Electronic and magnetic properties of Ga$_{1-x}$Mn$_{x}$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 photoem
ission experiments at ambient pressure, we find for $x=6.25%$ that non-hybridized Mn-3$d$ levels and Mn-induced states reside about 5 and 0.4 eV below the Fermi energy, respectively. For elevated pressures, the Mn-3$d$ levels, Mn-induced states, and the Fermi level shift towards higher energies, however, the position of the Mn-induced states relative to the Fermi energy remains constant due to hybridization of the Mn-3$d$ levels with the valence As-4$p$ orbitals. We also evaluate, employing Monte Carlo simulations, the Curie temperature ($T_{{rm C}}$). At zero pressure, we obtain $T_{{rm C}}=181$K, whereas the pressure-induced changes in $T_{{rm C}}$ are d$T_{{rm C}}$/d$p=+4.3$K/GPa for $x=12.5%$ and an estimated value of d$T_{{rm C}}$/d$papprox+2.2$K/GPa for $x=6.25%$ under pressures up to 6 GPa. The determined values of d$T_{{rm C}}$/d$p$ compare favorably with d$T_{{rm C}}$/d$p=+$(2-3) K/GPa at $pleq1.2$GPa found experimentally and estimated within the $p$-$d$ Zener model for Ga$_{0.93}$Mn$_{0.07}$As in the regime where hole localization effects are of minor importance [M. Gryglas-Borysiewicz $et$ $al$., Phys. Rev. B ${bf 82}$, 153204 (2010)].
