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

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 photoemission 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$p\approx+2.2$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 $p\leq1.2$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)].