F}\mathrm{M}}$ for two (a) V, (b) Fe, (c) Cr , (d) Mn in 64 atom GaAs cell using USP potentials [using PAW in (d) in parentheses]. The upper $x$ axis gives the direction of the vector joining the two TM atoms.

Figure 4

The distance/orientation dependence of $J_{ij}$ for Mn pairs in (a) 256, (b) 64 atom GaAs cell using PAW potentials. The expected dependence of $J_{\mathrm{R}\mathrm{K}\mathrm{K}\mathrm{Y}}$ for a hole in GaAs is given in the inset.

Figure 5

The up [(a) and inset] and down (b) spin Mn $t_2$ PDOS for $U=0$ (thin solid line), $U=6$ (dashed line), $U=10$ (dash-dotted line), and $U=15$ (thick solid line) eV. Hole wave function squared in the $⟨110⟩$ plane are shown for $U=0$, and $U=10$ in parts (c) and (d), respectively.