(Ga,Mn)As under pressure: A first-principles investigation

Electronic and magnetic properties of ${\mathrm{Ga}}_{1-}{}_x\text{Mn}{}_x\text{As}$, obtained from first-principles calculations employing the hybrid HSE06 functional, are presented for $x=6.25\%$ and 12.5% under pressures ranging from 0 to 15 GPa. In agreement with photoemission experiments at ambient pressure, we find for $x=6.25\%$ that nonhybridized Mn $3d$ levels and Mn-induced states reside about 5 and 0.4 eV below the Fermi energy, respectively. For elevated pressures, the Mn $3d$ levels, Mn-induced states, and the Fermi level shift toward higher energies, however the position of the Mn-induced states relative to the Fermi energy remains constant due to hybridization of the Mn $3d$ levels with the valence As $4p$ orbitals. We also evaluate, employing Monte Carlo simulations, the Curie temperature $\left({\mathit{T}}_{\mathrm{C}}\right)$. At zero pressure, we obtain ${\mathit{T}}_{\mathrm{C}}=181$ K, whereas the pressure-induced changes in ${\mathit{T}}_{\mathrm{C}}$ are $d{T}_{\mathrm{C}}/dp=+4.3$ K/GPa for $x=12.5\%$ and an estimated value of $d{T}_{\mathrm{C}}/dp\approx +2.2$ K/GPa for $x=6.25\%$ under pressures up to 6 GPa. The determined values of $d{T}_{\mathrm{C}}/dp$ compare favorably with $d{T}_{\mathrm{C}}/dp=+(2$–3) K/GPa at $p$ $\le 1.2$ GPa found experimentally and estimated within the $p\text{−}d$ Zener model for ${\mathrm{Ga}}_{0.93}{\mathrm{Mn}}_{0.07}\text{As}$ in the regime where hole localization effects are of minor importance [M. Gryglas-Borysiewicz et al., Phys. Rev. B 82, 153204 (2010)].

Figure 1

Spin-resolved DOS in logarithmic scale of ${\mathrm{Mn}}_{0.0625}{\mathrm{Ga}}_{0.9375}\text{As}$ (one Mn atom per supercell) at hydrostatic pressures of 0, 7, and 15 GPa. Light gray denotes the total DOS, whereas the Mn $3d$ projected DOS is shown in black. All the energy values are referred to the position of the main peak of the Mn $3d$ states. The dashed vertical line indicates the Fermi level.

Figure 2

Majority spin band gap of ${\mathrm{Ga}}_{0.9375}{\mathrm{Mn}}_{0.0625}\text{As}$ and the band gap of GaAs plotted as a function of pressure. In both cases, the direct-to-indirect band-gap transition occurs at $\sim 6$ GPa.

Figure 3

Nearest-neighbor distances $d$ plotted as a function of pressure for ${\mathrm{Mn}}_{\mathrm{S}}\text{−}{\mathrm{Mn}}_{\mathrm{I}\left(\mathrm{Ga}\right)}$ (circles) and ${\mathrm{Mn}}_{\mathrm{S}}\text{−}{\mathrm{Mn}}_{\mathrm{S}}$ (squares) pairs in GaAs.

Figure 4

Total energy difference per ion between the FM and AFM configurations for ${\mathrm{Mn}}_{\mathrm{S}}\text{−}{\mathrm{Mn}}_{\mathrm{I}\left(\mathrm{Ga}\right)}$ (circles) and ${\mathrm{Mn}}_{\mathrm{S}}\text{−}{\mathrm{Mn}}_{\mathrm{S}}$ (squares) pairs in GaAs as a function of pressure. For ${\mathrm{Mn}}_{\mathrm{S}}\text{−}{\mathrm{Mn}}_{\mathrm{S}}$, we have considered NN and NNN positions in the Ga sublattice.

Figure 5

Curie temperature of (Ga,Mn)As calculated within MFA (squares) and MC (circles) methods as a function of pressure. The given values of the pressure coefficients correspond to the region below 6 GPa marked by a dashed line.