The cubic spinel structure of prepared samples was estimated from the X-ray diffraction (XRD) details presented in Fig. 1. Sharp peaks were seen in XRD data. The XRD peaks for samples having composition x = 0.1 are wider with smaller intensity values. The diffraction planes (111), (220), (222), (311), (400), (422), (333), and (440) showed the cubic spinel structure of prepared samples. All these peaks were well-matched with standard JCPDS card (88-1942). All the samples possessed a simple cubic structure and were categorized in the Fd-3m space group. No secondary phases were seen in the XRD pattern. The formula for the measurements of lattice constant is given as [18];
(1)
In Eq. (1), the h k l are miller indices and d is inner planer spacing. Various numerical values for lattice constant, ionic radii, jump lengths as well as bond lengths of tetrahedral and octahedral sites were displayed in Table 1. The greater value of lattice constant for x = 0.1 sample is due to bigger size of Ho3+ as compared to Fe3+. These results are well matched with previous presented paper results [19, 20].
Table 1
Different structural parameters of spinel ferrites.
Concentration
|
a
[Å]
|
rA
[Å]
|
rB
[Å]
|
A-O
[Å]
|
B-O
[Å]
|
LA
[Å]
|
LB
[Å]
|
Room Temperature Resistivity [Ω-cm]
|
x = 0.00
|
8.310
|
0.449
|
0.727
|
1.799
|
2.077
|
3.598
|
2.938
|
7.07 × 107
|
x = 0.1
|
8.334
|
0.453
|
0.732
|
1.803
|
2.082
|
3.607
|
2.945
|
2.63 ×108
|
The inner atomic vibrations were estimated from Fourier-transform infrared spectroscopy (FTIR) spectra. The structural behavior of samples is dependent upon the lattice vibrations. These vibrations vary with bonding force and mass of cations. The IR spectrum for both samples was shown in the Fig. 2. The absorption peaks of manufactured system under room temperature were positioned at 435 and 581. The existence of basic two absorption bands confirmed the successful formation of ferrites [21]. Two major bands parallel to stretching vibrations of A and B sites positioned between 600cm− 1 and 400cm− 1[22]. The specific band at 581 cm− 1 and 582cm− 1 allotted to tetrahedral category complexes whereas the absorption bands at 435 accredited to tetrahedral category complexes [23].
The scanning electron microscopy (SEM) images for two samples were given in the Fig. 3. The nanoparticles are agglomerated and have spherical shape as seem in SEM micrographs. The inhomogeneous mixture can be seemed clearly from images. Similar facts were also reported in previous researches by some other authors [24, 25]. Two samples are selected for transmission electron microscopy (TEM) analysis. The TEM images were presented in the Fig. 4. TEM images showed that the particles have spherical shape and they formed clumps. The TEM data have good accordance with XRD data.
Table 1 shows the DC electrical resistivity at room temperature of Co0.6Zn0.4HoxFe2−xO4 (x = 0.0 and x = 0.1) spinel ferrites. Co-Zn ferrite is extremely resistant in spinel ferrites and has high activation energy. The methods for synthesizing doped cations at sites A and B, particulate size or morphology, as well as sintering conditions affect all of spinel ferrite's electro-power properties [26]. The DC electro-resistivity, as shown in Table 1, increases with the Ho3+ concentration. When Ho3+ (x = 0.1) is replaced, the electrical DC resistivity increases considerably. Due to electron hopping between Fe2+ and Fe3+, the Verwey mechanism could easily explain the electrical conduction of spinel ferrites. The replacement of Ho3+ with octahedral ions (B location) decreases the number of Fe3+ ions on B sites, along with the Fe3+↔Fe2+ trend, reduces the conductivity and increases the resistivity.
The graph of DC resistivity for temperature was given in Fig. 5. From this figure, it is cleared that the resistivity was reduced with the surge of temperature. The reason for the high resistivity value is the presence of Ho3+ion in the Co-Zn system. The quantity of Fe-ions reduced at the octahedral site due to Ho3+ substitution, which plays a central role in the conduction mechanism [26]. The DC resistivity value of pure Co-Zn-ferrites declined with the increase of temperature, obeying the eminent Arrhenius equation [27]. Thus, the Co-Zn system has semiconducting nature. More conduction electrons were originated with the upsurge of temperature, which in turn reduced the resistivity. The reduction in the resistivity with the activation of drift electrons followed the hopping conduction mechanism. The decrease of resistivity with the increase of temperature does not link the charge carrier's production. The conduction mechanism is mainly completed by the electrons hopping between ferric and ferrous ions, i.e., Fe2+ ↔ Fe3+ + e− 1.
The slope of the graph presented in Fig. 6 gives the value of activation energy. Usually, the activation energy of nano-ferrites depends upon the charge carrier's mobility. It is independent of the concentration of charge carriers. Charge carriers merely stay at vacant positions. The hopping process completes the conduction procedure. The hopping procedure is determined by activation energy associated with the electrical barrier experienced by the electrons during the procedure [24]. Figure 7 contains different dielectric constant values for frequency ranges from 0.1MHz to 20MHz under fixed temperatures. Up to 1MHz frequency, the dielectric constant value slowly decreases and then becomes constant at 6MHz. Beyond this limit, its value increases. The reduction of dielectric constant below a particular frequency can be demonstrated on dipole relaxation occurrence [25, 26]. The increase of dielectric constant beyond the specific limit can be explained on behalf of the resonance phenomenon at high frequency. The resonance happened when the applied field frequency matched with the charge exchanging frequency Fe3+↔ Fe2+. Wagner polarization model as well Maxwell theory, was used to clarify such type variations [27, 28].
The variation of dielectric constant for different temperature values under fixed frequency range was given in Fig. 8. For each value of frequency, the rise of temperature leads to an increase in the dielectric constant. The declined in dielectric constant was observed by substitution of the Holmium concentration. In decrease was observed through the ions substituted of the Holmium content also be clarified by the similar trend by the conduction technique of the electronic conduction. Here, the inter-conversion of electrons among Fe3+ and Fe2+ ions developed the displacement among charges increases, which supports finding out polarization of the charges through such ferrites. Therefore, the plenty of these Fe2+ ions at the octahedral site shows a competent role in the polarization of dielectric. Because of the greater ionic radius, the ions of Ho3+ take an octahedral site. Substitution of the Holmium ions for the ions of iron (site-B) blocks the mechanism of conduction because of its valence stability. It’s purposed that the transfer of electrons could not take between the Ho3+ and Fe2+ ions. Thus, a decrease in dielectric polarization is observed. However, the increase in temperature is faster in lesser frequency areas and slowed down in higher frequency areas. Usually, the dielectric constant is related directly to dielectric polarization. There are four main kinds of polarizations: electronic polarization, ionic polarization, dipolar polarization, and space charge polarization. The dipolar and space charge polarization plays a central role in the lower frequency section, and they are temperature-dependent [29].
The dielectric loss versus temperature values under the specified range of frequency was displayed in Fig. 9. The dielectric loss reduced with the rise of frequency. This variation trend is due to resonance and follows Koop's Model [30, 31]. The phenomenon of resonance occurred when the hopping frequency matched with the applied field frequency. The data relating to the conduction process presented by Hudson explains the dielectric losses in ferrites. The substances with more excellent conductivity would have high loss values. The dielectric losses versus several frequency values under specified temperature were shown in Fig. 10. The trend of variation of dielectric loss is similar to the trend of dielectric constant and explained similarly. The results showed that the involvement of Ho3+ ions in Co-Zn -ferrites increased DC resistivity and decreased dielectric constant and dielectric loss. These changes are demonstrated by using the concept of the hopping mechanism (Fe2+ ↔ Fe3+ + e− 1). The substituted ion (Ho3+) does not take part in the conduction mechanism. These ions only bound the hopping by stopping the Fe2+ ↔ Fe3+ + e− 1 exchange on the octahedral site [32]. The quantity of Fe-ion lessened with the substitution of Ho3+ion [33].
The measurements of magnetic factors were completed under the applied field of 2 kOe. Fundamentally that was ferromagnetic phenomenal. In the given magnetic field, we observed the explicit behavior of hysterics. Narrow loops indicate the soft type of such spinel ferrites. Moreover, we used the hysteresis loop to count the various magnetic parameters such as remanence (Mr), magnetization (Ms), and coercivity (Hc). The calculation of saturation magnetization is done with magnetization curve on the Hmax also observes a falling trend by raising the Holmium contents. We observed the behavior of soft magnetic through thin M-H loop because of their fewer coercivity values. The ferromagnetic nature was confirmed from the characterization results as given in Fig. 11. The coercivity value enlarged while the saturation magnetization dropped. The replacement of Ho3+ ions with Fe3+ ions reduced the quantity of Fe3+ ions at the octahedral site. The magnetic moment value of RE ion is significantly less than Fe-ion [32, 33]. Consequently, the magnetization values dropped.
The loss in flagging off the AB-exchange interfaces was the only cause of the loss in saturation magnetization and the remanence. The three types of negative exchange interactions occurred among both ions of those electrons that were unpaired on sites B and A. Among these three interactions, the interaction A-B predominates upon the remaining two, for example, interaction B-B and A-A. For the spinel ferrites given, we considered Ho3+ ions such as minimum magnetic substance value on the room temperature also attain to the sites-B(an octahedral site). In contrast, the ions of Fe3+ are occupied with both sites B as well as A. Like in the spinel ferrite, the total magnetic moments relay at the no. of the magnetic ions attaining to the octahedral (B) and tetrahedral (A) sites; create the saturation magnetization decreasing value. The Ho ions substitution (1.00 Å ionic radius) on the ions of Fe3+ (0.64 Å ionic radius) occurred on the octahedral sites also its existence on the sites of tetrahedral is founded very rare. Hence, the reduction of the octahedral site in the number of magnetic moments is expected. Thus we observed a reduction in the magnetic moment on lattice-B that consequently causes to decreases the magnetization, and eventually, in net magnetization, we observed a decrease. In the current study, by substituting Holmium, the reduction in magnetization is the best deal by the previously described work of many more researchers.