## 4 Conclusions  
In this work, the full Raman spectra of the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal, which is a promising material for laser radiation conversion, are recorded in the backscattering geometries \(x(zz,zy)\overline{x}\), \(y(zz,zx)\overline{y}\), and \(z(xx,yy,xy)\overline{z}\). We have given an interpretation of the registered Raman lines, including lines with ambiguous assignments. The Raman spectra show that, in the structure of the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\) (0.65 wt.%) crystal, oxygen-octahedral clusters of MeO\({}_{6}\) (Me-Li, Nb, Gd, and Mg) are slightly distorted, and in addition, the value of R = [Li]/[Nb] is increased compared to that for a congruent crystal. That is, during doping, an increase in the stoichiometry of the crystal occurs. The fact of the increase in stoichiometry is confirmed by the fact that the Raman spectrum of the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal lacks a low-intensity line with a frequency of 120 cm\({}^{-1}\), corresponding to two-particle states of acoustic phonons with a total wave vector that is close to zero. Its absence in the spectrum also indicates a small anharmonic interaction of the lowest-frequency fundamental vibration A\({}_{1}\)(TO)-symmetry type (quasi-soft mode) with the acoustic continuum. A low-intensity line with a frequency of 120 cm\({}^{-1}\) is confidently observed in the spectra of non-stoichiometric LiNbO\({}_{3}\) crystals, nominally pure and doped, and this is absent in the Raman spectra of a stoichiometric crystal [2]. The results obtained indicate a high degree of structural perfection of the crystal and allow us to state that the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal is close in some of its properties to the stoichiometric LiNbO\({}_{3}\) crystal. One of the properties of stoichiometric and magnesium-doped LiNbO\({}_{3}\) crystals that is important for creating materials for laser radiation conversion on periodically polarized submicron-sized domains with flat boundaries [4; 5; 6] is a low value of the coercive field (\(\approx\)2.3 kV/cm). In a congruent LiNbO\({}_{3}\) crystal, the coercive field is much higher, \(\approx\)23.0 kV/cm.  
Figure 4: Raman scattering spectra of the crystal LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) in the region of two-phonon states: 1—experimental curve, 2 and 3—calculated dependences.  
When the Raman spectrum of a LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal is excited by a laser line with a wavelength of 532 nm, the intensities of the lines corresponding to the second-order spectrum are significantly (by an order of magnitude or more) less than the intensities of the second-order lines observed at excitation with a 785 nm laser line. At the same time, in the Raman spectrum in the region below 900 cm\({}^{-1}\), no lines were found to correspond to the second-order spectrum, as well as lines with frequencies of 209, 230, 298, and 880 cm\({}^{-1}\) crystals of LiNbO\({}_{3}\):Mg [30]. A comparison of the second-order Raman spectra shows that the near-IR laser line makes it possible to detect more second-order Raman lines.  
Conceptualization, N.S. and A.S.; methodology, N.S., M.P. and A.S.; software, A.S.; formal analysis, A.S.; investigation, A.P.; resources, N.S. and M.P.; data curation, A.P.; writing--original draft preparation, A.S., A.P. and N.S.; writing--review and editing, M.P.; visualization, A.P.; supervision, N.S. All authors have read and agreed to the published version of the manuscript.  
This study was supported by Ministry of Science and Higher Education Russian Federation scientific topic No 0186-2022-0002 (FMEZ-2022-0016) and the RFBR and BRFBR (grant No. 20-52-04001 Bel_mol_a).  
Not applicable.  
Data Availability StatementData on this research will be available from the corresponding author, A.P., upon reasonable request.  
The authors declare no conflict of interest.