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Electronic and magnetic properties of Ga$_{1-x}$Mn$_{x}$As, obtained fromfirst-principles calculations employing the hybrid HSE06 functional, arepresented 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 non-hybridized Mn-3$d$ levels and Mn-induced states resideabout 5 and 0.4 eV below the Fermi energy, respectively. For elevatedpressures, the Mn-3$d$ levels, Mn-induced states, and the Fermi level shifttowards higher energies, however, the position of the Mn-induced statesrelative to the Fermi energy remains constant due to hybridization of theMn-3$d$ levels with the valence As-4$p$ orbitals. We also evaluate, employingMonte Carlo simulations, the Curie temperature ($T_{{\rm C}}$). At zeropressure, 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 estimatedvalue of d$T_{{\rm C}}$/d$p\approx+2.2$K/GPa for $x=6.25\%$ under pressures upto 6 GPa. The determined values of d$T_{{\rm C}}$/d$p$ compare favorably withd$T_{{\rm C}}$/d$p=+$(2-3) K/GPa at $p\leq1.2$GPa found experimentally andestimated within the $p$-$d$ Zener model for Ga$_{0.93}$Mn$_{0.07}$As in theregime where hole localization effects are of minor importance [M.Gryglas-Borysiewicz $et$ $al$., Phys. Rev. B ${\bf 82}$, 153204 (2010)].

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