Exchange and spin-orbit induced phenomena in diluted (Ga,Mn)As from first principles

Physical properties induced by exchange interactions (Curie temperature and spin stiffness) and spin-orbit coupling (anomalous Hall effect, anisotropic magnetoresistance, and Gilbert damping) in the diluted (Ga,Mn)As ferromagnetic semiconductor are studied from first principles. Recently developed Kubo-Bastin transport theory and nonlocal torque operator formulation of the Gilbert damping as formulated in the tight-binding linear muffin-tin orbital method are used. The first-principles Liechtenstein mapping is employed to construct an effective Heisenberg Hamiltonian and to estimate Curie temperature and spin stiffness in the real-space random-phase approximation. Good agreement of calculated physical quantities with experiments on well-annealed samples containing only a small amount of compensating defects is obtained.

Figure 1

The total magnetic moments in ${\mu }_{\mathrm{B}}$ as a function of the Mn concentration $x$ in (${\mathrm{Ga}}_{1-x},{\mathrm{Mn}}_x$)As alloys. (Left scale) Calculated magnetic moments (solid circles) and experiment [2] (open circles). (Right scale) Calculated values per Mn atom (solid diamonds) and experimental values [2] (open diamonds).

Figure 2

Calculated (solid circles) and experimental (open diamonds [2] and solid diamonds [5]) values of the Curie temperature (a) and the spin stiffness (b) plotted as a function of the concentration $x$ in (${\mathrm{Ga}}_{1-x},{\mathrm{Mn}}_x$)As alloys. The RPA approach which includes percolation effects for random spins in the simulation cell is employed.

Figure 3

Calculated ${\sigma }_{\mathrm{tot}}$ in the logarithmic scale (solid circles) for (${\mathrm{Ga}}_{1-x},{\mathrm{Mn}}_x$)As as a function of the Mn concentration $x$ is compared with experimental data [2] (open diamonds) and [5] (solid diamonds). The conductivities corresponding to compensating defects (the models A, B, and C in Table 1) are shown by various square symbols.

Figure 4

Calculated AHC ${\sigma }_{xy}$ (solid circles) as a function of the Mn concentration for (${\mathrm{Ga}}_{1-x},{\mathrm{Mn}}_x$)As are compared with results of two experiments: Ref. [5] (solid diamonds) and Ref. [36] (open diamonds).

Figure 5

The calculated values of ${\rho }_{xy}$ (solid circles) and corresponding experimental results, Ref. [5] (solid diamonds) and Ref. [36] (open diamonds). Note the opposite sign of ${\rho }_{xy}$.

Figure 6

(Left scale) The calculated Gilbert damping constants $\alpha$ (solid circles) as a function of the Mn concentration $x$ in (${\mathrm{Ga}}_{1-x},{\mathrm{Mn}}_x$)As alloys. Half-filled square symbols show values for 10% of spins with reversed orientation at $x=0.025$ and $x=0.06$ calculated in the framework of the uDLM approach (see the text). The experimental values [2] (open circles) are also shown for comparison. (Right scale) The ratio DOS($E_{\mathrm{F}}$)/$M_{\mathrm{spin}}$ of the density of states at the Fermi energy to the total spin magnetic moment (diamonds) is shown as a function of $x$.