**1. Introduction**

Nano-ferrites, which are currently being studied, have piqued curiosity on account of their remarkable electrical properties. Due to their extraordinary physical and chemical properties, spinel ferrites nanoparticles have become a significant field of research in nanotechnology, nanoscience, and nanoelectronics [1–6]. A kind of high resistance spinel ferrite with a conventional AFe2O4 formula, where A alludes to divalent (+2) metal ions. In deciding their significant applications, dielectric and

electrical examinations of spinel ferrites assume a vital role. Doping has a considerable impact on the semiconductive property of spinel ferrites. The high electrical resistance of soft ferrites, which prevents undesirable eddy current losses in AC fields, is the most important asset they create for being qualified for high-frequency applications. Spinel ferrites might be utilized in a MCS (microwave communication system) [7], magnetic transmitter feeder [8], pulsed current monitor [9] and gas sensor [10]. Spinel ferrites, on the other hand, have excellent chemical stability and biocompatibility under physiological conditions [11]. Impedance spectroscopy was used to explore the electrical characteristics of spinel ferries. Electrical similar circuits with inductors, capacitors and resistors are commonly utilized models for complex impedance. A comprehensive impedance examination can provide the necessary information of a material's dielectric characteristics. This research enables for the separation of distinct total impedance contributions arising from bulk conductivity and interfacial phenomena, such as grain boundary, grain, and other electrode interface results.

Mn-Zn ferrites are relied upon to be mixed ferrites with Fe2+/Fe3+ ions affecting dielectric characteristics at both A-site and B-site. As a result, Mn-Zn ferrites offer a wide range of electrical properties that can be applied to a wide range of technological applications, including telecommunications [12]. Few researchers are researching the effect of rare earth such as Sm, Gd, Eu, and Ce among others, on the varied properties of Mn-Zn ferrite, according to a thorough literature assessment [13, 14]. The dielectric properties of Zn0.2Ni0.8-xCuxFe2O4 (x = 0 to 0.6) can be enhanced by replacing Ni2+ with Cu2+, according to Houshair et al. Rao et al. [15] examined on the cation distribution of Ni-Zn-Mn ferrite NPs. Bharamagoudar et al. [16] reported that the Mn1 xZnxFe2O4 (where, x = 0, 0.25, 0.5, 0.75, 1) were prepared by solution combustion method and the dielectric constant decrements with enhancing of Zn content. In addition, Qian et al. [17] found that introducing Nd into Ni-Zn ferrite increased the dielectric properties. Impedance spectroscopy, in particular, has been carried out in various research. Rare earth (RE) metal ions (Dy&Ho) with larger ionic radii can cause crystal structure distortions [18]. As a result, replacing trivalent iron with RE metal ions at the Fe site improves dielectric and structural properties in Mn-Zn ferrites. There have been several studies on the integration of RE ions into Mn-Zn ferrites.

The main goal of this work is therefore to understand the dielectric constant, dielectric loss tangent, ac conductivity, cole-cole plot and impedance spectroscopy of Dy-Ho doped Mn–Zn ferrite. As indicated by the investigation accomplished, replacing of Fe3+ ions with a larger Dy3+-Ho3+ ions results in a significant rise in dielectric and ac conductivity. In our current paper, we investigated the structure, dielectric properties of the current systems.

### **2. Synthesis method and characterizations**

Stoichiometric quantity of metal nitrates such as manganese nitrate, zinc nitrate, ferrous nitrate, dysprosium nitrate, holmium nitrate and reducing agents as stoichiometry quantities of fuels glucose and urea were mixed in 30 ml distilled water, and the combined solution was taken in a borosil glass beaker. Then combined solution was continuously stirred for 60 min to achieve a homogeneous solution. At 450°C, this homogeneous solution was kept in a box style muffle furnace that had been preheated. The solution boils, froths, and then burns with a smoldering flame at first. The combustion process will be completed within 20 minutes. The flow chart of solution combustion method as shown in **Figure 1**.

The XRD was characterized by utilizing CuK<sup>α</sup> radiation (λ = 1.5406 Å) and the 2θ diffractogram was run from 20° to 80° with a stage size of 0.02 We can deduce crystalline phase and structure from XRD patterns. The surface morphology of the all *Synthesis and Study of Structural and Dielectric Properties of Dy-Ho Doped Mn-Zn Ferrite… DOI: http://dx.doi.org/10.5772/intechopen.99264*

#### **Figure 1.**

*Flow chart of solution combustion method for Dy-Ho doped M-Zn Ferrite NPs.*

samples were analyzed by SEM images and the images were carried out by using JEOL (model JSM-840). For dielectric studies, the pellet of the sample was prepared using hydraulic press. The silver was pasted on it to get the electrical contact and heated in an oven for 2 hours at 55°C. The impedance spectroscopy measurement was performed in the frequency range up to 10 MHz using an Novocontrol Alfa A impedance analyzer.

## **3. Results**

#### **3.1 Structural analysis**

The **Figure 2** depicts the XRD pattern of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs. The single-phase cubic structure was verified for all samples, and the pattern matched data card ICDD#10– 0319 perfectly. The miller indices (hkl) suggested a spinel cubic structure without appearance of secondary phases. The lattice constant (a) values of were estimated by using the following relation [19].

$$\mathbf{a} = \frac{\lambda\sqrt{\mathbf{h}^2 + \mathbf{k}^2 + \mathbf{l}^2}}{2\sin\theta} \tag{1}$$

For x = y = 0.005 to 0.03 concentration, the values of 'a' were found 8.3964 to 8.4245 Å, respectively. Eq. (1) was utilized to estimate the crystallite size of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs using the Debye Scherrer Equation [20, 21];

$$D = \frac{k \,\lambda}{\beta \cos \theta} \tag{2}$$

The "λ" denotes the X-ray wavelength, the "β" denotes the FWHM value, k is the Scherrer constant and θ denotes the diffraction angle. The crystallite sizes measured were 11.88 to 6.44 nm for x = 0.005 to 0.03, respectively. Large ionic radius of rare-

**Figure 2.** *The XRD patterns of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

earth ions increases the lattice parameter value while decreasing the average crystallite size, which is a popular trend [22]. However, in some cases, such as in our investigation, the researcher found different actions. The introduction of the Dy3+-Ho3+ ions cause increases in the lattice parameter in our analysis. As the large ionic radius of Dy3+ (0.912 Å) and Ho3+ (0.901 Å) ions replaces the small ionic radius of Fe3+ (0.645 Å) ion at the B-site position, the lattice structure becomes asymmetric [23]. The hopping length at tetrahedral and octahedral sites was estimated by using following equations

$$\mathbf{L}\_{\mathbf{A}} = \frac{\sqrt{3}\mathbf{a}}{4} \text{ and } \mathbf{L}\_{\mathbf{B}} == \frac{\sqrt{2}\mathbf{a}}{4} \tag{3}$$

and observed the increase of hopping lengths with the increase of Ho3+ content as the lattice parameter increased gradually [24].

#### **3.2 SEM analysis**

SEM micrographs of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) nanoparticles are shown in **Figure 3**. The existence of surface morphology with pores, holes, and on their surfaces can be seen in the figures. The development of the fuels during the combustion process resulted in the formation of the dry frothy powder. We are unable to measure grain size due to the porous nature of the samples. The micrographs show that the particles are agglomerated, showing that the magnetic nanoparticles in powder form have a strong connection [25].

#### **3.3 Dielectric studies**

#### *3.3.1 Real part of dielectric constant*

The variation of real part of dielectric constant (ε00) with applied frequency as shown in **Figure 4.** The ε' reduces as the frequency increases, stays constant at higher frequencies, and declines as the Dy3+ and Ho3+ content increases. This

*Synthesis and Study of Structural and Dielectric Properties of Dy-Ho Doped Mn-Zn Ferrite… DOI: http://dx.doi.org/10.5772/intechopen.99264*

behavior could be explained by using Koop's theory. In the lower frequency zone, the electrons exchange between ions follows the applied electric field and is responsible for high value of ε' [26]. Due of high conducting grains, the ε' is

**Figure 3.** *SEM micrographs of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) nanoparticles.*

#### **Figure 4.**

*The variation of real part of dielectric constant (*ε<sup>0</sup> *)with applied frequency of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

frequency independent at higher frequency region. The ionic and orientation polarizations weaken and eventually disappear as frequency rises, resulting in a drop in dielectric constant at higher frequency region [27]. Polarization is caused by electron exchange between Fe3+ and Fe2+ ions on the octahedral site in the ferrite lattice at lower frequencies.

#### *3.3.2 Imaginary part of dielectric constant*

The variation of real part of dielectric constant (ε00) with applied frequency as shown in **Figure 5**.

The concept of polarization and the hopping process can be used to understand the dielectric behavior of ferrite materials [28]. The following is the explanation for the observed dielectric loss in the ferrite samples: at lower frequency region the electron exchange between Fe2+ and Fe3+ is predominant and it follows the applied electric field. As the increase of frequency, the electron exchange between Fe2+ and Fe3+ ions does not follow the applied electric field.

#### *3.3.3 Dielectric loss tangent*

The variation of dielectric loss tangent (tan δ) with applied frequency as shown in **Figure 6**. Dielectric loss tangent in the ferrites is due to the lag of polarization with respect to the applied field [29, 30]. Ferrites with high tanδ are suitable candidates for the manufacturing of high frequency heating systems. Tanδ decreases with the applied frequency for each sample. This can be ascribed based on Koop's phenomenological model [31, 32]. At low frequencies region non conducting grain boundary gives maximum contribution for polarization. At lower frequency grain boundary contribution dominates results high resistivity and high value of dielectric loss tangent. Large quantity of energy is required for electron exchange

*Synthesis and Study of Structural and Dielectric Properties of Dy-Ho Doped Mn-Zn Ferrite… DOI: http://dx.doi.org/10.5772/intechopen.99264*

#### **Figure 5.**

*The variation of imaginary part of dielectric constant with applied frequency of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

#### **Figure 6.**

*The variation of dielectric loss tangent with applied frequency of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

between Fe3+ ions and Fe2+ ions at low frequency ensuing high value of loss tangent. At higher frequencies, small quantity of energy is enough for exchange of electron between Fe2+ and Fe3+ gives low resistivity and low value of loss tangent [33, 34]. At x = y = 0.005 concentration sample shows hump at mid of the frequencies, which

was happened due to exchange of electron between ions frequency is matched with the applied frequency [35].

## *3.3.4 AC conductivity*

The variation of AC conductivity (*σac*Þ with applied frequency as shown in **Figure 7**. The frequency enhances with diminishing in *σac* which can be explained due to hopping model. At lower frequency side independent of conductivity, so the *σac* is small at lower frequency side. The Ho3+-Dy3+ ions substitution on Fe3+ ions of B- site, here the electron exchange between ions and there is no electrons exchange between A site-B site. The electron exchange between A site-B site is most significant contrast with A site- A site and B site-B Site of spinel ferrite sample. The conduction mechanism enhances with enhancing the polarization there by enhancing the *σac* [36].

#### *3.3.5 Real part of impedance (Z*0 *) and imaginary part of impedance (Z )*

The variation of real part of impedance (Z<sup>0</sup> ) with applied frequency as shown in **Figure 8**. The spectra unmistakably shows that the Z<sup>0</sup> is diminishes with enhancing the frequency. Furthermore, because to the charge space polarization of the spinel ferrite sample [37], it remains constant at high frequency region. The imaginary part of impedance (Z″) varies with applied frequency, as shown in **Figure 9**. This spectrum (Z″ V/s log f) also named as loss spectrum. The frequency grows as Z″ decreases, and it reaches its maximum value at a certain frequency. The frequency then increases as Z″ decreases. Furthermore, the highest peak value rises as the concentrations of dysprosium and holmium rise. It results in the presence of relaxation time in the samples, which occurs as a result of space charge relaxation, which occurs when the sample is made up of grain borders and grain [38]. Furthermore, as the frequency shifts from low to high, the conduction mechanism shifts as well.

#### **Figure 7.**

*The variation of AC conductivity with applied frequency of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

*Synthesis and Study of Structural and Dielectric Properties of Dy-Ho Doped Mn-Zn Ferrite… DOI: http://dx.doi.org/10.5772/intechopen.99264*

#### **Figure 8.**

*The variation of real part of impedance (Z*<sup>0</sup> *) with applied frequency ofMn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

#### **Figure 9.**

*The variation of imaginary part of impedance (Z ) with applied frequency ofMn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

#### *3.3.6 Cole-Cole plot*

The Cole-Cole plots (Z″ along y-axis and Z<sup>0</sup> along y-axis) as shown in **Figure 10**. shows the and this plot is called Cole-Cole plots. The occurrence of a non-Debye kind of relaxation phenomenon in the Dy-Ho doped Mn-Zn ferrite NPs is confirmed by the Cole-Cole plots complex impedance spectra of the semicircle spectra.

#### **Figure 10.**

*Cole-Cole plots of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs.*

Further, the maximum peak increases with increasing the Dy-Ho concentration. For the analogous circuit model, three series sets of capacitance and resistance are created in parallel. The complex impedance formula of an equivalent circuit is shown in Eq. (4) [39, 40].

$$\mathbf{Z} = \mathbf{Z}\_0 + \mathbf{i}\mathbf{Z}'' = (\mathbf{1}/R\_b + i\alpha \mathbf{C}\_b)^{-1} + \left(\mathbf{1}/R\_{\mathbf{g}b} + i\alpha \mathbf{C}\_{\mathbf{g}b}\right)^{-1} + \left(\mathbf{1}/R\_{\mathbf{el}} + i\alpha \mathbf{C}\_{\mathbf{el}}\right)^{-1} \tag{4}$$

Where Rb is the resistance of the material and Cb is the capacitance of the material, Rel and Cel is the contact impedance between material in the electrode. The capacitance and resistance assigned by Cgb and Rgb, respectively and brought about by the combination of grain boundary.

### **4. Conclusions**

The synthesis of Mn0.5Zn0.5DyxHoyFe2-x-yO4 (x = y = 0.005, 0.010, 0.015, 0.020, 0.025 and 0.030) NPs by solution combustion technique. The lattice parameters increases with increase of Dy-Ho content due to ionic radius of Dy3+ (0.912 Å) and Ho3+ (0.901 Å) ions greater than of Fe3+ (0.645 Å) ions. SEM micrographs shows the porous nature for all samples. The development of the fuels during the combustion process resulted in the formation of the dry frothy powder. The Dielectric properties of all the samples were explained by using Koop's phenomenological theory. The ε<sup>0</sup> , ε00and tanδ were decreases with increase of frequency. Dielectric loss tangent in the ferrites is due to the lag of polarization with respect to the applied field. The AC conductivity rises as the frequency rises. For all samples, the real part of the impedance spectra diminishes as the frequency increases. Noticed that the maximum peak value increases with increase of dysprosium and holmium content in the imaginary part of impedance spectra. It gives a presence of relaxation time in the samples and it happened due to the space charge relaxation that overwhelms when the sample is composed of grain boundaries and grain. The appearance of a non-Debye type of relaxation phenomenon is linked to the presence of a single semicircle in the Cole-Cole plots for all samples. The high ac conductivity and low

*Synthesis and Study of Structural and Dielectric Properties of Dy-Ho Doped Mn-Zn Ferrite… DOI: http://dx.doi.org/10.5772/intechopen.99264*

dielectric loss noticed for all samples at high frequency region are reasonable for power transformer applications at high frequencies.
