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Scientific Reports
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10.1038/s41598-024-72026-6
Article
Comparative study on structural, morphological, and optical properties of MS/Fe3O4 nanocomposites and M-doped Fe3O4 nanopowders (M = Mn, Zn)
Soltanpour P.
Naderali R.
Mabhouti Kh. kh.mabhouti@urmia.ac.ir

https://ror.org/032fk0x53 grid.412763.5 0000 0004 0442 8645 Department of Physics, Faculty of Sciences, Urmia University, Urmia, Iran
12 9 2024
12 9 2024
2024
14 2128722 3 2024
3 9 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
In the present work, the un-doped, M-doped magnetite (Fe3O4); (M = Mn, Zn), and MS/Fe3O4 composite nanopowders with a cubic spinel-type structure and average crystallite size range from 8.30 to 12.33 nm were synthesized by co-precipitation method. The FESEM images revealed the shape of particles are spherical with a grain size in the range of 33.44–49.77 nm. Through the analysis of reflectance data using Tauc’s model, the direct band gap energies of 2.98 eV, 2.93 eV, 3.01 eV, 2.85 eV, and 2.95 eV were determined for Un-doped Fe3O4, Mn-doped Fe3O4, Zn-doped Fe3O4, MnS/Fe3O4 composite, and ZnS/Fe3O4 composite NPs respectively. The parameters such as extinction coefficient and refractive index of the nanoparticles were computed by the Kramers–Kronig (K–K) method. Non-linear optical (NLO) parameters were computed from DRS data using the Wemple–Di-Domenico (WDD) model. The calculated third-order NLO susceptibility χ(3) and also electrical susceptibility χe represented the maximum value for MnS/Fe3O4 composite NPs compared to the other samples. Considering the advanced optical parameters of MS/Fe3O4 composite samples, these particles can be suitable candidates for non-linear optical applications.

Keywords

Fe3O4 NPs
Tauc’s model
Urbach energy
Kramers–Kronig
Wemple–DiDomenico method
Subject terms

Nanoscale materials
Nanoparticles
Structural properties
Characterization and analytical techniques
Materials for optics
Theory and computation
Electronic properties and materials
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pmcIntroduction

Nanoscale-engineered materials, such as metal oxide nanoparticles, have impressive and innovative properties that are substantially different from their conventional bulk counterparts. Thus, they have grown into active research areas in various fields including physics, materials science, chemistry, medicine, and multidisciplinary sciences1. Meanwhile, magnetite (Fe3O4) NPs with remarkable properties such as low toxicity, high magnetization, biocompatibility, high photon absorption capacity, and strong molecular bonding have received significant attention2. In addition, they have various applications in drug delivery agents, magnetic resonance imaging (MRI), magnetic storage media, biosensors, magneto-optical devices, microwave absorption, sensors, catalysts, and high-frequency applications3–9.

Magnetite (Fe3O4) nanoparticles are inverse spinel ferrites and their unit cell has eight fcc cells. It consists of 32 closely packed oxygen atoms in fcc sites and 24 metal cations distributed between 64 divalent tetrahedral (A) and 32 trivalent octahedral (B) sites. In these sites, metal cations are inscribed by four oxygen ions in tetrahedral sites and six oxygen ions in octahedral sites. Fe3O4 spinel ferrite has an inverted spinel structure with 8 Fe2+ ions occupying preferentially B sites, while 16 Fe3+ ions are equally distributed between A and B sites as [Fe3+]A[Fe2+Fe3+]BO4. The cation distribution is a crucial parameter in the alteration of structural, optical, and magnetic properties of Fe3O4 spinel ferrite10. Magnetite (Fe3O4) NPs have various applications that can be improved by varying their properties through the control of essential qualities for instance shape, magnetic behavior, size, stability, and surface morphology11,12.

The appropriate factors involved in the synthesis process can leveraged to control the mentioned qualities of nanoparticles. In this regard, different chemical methods have been used to prepare magnetite (Fe3O4) NPs, such as sol–gel13, Novel flow injection14, electrospray15, microwave16, and co-precipitation. Compared with other techniques, the co-precipitation technique has attracted much attention due to the simplicity of the process and high efficiency17–20. For this reason, the co-precipitation technique has been employed for synthesizing the samples under consideration. Also, the most efficient methods to improve the qualities of magnetite (Fe3O4) NPs are doping it via cations of transition metals or making a nanocomposite containing Fe3O4 and various compounds21–25. Due to the unique properties of transition metals, many studies have been conducted on the dependence of optical, structural, electrical, and magnetic properties of magnetite (Fe3O4) NPs doped with ions such as Mn+2, Zn+2, etc.26–28. The first impurity considered is manganese, which, due to its catalytic activity and increasing effect on the surface of nanoparticles as well as different oxidation states from 3 + to 7 + , manganese-based nanostructures can be very stable and have numerous applications in various industries, including medical industries, and soil29,30. Mustafa Aghazadeh et al.12 reported that the Mn-doped Fe3O4 NPs are suitable for supercapacitor applications. Eventually, because of the minimal difference in the ionic radii of zinc and iron, Fe3O4 NPs can be easily doped by Zn without destroying the crystal structure. On the other hand, Fe3O4 nanostructures doped with Zn can have many clinical applications due to the compatibility of Zn2+ ions with the human body and also resulting in lower toxicity28,31. Rakhi et al.32 researched the characteristics of Fe3O4 NPs doped with Zn. Their research group reported that the studied nanoparticles could be used in biomedicine and electrochemical energy storage devices. Furthermore, manganese sulfide (MnS), a semiconductor with a broadband gap of approximately 3.1 eV, is widely utilized in various industries such as magnetic resonance imaging (MRI), solar cells, lithium-ion batteries, biologic, and catalysts because of its exceptional electrical and optical features33,34. In addition, ZnS, among II–VI semiconductors, stands out as an essential material due to its notable optical properties and direct energy gap of about 3.68 eV at room temperature. It has applications in various fields, including light-emitting devices, nonlinear optical devices, laser devices, and anti-reflection coatings35. As a result, manganese and zinc sulfide can be suitable candidates for making nanocomposites containing magnetite (Fe3O4) NPs. On the other hand, the theoretical study of nonlinear features of materials can be advantageous for investigating nonlinear applications. From the Optics perspective, not much research has been done on Fe3O4 NPs and their composites. For instance, Anirban Roychowdhury et al.36 investigated how magnetite nanoparticles influence the optical characteristics of ZnS in fluorescent magnetic Fe3O4/ZnS composite NPs. Their group stated that as the zinc sulfide content in the composite samples enhanced, the magnetization decreased. Recently, Khalid et al.37 examined the properties of Fe3O4 NPs and Fe3O4@SiO2 core–shell and concluded that the studied nanoparticles can be applied in biomedicine and solar cells. Furthermore, for evaluating the linear and also nonlinear characteristics of nanoparticles, the numerical relations of Kramers–Kronig (K–K)38 and the Wemple–DiDomenico (WDD) model38 can be used, respectively. The K–K dispersion relation has been used to obtain the optical parameters of NPs with the support of DRS data40. In addition, the WDD model has been used to obtain scattering energies and non-linear refractive indices41. Based on our knowledge, the optical properties of ZnS/Fe3O4 and MnS/Fe3O4 composite nanoparticles have not been thoroughly investigated. Furthermore, there are insufficient reports on the systematic characterization of the optical properties of undoped, M-doped (M = Mn, Zn) Fe3O4 NPs, and MS/Fe3O4 composites NPs by the K–K and WDD analyses. In addition, as we know, optical parameters can be affected by structural and morphological characteristics such as shape and size.

Hence, the current research aim is to examine the structural and morphological characteristics of Fe3O4 NPs contaminated with Mn and Zn ions, as well as ZnS/Fe3O4 and MnS/Fe3O4 composite NPs, and to assess their impact on optical parameters in terms of quantity, doping effect, and type of composite. Therefore, in this research, the structural parameters of the samples, such as size, phase, stacking faults, and dislocation density, were deduced from XRD data. Also, the optical properties of nanoparticles were investigated based on DRS data using (K–K) relations and (WDD) model. Besides, parameters such as band gap, Urbach energy, refractive indices, linear and non-linear absorption coefficients, third-order optical susceptibility, and electrical susceptibility were calculated, and a comparative study was presented.

Experimental details

Material

All the samples of this research are synthesized through the chemical co-precipitation technique. In this work, ≥ 99.0% (RT), puriss. p.a. Iron (II) chloride tetrahydrate (FeCl2·4H2O, 13478-10-9), 97.0% ACS reagent, Iron (III) chloride hexahydrate (FeCl3·6H2O, 10025-77-1), ≥ 97.0% (KT) purum p.a. Manganese (II) nitrate tetrahydrate (Mn(NO3)2·4H2O, 20694-39-7), 98% reagent grade, Zinc nitrate hexahydrate (Zn(NO3)2·6H2O, 10196-18-6), ≥ 99.99% trace metals basis, Sodium sulfide nonahydrate (Na2 S·9H2O, 1313-84-4), 99.9% Sodium hydroxide (NaOH), 99.8% ethanol (C2H6O), and double distilled water was used.

Preparation of un-doped Fe3O4, M-doped Fe3O4 and MS/Fe3O4 composite NPs

Synthesis of un-doped and M-doped Fe3O4 NPs

In the first step, the stoichiometric amounts of FeCl3 0.6H2O and FeCl2·4H2O with a ratio of 2:1 were dissolved in water at 80° C for 2 h under stirring. Afterward, to prepare 5 wt.% of M-doped Fe3O4, the required salt solution containing the dopant element (M = Mn, Zn), was added to the previous solution with an optimized concentration42,43. Then, a solution containing 2.0 M NaOH was continuously augmented to the previous solution until the pH of the solution reached 13. In the next step, until the pH of the solution achieves 6.5, the prepared sediment was separated using an external magnet and then washed with water and alcohol numerous times. Finally, the resultant powders were dried in an oven at 100 °C for 3 h and later milled to prepare nanoparticles. The above procedure was applied to prepare M-doped Fe3O4 NPs by adding Manganese nitrate and Zinc nitrate in stoichiometric ratios M: Fe = 0. 15: 2.85.

Synthesis of MS/Fe3O4 composite NPs

In the synthesis process of MS/Fe3O4 by co-precipitation procedure, specified amounts of FeCl3·6H2O and FeCl2·4H2O were dissolved in distilled water to provide iron components for Fe3O4 nanoparticles and dynamically stirred for 1 h at 80 °C. Afterward, a solution containing 2.0 M NaOH was added to adjust the pH of the solution between 9 and 11 and to form a Fe3O4 suspension, and it was stirred for 2 h at 80 °C. In the following, one of the required salt solutions (Manganese (II) nitrate tetrahydrate, Zinc nitrate hexahydrate) was added to the mixture with the specified percentage and stirred for 1h at the same temperature. In the next step, the 0.2 M sodium sulfide solution was poured dropwise into the obtained suspension under constant stirring for 1 h to the mixture to induce the precipitation of metal ions and form composite nanoparticles43,44. In the subsequent stage, the resulting precipitate was detached using an exterior magnet and also washed with distilled water and alcohol to obtain pH 6.5. Finally, the resultant powders at 80 °C for 5 h were dried in an oven and then ground to obtain composite nanoparticles. Supplementary Fig. 1 represents the synthesis process and the chemical reaction behind the formation of the synthesized nanoparticles.

Characterization

The structural characteristics of Un-doped, (M-doped magnetite (Fe3O4) NPs and MS/Fe3O4 composite NPs; M = Mn, Zn) were investigated through a high-resolution X-ray diffraction system (Philips PW 1730) provided with Cu-Kα radiation at a wavelength of λ = 0.154056 nm, from an angle of 2θ = 10°–80°. To determine the surface morphology and diameter of nanoparticles, field emission scanning electron microscopy (FE-SEM) (TeScan-Mira III, Czech Republic) and ImageJ analysis software were used, respectively. Also, to examine the presence of the desired phases in the matrix of synthesized nanoparticles and to identify functional groups, Fourier-transform infrared spectroscopy (FT-IR) (Thermo Scientific, Nicolet, Avatar, USA) was carried out over a wavenumber range of 400–4000 cm1. The evaluation of linear and nonlinear optical parameters of nanopowders was done using Diffuse Reflectance Spectroscopy (DRS) (Sinco S4100 Korea) and MATLAB coding.

Results and discussion

XRD

Typically, XRD is used to determine the crystal structure, as well as estimate the mean crystallite size (D) of the nanoparticles. The XRD diffraction patterns of the synthesized Un-doped, M-doped Fe3O4 NPs and MS/Fe3O4 composites NPs are demonstrated in Fig. 1a–c. Due to the X' Pert software calculations, the presence of the Brag diffraction planes (220), (311), (400), (422), (511), (440) and (533) in all samples indicate the cubic spinel phase of Fe3O4 (JCPDS card No. 075-0449). Hence, based on the samples containing Zn and Mn doping, it can be inferred that M+2 ions have been effectively substituted in the Fe3O4 lattice, resulting in the formation of samples with high phase purity. Moreover, phases indicating the formation of M-based structure were identified in the MS/Fe3O4 composite samples. The diffraction peaks observed in the MnS/Fe3O4 nanocomposite are attributed to the (100), (002), (101), (103), and (212) planes, which correspond to the hexagonal phase of the MnS nanoparticles (JCPDS card No. 040-1289). Also, for ZnS/Fe3O4 composite NPs, the presence of the Brag diffraction planes indicates the hexagonal phase of ZnS (JCPDS card No. 072-0163). It is observed from Fig. 1c that compared to the rest of the samples the peaks of ZnS/Fe3O4 composite NPs show more broadening, which indicates the ultra-fine nature of the nanoparticles.Fig. 1 The XRD spectra of (a) Un-doped Fe3O4 NPs; Mn-doped Fe3O4 NPs; Zn-doped Fe3O4 NPs; (b) MnS/Fe3O4 composite NPs; (c) ZnS/Fe3O4 composite NPs.

Based on XRD data, the presence of M+2 ions and also MS impurities do not alter the Fe3O4 lattice structure. Nevertheless, the existence of the impurities leads to the reduction in the spacing between the planes and the lattice constant, resulting in a slight shift towards higher 2θ values in the diffraction peaks. Also, apart from the shift of the peaks, the intensity of the diffraction peaks, which indicate the crystalline order of the synthesized materials, can alter under the influence of factors such as stress, synthesis temperature, crystal growth time, the number of crystal atoms, etc.45. In the present work, it seems that the shift of the peak towards higher 2θ is the cause of the decrease in the intensity of the diffraction peaks in the synthesized samples. The pattern depicts that the diffraction peak intensities decreased and peaks wide diminished in the Mn-doped Fe3O4 and ZnS/Fe3O4 samples compared to un-doped Fe3O4 NPs; this can imply the lowest crystallinity and increased crystallite size of Mn-doped Fe3O4 and ZnS/Fe3O4 NPs. The broadening and low-intensity peaks of Zn-doped can imply a decrement in crystallinity and crystallite size despite the Fe3O4 NPs. On the other hand, the pattern of the MnS/Fe3O4 sample shows a higher peak intensity and a smaller peak width, which means that this sample has a higher crystallite size and crystallinity46. The values of 2θ angles, interplanar distance (d), and full width at half maximum (FWHM) belonging to the Fe3O4 phase in all prepared nanopowders are given in Tables 1 and 2.Table 1 Peak positions (2θ), interplanar distances (d), and FWHM (β) of the JCPDS card, Un—doped Fe3O4 and Mn-doped Fe3O4 NPs.

(h k l)	JCPDS card	Un—doped Fe3O4	Mn—doped Fe3O4	
2 θ(∘)	dhkl(A∘)	2 θ(∘)	dhkl(A∘)	FWHM (˚)	2 θ(∘)	dhklA∘	FWHM (˚)	
(2 2 0)	3o.36	2.94	30.33	2.94	1.04	30.38	2.94	0.82	
(3 1 1)	35.76	2.5	35.67	2.51	0.88	35.77	2.5	0.85	
(4 0 0)	43.47	2.08	43.29	2.08	1.02	43.41	2.08	0.88	
(4 2 2)	53.94	1.69	53.68	1.7	1.23	53.78	1.7	0.68	
(5 1 1)	57.51	1.6	57.25	1.6	0.85	57.36	1.6	0.96	
(4 4 0)	63.16	1.47	62.91	1.47	1.08	62.94	1.47	1	

Table 2 peak positions (2 θ), interplanar distance (d), and FWHM ( β ) of the Zn – doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 nanopowders.

(h k l)	Zn—doped Fe3O4	MnS/Fe3O4	ZnS/Fe3O4	
2 θ(∘)	dhkl(A∘)	FWHM (˚)	2 θ(∘)	dhkl(A∘)	FWHM (˚)	2 θ(∘)	dhkl(A∘)	FWHM (˚)	
(2 2 0)	30.38	2.93	1.06	30.34	2.94	0.9	30.34	2.94	0.77	
(3 1 1)	35.73	2.51	1.16	35.68	2.51	0.86	35.7	2.51	1.14	
(4 0 0)	43.39	2.08	1.26	43.32	2.08	0.7	43.45	2.08	1.49	
(4 2 2)	53.76	1.7	1.09	53.68	1.7	0.8	53.8	1.7	1.03	
(5 1 1)	57.3	1.6	1.17	57.28	1.6	0.94	57.25	1.6	1.26	
(4 4 0)	62.92	1.47	1.45	62.89	1.47	0.89	62.91	1.47	1.04	

By analyzing the XRD spectrum, and by using Scherer and Williamson–Hall (W–H) methods, the effects of M doping and MS NPs on the structural characteristics such as crystallite size and microstrain of Fe3O4 nanopowders can be obtained.

The network structure's strain and crystallite size, which are categorized as physical and instrumental broadening, have an impact on the peak width in XRD patterns47. Therefore, we must consider the broadenings caused by the samples and instrumentals while calculating the crystallite size "D" of the nanopowders11,26. In this regard, the broadening of data standard (defect-free silicon crystals) as instrumental expansion (βinstrumental=βsilicon=0.196degrees) is used to correct and remove the detected peak width47. So, to attain the crystallite size, the corrected expansion can be determined by applying the following equation48.1 βC=βsample2-βsilicon2⇒βC2=βmeasured2-βinstrumental2

where βC is the value of peak broadening related only to the change in the size of crystallites, and βsample is the measured width value.

The mean crystallite size "D" of the prepared nanopowders was obtained by considering the average sizes of D220, D311, D400, D422, D511, and D440 in the X-ray patterns and using the Debye–Scherrer (D–S) relationship, as follows49,50:2 D=kλβhklcosθ;whichβhkl2=βmeasured2-βinstrumental2

Here, D denotes the average size of the crystallite, K = 0.9 represents the structure factor, λ = 1.5406 Å represents the wavelength of X-rays, β is considered as the FWHM, and θ known as the diffraction angle.

The average lattice parameter (a) associated with cubic structures and cell volume (V) can be computed from the XRD patterns by the following equations51:3 a=dhkl[h2+k2+l2]1/2

4 Vcell=a3

Here, (h k l) indicates the plane coordinates in reciprocal space (Miller indices), and dhkl represents the distance between crystal planes (dhkl= λ/2 sinθ).

Besides Scherer's method, the Williamson–Hall (W–H) relation can be used to determine the crystallite sizes and the micro strains of the synthesized samples. Disorders, crystal imperfections, and lattice misfits owing to the synthesis process can be some of the reasons for the generation of microstrain (ε) in the lattice structure of synthesized nanopowders. Therefore, in addition to the crystallite size, the strain induced in the lattice causes the broadening of the XRD peaks in all crystallographic orientations. Thus, based on W–H analysis using the uniform deformation model (UDM), total physical broadening (βtot) has been evaluated as follows52,53.5 βtot=βhkl=βs+βD=4εtanθ+KλDcosθ

6 βhklcosθ=kλ/D+4εsinθ

where βs represents the strain broadening and βD indicates the size broadening width. The mean particle size and lattice strain can be calculated by plotting βhkl cos θ (y-axis) vs. 4 sin θ (x-axis) for the diffraction peaks and extrapolating the y-intercept and slope of the linear fit.

Figure 2a–g displays the W–H diagrams of the nanopowders. In Table 3, the values related to the average crystal size, microstrain, network parameters, and volume cells of the cubic phase of the samples are presented. The crystallite size obtained by W–H is slightly different from the results obtained by the Debye-Scherer method, which can be related to the strain applied to the nanoparticles. From Table 3, it can be seen that the lattice parameter in doped and composite NPs decreased in comparison to Fe3O4 NPs. The decreasing of lattice parameters in doped samples can be associated with the cation distribution. When Fe3O4 is doped, the dopant ion is generally replaced in the sites that are proportional to ionic radii54. In Mn-doped Fe3O4 NPs, though the ionic radius of Mn2+ (0.81 Å) is larger than Fe2+ (0.77 Å), the lattice parameter can be increased, and the unit cell can be expanded. Also, in the Zn-doped Fe3O4 NPs, the Zn2+ ions have a preference to present in the tetrahedral sites with larger ionic radius (0.74 Å) to Fe2+ (0.645  Å) ions in A sublattice hence the lattice constant in Zn-doped Fe3O4 can be larger than Fe3O4. However, the reduction of the lattice parameters could be the result of the cation distribution between the A and B sites, which affects the inversion parameter, giving the percentage of doped ions in the octahedral (B) sites33,55. Furthermore, the reduction of the iron oxide phase lattice parameter in the composites can be attributed to the alternation in the structural order due to the presence of the secondary phases MnS and ZnS. It is evident that the examined (a) and (V) of the synthesized samples do not demonstrate considerable variation and are in good agreement with the standard value announced in JCPDS file No. 075-0449 (a = 8.320 Å, V = 575.93 Å).Fig. 2 W–H plot for (a) Un-doped Fe3O4 NPs; (b) Mn-doped Fe3O4 NPs; (c) Zn-doped Fe3O4 NPs; (d) Fe3O4 in MnS/Fe3O4 composite NPs; (e) Fe3O4 in ZnS/Fe3O4 composite NPs; (f) MnS in MnS/Fe3O4 composite NPs; (g) ZnS in ZnS/Fe3O4 composite NPs.

Table 3 The average crystallite sizes were computed by (using W–H relations and D–S method), (ε), (a), and (V) of the prepared samples.

Samples	Debye–Scherer (nm)	Williamson–Hall (nm)	10-3ε(W–H plot)	FE-SEM average particle size (nm)	a (A∘)	V (A∘3)	
Un-doped Fe3O4	10.91	8.83	0.741	36.51	8.3472	581.59	
Mn-doped Fe3O4	12.28	10.79	0.975	45.26	8.3325	578.55	
Zn-doped Fe3O4	8.58	8.3	1.75	33.44	8.3342	578.88	
Fe3O4 in MnS/Fe3O4	13.91	12.33	1.02	49.776	8.3455	581.26	
Fe3O4 in ZnS/Fe3O4	9.98	9.87	1.56	36.96	8.3377	579.62	

The dislocation density representing various types of defects can be introduced as the number of dislocation line lengths per unit volume in the lattice and estimated using the Williamson and Smallman relationship37:7 δ=1D2

In addition, in the structure of nanoparticles, the number of crystallites or particles can be expressed by the following relation:8 N=δD3

Another type of surface fault is the stacking fault (SF), which usually occurs during the preparation. In crystals, the fraction of planes that have accumulated defects is called SF and characterizes the disorder of crystallographic planes. Also, its value is measured according to the given form56:9 SF=2π2453tanθ0.5β

The computed values of (D), (δ), (N), and (SF) for all prepared nanopowders are tabulated in Table 4. Data in Table 4 displays that the doping of Mn in Fe3O4 structure and also the existence of ZnS NPs in ZnS/Fe3O4 composite sample leads to the reduction in dislocation density, N, and SF in comparison to Fe3O4 NPs. The decrement SF parameter in these samples conforms to the reduction of disorder and decreasing crystallinity that is evident from the decreasing of peaks wide and intensity in the XRD section. Besides, in the MnS/Fe3O4 composite sample, the existence of MnS NPs leads to the reduction in dislocation density, N, and SF in comparison to Fe3O4 NPs. Hence, the higher intensity peaks with less broadening were observed for the MnS/Fe3O4 sample indicating the large crystallite size with the increased crystallinity. Compared to the other samples, the higher SF and δ values ​​for Zn-doped Fe3O4 NPs confirm the reduced crystallinity, smaller crystallite size, and increment defects, which can be estimated from the larger peak width and lower peak intensity57,58. Furthermore, the highest (δ) value for the Zn-doped Fe3O4 sample displays that Zn doping increases the mechanical features such as the tensile and yield strength of the Fe3O4 NPs59.Table 4 Computed values of (D), (δ), (N), and (SF) of synthesized samples.

Sample	DW-H (nm)	δW-H(×1015 line/m2)	NW-H×1038particlem3	Avg.SF (×10-3)	
Un-doped Fe3O4	8.83	12.82	186.21	7.32	
Mn-doped Fe3O4	10.79	8.589	68.371	6.21	
Zn-doped Fe3O4	8.3	14.51	253.76	8.4	
Fe3O4 in MnS/Fe3O4	12.33	6.577	35.086	5.36	
Fe3O4 in ZnS/Fe3O4	9.87	10.26	106.7	7.04	
MnS in MnS/Fe3O4	53.72	0.3465	0.0235	1.09	
ZnS in ZnS/Fe3O4	23.39	1.827	1.427	2.356	

FE-SEM

The surface structure and morphology of the synthesized samples are revealed using the FESEM analysis. Figure 3a–e displays the FESEM micrographs of Un-doped Fe3O4, Mn-doped Fe3O4, Zn-doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 nanopowders, respectively. To measure the diameter of the nanoparticles, Image J software is used. It is evident from the images that Fe3O4 nanoparticles have a spherical shape with higher or smaller grain size compared to the pure Fe3O4 NPs, but due to the integration of different ionic radii and the presence of MS NPs, distortion is observed in the structure. Several factors, such as impurities in the preparation process, cations escaping from the samples, and oxygen deficiency in the samples, are attributed to the causes of these morphological changes60. Also, the value distribution histogram with Gaussian fit in Fig. 4a–e shows the average particle size of 36.51 nm, 45.26 nm, 33.44 nm, 49.77 nm, and 36.96 nm for Un-doped Fe3O4, Mn-doped Fe3O4, Zn-doped Fe3O4, MnS/Fe3O4 and ZnS/Fe3O4, respectively. It can be concluded from the graphs that the trend of changes in particle diameter obtained from FESEM is in the nano range and in accordance with the results obtained from XRD analysis. However, the crystallite size obtained from FESEM is slightly higher than the values computed from XRD data. This detected difference can be related to the surface structure of the aggregated grains, which leads to the growth of larger grains that exhibit porosity and surface roughness61. Considering that the main parameters of nanoparticles, including size, shape, and structure of individual particles, as well as their spatial distribution, affect the peculiarities of the nanoparticle system and lead to special optical features that can be used in new material applications62. Therefore, in the following, linear and non-linear optical properties affected by the structural and morphological characteristics of the nanoparticles will be investigated.Fig. 3 FE-SEM micrographs of (a) Un-doped Fe3O4 NPs; (b) Mn-doped Fe3O4 NPs; (c) Zn-doped Fe3O4 NPs; (d) MnS/Fe3O4 nanocomposites; (e) ZnS/Fe3O4 nanocomposites.

Fig. 4 Histograms of size distributions with Gaussian fit for (a) Un-doped Fe3O4 NPs; (b) Mn-doped Fe3O4 NPs; (c) Zn-doped Fe3O4 NPs; (d) MnS/Fe3O4 composite NPs; (e) ZnS/Fe3O4 composite NPs.

FT-IR analysis

Figure 5 depicts a comparison of FTIR spectra of Un-doped, Mn-doped, Zn-doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 nanopowders in the wave number range of 400–4000 cm−1. FTIR peaks related to the prepared nanopowders are arranged in Table 5. According to the values inserted in the spectrum of the Un-doped sample in Fig. 5, it can be seen that the transmittance bands indicating the vibrational modes are located in the wave numbers 448 cm−1, 600 cm−1, 1401 cm−1, 1619 cm−1, 2926 cm−1 and 3419 cm−1. The absorption bands identified at the wave numbers 448 cm−1, and 600 cm−1 are associated with the vibrational modes of the Fe–O bond, indicating the octahedral and tetrahedral sites63,64. Figure 5 shows that the band at 600 cm−1 consists of two distinct bands at 631 cm−1 and 593 cm−1 imputed to the Fe–O state extending from the tetrahedral sites14. The broadening or splitting of the band displays the increase of cation vacancies in the lattice structure and the decrease of the lattice constant value65. Also, the spectrum shows an influential band near 3418 cm−1, which is relevant to the stretching vibration of OH groups and surface water molecules and causes the foundation of hydrogen bonds. In addition, the bending vibration related to OH groups appeared in 1619 cm−137,66. The transmittance band at 1401 cm−1 is attributed to COO–Fe due to the presence of carbon pollution during washing with alcohol67, and the weakest observed band at 2926 cm−1 belongs to the C–H stretching vibration in the CH2 group68. According to Fig. 5, after the loading of different metals into the structure of Fe3O4 and the presence of MnS or ZnS NPs in the composite nanopowders, slight distinctions can be observed in the IR spectra of Un-doped, M-doped, and composite samples. This difference appears by the displacement of the absorption bonds to lower and higher frequencies in doped and composite samples compared to the Non-doped sample. In the doped samples, the new metal bonds all appear in the scope of 400–700 cm−1, which overlaps with the peaks of Fe3O4 species and cannot be identified. Furthermore, a broad peak in the range of 1000 cm−1–1300 cm−1 is observed in the composite nanopowders, which is relevant to the S=O bond vibrations69. Besides, the characteristic peak in the region of 1126 cm−1 can be imputed to metal-hydroxyl M−OH bonds70. Moreover, in nanocomposites, the characteristic peaks within the range of 450 cm−1 to 630 cm−1 can be attributed to metal-S bonds such as Zn–S and Mn–S bonds43. Therefore, it can be concluded that the characteristic peaks of MnS and ZnS nanoparticles overlap with Fe–O vibration modes located at 627 and 629, respectively71,79.Fig. 5 FTIR spectra of synthesized Un-doped Fe3O4, Mn-doped Fe3O4, Zn-doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 nanopowders in the range of 400 cm−1–4000 cm−1.

Table 5 Representation of functional groups of Un-doped Fe3O4, Mn-doped Fe3O4, Zn-doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 nanopowders from FTIR Spectra.

Mode of vibration	Wavenumber (cm−1)	
Un-doped Fe3O4	Mn-doped Fe3O4	Zn-doped Fe3O4	MnS/Fe3O4	ZnS/Fe3O4	
O–H stretching	3419	3417	3412	3418	3425	
H–O–H bending vibration	1618	1620	1619	1619	1636	
C–H stretching	2926	2925	2926	2925	2925	
COO–Fe	1401	1384	1400	1386	1385	
Fe–O stretching (tetrahedral vibrations)	593	592	589	594	593	
631	630	621	627	629	
Fe–O Stretching (octahedral vibrations)	448	445	436	463	449	

Optical results

Linear optical properties

Diffuse reflectance spectra of synthesized samples at room temperature in the wavelength range of 300–800 nm are displayed in Fig. 6. The reflectance values change with photon wavelength. From Fig. 6, the lowest value of the reflection spectrum in the visible region corresponds to the Zn-doped Fe3O4 at about 0.21%, while the highest value in the same region for the ZnS/Fe3O4 sample varies up to 26.40%. In fact, based on DRS data and the theory of P. Kubelka and F. Munk presented in 193173, the measured reflectance spectra can be converted to the corresponding absorption spectra by applying the Kubelka–Munk (K–M) function as follow74,75:10 FR=(1-R)22R=KS∝α

where K and S are known as K–M absorption and scattering coefficients, moreover, FR is the K–M function; R=(Rsample/Rrefrence) is the diffuse reflectance ratio between the reference and sample.Fig. 6 Variation of reflectance spectra as a function of wavelength (λ) for synthesized nanopowders.

Besides, it is supposed that the optical absorption coefficient (α) of the semiconductors depends on the energy (hv), according to the bellow equation76,77:11 αhv1/n=A(hv-Eg)

Incorporating the K–M function Eq. (10), with the Tauc relation Eq. (11), yields Eq. (12), which can produce the absorption spectrum from which Eg can be extrapolated75,78:12 FRhv1/n=A(hv-Eg)n

Here, A displays a constant, ν represents the photon frequency, h denotes Planck’s constant,Eg indicates band gap energy, and n is a constant that indicates the nature of electron transition can take the values of 2 and 1/2 for indirect and direct allowed transitions79. In Fig. 7, by plotting the FRhv2 in terms of (hv) and extrapolating the straight line of the graphs, the direct energy gap (Eg) of all samples has been estimated, and the deduced results are classified in Table 6. By adjusting the size of the NPs, the energy gap values of the NPs increased from 2.85 to 3.01 eV, which are inversely proportional to the particle size80,81. Furthermore, the data in the table indicate that Eg values for Mn-doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 samples decreased which may be advantageous in photocatalytic activity. In photocatalyst application, the bandgap energy must be in the range of 3.0>Eg>1.23 for visible light activity, so the narrow Eg values of composites and 5% Mn-doped in the structure (Fe3O4) can be a helpful candidate for photocatalytic applications82.Fig.7 Determination of direct band gap energy of prepared nanopowders using the Kubelka–Munk function.

Table 6 Computed energy parameters (Eg, Eu, E0, Ed) of synthesized samples.

Sample	Direct Eg (eV)	Eu(eV)	E0(eV)	Max.Ed(eV)	
Kubelka–Munk (see Fig. 7)	Kramers–Kronig (see Fig. 11)	
Un-doped Fe3O4	2.98	2.58	0.666	5.225	14.57 (λ=687.82nm)	
Mn-doped Fe3O4	2.93	2.53	0.425	5.162	14.32 (λ=687.82nm)	
Zn-doped Fe3O4	3.01	2.66	0.9134	5.262	14.00 (λ=686.02nm)	
MnS/Fe3O4	2.85	2.51	0.668	5.062	14.53 (λ=671.61nm)	
ZnS/Fe3O4	2.95	2.547	0.5368	5.187	14.37 (λ=687.82nm)	

In crystalline materials, vacancies and chemical defects cause strain in the material network, which affects the electronic structure of the material, and more localized states appear between the material's valence and conduction bands. These states are known as band tails, and the energy gap between them is called Urbach energy. Hence, the Urbach energy (Urbach tail) can be attributed to an electronic disorder near the band edge due to the random distribution of defects in the nanoparticle crystal structure64. On the other hand, the Urbach tail at the edge of the band can be caused by the density of electron states. Also, in nanomaterials, the structure created as a result of "electron–phonon" interactions is known as the quantum effect and can be described as a structure near the edges of the absorption band10,83.

The Urbach energy (Eu) is calculated with the following empirical relation84:13 α=αoexphνEu

Here, α≈F(R) defines the absorption coefficient, and αo represents a constant, and E=hν represents the incident photon energy. Then the logarithm function is applied to both sides of the Eq. (13), and the following relation can be obtained10,61:14 LnF(R)=Lnβ+hνEu

The Urbach energies of the synthesized samples are determined by linearly fitting plots of lnF(R) vs. (hv) and calculating the inverse slope of the lines as shown in Fig. 885. The slopes of linearly fitted plots are obtained as 1.50307, 2.35775, 1.09432, 1.30201, and 1.87023 for Un-doped Fe3O4, Mn-doped Fe3O4, Zn-doped Fe3O4, MnS/Fe3O4, and ZnS/Fe3O4 samples, respectively. Furthermore, the resulting values of the Urbach energy for the samples are evaluated and indexed in Table 6. Based on Table 6, It can be seen that compaired to other samples the highest value of Eu is obtained for Zn-doped Fe3O4 NPs, which indicates the generation of more impurity levels in the band gap of Zn-doped Fe3O4 NPs86,87.Fig. 8 The Urbach tail energy measurement from the slopes of the fitted linear straight lines of synthesized samples.

Also, in this work, K–K relations were used to estimate the optical parameters of nanopowders. By using K–K relations, critical information about scattering and absorption phenomena can be obtained. The typical quantity used in optical projects for determining the speed of electromagnetic wave propagation in materials is the complex refractive index (N), which is expressed as follows87:15 N=n(ω)+ik(ω)

The part of (N) which has essential significance for photonic applications and is a fundamental characteristic to describe the features of optical devices such as sensors, filters, and other optoelectronic instruments, is called the real refractive index (n). In addition, (k) as the imaginary part of the complex refractive index depends on the amount of light absorption and plays an important role in optical applications88,89.

Refractive index (n) and extinction coefficient (k) are computed according to the K–K relations with the following Eqs89.16 nw=1-R(w)1+R-2Rwcosθ(w)

17 kw=2Rwsinθ(w)1+R-2Rwcosθ(w)

Here, ω indicates the angular frequency, θ(w) is the phase division of the reflected and incident radiations, which is calculated by the Fourier transform and is expressed as follows90:18 θ(w)=-ωπ∫0∞lnRω′-lnR(ω)ω′2-ω2dω′

Graphs of n(w) and k(w) obtained by the k–k calculation method for all synthesized samples are demonstrated in Fig. 9. In nanomaterials, the value of n depends on the synthesis conditions and is variable. According to Fig. 9a, higher values of n are observed in the visible wavelength region for all synthesized samples and then decrease with increasing photon energy (1.5–4 eV). In Fig. 9, a slight difference amongst the n values is observed, which could be influenced by the permeability nature of the nanopowders or the distinct impurities created. Compared to the rest of the samples, it can be seen that the value of n changes widely from 0.54 to 1.82 as the wavelength decreases from 800 to 300 nm for the MnS/Fe3O4 nanocomposite sample. Since the value of the refractive index is decisive for solar cells, photocatalytic, and optoelectronic devices, and as can be seen, the refractive index MnS/Fe3O4 nanocomposite in the peak area has increased in the value of n compared to other synthesized NPs. Therefore, this sample could be a better candidate for optoelectronic applications91.Fig. 9 Curves of (a) n, and (b) k vs. energy (eV) for synthesized samples.

In addition, Fig. 9b provides the possibility to obtain the values of k as a function of the wavelength of the incident light. It is worth noting that k values increase in two regions, first around 400–420 nm and again more strongly at 80 nm, which indicates a substantial increase in photon absorption in these regions.

The stored energy, as well as the energy loss in the environment, which are respectively determined by the real ε1(ω) and imaginary ε2(ω) parts of the dielectric function, are defined by the following relations79:19 ε1=εr=n2-k2

20 ε2=εi=2nk

Also, the energy loss that occurs due to the electric field in the material is called dielectric loss and is expressed as follows92:tanδ=εiεr

21 Losstan(δ)=tan-1εiεr

The computed maximum values for n, k, ε1,ε2, and tan(δ) are given in Table 7. According to the variable values of n, k, and the obtained values for ε1 and ε2, it can be seen that the maximum values of ε1 for the samples are greater than ε2.Table 7 The calculated maximum values of n, k, ε1,ε2, Loss tan (δ), and α for synthesized samples.

Samples	n	k	ε1	ε2	Loss tan (δ)	α(nm-1)	
Un-doped Fe3O4	1.68

(λ = 687.8 nm)

	0.586

(λ = 782.9 nm)

	2.79

(λ = 687.8 nm)

	1.54

(λ = 763.5 nm)

	1.055

(λ = 796.0 nm)

	0.0094

(λ = 782.9 nm)

	
Mn-doped Fe3O4	1.66

(λ = 687.8 nm)

	0.688

(λ = 782.9 nm)

	2.68

(λ = 660.7 nm)

	1.80

(λ = 764.4 nm)

	1.217

(λ = 797.8 nm)

	0.011

(λ = 774.1 nm)

	
Zn-doped Fe3O4	1.50

(λ = 686.0 nm)

	0.448

(λ = 780.2 nm)

	2.25

(λ = 686.0 nm)

	1.09

(λ = 766.1 nm)

	0.842

(λ = 791.6 nm)

	0.0072

(λ = 773.2 nm)

	
MnS/Fe3O4	1.82

(λ = 671.6 nm)

	0.754

(λ = 785.5 nm)

	3.30

(λ = 671.6 nm)

	1.98

(λ = 771.4 nm)

	1.285

(λ = 796.9 nm)

	0.012

(λ = 783.8 nm)

	
ZnS/Fe3O4	1.66

(λ = 686.0 nm)

	0.624

(λ = 782.9 nm)

	2.70

(λ = 680.6 nm)

	1.58

(λ = 767.9 nm)

	1.119

(λ = 796.0 nm)

	0.010

(λ = 782.9 nm)

	

For all provided nanopowders, the absorption coefficient (α) was computed using Eq. (22), and the data are depicted in Fig. 1093.22 α=4πkλ

where λ is the incident light wavelength and k is the extinction coefficient calculated by K–K method. Besides, the maximum computed values for (α) are also given in Table 7. Furthermore, putting the absorption coefficient (α) resulting from the (k–k) relations in Eq. (11) is a different method for estimating the band gap energy (Eg) of nanoparticles, which was done in the present work93. Figure 11 shows the band gap determination curves and the data obtained from the mentioned curves are also listed in Table 6. According to the energy gap values listed from both methods in Table 6, it can be found that the results match well with each other (Fig. 12).Fig. 10 Plots of absorption coefficient (α) versus Energy for synthesized NPs.

Fig.11 Direct band gap energy determination of the Un-doped, M-doped Fe3O4, MS/Fe3O4 synthesized nanopowders using the Kramers–Kronig method.

Fig. 12 Dependence of absorption coefficient βc on wavelength (λ) for synthesized NPs.

Non-linear optical (NLO) properties

In addition to linear optical studies, determining the nonlinear characteristics of nanomaterials is vital for their use in optoelectronic devices. The induced polarization vector is used to determine the properties, which is the consequence of the power series expansion of the electric field vector (E) and the dielectric susceptibility (χ) of the material as follows94,95:23 P=εoχE=(χ(1)E+χ(2)E2+χ(3)E3+⋯)

P is polarization, εo refers to the permittivity of free space, χ(1) indicates the linear susceptibility, and in contrast, χ(2) and χ(3) denote the second and third-order non-linear susceptibility, respectively.

χ(1) and χ(3) are calculated by the Wemple–Di-Domenico (WDD) model and the generalized Miller's law with the following Eqs83,96:24 χ(1)=n2-14π=Ed4πE0

25 χ3=Aχ14=A4π4n02-14=6.82×10-15EdE04esu

where A is a constant given by 1.7×10-10esu and n0 specify the static linear refractive index at the hυ→0. Figure 13 displays the obtained third-order NLO susceptibility χ(3) versus (hv) for all prepared NPs.Fig. 13 Variation of non-linear susceptibility χ(3) in terms of energy (eV) for all prepared NPs.

Refractive index n(λ) consists of two parts: (n0) static refractive index and (n2) non-linear optical refractive index as follows:26 nλ=n0λ+n2E2

Also, the relation between n2, representative non-linear optical refractive index, and χ(3) is expressed in the following form:27 n2=12πχ(3)n0

Refractive index factors and scattering energies are significant in the design of spectral scattering devices and electronic optical systems97,98. As a result, the scattering behavior of the refractive index could be explored utilizing the theory of effective single oscillator model using the below relation97:28 n2w=1+EdE0E02-ℏw2

Here, Ed specifies the scattering energy, which indicates the capability of the interbond optical transition. This energy is associated with changes in the structural order of the material. In particular, it is related to the onion valence and cation coordination number. Besides, E0 is the energy of the single oscillator, which quantifies the average energy gap. In summary, optical communications and applications of dispersion spectra in optical materials depend on the evaluation of E0 and Ed parameters98. E0 and Ed are expressed in the following form:29 E0=Eg+1.20.8

30 Ed=βNcZαNe

Here β is a constant, Nc is related to the coordination number of the cation, Zα is the chemical valance of the anion, and Ne indicates the number of valence electrons per anion. The computed maximum values of Ed and E0 can be seen in Table 6.

The amounts of n2 and χ(3) listed in Table 8 demonstrate the highest value for the MnS/Fe3O4 composite NPs compared to other samples.Table 8 The resultant maximum values of n0, n2, f, χ(3), and βc for Un-doped Fe3O4, M-doped Fe3O4, and MS/Fe3O4 composite NPs.

Samples	n0	ε	f (eV)2	n2esu×10-10	χ(3)esu×10-11	βc(m/w)×10-20	
Un-doped Fe3O4	2.96

(λ=687.8nm)

	8.761	76.13	3.17

(λ=687.8nm)

	2.49

(λ=687.8nm)

	6.62

(λ=624.4nm)

	
Mn-doped Fe3O4	2.94

(λ=687.8nm)

	8.643	73.92	3.06

(λ=687.8nm)

	2.39

(λ=687.8nm)

	6.53

(λ=624.4nm)

	
Zn-doped Fe3O4	2.84

(λ=686.0nm)

	8.065	73.66	2.28

(λ=686.0nm)

	1.72

(λ=686.0nm)

	5.73

(λ=623.5nm)

	
MnS/Fe3O4	3.04

(λ=671.6nm)

	9.241	73.44	3.90

(λ=671.6nm)

	3.15

(λ=671.6nm)

	7.25

(λ=603.4nm)

	
ZnS/Fe3O4	2.94

(λ=687.8nm)

	8.643	74.53	3.04

(λ=687.8nm)

	2.38

(λ=687.8nm)

	6.57

(λ=623.5nm)

	

Based on previously reported papers, nanoparticles with high χ(3) values can have potential applications in nonlinear optics, especially in information processing elements, optical power limiters, and photonic applications94,99.

Furthermore, the refractive index of zero-frequency (n0) along with the zero-frequency dielectric constant (ε) were investigated through the following formulas, respectively98.31 n0=1+EdE0

32 ε=(n0)2

The ability of electrons to absorb photons between the initial and final states is known as the optical oscillator strength (f), which can be computed from the following relation37:33 f=E0Ed

Along with the values of parameters ε, n0, n2, and χ(3) listed in Table 8, the nonlinear absorption coefficient (βc) can be evaluated with the bellow equation96:34 βc=48π3χ(3)n2cλ

According to the data in Table 8, we find that Zn-doped Fe3O4 NPs have the lowest values of non-linear parameters, while the highest values of n0, n2, χ(3) and βc parameters related to the MnS/Fe3O4 sample. Therefore, MnS/Fe3O4 composite nanoparticles can be considered in nonlinear optics and used in information processing elements or optical power limiters98,100. Besides, the maximum value of f and Ed is assigned to Un-doped Fe3O4 NPs. Also, localized defect states can impact the nonlinear optical properties of materials, including nonlinear absorption. Therefore, increasing βc (Fig. 12) could be linked to a decrement of the Urbach energy and the number of defect states94. In the present work, it is observed that larger particles have a high nonlinear refractive index, third-order susceptibility, and absorption, which illustrates a good consistency among XRD and FESEM results with NLO properties. The maximum value of the calculated non-linear parameters for all samples is given in Table 8.

With the help of available optical data, electrical parameters such as electrical susceptibility (χe) and relative permittivity (εr) can be evaluated. which are determined as follows96:35 χe=n2-k2-ε04π

36 εr=χ(e)+1

Figure 14 depicts the measured electrical susceptibility χe in terms of (hv) for the samples studied. As seen in Fig. 14, the electrical susceptibility behavior in terms of wavelength (λ) within the scope of 300–700 nm for all samples is an increasing trend, indicating an increase in the speed of electron mobility with increasing wavelength then a sharp decrease around 750 nm is experienced. Moreover, the maximum calculated values of χe and εr are given in Table 9. From the obtained data, it is evident that the highest value of χe and εr among the synthesized samples is related to MnS/Fe3O4 composite NPs, which means that this sample has the highest electron mobility.Fig. 14 Electrical susceptibility χe, as a function of energy (eV) for all prepared NPs.

Table 9 Calculated maximum values of χe and εr.

Samples	χe	εr	λ(nm)	
Un-doped Fe3O4	0.222249	1.222249	687.82	
Mn-doped Fe3O4	0.213835	1.213835	660.77	
Zn-doped Fe3O4	0.179228	1.179228	686.02	
Mn S/Fe3O4	0.262765	1.262765	671.61	
Zn S/Fe3O4	0.215338	1.215338	680.62	

According to the literature review, the lack of articles presented a comprehensive discussion on the optical properties of Fe3O4 related to their application in various fields. Any physical information about the optical properties of Fe3O4 at the nanoscale is very important. Therefore, further studies of optical constants are useful for their application in optical systems. So, the aim of this work is to provide a comprehensive discussion of optical constants. As an instance, for recently published studies, with reported data on optical properties, Table. 10 is presented to create an index to compare the results of the present work with previous research. Khalid et al.37 studied the structural, morphological, linear, and nonlinear optical properties of Fe3O4 and Fe3O4 @SiO2 core–shell nanoparticles. The comparison of the results of these two studies shows that the values ​​obtained for ​​the non-linear parameters of the present study are higher than those of the literature37 Table 10. This indicates that the nanoparticles synthesized in the present study can have more capabilities in nonlinear optics. Also, the Urbach and band gap energy values ​​obtained in our work for the iron oxide samples are comparable with the values ​​of literature102 and there is a good match between the results.Table 10 Structural and optical properties of Fe3O4 nanoparticles synthesized by co-precipitation method.

Material	Structural properties	Optical properties	Energies (Ev)	
D (nm)	δ (nm-2)	n	k	χ3(esu)	n2(esu)	Eg	Eu	Ed	
Fe3O4	7.79	0.0164	–	–	1.65E−14	4.14E−13	5.61	0.53	3.29	
Fe3O4 @SiO237	7.99	0.0157	–	–	3.29E−13	6.51E−12	5.97	0.72	8.01	
Fe3O4101	5.39	–	2.187	1.68E−05	–	–	–	1.02	–	
	15.96	–	2.642	4.38E−05	–	–	–	1.63	–	
Fe3O4102	10	–	–	–	–	–	2.87	0.7	–	
Pure Fe3O4	13.2943	–	–	–	–	–	2.25	–	–	
Zn-doped Fe3O432	9.5766	–	–	–	–	–	2.4	–	–	
Fe3O464	15.7	4.05E−03	–	–	–	–	3.43	0.22	–	

Conclusion

In summary, transition metals (M)—doped Fe3O4 of Fe2.85M0.15 O4 and (MS)0.05 (Fe3O4)0.95 ; (M: Mn, and Zn) with a cubic spinel-type structure were synthesized by co-precipitation technique. In the composite samples, the presence of MnS and ZnS phases led to changes in the structural parameters of the Fe3O4 phase of the samples. Besides, the doping of Mn and Zn ions in the Fe3O4 lattice did not alter the structure and phase of the produced NPs, but their crystal size and dislocation density changed. These measurements were made using the XRD technique and the software X'Pert HighScore Plus. The samples' crystallite size (D) were computed using the Debye–Scherrer and Williamson-Hall methods, and the Zn-doped Fe3O4 and MnS/e3O4 samples yielded the lowest and highest average values of (D), respectively. Also, the relation between dislocation density (δ) and stacking fault (SF) of the studied nanopowders, with their Urbach energy (Eu) and non-linear optical (NLO) parameters, was investigated. The results of FESEM morphological studies demonstrated that the particle diameter size is consistent with the XRD results, and the synthesized samples are spherical and agglomerated. The values of the optical energy gap for Un-doped, Mn-doped, Zn-doped, MnS/Fe3O4 composite, and ZnS/Fe3O4 composite NPs were found to be 2.98 eV, 2.93 eV, 3.01 eV, 2.85 eV, and 2.95 eV respectively. Furthermore, these values were inversely proportional to the nanoparticle size. Besides, the computation of the Urbach energy (Eu) of the NPs revealed that as the particle size enhances and the optical band gap of the nanoparticles decreases, the amount of Eu also reduces. The linear optical parameters obtained from the K–K method exhibited the highest values of (k), (n), (ε1, ε2), and (α) for MnS/Fe3O4 composite NPs. Also, among the synthesized samples, the highest amount of (NLO) parameters such as βc, n2, and χ3 calculated by utilizing the WDD model was related to the MnS/Fe3O4 sample. This indicates that the MnS/Fe3O4 sample has a great capacity to modify (NLO) characteristics. Furthermore, the high electron mobility in the MnS/Fe3O4 composite NPs leads to the highest values of χe and εr. These findings could apply to a variety of non-linear and optoelectronic applications.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-72026-6.

Author contributions

P.S.: Investigation, Formal analysis, Conceptualization, Writing original draft, Data curation. K.M.: Supervision, Conceptualization, Data curation, Software. R.N.: Supervision.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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