First-Principle\nCalculations and Experimental Investigation\nof Structure, Defect, and Spectra Properties of Yb<sup>3+</sup>-doped\nNaGd<sub>(1–<i>x</i>)</sub>La<sub>(<i>x</i>)</sub>(MoO&lt

Inhomogeneous broadening in disordered\ncrystals has been\nwidely\nrecognized as a successful approach to enhance the spectral bandwidth\nof rare earth ions in optical spectra, and the Yb<sup>3+</sup>-doped\nmixed laser crystals are known as ultrafast pulse materials and have\nemerged as a hotspot recently. In this study, mixed sodium gadolinium/lanthanum\ndouble molybdate disordered laser crystals NaGd<sub>(1–<i>x</i>)</sub>La<sub>(<i>x</i>)</sub>(MoO<sub>4</sub>)<sub>2</sub> with <i>x</i> = 0.3, 0.5, and 0.9 were grown\nby the Czochralski (Cz) method. The structure of as-grown crystals\nwas investigated by XRD, SEM, FT-IR, and Raman experiments. The spectroscopic\nproperties, including absorption, emission, and fluorescence decay\ncharacteristics, were investigated thoroughly. The NaGd<sub>0.5</sub>La<sub>0.5</sub>(MoO<sub>4</sub>)<sub>2</sub> (NGLM) composite crystal\nexhibited an exceptionally broad absorption which reaches 70 nm (fwhm)\nat 980 nm, exceeding those of NaGd(MoO<sub>4</sub>)<sub>2</sub> (NGM)\nand NaLa(MoO<sub>4</sub>)<sub>2</sub> (NLM). Additionally, the electronic\nstructures (band structure and density of states) of NGM, NGLM, and\nNLM were determined from the first-principles method combined with\nthe PBE function. The calculations of defect formation energies under\nO-poor and O-rich conditions demonstrate that the +2 defects are easily\ngenerated in the undoped NGM crystal prepared under reducing atmospheres,\nand the calculation of absorption properties reveals that the black\ncolor of NGM without annealing is mainly attributed to intraband transitions\nbetween defect induction states and VBM or CBM. Moreover, the lifetimes\nof excited energy level <sup>2</sup>F<sub>5/2</sub> of Yb<sup>3+</sup> were examined under different experimental environments to obtain\nthe intrinsic radiative lifetime, and the emission cross section was\ncalculated as 2.25 × 10<sup>–20</sup> cm<sup>2</sup> at\n1016 nm. The features of the Yb<sup>3+</sup>:NaGd<sub>(1–<i>x</i>)</sub>La<sub>(<i>x</i>)</sub>(MoO<sub>4</sub>)<sub>2</sub> crystal indicate the potential applications for ultrafast\nand broad tunable laser through slight regulation of the composite\nengineering strategy.