###### Abstract  
A compositionally homogeneous nonlinear optical single crystal of double-doped LiNbO\({}_{3}\)Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) was obtained. Fine features of the LiNbO\({}_{3}\)Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal structure were studied from the Raman spectra of the first and second orders upon excitation by laser lines in the visible (532 nm) and near-IR (785 nm) regions. When the Raman spectrum was excited by a 785 nm laser line in the frequency range of 1000-2000 cm\({}^{-1}\) for the first time, a number of low-intensity lines in the range of 900-2000 cm\({}^{-1}\), corresponding to the second-order Raman spectrum, were discovered. The same lines also appear in the spectrum upon excitation by a laser line with a wavelength of 532 nm, but their intensities are significantly (by an order of magnitude or more) lower. It is shown that in the structure of the double-doped LiNbO\({}_{3}\)Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%), the crystal oxygen-octahedral clusters MeO\({}_{6}\) (Me-Li, Nb, Gd, Mg) are slightly distorted, and in addition, the value R = [Li]/[Nb] \(\approx\) 1 is close to that for a nominally pure stoichiometric crystal. Footnote †: journal: _Applied Sciences_  
for traditional applications, and the optimization of photorefractive properties; for example, increasing the sensitivity and speed of information recording. For practice, the first task is much more important, since the use of a lithium niobate crystal in nonlinear optics as an active nonlinear laser medium, as well as for converting and modulating laser radiation, remains dominant. This task is especially relevant in the current intensive development of the method of optical frequency conversion in the regime of phase quasi-phase matching on regular domain structures (PPLN--\"periodically-poled LiNbO\({}_{3}\)\") [3]. LiNbO\({}_{3}\):Mg crystals are currently the most promising for the creation of highly advanced materials for radiation conversion [3; 4; 5; 6; 7; 8]. In the case of double doping, when one of the alloying elements is magnesium, it can be used to create optical materials of increased compositional homogeneity with a minimum photorefractive response time and a high resistance to optical damage [9; 10; 11; 12; 13; 14; 15; 16]. In highly perfect double-doped LiNbO\({}_{3}\) crystals, the fundamental absorption edge shifts to shorter wavelengths, and a noticeable increase in nonlinear optical coefficients is observed vs. one-time doped crystals [11; 12; 14; 16; 17]. Co-doping simultaneously with two \"non-photorefractive\" cations (Mg\({}^{2+}\) and Gd\({}^{3+}\)) makes it possible to control the ordering of structural units of the cationic sublattice along the polar axis and the polarizability of MeO\({}_{6}\) clusters (Me-Li, Nb, vacancy, and impurity metal) more finely than single doping. It also allows one to control the type and concentration of point and complex defects with localized electrons, which determine the magnitude of the photorefraction effect (optical damage) [1; 11]. This is due to the fact that both the Mg\({}^{2+}\) and Gd\({}^{3+}\) cations occupy mainly lithium positions in LiNbO\({}_{3}\) crystals [2]. Therefore, in co-doped LiNbO\({}_{3}\):Gd:Mg crystals, there is competition for the lithium positions between the Mg\({}^{2+}\) and Gd\({}^{3+}\) cations, which leads to a change in the number and type of defects, which are shallow and deep electron traps that increase the photorefraction effect. There is no such competition in LiNbO\({}_{3}\):Mg and LiNbO\({}_{3}\):Gd [1; 2]. Thus, it is of considerable interest to establish the possibility of controlling the optical and electrical properties of a LiNbO\({}_{3}\) crystal by doping LiNbO\({}_{3}\) crystals with various cations or groups of cations. Raman spectroscopy (RS) is a well-known method for studying various organic and inorganic compounds. This method has a high sensitivity, which makes it possible to study objects under difficult conditions.