Structural, electrical, and magnetic properties of nano Sr1−XLaXFe12O19 (X = 0.2–0.8)

The current work is mainly devoted to the synthesis, structural, electrical, and magnetic characterization of Sr1−XLaXFe12O19 (X = 0.2–0.8) (SLFO) nanoparticles synthesized via the hydrothermal technique. The hexagonal peaks were determined using X-ray diffraction analysis. The obtained results indicated that the lattice constants were noted to be increasing from 0.58801 to 0.58825 nm (a = b), and 2.30309 to 2.30341 nm (c) with increase of in ‘X’. The morphological studies ensured that the grains as well as nanoparticles of SLFO acquired almost spherical shape. The optical properties were investigated using FTIR and UV–Visible spectra. The optical bandgap (Eg) of SLFO was found to be increasing from 1.866 to 2.118 eV with increase of dopant content. The electrical properties of SLFO were studied in detail as a function of temperature, and frequency. In addition, the dielectric modulus, and impedance spectroscopy analysis was carried out to describe the space charge polarization, and electric conduction mechanism, respectively. The hysteresis loop (M–H curves) of SLFO revealed the decrease of magnetization from 36.34 to 7.17 emu/g with increase in ‘X’.


Materials and experimental method
Hydrothermal synthesis technique is considered as one of the simplest and cost-effective technique to synthesize nanoparticles. The Sr 1−x La x Fe 12 O 19 (x = 0.2-0.8) (SLFO) nanoparticles were prepared using hydrothermal technique. In order to synthesize the SLFO nanoparticles, the precursor materials SrN 2 O 6 , LaN 3 O 9 , and FeN 3 O 9 (each of 99.88% from Sigma-Aldrich) as mentioned in flow chart ( Fig. 1) were chosen as per the stoichiometricratio. Different mass of nitrate materials was considered for x = 0.2-0.8 samples. Further, the precursors were taken into glass beaker containing 50 ml of deionized water. In order to mix the precursors, the glass beaker was kept on the magnetic stirrer. The solution was stirred for about 3 h. At the time of stirring, the NaOH-solution Results and discussion X-ray diffraction (XRD) spectra. Figure 2 represents the XRD-spectra SLFO nanoparticles confirming the phase identification of prepared nanoparticles. These phases were indexed and compared with the standard JCPDS: 80-1198. From this, it was noted that all the diffraction phases were in consistent with the standard JCPDS. In addition, the highest counts were recorded for (114) reflection plane. The average crystallite diameter was calculated using Scherrer Eq., D avg = 0.9λ CuKα /βcosθ, where λ CuKα is the CuKα wavelength (0.15406 nm), β refers to full width half maxima (FWHM), and θ is associated to the diffraction angle 24 . The obtained D avg values of x = 0.2-0.6 were found to be increasing from 4.5 to 14.8 nm. However, at x = 0.8, it was decreased to 5.2 nm. This can be usually attributed to the decreasing trend of microstrain (ε s ) (from 0.0282 to 0.0210 rad) for x = 0.2-0.6 contents and increasing nature of the same to 0.0276 rad for x = 0.8 content. Likewise, the FWHM also followed the same trend as that of microstrain for all SLFO contents. This kind of behavior was earlier observed in the literature [25][26][27][28][29] . Besides, to provide a good agreement with these values, the microstrain (ε W-H ), and average crystallite size (D W-H ) parameters were calculated by plotting Williamson-Hall (W-H) plots as depicted in Fig. 3. These results were reported in Table 1. The achieved data suggested that both the D W-H and ε W-H values were in good consistent with the same parameters attained using the Scherrer method 24 .
Moreover, the lattice-parameters (a = b & c) were calculated using the equation: 1/d 2 = [1.333/a 2 ] [h 2 + hk + k 2 + (l 2 /c 2 )] 25 and listed in Table 1. The obtained results indicated that the lattice-constants were noted to be increasing from 0.58801 to 0.58825 nm (a = b), and 2.30309 to 2.30341 nm (c) with increase in 'X' . A detailed discussion can be given like this. Shannon ionic-radii table 30 showed that the ionic-radii of cations of SLFO are noted as Sr +2 = 0.127 nm, La +3 = 0.122 nm, Fe +3 = 0.0645 nm, and Fe +2 = 0.080 nm. This data ensured that the La +3 ions have lesser ionic radii than Sr +2 ions and greater than the ionic radii of ferric and ferrous ions. Therefore, La +3 cations will have probability to occupy the Sr-site rather than the rest of the cationic sites. In the literature [31][32][33][34][35] , it was observed that the incorporation of rare earth cations into the site of divalent element     www.nature.com/scientificreports/ of La +3 cations, and defects may also become accountable for present variation trend of unit-cell dimensions as well as its volume (V cell ) 35 . The c/a ratio was found to be decreasing with increase in 'X' . Furthermore, X-ray (ρ x = ZM.W/N A V cell , where Z = effective-number of atoms per unit-cell, M.W = molecular-weight, N A = Avogadro's number, and V cell = volume of the unit cell) and bulk densities (ρ b is attained from Archimedes principle) 25 were evaluated (see Table 1). The accomplished outcomes manifested that both the density parameters were noticed to be increasing with increase of La-content in SFO system. This was ascribed to the increase of molecular weight from 1072 to 1102.8 g/mol., as a function of 'X' . In addition, the porosity (P = 1 − (ρ b /ρ x )) was calculated and found to be decreasing from 18 to 8%. This confirmed a fact that the pore content was reduced upon increasing the La-content. Finally, the specific surface area (S) established the decreasing trend from ~ 258 to 77 m 2 /g (for X = 0.2-0.6). Beyond X = 0.6, the 'S' was about 217 m 2 /g. This nature was attributed to the increasing trend of crystallite size up to X = 0.6 and decreasing manner beyond X = 0.6. Similar reports were noticed in the literature 25 .
Surface morphology. Figure 4 showed the FESEM pictures of SLFO nanoparticles. In FESEM pictures, one can obviously notice that there were well-defined spherical shaped grains. Besides, these grains were distributed homogeneously. Comparatively, the X = 0.2 content acquired low apparent grain size while it seemed to be increasing from X = 0.2-0.6. But, for X = 0.8, it was decreased. Later, using linear intercept method, the average grain-size (G avg ) was computed. In this technique, for each composition ten test-lines were drawn containing different test-lengths (L) at a specific working distance (WD) and magnification (M). Then, the total number of intersecting grains (N) was counted. Besides, all the parameters were inserted into the relation: G avg = 1.5L/MN, where the symbols have their usual meaning. Thus, the experimental grain-size was accomplished and observed to be increased from 23.5 to 117.6 nm for X = 0.2-0.6. Furthermore, for X = 0.8, it was reduced to 102.4 nm. Similar kind of variation was noticed in average crystallite-size with increase in 'X' of SLFO-nanoparticles.
The TEM pictures as shown in Fig. 5 revealed the slightly distorted spheres like nanoparticles. Herein, the distribution of nanoparticles was seemed to be almost homogeneous. In addition, the average particle-size (P avg ) was computed and noticed to be upsurging from 16.2 to 44.1 nm for X = 0.2-0.6 whereas the same was reduced to 37.2 nm for X = 0.8. This manner was identical to the variation of D avg and G avg . Besides, the nanoparticles were appeared to be very close to each other. This can be normally attributed to various factors like magnetic interactions, agglomeration, size, charge etc. 25 . The samples are of same group of synthesized nanoparticles and processed with identical conditions. In general, the agglomeration of nanoparticles is responsible for little nonuniformity followed by distortions in the shape of nanoparticles shown in TEM pictures.
Optical properties. The Fourier-transform infrared-spectra (FTIR) of SLFO-nanoparticles were shown in . Hence, for the prepared SLFO samples, the absorption bands noticed at ν 1 were associated to the M-site while 'ν 2 ' was associated to Fe-O bond. Therefore, this can indicate the development of hexagonal structure of prepared samples. Furthermore, as observed in Fig. 6, the formed additional bands on either side of iron-oxygen stretching vibrational site were ascribed to the presence of Fe +2 -ions. Generally, this may be happened due to heat treatment of the samples. Also, few band sites were observed at 1632.5 & 2109.5 cm −1 and 3358.2 & 1338.6 cm −1 . These sites were developed due to vibrational stretching which were appropriate to the contortion of water molecules and O-H bonds [25][26][27] . Figure 7 expressed the diffuse reflectance spectra (DRS) of SLFO nanoparticles. It was seen that the maximum absorption wavelength (λ max ) was noted to be diminishing from 553.66 to 529.3 nm with increase of La-content.   www.nature.com/scientificreports/ Furthermore, (αhυ) n vs hυ plots (where 'α' is absorptivity, and 'hυ' is the photon energy) were drawn to obtain optical band gap energy (E g ) of as prepared samples by considering n = 2. For n = 2, it allows the direct-transition of charge-carriers between the energy-bands [25][26][27] . Therefore, as shown in Fig. 8, we can mention (αhυ) 2 versus hυ instead of (αhυ) n versus hυ. From Fig. 8, it is clear the value of E g was progressively increased from 1.866 to 2.118 eV with respect to dopant concentration. The value of E g was obtained through extrapolation of linear portion of graph ( Fig. 8) towards the axis of photon-energy, where the absorptivity tends to zero 26 . Therefore, the outcomes are evinced that the increasing La-content causes the enhancement in the value of E g .

Magnetic behavior.
In case of SLFO nanoparticles, the magnetic nature was confirmed by hysteresis loops.
These curves were plotted (see Fig. 9) using the magnetization (M) versus magnetic-field (H) data. In general, one can expect that the magnetization should be decreased upon increasing the nonmagnetic La-composition. From Fig. 9, it was seen that the saturation magnetization was decreasing from 36.34 to 7.17 e.m.u./g (see Table 2) with increase of La-content. Thus, the expectations became true in this case. As discussed in the "X-ray  www.nature.com/scientificreports/ diffraction (XRD) spectra" section (XRD analysis), to replace the strontium site of large ionic radii by lanthanum of small ionic radii, there was an occurrence of conversion of ferric ions to ferrous ions. It was an established fact that Fe +3 ions contain the magnetic moment of 5μ B /f.u., while the Fe +2 -ions attain magnetic-moment of 4 μ B /f.u. Indeed, this aspect implied a fact that the increasing La-content reduced the resultant magnetic moment thereby increasing the concentration of Fe +2 ions in SLFO. This manner was discussed earlier in the literature 31,32 in case of bulk SLFO. Moreover, the increase of lattice constants with 'X' can be a second reason for the expansion of unit cell. Consequently, the magnetic exchange interactions will be decreased. This could be responsible for the reduction of magnetization thereby decreasing the magnetic moment of the spins. In addition, the high coercivity (H c ) of SLFO was estimated to be changing from 490 to 820 G with dopant. This can be an indication for the hard ferrite nature of SLFO. Besides, the retentivity (M r ) was found to be altering from 2.8 to 9.0 e.m.u./g. This suggested a fact that the variation of retentivity was unsystematic with increase in 'X' .
Temperature and frequency dependence of dielectric parameters. As a part of dielectric parameters, the dielectric constant (ε′), dielectric loss (ε″), ac-electrical conductivity (σ ac ), and complex dielectric modulus (M*) were elucidated with respect to the variation of temperature (T) and frequency (f). It was a known fact that these parameters can mainly depend on distinct factors like sample preparation method, type of dopant, resultant compound, grain size, porosity, strain, density, and ionic radius 25 . Figure 10 depicted the ε′ versus T plots. It was observed from the ε′-T plots (at f = 1 MHz) that the ε′ of SLFO was remained constant until 400 K. It was attributed to weak and constant response of the charge carriers at these temperatures. Beyond 400 K, there was a gradual increasing trend of dielectric constant for X = 0.2-0.6. In contrast, X = 0.8 revealed an abrupt increasing manner of dielectric constant without any intermediate dielectric relaxations. Meanwhile, X = 0.2-0.6 contents exhibited dielectric relaxations between 533 and 583 K temperatures. These dielectric relaxations were established owing to high thermal agitations among the electric dipoles. As a result, the entropy becomes predominant at the relaxation temperatures which can in turn acquire the high magnitude of dielectric constant. Above 600 K, different compositions performed different Curie transition temperature (T c ) values. That is, the T c values were decreased from 743 to 643 K with increase of 'X' from 0.2 to 0.8. This kind of trend was obtained due to reduction in exchange-interactions between two sites of SLFO thereby increasing the lattice constants with increase of dopant concentration. Likewise, ε″ versus T plots (Fig. 11) stated almost similar T c values as in case of dielectric constant versus temperature plots. Even, the variation trend of ε″−T plots was also identical to the ε′−T plots. The frequency variation of dielectric constant and loss was described by means of ε′−f (Fig. 12) and ε″−f ( Fig. 13) plots, respectively. In Fig. 12, it was noticed that the dielectric constant of X = 0.2-0.8 was decreasing   36 . This theory reported that the polycrystalline material can be composed of two-layers such as (i) grain & (ii) grain-boundary. Indeed, these two layers are responsible for the higher and lower values of dielectric constant at lower and higher frequencies. The analysis of Koop's theory suggested that the grain-boundaries are more resistive (low conductive) than the polycrystalline grains. Thus, at lower frequencies the charge carriers may not move and further they will be confined to certain microscopic region of the material. At this moment, the overcrowded nature of charge carriers usually takes place. This implied a fact that all the charge carriers were not able to break the barrier (grain boundary layer) due to its high resistance. Therefore, the grain boundaries were predominant at the low frequencies and consequently, it induced the huge amount of space charge or Maxwell-Wagner interfacial polarization. As a result, the maximum value of dielectric constant was possible at low frequencies. This type of discussion was earlier reported by Wagner 37 . On the other hand, with increase of input field frequency, the electric dipoles become more active after absorbing sufficient energy from the input field. Hence, the charge carriers can break the grain boundary layer which subsequently reduces the resistance of barrier. This kind of approach of carriers will induce to obtain the high conductivity. At this moment, the grains (referred as low resistive or conductive segments) become more active. Therefore, the space charge polarization will be diminished to larger extent. This in turn leads to achieve low dielectric constant value at high frequencies. After 20 kHz, the dielectric constant of all samples was seemed to be constant. However, the inset figure of Fig. 12 showed that X = 0.6 content revealed the high ε′ of ~ 18 at 1 MHz while the rest of the contents expressed moderate ε′ values varying from ~ 5 to 9. In Fig. 13, the ε″-f plots indicated that there was an observation of huge ε″ value altering from 1830 to 34 between 100 Hz and  . The X = 0.6 content can be suitable for dielectric absorber applications at 1-5 MHz. Furthermore, this content may also work as microwave absorber at high frequencies. Figure 14 indicated the behavior of σ ac with temperature. It was clearly found that the conductivity was enhanced as a function of temperature. This was attributed to the thermal activation of charge carriers during the applied temperature range. Accordingly, hopping of electrons take place between ferric and ferrous ions. At very high temperatures, this electron hopping can be predominant and therefore, the conductivity goes to larger extent. Herein, the values of T c were noticed to be decreasing from 743 to 643 K. Hence, one can expect the change of conduction mechanism before and after transition temperature. In view of this, the activation energies were determined by drawing Arrhenius-plots (see Fig. 14). In the plots, H-region corresponds to the high temperature while L-region is associated to the low temperature. In both the regions, the slopes were considered into an account. Furthermore, with the help of a standard equation E a = 0.086 (slope), the activation energies (E a ) were computed and depicted in Table 2. The obtained outcomes manifested that the values of E a in H-region were detected to be increasing from 0.154 to 0.190 eV for X = 0.2-0.6 contents. But for X = 0.8 content, it was decreased to 0.147 eV. In the same way, the activation energies of L-region were also decreased from 0.0376 to 0.0443 eV for X = 0.2-0.6 compositions whereas, X = 0.8 exhibited E a of ~ 0.0274 eV. From the results, one can understand that the E a values of H-region seemed to be larger than that of L-region. This kind of low E a values were obtained owing to the limited availability of charge carriers caused by magnetic disordering 25 . However, the  www.nature.com/scientificreports/ L-region was evolved owing to the electrical conduction process produced by the extrinsic charge carriers while H-region was formed because of polaron hopping 25 . Previously, it was reported that there must be a change of slope of gradient line on passing through the T c 25 . In addition, the magnetic exchange interactions between the inner and outer electrons (e − ) on either side of T c 25 were responsible for the different activation energies. In other words, the change of magnetic state from ferri to para at the T c can offer two different E a values.
As depicted in Fig. 15, the power-law fit was accomplished to log σ ac − logω plots of X = 0.2-0.8 at various temperatures ranging from 313 to 813 K. Actually, the graphs from Fig. 15 can provide dc-conductivity (σ dc ) and exponent (n) values. It was well-known fact that σ ac is the combination of σ dc (T) (temperature-dependent) & σ ac (f) (frequency-dependent) terms. Mathematically, it can be written as follows: σ ac (f, T) = σ dc (T) + σ ac (f) 25 . For all the temperatures, the frequency-independent term in Fig. 15 can be identified from the invariant portion of the log σ ac -logω plots. The computed σ dc was found to be increasing from lower values to higher values as depicted in Table 4. That is, for X = 0.2-0.8, the σ dc was noticed to be almost increasing from 4.18E−07-2.54E−04, 1.72E−08-7.19E−05, 2.75E−08-6.51E−05 and 1.59E−08-1.95E−04 S/cm, respectively. This established a fact that low σ dc was recorded for x = 0.6 & 0.8 (large La-content). Moreover, exponent (n) values were also calculated and reported in Table 3. It was clear from the obtained 'n' values that it was decreasing from high value to low value for all La-contents. This was in consistent with the reports made by Hiti 38 . As a whole, the 'n' value offers the ratio between back hop-rate and site-relaxation. Therefore, it can achieve a maximum value of '1' & minimum value of '0' . In current work, the value of 'n' was accomplished to be less than one for all 'T' values (313-813 K). This established a fact that site-relaxation happened in SLFO-nanoparticles was quicker than the hopping of polarons 25 . Dielectric and impedance spectroscopy analysis. The complex dielectric modulus (M * ) is normally written as M* = M′ + j M″, where M′ = (ε′/(ε′ 2 + ε″ 2 )) and M″ = (ε″/(ε′ 2 + ε″ 2 )). The electrical conduction as well as the space charge polarization effect can be well understood by studying the complex dielectric modulus formalism. The real and imaginary parts of dielectric modulus (M′ & M″, respectively) were deliberated in case of SLFO nanoparticles. The related graphs were depicted in Figs. 16 and 17. Figure 16 indicated that the real part of dielectric modulus versus input field frequency plots (M′−f) of X = 0.2-0.8 showed relaxation (resonance) behavior. Therefore, the complete plots were divided into couple of regions and the corresponding frequency was considered as relaxation frequency (f r ). These two regions were denoted as region-a (< f r ) and region-b (> f r ).
The M′−f plots of X = 0.2-0.8 contents established a fact that the resonance frequencies were increased towards higher frequencies as a function of temperature from 313 to 813 K. It was practically seen that in case of X = 0.2-0.8, the f r values were (≥ log f) observed as 6.27, 6.16, 5.81, and 6.22, respectively. These f r values were noted to be decreased from X = 0.2-0.6 and beyond that it was increased to log f = 6.22 at room temperature. Usually, it was an established fact that the relaxation frequencies can be identified owing to the charge carrier accumulation at the grain-boundary interface. Thus, the space-charge polarization becomes predominant, and it can further show huge value of M′. In the same way, these kinds of relaxation were recorded in M″−f plots (see Fig. 17) up to smaller extent. That means, the significant relaxations were seen at low temperatures (see X = 0.4 content) while small relaxations were observed at large temperatures. However, the space charge polarization mechanism was found in these materials. Herein, the low frequency relaxations specified a fact that the space-charges were triggered for small input field frequency of log f = 5 and further accumulated at the interface. Further, it was found that the small M′-values were recorded at low f-values (< 1 kHz). This was attributed to the electrode polarization effect. Moreover, the regions below log f = 6.27, 6.16, 5.81, and 6.22 (see M′-f plots) can be dedicated to the region of long-range polarization. Inside this region, one can recognize the long-range hopping conduction mechanism which was grown due to the long-range mobility of charge-carriers. Likewise, M″−f plots disclosed the small  www.nature.com/scientificreports/ relaxations owing to long-distance motion of ions. Conversely, high f r -values were determined in case of M′−f & M″−f plots. These were formed owing to presence of ions confined to potential well. This approach was found in the previous reports 25 . Moreover, the region beyond f r was noted as short-range polarization region where the short-range mobility of charge-carriers can be originated. Also, this can reflect the short-range hopping conduction mechanism. In order to discuss the behavior of electrical conduction and relaxation, the M′ versus M″ plots were drawn as shown in Fig. 18. In Fig. 18, the semicircular arcs were associated to the contribution of grain & grain-boundaries in the electrical conduction-mechanism. Nevertheless, the noticed relaxations were partial in nature. Usually, these were developed due to partial relaxation-strength. Further, the presence of non-Debye relaxations in the prepared samples were confirmed from Fig. 18 i.e., the centers of semicircles were existed below the M′-axis. Specifically, the first semicircular-arc was connected to induced electrical-conduction owing to grain-contribution whereas the second one was related to the contribution of grain-boundary in the conduction mechanism. Also, some distortions were noticed in M′ versus M″ plots, which were evolved owing to intrinsic factor such as microstrain, pores, temperature, grain-size and moisture 25 .
As we know that the complex impedance (Z*) parameter can provide the information about the behavior of microstructure of polycrystalline materials. Further to elucidate the electrical conduction mechanism of as prepared SLFO-nanoparticles. The complex impedance relation of Z* = Z′−jZ″, where Z′ & Z″ are real and imaginary parts of complex impedance parameter can be useful to discuss impedance spectroscopy. Besides, the Cole-Cole plots (Nyquist plots) were plotted as displayed in Fig. 19. Nyquist plots were used to describe the conduction mechanism as a function of increase of La-concentration in SLFO samples at various temperatures ranging from 313 to 813 K. Clearly, two semicircular arcs were found for X = 0.2-0.8 contents. In particular, X = 0.2 composition exhibited two semicircles, whereas the remaining compositions showed slightly weak arcs. www.nature.com/scientificreports/ The partial relaxation strength may be accountable for the presence of weak arcs 25 . Similarly, the ions moving for longer distances can induce the formation of partial arcs. The X = 0.2 content attained complete relaxation strength owing to the existence of few ions confining to potential well 25 . The existence of semicircles indicated the magnetic semiconducting behavior for X = 0.2 samples. In case of two arcs, the first arc indicates the nature of grain whereas second one connected to grain-boundary. Normally, grain is high conductive layer and its boundary acts as low conductive layer. In current work, the Nyquist-plots were thoroughly examined via Z-view software (utilizing two RC-circuits). Accordingly, the accomplished values of grain/grain-boundary resistance (R g (R 1 )/R gb (R 2 )) with their respective capacitances ((C g (C 1 )/C gb (C 2 ))). The obtained values were tabulated in Tables 4, 5, 6 and 7. This was evident that for all 'X' values, the values of grain-resistance and grain-boundary resistance were observed to be decreasing with increase of temperature (from 313 to 813 K). Consequently, the corresponding capacitance values (C g & C gb ) were noticed to be increasing with temperature. Comparatively, the grain boundaries exhibit large resistance than the grains. Using the intersecting portion of first and second arcs at Z′-axis, the parameters like R g and R gb were elucidated. Therefore, first arc delivered R g , whereas second one showed R gb . This established a fact the grain boundaries consist of few conductive layers while the grains constitute more conductive layers. Practically this was demonstrated from bulk conductivity of grain (σ g = t/R g A, where 't' = thickness, and ' A' = area of cross section of pellet) and its boundary (σ gb = t/R gb A) (See Tables 4, 5, 6, 7). The obtained results confirmed that grains accomplished larger electrical conductivity than grain boundaries. Hence, it was clear that the current results satisfied the Koop's theory 36 . In addition, the electrical conductivity of X = 0.2-0.8 contents were found to be increasing with temperature and hence, it obeyed the Arrhenius law as mentioned in the previous work 25 . Apart from this, the induced relaxations were also observed. For this, we www.nature.com/scientificreports/ assumed the centers of arcs and noticed that if the centers of arcs were placed below real axis. Therefore, it can be recommended that the non-Debye relaxations were observed for x = 0.2-0.8 25 . In this view, the relaxation time constants (τ) of grains (τ g ) and grain-boundaries (τ gb ) were computed. The obtained results (see Tables 4,  5, 6, 7) ensured that the time constant was increased with increase of 'T' . Moreover, the second arcs expressed high 'τ gb ' values.

Conclusions
In this study, the SLFO nanoparticles were prepared using the hydrothermal method varying the La-content from X = 0.2-0.8. The diffraction pattern evidenced the hexagonal crystal structure. In addition, the lattice constants were observed to be increasing from 0.58801 to 0.58825 nm (a = b), and 2.30309 to 2.30341 nm (c) with increase in 'X' . The FESEM and TEM pictures indicated the spheres like grains as well as particles in the morphology. Furthermore, the E g values were identified to be increasing from 1.866 to 2.118 eV with increase in 'X' . The M-H loops of SLFO revealed the decreasing trend of magnetization from 36.34 to 7.17 emu/g with increase in 'X' . The X = 0.6 content revealed the high dielectric constant (~ 18) and dielectric loss (10.85) at high frequencies.
Therefore, this composition can be suitable for dielectric absorber applications at 1-5 MHz. The E a values of H-region were altered from 0.147 to 0.190 eV while the L-region showed the same trend changing from 0.0274 to 0.0443 eV. Using the power law fit, the dc-conductivity and exponents were computed. The dielectric modulus formalism provided the clear evidence for the space charge polarization mechanism. Besides, the short range and long-range hopping conduction mechanism was described. The Cole-Cole plots showed the elucidation of grain and grain boundary contribution in the electrical conduction mechanism. The obtained results indicated that the grains accomplished more electrical conductivity than the grain-boundaries. www.nature.com/scientificreports/ Table 4. Impedance spectroscopy parameters of X = 0.2 content. T (K) R g (Ω) R gb (Ω) C g (F) C gb (F) σ g (S/cm) σ gb (S/cm) τ g (s) τ gb (s) www.nature.com/scientificreports/ Table 5. Impedance spectroscopy parameters of X = 0.4 content.

Data availability
Date will not be provided publicly by all authors, and it will be provided immediately based on suitable request to the corresponding author.  Table 7. Impedance spectroscopy parameters of X = 0.8 content.