Abstract
Abstract In this thorough investigation, we analyze the complex electronic, magnetic, and structural properties of wurtzite-structured aluminum gallium nitride (Al0.125Ga0.75N) when co-doped with the rare-earth elements erbium and europium. Leveraging a modified LSDA+U approach that adeptly captures the pivotal interactions within the 4f shell, our findings unveil that the co-doped AlGaN exhibits distinct semiconducting behavior. Remarkably, in stark contrast to its pristine Al0.125Ga0.75N counterpart, the co-doped material manifests an indirect band gap whose value is notably reduced. This intriguing phenomenon of ferromagnetism observed in the co-doped system can be attributed to the intricate interplay between the f-p and p-d states, culminating in the formation of hybridized f-p-d orbitals. Our investigation further elucidates the intricate hybridization of various orbitals at the valence band maximum (VBM), including the harmonious fusion of p-d orbitals derived from Eu-5d, Er-5d, and N-2p. Notably, the magnetic moment exhibits a pronounced localization at the Eu and Er sites, attaining substantial values of 5.90 μB and 2.99 μB, respectively. Moreover, our comprehensive exploration encompasses the calculation of the real and imaginary components of the dielectric function, refractive index, and extinction coefficient, spanning an impressive photon energy range of up to 12 eV. Significantly, in the ultraviolet region of the optical spectrum, the imaginary part of the Eu and Er co-doped Al0.125Ga0.75N unveils a pronounced absorption coefficient, a pivotal property with far-reaching implications for optoelectronic applications.

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