Synthesis, Characterization, and Second Harmonic Generation of Multiferroic Iron‐Doped Lithium Niobate Powders

Random granular media can exhibit characteristics that are often related to ordered media. In the present work, this feature is observed in the polarized Second Harmonic Generation (SHG) response from reduced iron‐doped lithium niobate (LN:Fe) powders, which is an unexpected effect due to multiple scattering. In addition, the subsisting‐order properties of the powders can be further controlled by magnetic induction to tailor the SHG response. The samples are characterized by X‐ray Diffraction (XRD), X‐ray Photoelectron Spectroscopy (XPS), and confocal Raman Spectroscopy. The SHG response in the absence and presence of an external static magnetic field is then studied as the fundamental beam focus is translated from air into the powder. The SHG intensity polarization state is studied as a function of the linear polarization of the fundamental beam at the focus depth position, where the maximum SHG recorded intensity is observed. These results demonstrate that the SHG response of LN:Fe powders can be modified by post‐thermal treatment in a reducing atmosphere for photonic applications.


Introduction
Lithium niobate (LN, chemical formula LiNbO 3 ) is a synthetic bi-metallic oxide that exhibits high chemical stability and high DOI: 10.1002/aelm.202300450melting point.It is insoluble in water and in other organic solvents.Intrinsically, LN adopts a crystalline ferroelectric phase for a wide range of temperatures, from room temperature (RT) to ≈1200 °C.Large electro-and acoustooptical coefficients are ascribed to this phase, lending to this material attractiveness for applications in the fields of actuators, sensors, or transducers, notably for medical ultrasound devices, thermal sensors, sonar systems, or precise positioners among others. [1,2]Ferroelectric LN also exhibits high nonlinear optical coefficients.Efficient coherent Second Harmonic Generation (SHG) can be obtained from this material within a broad range of fundamental excitation wavelengths with the corresponding second-order susceptibility tensor possessing three non-zero and independent tensor elements, namely d 33 , d 31 , and d 22 . [3]Coherent SHG is lost in the case of polycrystals, that is, thin films or powders, owing to intrinsic material randomization which could be twofold: spatial randomization (single nanocrystals in larger grains can have any possible orientation with respect to each other) and randomization of the refractive index (it can vary from nanocrystal to nanocrystal according to the flexibility that characterizes the crystal structure of LN in adopting a continuous chemical composition within the range of ratios Li:Nb from 50.0:50.0to ≈48.4:51.6,RT conditions).
Recent developments have put LN into the scene in the rapidly growing field of applications in photonics, [4] to the extent that the once coined term "the silicon of photonics" (2009) reverberates.LN has been highlighted as a potential cornerstone in photonics, similar to the use of Si in electronics. [5,6]But none of these applications can be envisioned for polycrystals, as incoherent light is a serious hindrance for any thinkable optical application.However, profits can still be obtained by studying the optical SHG response of the polycrystalline solid solutions of LN.The incoherent feature of the response signal can be overcome by combining an appropriate experimental apparatus and ultrasensitive detection devices, such as cooled photomultipliers and charge-coupled device cameras.Any surface or interface can then be assessed by analyzing the SHG response. [7,8]n this work, LN powders are being tested as they exhibit important ferromagnetic properties at RT when suitably doped with Fe ions and post-thermally treated in a reducing atmosphere. [12]The connection between RT ferromagnetism in Fe-doped LN (hereafter referred to as LN:Fe) powders can be formally described based on the framework of the Diluted Magnetic Oxides. [13]Our group has recently reviewed the subject, and earlier and current investigations regarding the manifestation of magnetic and ferromagnetic behavior in LN:Fe (single crystals and polycrystals) have been discussed in detail. [14]In the present study, the consequences of the ferromagnetic properties of LN:Fe powders were investigated, and the order/disorder of the powders was discussed using the SHG process and the deviation from the expected responses from purely random powders. [15,16]

Results and Discussion
In total, 21 samples were obtained.They can be classified into three main groups after post-thermal treatment: untreated, reduced, and oxidized.According to this classification, the samples were labeled as shown in Table 1.
Controlling the oxidization state of the samples is important because the reduced LN:Fe powders exhibit a saturation magneti-zation that is approximately two orders of magnitude higher than that of the corresponding oxidized samples. [12]The coexistence of valence states Fe 2+ and Fe 3+ in LN:Fe nanocrystalline powders has been reported where a ratio of 0.15 holds for untreated samples. [17]This value can be lowered by applying a suitable oxidizing thermal treatment; alternatively, a reducing atmosphere can be used to reach a stable thermodynamic state for which the fraction of the Fe 2+ population is ≈1.Oxidized samples are regularly considered passivated samples because V O oxygen vacancies are not expected in these samples.Thus, the redox state of the samples could be effectively controlled if reducing treatments were applied first, followed by oxidation.All the oxidized samples studied in the present investigation were first reduced.Reproducible and consistent results are obtained using this approach.However, because LN is tacitly acknowledged to be a unique oxide without V O 's, [18] no significant differences are expected between untreated LN:Fe and oxidized LN:Fe-ox powders, neither structurally nor in their performance in nonlinear optics.To observe the impact of the state of the LN:Fe powders, thorough characterization was performed.

X-Ray Diffraction
Figure 1 displays the recorded X-ray Diffraction (XRD) patterns of a) untreated pristine LN powders (sample pLN), b) raw iron oxide powder used for Fe-doping and its evolution after being reduced and oxidized, and c) reduced LN:Fe samples.In Figure 1a, the Bragg reflections comprise only the peaks of a trigonal crystal structure with a hexagonal basis (lattice constants a = b = 0.515, and c = 1.386 nm) indicating the formation of a stable crystal structure LiNbO 3 (COD 2 101 175).The original diffraction data were obtained from the Crystallographic Open Database. [19]he average Li:Nb = 48.9:51.1 was determined after structural refinement using the Rietveld method and equation 2 in ref. [20]  Thus, the pristine samples are off-stoichiometric with a chemical composition close to the congruent point, namely Li:Nb = 48.5:51.5.Therefore, the population of intrinsic point defects is rather high because the doping process becomes synergetic when the cationic vacancies are disposable.However, Figure 1b shows that the Fe 2 O 3 powder, when undergoing phase transitions into metallic iron (-Fe, JCPDS PDF 00-006-0696), recovered its structural characteristics (hematite-Fe 2 O 3 , JCPDS PDF 04-015-6943) after being subjected to the same thermal treatments as those used for the pLN and LN:Fe samples, that is, reduction and oxidation.The original diffraction data were obtained using the Powder Diffraction File (ICDD). [21]In Figure 1c, it is worth noting that in the ≈50-65°2 range, four peaks of intermediate intensity are located close to six peaks of the LN phase, which are also of intermediate intensity.These data show the unaltered XRD patterns recorded for the three cases with higher doping concentrations.Identical curves of nearly constant intensity over the entire studied 2 range are shown for sample 22LN:Fe-re to sample pLN-re, which were processed simply by calculating the quotient (normalized data in both inputs) between the corresponding sample and the pLNre sample.The observed common baseline was interpreted as the retention of the LN solid solutions.Thus, chemical solubility was achieved beyond a doping concentration of 3.3 wt.% Fe 2 O 3 .The XRD pattern of sample 33LN:Fe-re was also clean, similar to that of the pure ferroelectric LiNbO 3 phase; neither the Bragg reflections of the secondary phases related to Fe nor those of the precursors used for the synthesis could be tracked.However, an additional reflection of low intensity can be observed at ≈2 = 45°for the 45LN:Fe-re and 60LN:Fe-re samples.It pertains to the main diffraction peak of metallic iron (-Fe, JCPDS PDF 00-006-0696) and its intensity increased with the doping concentration.Interestingly, the lack of distinctive features indicating that the solubility limit at a doping concentration of 4.5 wt.% Fe 2 O 3 had been reached, could be observed in the XRD patterns of the untreated and oxidized sets of samples (Figure S2, Supporting Information).This was possible owing to the overlapping of the diffraction peaks ocurring in the 2 range ≈50-65°.Hence, possible misconceptions could arise regarding the structural characteristics of LN:Fe powders if they are not subjected to a reducing post-thermal treatment.However, as shown in Table 2, such an undesirable fact can be overcome with structural refinement, because a phase quantification analysis leads to correct conclusions irrespective of the oxidation state.
From the data available in Table 2, it can be argued that a maximum of 1% (3%) of the secondary phase was present in the powders doped with a 4.5 (6.0) wt.% Fe 2 O 3 .It is worth mentioning that, in view of the Second Harmonic Generation (SHG) response, another classification of the synthesized materials holds in terms of the concentration of doped iron, as it can be the lowest, intermediate, or highest.For practical purposes, the 1% of the second phase was considered marginal within the scope of this research; thus, the 45LN:Fe samples were denoted as the highest cases in the SHG analysis.Meanwhile, refinement of the crystal  structures also sheds light on the local environment of the unit cell, that is, a glance at the distribution of intrinsic and extrinsic point-defect complexes. [2]The evolution of the structure in terms of the synthesis parameters is conventionally assessed by extracting the resulting lattice constants (a, b, c) for a given number of experimental points.Usually, small differences in plots with a lattice parameter as the ordered axis are more discernible or significant when the entire set of parameters is circumscribed into the unit cell volume defined by formula √ 3a 2 c/2 for a hexagonal setting. [2,18]The unit cell volumes of all polycrystalline samples synthesized in this study are shown in Figure 2a.Correspondingly, Figure 2b shows that the mean crystallite size is on the order of 60-100 nm whereas Figure 2c indicates that the executed routines converged giving satisfactory agreement between the empirical and calculated patterns.The continuous relaxation of the crystal structure holds for the reduced samples, as inferred from the observed monotonic increase in the unit cell volume with the doping concentration.A change in the rate occurred at point 22LN:Fe-re.On the other hand, as expected, the untreated and oxidized crystal structures show identical local environments up to a critical point of 45LN:Fe(-ox): relaxation of the structures takes place first, followed by a contracting mechanism as the doping concentration increases (inflection points can be noted at 1.5 and 2.2 wt.% Fe 2 O 3 samples).
The most widely accepted defect scenario is the lithiumvacancy model. [14]Within this framework, neither oxygen vacancies (V O ) nor niobium vacancies (V Nb ) are assumed to exist, and the formation of a single Nb antisite defect (Nb Li ) is compensated by the formation of four Li vacancies (V Li ); whose constitutional formula is [Li 1−5x V 4x Nbx]NbO 3 , x = 0.01. [22]Although it is acknowledged that debate still prevails on the most appropriate defect model that solves electronic charge neutrality in off-stoichiometric LN, it must also be stated that all the available evidence, collected either empirically, or by ultimate computer simulations, points toward the univocal existence of Nb Li antisites. [23]Such an intrinsic point defect in LN denotes the occurrence of a stacking fault that compensates for the charge imbalance, which is compromised by the inexorable tendency of this compound to crystallize and form solids with a Li deficiency (or Nb surplus). [2,14]In consequence, for extrinsic defects in the case of elemental doping, the inserted cations occupy the first V Li vacancies while substituting Nb in Li sites (replacement of Nb Li ) before it takes place a substitution mechanism for Li Li and Nb Nb entities.
Many factors influence the observed trends in site occupancy and doping mechanisms (dopant concentration, ionic radii, valence states, etc.); however, there seems to be concomitant evidence that all types of dopants (irrespective of their nature or functionality when doped in LN) are predominantly localized at the Li sites when small doping concentrations are used.Two statements can be made regarding the occupancy/substitution mechanisms in doped LN.One is that the dopant ions tend to occupy Li sites first, either V Li or Li Li . [14]Second, if the content is being added continuously, a critical instance is reached where the dopants begin to substitute Nb in Nb sites just before the chemical solubility of the pristine LN crystal structure is exhausted. [14]aturally, the latter depends on the initial intrinsic defect structure, that is, the number of available V Li and Nb Li vacancies, which is characterized by a macrostate chemical composition with a given ratio [Li]/[Nb] < 1.This picture was constructed based on several reports in which Mg 2+ and other optical damageresistant ions (ODRI) have been used as doping entities.Recently, Kovacs et al. observed the same ODRI trend for some transition metals and lanthanide trivalent rare-earth ions. [24]There is evidence that Fe tends to occupy Li sites rather than Nb sites, irrespective of the oxidation state, in similar LN:Fe systems. [25]Some pioneering studies focused on controlling the Fe 2+ and Fe 3+ populations employing annealing (post-thermal treatments) are also worth mentioning. [26]lthough various counter examples can be found in the available literature, [14] it is thus possible to conceptualize that all kinds of impurity ions adjust to the following order: 1) simultaneous occupation of Li vacancies and substitution of Nb antisites (once depleted); 2) substitution of Li in Li sites; 3) substitution of Nb in Nb sites; and 4) soon afterward, the limit of solubility is reached and segregation follows upon adding further doping content.If such a depiction is adopted, it is convenient to define the critical instances of the starting points of stages ( 2) and (3) as the first concentration threshold (FCT) and second concentration threshold (SCT), respectively.The significance of the term ´concentration threshold ´has been proposed in earlier studies, ref. [18,24b]  and it must also be noted that this differs slightly from the sense that is usually attributed to it within the subfield of knowledge regarding LN-doped (only) with ODRI.
Hence, considering the discussion in the preceding paragraphs, the trends shown in Figure 2a can be interpreted as follows: The FCT of the synthesized LN:Fe powders was reached between the doping concentrations of 1.5 and 2.2 wt.% Fe 2 O 3. The post-thermal treatment in a reducing atmosphere is only sensitive to the chemical/physical instance in which all the Li vacancies have been filled, while all the Nb antisites have been completely removed, whereas the untreated and oxidized curves discriminate between both occupancy/substitution mechanisms.Under the assumption that most of the doped Fe ions share a common 3+ oxidation state for the untreated and oxidized samples, the observed increasing-decreasing-constant behavior in Figure 2a can be understood in terms of atomic size effects and their influence within the crystal structure (Table S1, Supporting Information file for the effective ionic radii for the species of interest with sixfold coordination). [27]The relaxation of the crystal structure follows the filling of vacant Li sites (V Li − ) with Fe 3+ of comparable larger dimensions,≈64.5 pm, up to point 15LN:Fe(ox).Then, it contracts owing to the cationic interchange with slightly larger Nb Li 4+ (size of ≈69 pm) up to point 22LN:Fe(-ox), where a change in the rate of the ongoing contracting mechanism results from the tuning of the interchange to Li Li + (size of ≈74 pm).At some stage between points 33LN:Fe(-ox) and 45LN:Fe(-ox), the atomic size effects should be minimal because of the inferred cationic interchange with the regular Nb sites (Nb Nb 5+ , with a size of ≈64 pm), as confirmed by the observed nearly constant behavior.The quotient between the atomic radii of Nb 5+ and Fe 3+ was 0.99.Similarly, if a multitudinous change in the oxidation state Fe 2+ → Fe 3+ is assumed after the application of the reducing treatment, the same comparative analysis can provide a satisfactory explanation for the observed trend in the reduced samples (line with empty squares).However, besides the fact that Fe 3+ possesses the largest ionic radius among the ions discussed, it should also be considered that thorough relaxation of the structure may be assisted by volumetric electronic charge redistributions arising from the multitudinous creation of oxygen vacancies at the surface.
LN powders with an overall stoichiometric composition were used as pristine samples and fitted into the present discussion (ref.[12]).However, the SCT cannot be resolved explicitly by refining the XRD results (Figure 2a), although it is expected to lie somewhere between points 3.3 and 4.5 wt.% Fe 2 O 3 .The analysis of the Raman spectra not only confirms the entailed arguments concerning the FCT but also that sensitivity to SCT can be reached.Finally, Figure 2a can also be considered an excerpt of evidence that neglects the aesthetic idea that off stoichiometric LN can be turned stoichiometric through suitable doping, that is, by the effective elimination of intrinsic defects by filling the vacancy sites. [14,28]This could only be strictly correct if, for a given doping concentration, the unit cell volume is smaller than that of the pristine sample (off stoichiometric in this work), because undoped (and post-thermally untreated) LN shows a characteristic structural relaxation from the stoichiometric chemical position to any off-stoichiometric point (for example Figure 3 in ref. [20]).

X-Ray Photoelectron Spectroscopy
Further characterization of a small set of reduced and oxidized samples was performed using X-Ray Photoelectron Spectroscopy (XPS) to demonstrate that the doped Fe ions reached a population fraction ≈1 with oxidation states of 2+ and 3+, respectively.The samples selected for analysis were pLN-ox, pLN-re, 22LN:Feox, and 22LN:Fe-re.Figure 3 and Table 3 present the photoelectron spectra and binding energy values, respectively.The graphs show the O 1s core level spectrum, which is typical of oxides.All spectra showed a shift in the binding energy, and after curve fitting, the observed peaks were c.a. 529.1 eV, which is associated with the regular lattice of lithium niobate.In the pristine reduced sample, the peaks ≈530.1 and 528.1 eV were associated with lattice distortion, as discussed previously in the results obtained by structure refinement.In the synthesis process, the first stage involved the application of a reduction treatment, followed by an oxidation treatment.During the reduction treatment, oxygen loss occurred, creating oxygen vacancies, and reducing Nb 5+ to Nb4 + .In contrast, oxygen diffusion causes changes in the binding energies observed in the XPS spectra.On the other hand, for the iron-doped sample with reduction treatment, the 531.2 eV peak is assigned to the vacancy region. [29]The highest energy observed in the present study corresponds to sample 2LN:Fe-re, as shown in Table 3. Owing to the charge compensation, higher proportions of Fe 2+ induced the formation of oxygen vacancies. [29,30]igure 4 shows that the spin-orbit doublet corresponding to Nb 3d, has contributions from 3d 3/2 and 3d 5/2 .In this case, the binding energies for most of the samples are ≈206.1 and 206.8 eV, which correspond to stable niobium Nb +5 .However, in the sample doped with an oxidation treatment, a reduction in the binding energy was observed, particularly for the contribution 3d 3/2 .This causes a change in the density of charge for the Nb─Li bond, which agrees with the discussion based on the XRD results, namely, the observed reduction in the cell volume.On the other hand, the binding energies for the contributions 3d 5/2 and 3d 3/2 increased in the case of sample 22LN:Fe-re, indicating the presence of oxygen vacancies produced during the reduction treatment and the presence of Fe 2+ when Li was replaced from its regular sites.33]  Finally, Figure 5 shows the Fe 2p core level spectra of the 22LNFe-ox and 22LN: Fe-re samples.The two peaks correspond to Fe 2p 3/2 and 2 p 1/2 and, according to the obtained values, these samples have a mixture of both valences: Fe +2 and Fe +3 .As shown in Table 3, the values of the peaks Fe 2p 3/2 and Fe 2p 1/2 are 711.5 and 725.1 eV for the oxidized sample with a binding difference of 13.6 eV.These values are consistent with the trivalent oxidation state of Fe.Similarly, for the reduced sample, the values of the peaks of Fe 2p 3/2 and Fe 2p 1/2 are 711.3 and 724.2 eV, respectively, with a binding energy difference of 12.9 eV.6]

Confocal Raman Spectroscopy
The structural evolution of all samples was also investigated using Raman Spectroscopy.The representative data are shown in Figure 6.All spectra were plotted in the 100-1000 cm −1 range.Raman spectra resembling those of (pure ferroelectric) LiNbO 3 were recorded under the same experimental conditions for all  the pristine and LN:Fe samples.Small deviations were observed when the functional forms were compared to those corresponding to the Raman spectra of the untreated pristine sample, as shown in Figure 6a.These can be ascribed to slightly registered differences in the centers and linewidths of certain individual Raman bands or polar modes from sample to sample.Such differences are likely to merge with the controlled defect structure or lattice re-ordering induced through elemental doping, that is, the tuning of phonon damping within the framework of damped harmonic oscillators.They hold for all instances, but are more notorious for the reduced samples, as shown in Figure 6b.
In the framework of group theory, lattice vibrations pertaining to the LN system (space group R3c, point group 3m, RT) with vanishing k wave vectors can be divided into 5A 1 , 5A 2 , and ten (twofold degenerate) E phonon branches. [37]Of these, one A 1 and E are the acoustic branches, five A 2 fundamentals are Raman and infrared inactive, and the remaining 4 A 1 and 9 E optical branches are both Raman-and infrared-active. [38]Accordingly, with two molecules per unit cell, the irreducible representation of the optical modes can be expressed as Γ = 4 A 1 + 5A 2 +9E.Although the assignment of phonon modes in LN has been the subject of debate for a long time, the above description has only been adopted in a few reports. [37,38]Because A 2 is nonpolar and inactive, there are 13 directional dispersion branches of the phonons.
LN plays a strong ionic role in terms of its overall chemical binding characteristics. [2]Hence, the incident macroscopic   2015). [37]However, this type of analysis is only consistent with single crystals that have definite principal axes; thus, knowledge of the state of linear polarization of scattered light is of great importance.Although the so-called selection rules for Raman-active phonons can be univocally determined by the standard methods of group theory, the relative intensities of the given Raman modes can be rationalized according to the polarization directions of the incoming and scattered light. [38]In contrast, the distinction between LO and TO components is not applicable to random media, such as powders composed of myriads of single nanocrystals.The polarization information is lost because of the arbitrary orientations of each given crystallite, whereas LO and TO can be assumed to overlap.Therefore, it is not necessary to use polarized Raman Spectroscopy to resolve all 13 fundamental lattice vibrations of the LN powders (Figure 6a inthe Experimental Section).Pezzotti (2013) provided an overall description of the main LN features of cation displacements in terms of the relative wavenumber, as summarized in Table S2 (Supporting Information).
The small deviations shown in Figure 6b can be analyzed by rationalizing the characteristics of a given Raman band into the dimensionless parameter FWHM/2x c where the numerator represents the Full Width at Half Maximum and the denominator represents twice the spectral center of the Raman band.Both entries are influenced by the substitution mechanism that follows the doping of the pristine LN structure with Fe ions and are determined numerically after performing a multi-peak fitting of the Raman spectra using a Lorentzian line shape.Small deviations were also observed for the untreated and oxidized samples, although in minor proportions.This type of analysis was performed for all the samples.This was performed once for each relative wavenumber domain of interest, namely the 200-300 zone, the 550-700 zone, the 100-200 zone, and ≈877 cm −1 .In each case, the experimental data were abridged to specific limits sharing a common baseline (enlargement of the spectra around the zone of interest), and the number of peaks on the fitting varied from one to three, depending on the analysis case.The first two zones are those where the doping effect on the different modes of lattice vibration is more evident, as highlighted in Figure 6b by dashed vertical lines.The remaining two zones were also studied so that the analysis could effectively cover the entire domain of fundamental Stokes modes, dividing it into low-, mid-, and high-Raman shift zones.They can also be considered as isolated contributions to the full Raman spectra compared to the first two zones.
The results of this analysis are shown in Figure 7. Initially, only the most intense Raman bands of each zone were targeted (solid curves in Figure 7a,b).However, their respective adjoining polar modes were also accounted for (dashed curves) to quantitatively assess any possible correlation between the two contributions.Only the results for the most intense Raman bands of each zone (153, 623, and 877 cm −1 ) are shown in Figure 7c, where the untreated and oxidized samples are represented by solid and dashed curves, respectively.It is also worth mentioning here that the trends resulting from using only the half-width (FWHM/2) are very similar to those shown in Figure 7, indicating that the latter can be interpreted based on the same mechanisms involved in the broadening of spectral bands, namely, the increasing disorder in the lattice due to compositional inhomogeneity, crystal imperfections, and insertion of impurities and dopant ions, among others.
Interestingly, most curves shown in Figure 7a,b show identical behavior, excluding only the one obtained for the polar mode centered at x c = 238 cm −1 (inset figure), and perhaps more rigorously, the one for x c = 177 cm −1 as well.Furthermore, following the arguments given in the previous subsection, these results confirmed the existence of the FCT at a doping concentration of 1.5 wt.% Fe 2 O 3 , as predicted to lie between this point and 2.2 wt.% Fe 2 O 3 by XRD measurements plus structure refinement.The SCT was determined at 3.3 wt.% Fe 2 O 3 , within the given absolute accuracy (doping concentration increments of Δ≈ 3.3 wt.% Fe 2 O 3 ).This inference is in agreement with the fundamental fact that the SCT should be close to the limit of chemical solubility. [14,18,24]Also, this information can only be extrapolated from the reduced samples, as no clean trends or "well-behaved" curves were obtained for the oxidized or untreated samples, as shown in Figure 7c.Thus, the application of post-thermal treatment in a reducing atmosphere is not only essential to avoid possible misfits in the interpretation of the XRD patterns (Figure 1c and the derived discussion), but also to have more elements in hand for a deeper understanding of the dynamics behind the defect structure of LN:Fe. [37]Reduced LN:Fe can also be used for applications, specifically in the development of new generation materials for nonlinear optics.

SHG Response
The SHG response from the zero, lowest, intermediate, and highest concentrations of the Fe-doped samples in their powder form was then obtained.The complete set of analyzed data was placed at reach in the attached Supporting Information file, along with a short video showing the strong sensitivity of sample 45LN:Fere to an applied magnetic field (MF).A not-too-strong applied MF may effectively alter the SHG response of the LN:Fe powders.Figure 8 shows the results obtained for the reduced pristine samples.Depth-SHG-intensity profiles were recorded when the fundamental beam focus was translated from air into the powder.Then, two crossed-polarization plots of the SHG intensity were recorded at z = 0, both in the absence (black and gray data points) and presence (blue and red data points) of the MF, as shown in Figures 8b,c.Here, z = 0 was defined as the maximum intensity of the SHG depth profile.
The nonlinear polarization of a non-centrosymmetric material is of electric dipole origin.Higher-order terms, such as quadrupole electric and dipole magnetic nonlinear polarization contributions, can be neglected if the crystal structure is assumed to remain non-centrosymmetric after metal doping and postthermal treatment. [40]It should be noted that the continuous relaxation of the crystal structure observed for the reduced samples (Figure 2a) may, to some extent, leave open further discussion on the possibility of an evolving system that becomes more symmetric as the doping concentration increases.Thus, the origin of SHG in the present LN:Fe powder is essentially its electric dipole character.It is then expected that the material orientational randomness drives the SHG response and that the ferromagnetic/electric properties provide a minor contribution.
The polar plots shown in Figure 8 exhibit a constant response at z = 0 irrespective of the incident linear polarization state of light, detection configuration, or MF application.Similar SHG intensity depth profiles and polarization plots were obtained for the pLN and pLN-ox samples.The observed polarization graphs exhibit circular plots or constant SHG as a function of the fundamental beam polarization resulting from the random nature of the granular medium from an optical perspective.Scattering, including single and multiple events, leads to complete loss of  the polarization state of the emerging photons at the harmonic frequency.However, it was concluded that in this system, centrosymmetry owing to the random nature of the powder was not perfect and appeared to be broken.Hence, a net non-zero SHG response can still be observed.This imperfect cancelation of the many single-powder grain dipolar contributions is a result of the combination of imperfect random orientational organization, differences in size, and chemical composition for different nano-grains.The same arguments can be used to explain the observed differences in the SHG efficiency for larger polycrystalline LN grains ≈2 μm in size, composed of several aggregated nanocrystals. [39]It is also worth mentioning that the polar plots reported in Figure 8 do not reproduce the results reported in ref. [15], where more pronounced two-lobe polarization patterns were observed for the pristine LN powders of stoichiometric composition at equivalent physical instances of z = 0.This feature may be ascribed to a different relative efficiency in the collection of photons that undergo linear scattering events, the socalled multiply scattered photons, as opposed to almost no linear scattering events, the so-called ballistic photons.In the present case, the contribution from multiple scattered photons domi-nates, which is similar to the undistorted circular polarization plots. [15]ample 8LN:Fe-re exhibited an important residual polarized SHG intensity with clear two-lobe patterns (Figure 9).Therefore, the powder nano-grains illuminated during the SHG intensity depth profiles, and their corresponding polarization plots appeared to preserve some orientational order.This may be due to the presence of intrinsic ferroelectric domains.Interestingly, this initial orientational ordering characteristic appears to be modified by the introduction of a magnetic field, as seen through the changes in polarization, as shown in Figure 9b,c.Interestingly, the application of MF changed the polarization plots, but did not change the SHG intensity depth profiles; the measured MF strength was of 600 G.The SHG intensity depth profiles are also much narrower.The pristine LN powder was colorless or white, regardless of the post-thermal treatment, whereas the untreated and oxidized LN:Fe samples appeared pink and orange, respectively, to the naked eye.Hence, the absorption and multi-photon absorption processes also alter the relative weight of the detected ballistic and multiply scattered photons.The mean free path for the latter is longer for the sample.A comparison between the  SHG intensity depth profiles of samples 8LN:Fe-re in Figure 9a and pLN-re in Figure 8a shows that this feature induces a collected intensity at z = 0 of the SHG intensity maximum, which is much weaker in the former case.
Figure 10 shows the results obtained for the sample with an intermediate Fe doping concentration, that is, sample 22LN:Fe-re.The polarization distortions observed for sample 8LN:Fe-re persisted, although they exhibited different behaviors.Before the application of a constant MF, the polarization plots exhibited some initial ordering although this was incomplete.In the presence of an applied MF, the polarization is modified and tends toward a more organized system with a more defined polarized SHG response.
Thus, at this doping concentration rate, re-orientation affects the orientation distribution of the powder nano-grains.This feature can be suggested as a potential mechanism for optimizing the SHG response of the randomly oriented grains.In addition, the SHG intensity depth profile appears rather asymmetrical, with a slow increase and a plateau in the SHG intensity as a function of depth.This feature further underlines the possible role of MF. Figure 11 shows another run with this sample (run B in this series of experiments; see the Experimental Section and Supporting Information file for details), exhibiting an important SHG signal enhancement and more dramatic changes in the polarization plots.This shows a strong alignment effect upon the application of an external MF on the nano-grain powder.Therefore, the SHG response appeared to be tailored by controlling the number of intrinsic and extrinsic point defects within the pristine host structure, thereby setting the magnetization to an optimal value using doping concentration rates between 0.8 and 2.2 wt.% Fe 2 O 3 .
Photo-induced changes in the material appeared to be another mechanism to be considered in the overall SHG response of the samples.This was more clearly observed for the 45LN:Fe-re sample, as shown in Figure 12.The recorded profiles are no longer invariant to repeated profiles.The SHG intensity almost entirely collapsed to the baseline.Polarization distortions were also discernible but were neither well resolved nor reproduced from sample preparation to sample preparation.In this case, the incident fundamental beam continuously transforms the material over time.Such photo-induced changes can be qualitatively explained in terms of the photo-refraction process.Photo-refraction is the process by which inhomogeneity in the refractive index is optically induced.This is characteristic of most insulators, and an irreversible change is generated by the application of intense laser light. [14]LN is a photorefractive material with an excellent performance.Accordingly, irradiance as low as 20 W cm −2 at a wavelength of 532 nm was sufficient for its manifestation in a congruent crystal. [41]Photo-refraction in LN can be either suppressed or enhanced by proper elemental doping.Transition metals are primarily employed in the latter case, and some devised applications include holographic storage, beam coupling, information processing, and computation.] Thus, although the input power was kept constant for all experiments performed in this study, the sample 45LN:Fe-re is more susceptible to optical damage simply because it supports more Fe in its structure, combined with the fact that the population of oxygen vacancies is also large.
In contrast, the 45LN:Fe and 45LN:Fe-ox samples did not exhibit significant photo-induced changes.In 45LN:Fe-re, the innumerable coexistence of oxygen vacancies and Fe 3+ ions promotes charge transport and trapping phenomena, which are the main factors at play in photo-refraction.Finally, in the polarization plots of the SHG responses of the untreated and oxidized samples, weak distortions could seldom be traced.The same can be said for the doping concentration of 2.2 wt.% Fe 2 O 3 .Nevertheless, for practical purposes, samples 22LN:Fe, 22LN:Fe-ox, 45LN:Fe, and 45LN:Fe-ox can be assumed to be random or granular from an optical point of view, similar to the pristine LN samples.The application of a post-thermal treatment in a reducing atmosphere thus provides a deeper insight into some fundamental scientific problems in LN:Fe, but also entails a modification of some of its intrinsic capabilities in the realm of nonlinear optics.

Conclusion
In this study, the SHG intensity depth profiles and polarization analysis of iron-doped LN powders were performed at several Fe doping rates.All the powders exhibited similar SHG intensity profiles driven by the competition between the Gaussian beam focus translation into the powder from the air side, providing a SHG signal increase, and multi-scattering with possible absorption, leading to loss of the SHG signal.The powders generally appeared randomly oriented, especially for the undoped and weakly doped ones, indicating a weak remaining order, possibly owing to the ferroelectric properties of LN.As the iron doping rate increased, changes in the polarization graphs were observed upon the application of a static magnetic field (600 G).Finally, the photo-refractive effects were observed at the highest doping rates.The following conclusions can be drawn from the measurements of all the samples: 1) For a given doping concentration (zero concentration included), the untreated and oxidized samples exhibited an SHG response of comparable intensity, whereas the intensities of their corresponding reduced samples were approximately one order of magnitude lower.
2) The SHG intensity depth profiles were slightly asymmetric, corresponding to an increase obeying the wave propagation of a TEM 00 Gaussian beam along the z-optical axis at negative z values, and a more rapid decay resulting from the convolution between the same propagation phenomena and exponential decay due to the strong optical extinction and scattering, including multiple scattering, at positive z values.3) For middle and low doping concentrations, no material degradation was observed from the invariance of the four repeatedly recorded profiles within a given set of experiments.4) The SHG intensity depth profiles were not modified upon the application of the MF, and the definition of the z = 0 depth through the maximum SHG intensity was the same, independent of the presence or absence of the MF.
Post-thermal treatment in a reducing atmosphere is essential for a deeper understanding of the static and dynamic characteristics of defect complexes in iron-doped lithium niobate (LN:Fe) powders.It can also enable the development of a new-generation characterization tool for random or granular media based on nonlinear optics.Some specific aspects described in the discussion of the results should be addressed for formal explication, such as the origin of the apparent order in reduced LN:Fe powders before the application of the magnetic field (probably due to the intrinsic ferroelectricity in bulk LN) or its apparent loss after the first run of polarization analysis (again, without application of the magnetic field), where the loss of polarization information due to multiple scattering of the SHG photons has been neglected here based on arguments related to the inferred absorption properties of the studied materials.

Experimental Section
Synthesis: High purity lithium carbonate (Li 2 CO 3 ) and niobium pentoxide (Nb 2 O 5 ), from Alpha Aesar, were used as starting reagents in a 1:1 molar ratio.The masses of the precursors were determined such that 3 g of congruent lithium niobate was produced using the following balanced chemical equation: Li 1.9 CO 3 + Nb 2.02 O 5 → 2Li 0.95 Nb 1.01 O 5 + CO 2 (1)   where the most widely accepted defect model for describing congruent solid solutions of LN is the lithium vacancy model.The heterogeneous mixture of the precursors was then mechanically activated using a high-energy milling process carried out in a SPEX Sam-plePrep 8000 M Mixer/Mill (New Jersey, USA), using nylon vials with yttriastabilized zirconia (YSZ) balls, and a powder-to-ball mass ratio of 0.1 was used for each sample preparation.Milling was performed in 30 min cycles with 30 min pauses to avoid excessive heat inside the milling chamber until 180 min of effective milling time were reached.The resultant activated powders were then isothermally calcinated in an air atmosphere at 850 °C for 180 min using a tubular GSL1100X furnace (MTI Corporation, USA); no ramp was used, and the samples were cooled down slowly to RT. High-quality, pure ferroelectric LN powders, with a near-congruent chemical composition, were obtained at this stage of synthesis, as confirmed by X-ray Diffraction (XRD) and Raman Spectroscopy.A combination of characterization techniques yielded an average Li:Nb = 48.9:51.1 (the congruent point was described by the Li:Nb ratio of 48.5:51.5).The steps described thus far had been repeated several times (including characterization) to produce a sufficient mass of pristine powder, which was later doped with Fe ions, as described in the following paragraph.
During the doping stage of the synthesis, heterogeneous mixtures of pristine LN and commercial Fe 2 O 3 (Alpha Aesar, Puratronic 99.998%) were prepared at rates of: 0.8, 1.5, 2.2, 3.3, 4.5, and 6.0 wt.% Fe 2 O 3 .Mixing, homogenization of the particle size distribution, and lowering of the surface energy were simultaneously achieved after milling with the SPEX SamplePrep 8000 M Mixer/Mill (New Jersey, USA) for an effective time of 60 min.Subsequently, Fe ions were doped via diffusion after calcination for 60 h at 850°(air atmosphere).The resultant materials were labeled as follows: 8LN:Fe, 15LN:Fe, 22LN:Fe, 33LN:Fe, 45LN:Fe, and 60LN:Fe.During the final stage of the synthesis, reduction and oxidation treatments were performed for 60 min at 850 °C in controlled atmospheres of ultrahigh-purity hydrogen and oxygen, respectively.
Characterization: The XRD patterns of all the samples were recorded in air at RT using a Panalytical X-Pert system (Almelo, The Netherlands) with a Bragg-Brentano - geometry, a radiation source of CuK ( = 1.54 † A), a Ni 0.5% CuK filter in the secondary beam, and a 1D positionsensitive silicon strip detector (Bruker, Linxeye, Karlsruhe, Germany).The diffraction intensity, as a function of the 2 angle, was measured between 10.00°and 80.00°, with steps of 0.016°every 30 s. Structural refinements using the Rietveld method were performed using the computational package X'Pert HighScore Plus from PANalytical, version 2.2b (2.2.2), released in 2006. [44]Diffraction data for phases LiNbO 3 (COD 2 101 175), hematite-Fe 2 O 3 (JCPDS PDF 04-015-6943), and -Fe (JCPDS PDF 00-006-0696) were obtained from the Crystallography Open Database and Powder Diffraction File (ICDD), respectively. [19,21]To determination of the average crystallite size, a lanthanum hexaboride (LaB 6 ) single crystal was used as the standard sample, refined with the diffraction data available in the ICSD-194636 card (FIZ Karlsruhe, Germany).X-ray Photoelectron Spectroscopy (XPS) analysis was performed using a spectrometer equipped with an AL k (1486.7 eV) monochromator and a detector 1D DLD with a Phoibos 150 analyzer.The electron energy analyzer was operated at a pass energy of 15 eV.The step size used was 0.1 eV and the powders were deposited on Cu on Mo tape.The binding energy of peak C 1s 284.8 eV was used as the reference for calibration.
The structural evolution of all samples was also analyzed by Raman Spectroscopy.Unpolarized Raman spectra were recorded in air using a WITec confocal Raman microscope (Alpha 300R, Germany) with a 532 nm source of excitation wavelength (continuous wave diode laser) and 2-3 cm −1 spectral resolution.A CCD detector (cooled to −60 °C) was used to collect Stokes Raman signals in a backscattering configuration using a 0.4NA:20x objective lens (ZEISS, Germany).With this equipment, the spectra were recorded over the wavenumber range 100-3600 cm −1 at RT, and light was incident on the normal component of the sample with a power of 0.50 mW.
Depth Profiling and Polarization-Resolved SHG: A picosecond laser (EKSPLA PL2231-50-SH/TH Nd:YAG pulsed laser System, University Laboratory of Optics at Surfaces (Laboratorio Universitario de Óptica de Superficies) at the Physics Institute of UNAM (LOS-UNAM)) delivering 26 ps pulses at a repetition rate of 50 Hz was used as the source of light for excitation.The fundamental wavelength was set to 1064 nm and no resonance features were observed.The laser beam was then passed through a halfwave plate (HWP) and polarizing cube to select the linear input polarization angle and precisely control the input power.For control and automation purposes, a reference arm was generated from the reflected light on a transparent slide placed on the beam propagation with an arbitrary orientation, which was aimed toward a Thorlabs DET 10A fast photodiode coupled with a Tektronix MSO 4034 oscilloscope (USA).The transmitted light was defined as the experimental optical axis.Depth-SHG-intensity profiles resulted from z-sectioning of the SHG response of the samples along the optical axis; a microscope-like experimental setup was constructed on a vertical plane for this purpose.At the entrance, the light at the fundamental wavelength propagates downward, passes through a filter to reject any unwanted harmonic light ( SHG ≈ 532 nm), and then passes through an HWP mounted on a motorized rotation stage.A long-pass dichroic mirror (650 nm cut-on) was positioned at ≈45°with respect to the optical axis.The excitation beam propagated unaltered until it entered a 0.25NA:10× objective lens (Newport, USA), and afterward, it impinged from the top into the powders supported on a microscope coverslip.The objective lens was mounted on a motorized linear-translation stage with a minimum incremental step of 0.05 μm, which allowed the probing of the nonlinear optical response under several experimental conditions, distinguishing be-tween pre-focal (z<0, beam waist in air medium), focal (z = 0, beam waist at the air/powder interface), and post-focal excitation conditions (z>0, the physical instances for which a hypothetical undistorted propagation would lead to focused beam penetrating the sample).However, considering the stage just before the light beam entered the objective lens, all experimental procedures of this investigation were performed at a fixed input power of (1.65 ± 0.01) mW.The value represents the weighted average of several independent measurements performed routinely once or twice per day in a 2-3 week time interval.
Harmonic light from within the powders and from the air-powder interfaces propagates randomly in all possible directions.Depending on the objective lens used and the scattering properties of the samples, a given fraction of harmonic light backscatters ,or was retro reflected into the objective lens.It propagates upward along the optical axis until it reaches the dichroic mirror, where its wavevector rotates ≈90°.A long-pass filter was placed on the propagation line to reject any fundamental light (if it leaked from the dichroic mirror).A set of three "blue" mirrors (with high reflectance at  SHG ≈ 532 nm) was employed to reset the propagation axis on a horizontal plane and direct it toward the detection stage.The latter was composed of an analyzer (HWP plus polarizing cube) and a monochromator (Princeton Instruments, Acton SP2300, USA) coupled to a photo-multiplier tube (PMT, Hamamatsu H5784-04, Japan) operating in the photon-counting regime.The output signal was decoded by using a digital oscilloscope (Tektronix).A biconvex lens (f = 150 mm) was used to focus harmonic light at the entrance of the monochromator, which was operated at a fixed spectral position of 532 nm in all instances.
The cubic polarizer sets the detected light as linearly polarized and parallel to the horizontal plane, defining the cross-section (or top surface) of the optical table.With respect to the detection stage, the zeroth or original configuration is defined by placing the HWP fast-axis perpendicular to the transmission axis of the polarizer, that is, parallel to the normal component of the top surface of the optical table.Hereafter, this is referred to as V-pol (where V stands for vertical polarization).The horizontal H-pol configuration was also of interest, only in the polarization analysis of the SHG response; it can be easily obtained by the clockwise rotation of the HWP with  HWP = 45°( pol.angle = 90°).All the recorded intensity depth profiles were obtained using the zeroth-zeroth experimental configuration, namely, the V-pol configuration at the detection stage and the setting of the first HWP (excitation stage, fundamental wave) at position  HWP =  pol.angle = 0°.The scanning resolution in the depth profiling was set to either 5 or 2 μm, depending on the optical absorption properties of the samples: wide profiles (untreated and oxidized powders) or narrower profiles (reduced powders).Recall that strong absorbance in the visible region could be interpreted as a lower probability of the harmonic photons being retro reflected and reinserting the objective lens, that is, a shortened detection efficiency (narrower profiles).
The polarization analysis of the SHG response conveys an effective inplane rotation of the linear polarization state of the fundamental wave impinging on the sample.A full-range analysis (0-360°) can be performed by rotating the first HWP in the 0-180°range.This was performed in the present investigation for all polarization-resolved SHG experiments, with a resolution of 2°on the polarization angle (the incremental step used in every experiment was of Δ HWP = 1°).Signal detection is performed in the same fashion as for the case of the depth profiles, but now using both configurations, V-pol first and H-pol afterward.These polarizationresolved measurements were performed at the physical instance of the maximum SHG intensity, by setting the motorized linear translation stage at such a position (defined as z = 0).

SHG Data Recording and Sample Preparation Steps:
1) Recording of the first depth-SHG-intensity profile (detected in the Vpol configuration; black color in graphics).See the Experimental Section for the precise meanings of the V-pol and H-pol.2) Repetition of the previous step (to evaluate possible sample modification or damage due to laser excitation; gray color in the graphics).
3) Determination of the z-position corresponding to the maximum SHG intensity and setting of the motorized linear translation stage at this position (defined as z = 0).4) Recording of the first polar plot in the V-pol configuration (black color in graphics).5) Recording of a first polar plot in H-pol configuration (black).6) Repetition of step 4) (to evaluate possible plowing of the material, either by light intrinsic electric or magnetic fields; gray).7) Repetition of step 5) (gray).8) The set of two magnets was moved closer to the sample from bottom to top along the optical axis; a fine gap of air scarcely separated the edges of the magnets from the coverslip that supported the sample.
A constant amplitude of roughly 600 G was measured for an applied magnetic field (MF) at the laser excitation point.9) Repetition of step 4) (measurement in the presence of the applied MF; -MF, blue).10) Repetition of step 5) (-MF, blue).11) Repetition of step 9) (-MF, red).12) Repetition of step 10) (-MF, red).13) The motorized rotation stage controlling the linear polarization state of the incident light was restored to the zeroth position and the V-pol configuration was reset.14) Repetition of step 1) (-MF, blue).15) Repetition of step 2) (-MF, red) .16) Removal of the studied sample and magnets.Another sample was prepared and placed in the optical setup for a new set of experiments.
The procedure was performed three times for each sample, so three distinct points were probed randomly from the same sample (runs A, B, and C).In each subsequent sample preparation after the first one, the recently studied sample was recovered back into its container and recombined with the rest of the synthesized powder, prior to studying the SHG response of the same powder for the second and third time.The powder was systematically chopped with a coverslip to cancel any possible grain orientation induced by the MF applied in the previous set of experiments.In this study, only the pristine samples (pLN) and doped samples 8LN:Fe, 22LN:Fe, and 45LN:Fe were studied, three available states of oxidation were considered (untreated, oxidized, and reduced samples), and a total of 36 independent sets of experiments were performed.

Figure 1 .
Figure 1.XRD characterization of the LN samples.a) As obtained (without post-thermal treatment) pristine lithium niobate powders with near-congruent chemical composition denoted by a ratio Li:Nb = 48.91:51.1.b) Iron oxide powders converted into powdered metallic iron and then recovered in their initial phase when first reduced and oxidized afterward.c) Reduced Fe-doped lithium niobate powders where the two samples of the highest doping concentration show the existence in small proportions of metallic iron as a secondary phase (2 ≈45°).For a doping concentration of 3.3 3 wt.%Fe 2 O 3 , and below, lithium niobate phases were obtained as inferred from the straight lines resulting from a direct comparison between the corresponding patterns and that of the untreated pristine sample.

Figure 2 .
Figure 2. Crystal structure refinement using the Rietveld method.As a function of the doping concentration and the applied post-thermal treatments: a) Unit cell volumes in angstrom units.b) Mean crystallite sizes calculated by the implicit use of the Scherrer equation and weight averaging of all the contributions to line broadening.c) The estimated Rietveld error indices are < or ≈10%.

Figure 3 .
Figure 3. XPS spectra for O 1s in the LN samples with oxidation and reduction treatment.

Figure 4 .
Figure 4. XPS spectra for Nb 3d in the LN samples with oxidation and reduction treatment.

Figure 6 .
Figure 6.Raman spectra in the Stokes-frequency domain containing the fundamental lattice vibrations of lithium niobate (normalized to the highest intensity).a) Pristine powders: The dotted curves show the individual polar modes that contribute to the full spectra.b) The doping effect on the different modes of lattice vibration is more evident for the reduced LN:Fe powders, particularly near to ∆ṽ = 250 cm -1 and ∆ṽ = 600 cm -1 .

Figure 7 .
Figure 7. Half-width divided by the center of individual Raman bands of interest.In function of the doping concentration and of the applied post-thermal treatments: a) Reduced samples ca.238-260 and 585-623 cm −1 , data for the 238 cm −1 band are shown in the inset figure.b) Reduced samples at ca. 153-177 and 877 cm −1 .c) Some results for the untreated and oxidized (solid curves) samples show that no systematic behavior or characteristic trend can be ascribed to these cases.

Figure 8 .
Figure 8. a) SHG intensity depth profiles of sample pLN-re, b) Polar plot of the Vertically polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0,and c) Polar plot of the Horizontally polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0.The blue and red points correspond to the data collected after the application of the constant magnetic field, whereas the black and grey points correspond to the data collected prior to the application of a constant magnetic field.The angular entries of the polar plots describe the input polarization angle with respect to the Vertical polarization configuration.

Figure 9 .
Figure 9. a) SHG intensity depth profile of sample 8LN:Fe-re.b) Polar plot of the Vertically polarized SHG intensity as a function of the polarization angle of the fundamental beam, collected at depth z = 0. c) Polar plot of the Horizontally polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0.The blue and red points correspond to the data collected after the application of the constant magnetic field, whereas the black and grey points correspond to the data collected prior to the application of a constant magnetic field.The angular entries of the polar plots describe the input polarization angle with respect to the Vertical polarization configuration.

Figure 10 .
Figure 10.a) SHG intensity depth profile of sample 22LN:Fe-re.b) Polar plot of the Vertically polarized SHG intensity as a function of polarization angle of the fundamental beam collected at depth z = 0. c) Polar plot of the Horizontally polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0.The blue and red points correspond to the data collected after the application of the constant magnetic field, whereas the black and grey points correspond to the data collected prior to the application of a constant magnetic field.The angular entries of the polar plots describe the input polarization angle with respect to the Vertical polarization configuration.

Figure 11 .
Figure 11.a) SHG intensity depth profile of sample 22LN:Fe-re, second run.b) Polar plot of the Vertically polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0. c) Polar plot of the Horizontally polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0.The blue and red points correspond to the data collected after the application of the constant magnetic field, whereas the black and grey points correspond to the data collected prior to the application of a constant magnetic field.The angular entries of the polar plots describe the input polarization angle with respect to the Vertical polarization configuration.

Figure 12 .
Figure 12. a) SHG intensity depth profile of sample 45LN:Fe-re.b) Polar plot of the Vertically polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0. c) Polar plot of the Horizontally polarized SHG intensity as a function of the polarization angle of the fundamental beam collected at depth z = 0.The blue and red points correspond to the data collected after the application of the constant magnetic field, whereas the black and grey points correspond to the data collected prior to the application of a constant magnetic field.The angular entries of the polar plots describe the input polarization angle with respect to the Vertical polarization configuration.

Table 1 .
Nomenclature of the synthesized samples.
a) The pristine samples.

Table 2 .
Phase percentages in the synthesized samples, as obtained by simultaneous insertion of cards containing the Wyckoff positions of the involved crystal structures.

Table 3 .
Binding energy values obtained from peak fitting of XPS spectra.