Evolution of Fe 3 d impurity band state as the origin of high Curie temperature in the p -type ferromagnetic semiconductor (Ga,Fe)Sb

$({\mathrm{Ga}}_{1\ensuremath{-}x},{\mathrm{Fe}}_{x})\mathrm{Sb}$ is one of the promising ferromagnetic semiconductors for spintronic device applications because its Curie temperature $({T}_{\mathrm{C}})$ is above 300 K when the Fe concentration $x$ is equal to or higher than \ensuremath{\sim}0.20. However, the origin of the high ${T}_{\mathrm{C}}$ in (Ga,Fe)Sb remains to be elucidated. To address this issue, we use resonant photoemission spectroscopy (RPES) and first-principles calculations to investigate the $x$ dependence of the Fe $3d$ states in $({\mathrm{Ga}}_{1\ensuremath{-}x},{\mathrm{Fe}}_{x})\mathrm{Sb}$ ($x=0.05$, 0.15, and 0.25) thin films. The observed Fe $2p\text{\ensuremath{-}}3d$ RPES spectra reveal that the $\mathrm{Fe}\text{\ensuremath{-}}3d$ impurity band (IB) crossing the Fermi level becomes broader with increasing $x$, which is qualitatively consistent with the picture of double-exchange interaction. Comparison between the obtained $\mathrm{Fe}\text{\ensuremath{-}}3d$ partial density of states and the first-principles calculations suggests that the $\mathrm{Fe}\text{\ensuremath{-}}3d$ IB originates from the minority-spin ($\ensuremath{\downarrow}$) $e$ states. The results indicate that enhancement of the double-exchange interaction between ${e}_{\ensuremath{\downarrow}}$ electrons with increasing $x$ is the origin of the high ${T}_{\mathrm{C}}$ in (Ga,Fe)Sb.