1 Introduction

The study of existing materials with varied physical properties enhances the possibilities for creating novel research materials [1,2,3,4,5]. To create new composite materials with highly noticeable electrical and magnetic properties, the research of ferroelectric materials serves as the foundation. Research reveals that adding diamagnetic elements to ferroelectric materials results in the creation of novel functional materials [6,7,8,9,10,11]. Multiferroics are the name given to such compounds because they have both electrical and magnetic properties. Multiferroics became extremely useful in contemporary sectors of electronics as a result of the development of the interaction of both magnetic and electrical characteristics. Compounds having diverse features, such as strong coercivity, high magneto-crystalline anisotropy, high resistivity, etc., are known as ferrites, a type of ferromagnetic metal oxide [12]. These ferrites are divided structurally into three categories such as hexagonal, spinel, and garnets. Hexagonal ferrites shortly called hexaferrites too have many types depending upon their compositions which include M-type hexaferrites, U-type hexaferrites, W-type hexaferrites, X-type hexaferrites, Y-type hexaferrites, and Z-type hexaferrites [13,14,15,16,17,18]. Most commonly used ferrites, M-type hexaferrites with the chemical formula MFe12 O19 (where M = Ba, Sr, Pb) have attracted the interest of many researchers because of their vast applications in electronics especially in ultra-high frequency ranges due to their high saturation magnetization, chemical stability perfection [2, 3, 19]. Due to their numerous uses and outstanding performance-price ratio, barium M-type hexaferrites (BaM) are significant since they account for half of the overall products of magnetic materials created worldwide. They have a wide range of applications as electromagnetic wave absorbers, magnetic storage media, magnetic filters, spintronics, and recording media [20,21,22,23,24]. In addition to their typical magnetic properties researchers are also interested in their utilization of the gigahertz and microwave frequency bands [14]. The magnetocrystalline anisotropy of hexagonal ferrites, which is a result of strong exchange coupling of Fe3+ spin at various areas, is tightly correlated with their high coercivity values [25,26,27,28].

Previous studies have shown that with partial substitutions of Sr2+ or Ba2+ and Fe3+ ions by several ions, such as La3+, Zn2+, Al3+, Cu2+, Ce2+, Co2+, Ti4+, Mn2+, Mo6+, etc. affect the basic properties of barium hexaferrite [5, 7,8,9,10, 29,30,31]. Atendra et al. prepared the nickel-doped M-type hexaferrites with a chemical reaction method. The magnetic hysteresis curve showed that the material’s ferromagnetic behavior was temperature dependent [32]. Makhdoom et al. reported that doping of Ce-Al ions in M-type hexaferrites showed shrinking of iron surroundings at different sites that enhanced the magneto crystalline anisotropy and an increase in coercive forces at different sintering temperatures [33,34,35,36]. Khalid et al. reported that the doping of yttrium and cobalt on M-type hexaferrites showed the enhancement of magnetic properties. They observed an increase in coercivity with an increase in the doping concentration of yttrium and decreasing the doping concentration of cobalt. Saturation magnetization first increased and gradually decreased after a sintering temperature of 1250 °C [37]. Furthermore, indium-doped barium hexaferrites were investigated to see the effect of In against Fe and it was observed that magnetic moments decreased as the substitution level rises because the superexchange connections between the magnetic positions both within and outside the sublattices are broken. Due to the weakening of the Fe–O-Fe exchange interaction, the Curie temperature appeared to fall as the concentration of diamagnetic cations increased, which destroyed magnetic order at lower temperatures [18, 38, 39].

In this work, we have reported the impact of ferromagnetic nickel substitution on structural and magnetic parameters of synthesized Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites. The base compound was prepared by considering charge compensation mechanism as it is a unique way to alter properties. Microstructural parameters were calculated using XRD refinement, W–H plot and magnetic properties including the different magnetic anisotropic parameters such as K, Ha, B, were estimated etc. The results showed an increase in the magnetic saturation with increasing doping of ferromagnetic nickel. The coercivity values were found in a specific range showing a small change for different values of concentration (x).

2 Experimental Work

2.1 Sample Preparation

All of the samples of M-type hexaferrite Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) used in this investigation were made using the conventional solid-state reaction method. The starting materials BaCO3, Al2O3, In2O3, and Fe2O3, purchased from Aladdin chemicals and contained a purity level of 99.9% were mixed according to the stoichiometric ratios by using a planetary ball mill, and the sample was ground for 10 h while the components were combined with zirconia balls and ethanol as a medium in nylon jars. To remove any remaining moisture before further processing, the material was removed from the ball mill, dried, and ground. To remove the carbonates, the material was calcined at 1100 °C. After that, it was exposed to a 6-h ball milling process before being dried and powdered once more. Using a vibration mill, the material was further broken down into particles smaller than 90 nm. The material was then sintered for 2 h at a temperature of 1250 °C. The resultant solid solution was pressed into pellets of 12 mm diameter and 1.2 mm thickness for scanning electron microscopy investigation. The pellets underwent another sintering procedure at 900 °C to remove any PVA binder leftover. The generalized chemical equation for the reaction can be as:

$${\text{BaCO}}_{{3}} + {\text{ In}}_{{2}} {\text{O}}_{{3}} + {\text{ Fe}}_{{2}} {\text{O}}_{{3}} + {\text{ NiO }} + {\text{ O}}_{{2}} \; \to \;{\text{Ba}}_{{0.{8}}} {\text{In}}_{{0.{2}}} {\text{Fe}}_{{{12} - {\text{x}}}} {\text{Ni}}_{{\text{x}}} {\text{O}}_{{{19}}}$$

where x is the amount of Nickel oxide added and can be varied depending on the requirement of the desired material.

2.2 Properties Measurements

An analytical X'Pert Pro X-Ray diffractometer was used to examine the sample's structural makeup. With the use of a HITACHI S-4800 scanning electron microscope, measurements of the structure of the samples were performed utilizing the sample pellets. The sample's magnetic characteristics were then assessed at room temperature using Chinese-made NIM-2000HF magnetic measuring equipment.

3 Results and Discussions

3.1 Structural Analysis

A crucial tool for examining the properties of the material is structural analysis [40, 41]. The X-ray diffraction analysis of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) was carried out in a range (20–80) degrees throughout the data gathering by using an x-ray diffractometer. The XRD pattern matched JCPDS card #43-0002 and indicated that the hard phase of barium ferrite had formed [42]. The formation of a magnetoplumbite structure with a space group of P63/MMC (No. 194) was confirmed by the observed diffraction pattern [43]. Every diffraction pattern exhibited an M-type or magnetoplumbite structure. No additional peaks related to other phases were found except Fe2O3. The high peak intensity indicated that the samples seemed to be of excellent quality and had a good crystalline phase. Figure 1(a-c) shows the XRD patterns of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites along with lattice parameters and expected crystal structure obtained through structural refinement.

Fig. 1
figure 1

a XRD patterns of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites. b Lattice parameters a and c vs doping level (x). c Expected crystal structure based on refinement results

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The lattice parameters were calculated by refinement of the XRD patterns of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) by using Celref software based on the five iron sites [41, 44,45,46]. The variation in intensity peaks could be well observed as a result of doping. Table 1 reveals the overall lattice parameters determined for the Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites. “Fe” generally possesses five uneven sites, including three octahedral sites (2a, 12 k, 4f2), one tetrahedral site (4f1), and a trigonal bipyramidal site (2b) [47, 48]. Figure 2a shows the volume of the samples along the c/a ratio for the synthesized samples. The c/a value ranging between (3.8781 to 3.9629) as indicated in Table 1 and less than 3.98 as reported earlier could also serve as confirmation of the formation of M-type hexaferrites [49].

Table 1 Refined Lattice parameters of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites
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Fig. 2
figure 2

a c/a ratio and volume (V) vs different doing levels of Ba0.8In0.2Fe12−xNixO19 hexaferrites. b–f W–H plots for the Ba0.8In0.2Fe12−xNixO19 hexaferrites

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It could be seen that ‘a’ initially increased with increasing doping levels but declined at the highest levels of doping. Additionally, for the maximal doping level, ‘c’ showed a drop earlier and then a rise. As a result, the parameter changes suggested that as the quantity of doping is increased, the lattice initially contracted before expanding towards the c-axis. These patterns could portend significant developments in the present magnetic material system [50]. Additionally, the difference in the ionic radii of the dopants (Indium and Nickel) in the synthesized samples was what caused the shift in lattice characteristics. The non-linear dependence in lattice parameters with increasing Ni2+ content in M-type Ba0.8In0.2Fe12−xNixO19 hexaferrites could be attributed to the competition between the substitution of Ni2+ for Fe3+ and the distortion of the crystal structure due to the size mismatch between the dopant and host ions. The ionic radii of the Fe3+ and Ni2+ ions vary depending on the coordination number and oxidation state of the ion. For the oxygen coordination number of 6, the ionic radii of Fe3+ and Ni2+ are approximately 0.645 Å and 0.690 Å, respectively. For the oxygen coordination number of 12, which is typical for M-type hexaferrite, the ionic radii of Fe3+ and Ni2+ are approximately 0.645 Å and 0.780 Å, respectively. When Ni2+ is substituted for Fe3+ in the lattice, the larger size of the Ni2+ ion could distort the crystal structure due to the size mismatch with the neighboring Fe3+ ions. This distortion can cause changes in the lattice parameters a and c, which describe the lengths of the crystallographic axes along the hexagonal plane and the c-axis perpendicular to the plane, respectively. Micro strains play a key role in the discussion of deformation in the crystal. Furthermore, Williamson Hall (W–H) method is employed to calculate strain among the crystallites. Figure 2b–f showed the W–H plots of the M-type Ba0.8In0.2Fe12−xNixO19 hexaferrites, along with the micro strain in Table 2. The micro strain showed an increase with increasing content of Ni, well-linked to the deformation due difference in the ionic sizes of the dopant and host cation in the synthesized sample [51,52,53]. Lattice is usually distorted to accommodate the dopant atom in the crystal lattice.

Table 2 Microstructural parameters average crystallite size D, Micro strain (ε), bulk density db, X-ray density dx, dislocation density (δ), and porosity P of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites
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Additional microstructural variables of the synthesized samples, including average crystallite size D, micro strain, bulk density db, X-ray density dx, and porosity P, were also investigated [54]. The average crystallite size was calculated using the well-known Scherrer formula and the following formulas were used to determine the other parameters, db, dx, and P [33, 55, 56].

$$D=\frac{K\lambda }{\beta Cos\theta }$$
(1)
$${d}_{x}=\frac{Z{M}_{w}}{{N}_{A}V}$$
(2)
$${d}_{b}=\frac{m}{\pi {r}^{2}h}$$
(3)
$$P=\left(1-\frac{{d}_{b}}{{d}_{x}}\right)\times 100$$
(4)

where k = 0.9, λ = 1.5409 Å, β refers to full-width half maximum (FWHM), the diffraction angle is referred to as θ, Mwt represents the molar weight and ‘r’ represents the radius, and ‘h’ represents the thickness of the pellet. The calculated parameters are shown in Table 2.

To determine the vacant spaces, present in the material, dislocation density (δ) was calculated from crystallite size by the equation given below [57].

$$\delta \; = \;1/D^{2}$$
(5)

Most often, smaller crystallites merging into larger ones and clusters creating new grain boundaries were the principal causes of dislocation. The plot of estimated microstructural parameters against different doping levels (x) was shown in Fig. 3(a-b). Both densities showed a decrease for the starting values, but when the concentration of the dopants was increased, both started increasing.

Fig. 3
figure 3

a X-ray density, and Bulk density variation with doping level (x). b Porosity and dislocation density for different doping concentrations of Ba0.8In0.2Fe12−xNixO19

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The trends could be further explained based on the Mwt of the samples. The higher X-ray density results implied that the materials contain pores. While variations in dislocation density (δ) and porosity ‘P’ may also be closely related to variations in oxide vacancies [40, 58]. In general, these variations in micro parameters may lead to a change in the material's magnetic properties.

3.2 Morphological Analysis

Samples of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) were subjected to scanning electron microscopy to ascertain the creation of shape and the existence of secondary phases. The findings demonstrated that the material lacked any secondary phases and that the particles' hexagonal shape could be seen in the micrographs. The sample’s uniform and homogeneous distribution was further confirmed by the SEM images in Fig. 4. The loss of the PVA binder was seen in the photographs as pores. Doping may impact the form of the hexaferrites instead of their size because the addition of dopants did not cause appreciable changes in grain size. The shape of the particles was observed to be spherical. However, some agglomeration could be well observed with increasing doping levels as well. Furthermore, the morphological images demonstrated that pure hexaferrites were successfully formed. The range of the grain size was between 500 to 2000 nm.

Fig. 4
figure 4

SEM images of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) hexaferrites

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4 Magnetic properties

Magnetic characteristics of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) were investigated using applied magnetic fields of about 30 kOe. The combined M-H loops of all samples are also displayed in Fig. 5 showing that Ms increased for the doping concentration till x = 1.5 but then decreased for the dopants at x = 2.0. The magnetic parameters including magnetic saturation (Ms), coercivity (Hc), remanence (Mr), crystalline anisotropic constant (K) in terms of magnetic susceptibility, the magnetic moment per formula unit (mB), and anisotropy field (Ha), are presented in Table 3. Parent compound Ba0.8In0.2Fe12−xNixO19 (x = 0.00) was found to have a coercivity value of Hc of 5.129 kOe and a magnetic saturation Ms value of 48.01 emu/g. The results could be fairly comparable to those for M-type hexaferrites that have already been published [5, 28, 59,60,61,62]. Moreover, a little variance in the parent composition findings may be directly related to the diversity in material synthesis techniques.

Fig. 5
figure 5

Combined magnetic loops of Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00)

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Table 3 Magnetic parameters saturation magnetization (Ms), Remanence magnetization (Mr), Coercivity (Hc), Mr/Ms. Ratio, Magnetic anisotropy constant (K) and magnetic moment per formula unit (mB), and Anisotropy Field (Ha) obtained by analysis of M-H loops
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Ms and Hc values for the synthesized samples Ba0.8In0.2Fe12−xNixO19 (x = 0.00, 0.50, 1.00, 1.50, 2.00) increased as the doping level increased. From 0.0 to 1.5, a maximum value of 58.32 emu/g was observed for Ms, while the Hc displayed a minor change and its highest value of 5.512 kOe was observed at concentration x = 1.5 and subsequently started to decline at x = 2.0.

The changing trend in the values of Ms and Hc after the introduction of dopants could be well linked to the weakening of octahedral and tetrahedral superexchange mechanisms [63]. Furthermore, the incorporation of diamagnetic In2+ against Ba2+ and ferromagnetic Ni against Fe3+ may lead to an increase in saturation magnetization Ms by making iron ions unbalanced at 2a sites, producing a nonlinear ferromagnetic arrangement.

Furthermore, the difference between the ionic radii of the dopants and the host atoms creates spaces between magnetic ions and affects the superexchange interaction [3]. The basic building block of the M-type hexaferrite crystal is a cation–anion cluster in which Fe3+ ions occupy the interstitial sites between the octahedrons. Figure 6(a,b) showed the variation of different magnetic parameters against different doping levels of Ba0.8In0.2Fe12−xNixO19 hexaferrites.

Fig. 6
figure 6

a Variance in Ms, Mr, Mr/Ms vs doping level (x). b Variation in H, mB, and K for different doping levels in Ba0.8In0.2Fe12−xNixO19 hexaferrites

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Normally hexaferrites have five nonequivalent sites, 2a,2b, and 12 k spin up while 4f1 and 4f2 spin down. Introducing the Ni in the iron sublattice increased the superexchange interaction causing an increase in magnetization. Usually, Ni prefers to occupy 2a and 12 k sites by disturbing the upward spins of Fe ions, causing a large increase in magnetization and a smaller change in coercivity as well. Another confirmation for the single domain structure of the synthesized material was the Mr/Ms ratio observed to be greater than 0.5 [64]. These results could make the material more useful in magnetic applications such as magnetic filters, recording media, spintronics, etc. The magnetic moment per formula unit in terms of Bohr magneton was also calculated as [65]:

$${m}_{B}=\frac{Mw\times Ms}{5585}$$
(5)

Furthermore, magnetocrystalline anisotropy constant K was also determined and shown in Table 3. The charge compensation mechanism that results from the difference of ionic radii, caused the trends of K to match with the Ms and Hc values, which is another important component that influences the characteristics. The anisotropy field (Ha) and anisotropy parameter (B) were also calculated from magnetic parameters as [59]:

$${H}_{a}=\frac{2K}{{\mu }_{^\circ }{M}_{s}}$$
(6)
$$B=\frac{4{K}^{2}}{15{{\mu }_{^\circ }}^{2}{{M}_{s}}^{2}}$$
(7)
$$K=\frac{{M}_{s}Hc}{5096}$$
(8)

where µo is the permeability of the vacuum, K is the magneto-crystalline anisotropic constant. Anisotropy parameter B instigates from the resistance of magnetocrystalline anisotropy on domain wall rotation. Figure 7 showed the variation in Ha and B for different doping levels of Ba0.8In0.2Fe12−xNixO19 hexaferrites.

Fig. 7
figure 7

Variance in anisotropy parameter B, crystallite size D and magnetic anisotropic field vs doping level (x) in Ba0.8In0.2Fe12−xNixO19 hexaferrites

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The results show that K and Ha both increase for an increase in doping concentrations and then dropped for x = 2.0. Overall Magnetic saturation showed a significant increase with no significant change in coercivity values. Crystallite size also showed a minor change along with other parameters. Furthermore, results suggest that the material has a significant competitor for use in magnetic applications.

5 Conclusions

In this work, M-type hexaferrites Ba0.8In0.2Fe12−xNixO19 (x = 0.00–2.00) were synthesized and microstructure was analyzed from the X-ray diffraction data. Lattice constant ‘a’ was increased from 5.8958 to 5.9535 nm then decreased to 5.8495 but ‘c’ decreased from 23.0907 to 22.9950 nm, then increased to 23.1812. Morphology showed a uniform and homogenous distribution of particles, with grain sizes ranging from 500 to 2000 nm. W–H plots showed that micro strains were increased upon the introduction of dopants in the crystal lattice. VSM results showed that Magnetic saturation increased from 48.01 to 58.32 emug−1, and the coercivity values remained relatively confined in a range. The highest value observed for different magnetic parameters, such as magnetocrystalline anisotropy constant was 0.06308 emug−1kOe, anisotropy field was 1.722 kOe, and magnetic moment per formula unit was observed 11.603µB. Overall, this study provides valuable insights for future research and development for magnetic applications.