Electronic structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>?</mml:mi><mml:mo>?</mml:mo><mml:msub><mml:mi mathvariant="normal">Al</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Mg</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Al</mml:mi><mml:mn>13</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>4</mml:mn></…

We report a comparative study of the bulk electronic structure two Al-based complex metallic alloys (CMAs), $\ensuremath{\beta}\ensuremath{-}{\mathrm{Al}}_{3}{\mathrm{Mg}}_{2}$ and ${\mathrm{Al}}_{13}{\mathrm{Fe}}_{4}$ using hard x-ray photoemission spectroscopy (HAXPES) interpreted on basis density functional theory (DFT) calculations. An experimental confirmation role Hume-Rothery mechanism for stability phase is established by identification shallow pseudogap near ${E}_{F}$ from HAXPES that corroborated DFT. almost parabolic shape states (DOS), large $n$(${E}_{F}$), plasmon loss features are similar to Al metal show its nearly free-electron-like nature. In case total DOS exhibits due $s$ -- Fe $d$ hybridization, which results in at [$n$(${E}_{F}$)] being states. However, deep this revealed because cross section high photon energies. The overall valence band excellent agreement with DFT both CMAs. larger width core-level main peak peaks as well suppression intensities latter respect further underline importance $sp\text{\ensuremath{-}}d$ hybridization ${\mathrm{Al}}_{13}{\mathrm{Fe}}_{4}$.