1 Introduction

Ferrites are a class of ceramic materials consisting of mixtures of various metal oxides. It finds many potential applications in the modern world [1,2,3,4]. Nowadays, a significant attention has been given to lanthanum ferrites (LaFeO3) due to its exchange bias, opto-magnetic and multiferroic properties. These ferrites are candidates for memory devices, low power-consuming spintronic devices, oxygen permeation membranes, opto-magnetic sensors and electrode material in solid oxide fuel cells (SOFCs) [5, 6]. Manikandan et al. [7,8,9,10] also reported pure and doped ferrite nanomaterials for different applications such as photocatalyst for the degradation of dyes, catalytic oxidation of alcohols, antibacterial activity and sensor materials.

The rare-earth-based orthoferrites, RFeO3 (R denotes rare-earth element), are orthorhombically distorted perovskites with four formula units per unit cell. In this structure, Fe3+ occupies the orthorhombic site and R3+ situates on the twofold axis [11,12,13, 13,14,15,16,17,18,19].

The orthorhombic structure of LaFeO3 belongs to Pbnm space group displaying p-type semiconductor. It is an attractive electroceramics due to mixed ionic/electronic conductivity and chemical stability at high temperature [20]. It exhibits antiferromagnetic phenomena with Neel temperature (TN) at 750 K [21]. Neutron diffraction studies on model LaFeO3 proved that each Fe3+ ion is confined to six(6) Fe3+ ions with spins pair antiparallel [22]. Recently, ferromagnetism has also been reported for LFO nanoparticles. The effects of length scale, shape and anisotropy prevailed at surface which shows the magnetization increased with decreasing particle size [23,24,25].

Significant research efforts are being made to search for new class of oxide materials with smaller band gaps to enhance visible light absorption. The doping at La and/or Fe site of LaFeO3 conducted by researchers is shown to display significant effects on many properties of LaFeO3. Some investigations have been reported for LFO bulk ceramics [26,27,28,29,30,31,32,33,34,35,36]. Improved dielectric and optical properties of doped LFO are important for its practical applications. In this context, for the first time we thoroughly investigated the effect of Ni doping on the structural, dielectric and optical properties of LaFeO3 nanoparticles. La1−xNixFeO3 (x: 0.0, 0.10 and 0.20) nanoparticles were synthesized with the variation in Ni doping level by solid-state reaction technique.

2 Experimental techniques

La1−xNixFeO3 (x = 0.0, 0.10 and 0.20) nanoparticles were synthesized by a solid-state reaction technique. The analytical-grade base materials, namely La2O3, NiO and γ-Fe2O3, were taken in stoichiometric proportion. Then, it was milled using in zirconia balls for 24 h to obtain homogeneous mixture. Next, calcination was carried out at 700 °C for 2 h followed by remilling in alcoholic media for 10 h. Next, the suspensions were dried at 120 °C. Then, obtained powders were pressed into disk-shaped samples of 15 mm in diameter under a compressive force of 40 kN. The pressed pellets were sintered at 750 °C for 2 h embedded in corresponding powders to avoid volatilization. The phase structure of the sintered powders was determined by X-ray diffractometry (XRD; PANalytical Empyrean). The microstructure of the polished samples was investigated by scanning electron microscopy (JSM-7600F, JEOL). For dielectric measurement, the sintered samples were properly flattened to obtain parallel and smooth surfaces. Then, a silver paste (SPI Flash-Dry Silver Paint) was applied on both polished surfaces and dried at 250 °C for 4 h to provide connection of electrodes. Dielectric property measurement was conducted by a precision impedance analyzer (6500B, Wayne Kerr Electronics, UK) at ambient condition at frequency ranging from 10 Hz to 100 MHz. Optical properties were measured by UV–VIS–NIR spectrometry (Lambda-1050, PerkinElmer, USA).

3 Results and discussion

3.1 X-ray diffraction

X-ray diffraction (XRD) patterns were captured at Bragg angle (2θ) ranging from 20° to 80°. Figure 1 shows room temperature XRD patterns of La1−xNixFeO3 (x = 0.0, 0.10 and 0.20) samples. The peak intensity was shown to modulate with Ni content compared to pure LaFeO3. However, all samples were shown to confirm single-phase orthorhombic crystal structure with Pbnm space group.

Fig. 1
figure 1

X-ray diffraction (XRD) patterns of La1−xNixFeO3 (x = 0, 0.1, 0.2) samples

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Evidently, a small trace of secondary phase γ-Fe2O3 was found to present in XRD patterns of both pure and Ni-doped samples. However, the apparently unavoidable formation of secondary phases during the synthesis of LaFeO3-based materials has been reported in several articles [37, 38].

Obtained patterns were also further analyzed by the Rietveld refinement using Xpert HighScore plus with ICDD database. The crystallite size and strain are presented in Table 1. Average crystallite size was found to vary from 19 to 21 nm with the variation in Ni dopant level.

Table 1 Crystal parameters, crystallite size and lattice strain of LFO and Ni-doped LFO
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The ionic radius (0.69 A) of Ni2+ is much less than the ionic radius (1.03 A) of La3+ [39]. Thus, a significant strain is generated in parent LFO, which is found to be increased with Ni2+ content concomitant with the Rietveld refinement strain data as shown in Table 1. Crystallite size was found to decrease with increasing Ni2+ doping concentration. Similar result was reported for Ni-doped BiFeO3 [40]. In contrast, with increasing Ni2+ doping concentration crystallite size was shown to increase in ZnFe2O4 [10, 41,42,43,44]. In this context, we postulate that the initial crystal structure of parent material might play an important role. However, it is established through density functional theory (DFT) calculations that Mn2+, Co2+, Ni2+ and Cu2+ are both the A- and B-site dopants [45]. Ca2+, Sr2+, Ba2+ and Fe2+ are found to be A-site and Mg2+ is considered to be B-site dopants. We doped Ni2+ to substitute A-site La3+ ion, but the increase in cell parameters and the volume of unit cell obtained from Rietveld analysis contradicts with our initial prediction. Thus, we postulate that that Ni2+ substitutes B-site Fe3+ ion of radius 0.55 A which demonstrates a good agreement with observed cell expansion and may rule out the possibility of the A-site substitution by Ni2+ dopant.

3.2 Scanning electron microscopy

Shown in Fig. 2 are the scanning electron micrographs of the polished samples of La1−xNixFeO3 (x = 0, 0.1, 0.2) nanoparticles which were calcined at 700 °C for 2 h. Evidently, all micrographs exhibit irregular particle shapes with a wide range of particle size distribution. The mean particle size of La1−xNixFeO3 (x = 0, 0.1, 0.2) ceramics decreases with increasing Ni content. That means Ni doping was found to suppress grain growth. Inhibition of grain growth was also reported for Ni-doped BiFeO3 [40]. The decreasing grain size of Ni-doped LFO can be resulted from the suppression of O2 vacancy concentration (the slower the O2 ion movement, the smaller the grain growth rate) and due to the difference in ionic radius of La3+ and Ni3+ [46,47,48]. In addition, oxygen vacancies are presumably generated due to Ni doping in LFO resulting structural distortion with concurrent reduction in crystallinity hence reducing the grain size.

However, during calcining the compositions at 700 °C high surface energy leads to neck formation by diffusion in solid state and nanoparticles agglomerate by the process of evaporation–condensation. In addition, both the particle size and crystal size of Ni-doped LFO nanoparticles reduce with increasing Ni content demonstrating the retardation of grain growth.

Fig. 2
figure 2

FESEM micrographs of La1−xNixFeO3: a x = 0.0, b x = 0.10 and c x = 0.20

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3.3 Dielectric properties

The room temperature measurement of dielectric behavior is presented in Fig. 3. Figure 3a shows how the dielectric constant varies with frequency (102–107 Hz). The increase in dielectric constant at low frequency is remarkable. The frequency regions may be subdivided into three regimes: (I) the first region (up to 103 Hz) in which the dielectric constant sharply decreases with frequency, (II) the region in which the dielectric constant decreases comparatively slowly with frequency and (III) the frequency region in which the dielectric constant remains almost constant.

Fig. 3
figure 3

Frequency dependency of La1−xNixFeO3 (x = 0.1, 0.2) recorded at RT in the wide frequency range from 100 Hz to 120 MHz: a real part of the dielectric constant (\(\epsilon ^{'}\)), b imaginary part of the dielectric constant (\(\epsilon ^{''}\)) and c tangent losses (tan δ)

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Similar type of dielectric behavior has also been observed in our investigated other dielectric materials [49, 50] and may be exemplified by polarization mechanism. At low frequencies, the dielectric constant is attributed to all types of polarization mechanisms and the contribution from various types of polarizations start to decrease with the increase in frequency. The dipolar including interfacial polarizations play role to dielectric constant at low frequencies. Basically, Fe3+/Fe2+ ions bring about dipolarity in ferrites. The electron exchange between these ions results the dipolar polarization, and the dipole alignment takes place by AC field. After a certain frequency of AC field, the dipolar polarization does not contribute to the dielectric constant. This is because the electron exchange between Fe2+ and Fe3+ cannot follow alternating field. The dielectric constant is attributed only to the electronic polarization at very high-frequency region [51]. The electronic polarization is independent on frequency, resulting in a constant value of dielectric constant at high frequency. The effect of trace secondary phase may also be noted. The dielectric dispersion of γ-Fe2O3 was absent after annealing above 550 °C [52]. Thus, the observed dielectric behavior of LFO was not expected to alter remarkably.

The lagging in the polarization with respect to the AC field can be represented by the dielectric loss (tanδ). Figure 3b shows the frequency dependence of tanδ for La1−xNixFeO3 system where no loss peak is observed. The nonexistence of any peak in tanδ defines the system as charge carrier-dominated system where the dominant contribution to polarization stems from electronic or ionic charges [53]. The similar type of behavior was also observed for EuFeO3 [51].

3.4 AC conductivity

With the purpose of further studying the transport mechanism, the AC conductivity at different Ni contents is investigated. Figure 4 presents the frequency-dependent conductivity for different doping concentrations at room temperature. A plateau regime was observed at lower frequency while a dispersion region was found at higher frequency.

Fig. 4
figure 4

a Frequency dependence of AC conductivity for La1−xNixFeO3 (x = 0, 0.1, 0.2) ceramic and b log\(\sigma _{{\rm ac}}\) vs log\(\omega\)

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The Maxwell–Wagner two layers formalism can be applied to the observed phenomenon [54]. The plateau region characterizes the dc conductivity. The frequency-independent conductivity may be attributed to the random diffusion by activated hopping of ionic charge carriers. Therefore, the conductivity can be described by Jonscher’s universal power law [55]

$$\sigma _{{\rm ac}} (\omega ) = \sigma _{{\rm dc}} + D\omega ^s$$
(1)

where the first part (\(\sigma _{{\rm dc}}\)) of right-hand side is defined as the dc conductivity and the left part of the above equation is the frequency-dependent conductivity [56]. The frequency exponent ’s’ has the value in the range of 0 < s < 1 while the of s is 1 suggesting an ideal Debye-type behavior. The value of s can be calculated from the log\(\sigma _{{\rm ac}}\) versus log\(\omega\), and the calculated values are 0.55, 0.71, 0.65 for x = 0.0, 0.10 and 0.20, respectively.

A hopping mechanism for the direct current electrical conductivity is associated with a small value of activation energy. The small polaron can migrate by thermal activation from Fe2+ to Fe3+ sites contributing to the change in mobility. This phenomenon requires the reduction in a small fraction of Fe3+ to Fe2+ with a simultaneous creation of coordinated oxygen vacancy to satisfy the neutrality of a γ-Fe2O3 crystallite [57]. Thus, the effect of trace secondary phase would not significantly deteriorate the dc conductivity (ac conductivity at low frequencies) of parent LFO.

3.5 Band gap tuning

With small band gap energy, LFO is a plausible attractive visible light irradiator. The photovoltaic (pv) absorption capacity of LFO is correlated with its electronic structure and thereby major contributor to their band gaps [58]. In this context, the diffused reflectance spectra captured by UV–Vis–NIR spectrophotometry (PE-1050) were used to obtain band gap energy, Eg of synthesized all nanomaterials. Eg was calculated by applying Kubelka/Munk function defined as: \({F}({R}) = (1-R)^{2}/2{R}\), where R is the diffused reflectance. Shown in Fig. 5 are \([{F}({R}){h}\nu ]^{2}\) versus \({h}\nu\) graphs.

Fig. 5
figure 5

\([{h}\nu {F}({R})]^{2}\) versus \({h}\nu\) (photon energy, eV) plots to calculate band gap energy for Ni-doped LFO

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Eg is obtained from the plots by drawing tangent lines at upper linear part of the curves. The point of intersection of a tangent at \([{F}({R}){h}\nu ]^{2}= 0\) is Eg [59]. Basically, Eg is the differentiate energy between (O:2p) valence band and (Fe:3d) conduction band of LFO. Table 2 summarizes obtained band gaps of pure LFO and Ni-doped LFO.

Table 2 Band gap, mean particle size and lattice strain of LFO and Ni-doped LFO
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The observed reduction in Eg may stem from many contributors. The Fe–O octahedral restructuring of molecular orbital can reduce Eg [60]. The length scale of nanoparticles also affects the value of Eg [61], i.e., Eg scales with the size of particles. Theoretical calculation claimed that generation of new energy level between Fe:3d and O:2p by doping can reduce the effective Eg of LFO [62]. In addition, the Ni content in LFO might change the Fe–O bond length and Fe–O–Fe bond angle resulting in impact on Eg by modulating one-electron band width (w) [63]. Ecb of Ni2+ is − 4.39 eV, and Ecb of Fe2+ is − 4.33 eV; thus, \({E}^{\mathrm{Ni}}_{{\rm cb}} < {E}^{\mathrm{Fe}}_{{\rm cb}}\) [64] that may also reduce Eg. The experimental formula correlating w with bond length and bond angle reads

$$w= \frac{cos\omega }{d^{3.5}_{Fe-O}}$$
(2)

where \({d}_{{\rm Fe-O}}\) is Fe–O bond length and

$$\omega = \frac{1}{2}(\pi -({{\rm Fe-O-Fe}}))$$
(3)

Eg is linked to w by \({E}_{{\rm g}}= \Pi \hbox {-w}\). Here, \(\Pi\) is the energy related to charge transfer [65]. Thus, the increase in bond angle, Fe–O–Fe, and the reduction in bond length, \({d}_{{\rm Fe-O}}\), by Ni doping resulted in the increase in the value of w and thus the reduction in Eg. However, the band gap of γ-Fe2O3 is reported to be 2.0–2.2 eV [66, 67]; thus, it would interfere negatively with the purpose of lowering the band gap of LFO by doping.

4 Conclusions

Pure LFO and La1−xNixFeO3 (Ni-doped LFO) nanoparticles were successfully synthesized by conventional solid-state method. The parent crystal structure of LFO was found to retain in doped LFO. The size of crystallite was shown to decrease with increasing Ni doping level. The concurrently induced lattice strain increased with the reduction in crystallite size. However, the presence of clusters cannot be ruled out within the scope of XRD and FESEM experimental techniques. A significant agglomeration effect was thus presumably present in all synthesized nanostructured samples as confirmed by the disagreement between the crystallite size estimated from XRD patterns and the particle size calculated from FESEM images. Ni doping in LFO enhances its optical properties. The optical band gap was shown to decrease to 1.70 eV with 20 (at.)% Ni doping. Higher values of dielectric constant were obtained at low frequencies due to the conduction mechanism of heterogeneous nature. The observed dispersion at low frequencies may resulted from electronic polarization by the underlying hopping mechanism of polaron. The AC conductivity (\(\sigma _{{\rm AC}}\)) was found to increase with increasing Ni concentration. When the frequency of the applied field increases, the conduction process might be affected by 3d hopping electrons between Fe2+/\({Fe}^{3+}\) ions and Ni2+/Ni3+ ions. The improved properties of synthesized Ni-doped LFO provide a scientific implication for its plausible applications in magnetically tunable filters and oscillators.