Electrical and dielectric characteristics of magnetic ceramics of Mn 1−x Ni x Fe 2 O 4 spinel nanoferrites

Abstract

Ceramics materials of the class of spinel nanoferrites of Mn_1−xNi_xFe₂O₄ (x = 0·00, 0·025, 0·50, 0·75 and 1·00) of 13–25 nm particle sizes have been investigated for their electrical and dielectric characteristics. The dc electrical resistivity was measured and found to decrease with an increase in x to follow the Verwey mechanism because of the increase in electron hopping between the Fe²⁺ tetrahedral site (A site) and the Fe³⁺ octahedral site (B site). In addition, the resistivity of ferrites was observed to decrease with an increase in temperature, confirming their semiconductor characteristics. The dielectric constant and the dielectric loss factor were found to decrease as the frequency increased, following the Maxwell–Wagner interfacial type of polarisation. The study of the electrical properties of the prepared ferrites suggests their usefulness in important applications in electronic devices in reducing power losses due to an increase in conductivity caused by the increment in Ni concentrations in various electronic circuitries, such as those in computers and transformer coils.

Keywords

Activation energy Dielectric constant Ferrites Loss tangent factor Resistivity Magnetic ceramics Nanoparticles Spinel

Introduction

The advent of nanotechnology has generated renewed interest in the study of the synthesis, functionalisation, structural, electrical and magnetic properties of an important class of ceramics materials, known as spinel ferrites.1 These studies assist in understanding the chemical and physical properties to tailor these materials for modern nanotechnology applications in a large number of devices and components.2 Considering these, to obtain desirable electrical and dielectric characteristics of the ferrites, research efforts have been made to develop and study various combinations over the years by incorporating metal cations such as Mn, Ni, Co, Cu and Zn.3 The current work is also part of our continuous efforts to study the electrical characteristics of nanoparticles of manganese–nickel spinel nanoferrites of Mn_1−xNi_xFe₂O₄ with varying nickel concentrations: x = 0·00, 0·25, 0·50, 0·75 and 1·00. Our recent work has described in detail the synthesis, structural and magnetic characteristics of these Mn_1−xNi_xFe₂O₄ nanoferrites.4 The crystallised sizes of the spinel ferrites measured by X-ray diffraction were found in the range of 13–26 nm, and the lattice constant a decreased with an increase in Ni concentration x. In the present work, we further investigated the prepared nanoferrites to describe their electrical and dielectric characteristics. The study of these characteristic is important due to several reasons. First, most of the fundamental properties of ferrites based on Mn or Ni are made of simple binary alloys such as MnFe₂O₄ or NiFe₂O₄.5, 6 On the other hand, most of the commercially important ferrites are ternary alloys of mixed variety, and in this category, again, most of the published works described Mn–Zn and Ni–Zn ferrites able to attain high resistivity as well as high initial permeability.7, 8 These ferrites are usually marked under the trade name Ferroxcube, and the presence of Ni or Mn along with Zn enables these to be used in a wide variety of applications, such as a core for receiving antennas and inductors, wide band and pulse transformers, cores of recording heads and several components of television set and portable radio.9, 10 Second, several reports are available on the magnetic and electrical properties of the nanocrystalline binary alloy of MnFe₂O₄ and NiFe₂O₄ and its ternary alloy, such as NiZnFe₂O₄ and MnZnFe₂O₄. On the contrary, to the best of our knowledge, other related ferrites of the type of MnNiFe₂O₄ have not yet been investigated in much detail, and detailed electrical and dielectric properties of nanocrystalline spinel ferrites of MnNiFe₂O₄ are lacking. Finally, the dielectric properties of Mn_1−xNi_xFe₂O₄ for a whole range of Ni concentration x and frequency have not been reported before to reveal their influence on the characteristics of these nanoferrites. Therefore, it would be interesting to explore the effect of substitution of Mn or Ni ions in Mn_1−xNi_xFe₂O₄ for the whole concentration range on the electrical characteristics of these nanoferrites. This is because with the variation in the Ni²⁺ and Mn²⁺ concentrations, the resident amount of Fe²⁺ and Fe³⁺ ions on the tetrahedral and octahedral sites in the lattice structure can be rearranged to subsequently influence the electrical characteristics of Mn_1−xNi_xFe₂O₄ ferrites.

Keeping in view the above mentioned factors, the principal motivation of this work was to further study the prepared nanoferrites of Mn_1−xNi_xFe₂O₄ and describe in detail the specific influence of varying Ni concentrations x (x = 0·00, 0·25, 0·50, 0·75 and 1·00), different temperatures (373–573 K) and frequency (0·1–5 MHz) dependence on their electrical and dielectric properties. The detailed study reported here offers valuable information about the mechanism of electrical resistivity and conduction in the prepared Mn–Ni nanoferrites, which, in turn, help to explain their electrical characteristics, such as dc resistivity, influence of varying Ni concentrations x, different temperatures, activation energy and drift mobility. In addition, the present work also investigated the prepared nanoferrites of Mn_1−xNi_xFe₂O₄ considering the effect of the applied frequency on their dielectric properties, such as dielectric constant ϵ′, dielectric loss ϵ″, dielectric loss factor tan δ and ac conductivity σ_ac. The study of the dielectric characteristics indicates that the properties of Mn–Ni ferrites are strongly influenced by the applied frequency. In order to gain an insight into the properties of the prepared ferrites, dielectric behaviours are evaluated, and the results are correlated to the varying applied frequency regimen of 0·1–5·0 MHz.

Experimental

Previous work described in detail the synthesis by chemical coprecipitation procedure and structural and magnetic characterisation of a series of Mn_1−xNi_xFe₂O₄ (with x = 0, 0·25, 0·50, 0·75 and 1·00) spinel nanoferrites.4 Briefly, coprecipitation reactions yield ferrites in powder form, which were sintered at a temperature of 800°C for 5 h, and the prepared nanoferrites were characterised by X-ray fluorescence, X-ray diffraction, infrared spectroscopy, scanning electron microscopy and atomic force microscopy to study the compositional, structural and morphological changes taking place with varying Ni concentrations x. In addition, magnetisation measurements were made using a commercial vibrating sample magnetometer.4 The present work specifically focuses on the study of the electrical and dielectric characteristics of the previously well characterised nanoferrites. Electrical and dielectric parameters of the prepared ferrites were calculated using the standard relationship as described elsewhere and discussed below.11, 12

The dc electrical resistivity ρ_dc was measured with a custom made two probe method set-up in the temperature range of 373–573 K for various compositions of Mn–Ni nanoferrites. Disc shaped samples of ∼8 mm diameter and 3 mm thickness were used for the measurements. Standard Arrhenius relation in accordance to equation (1) was used to obtain the dc electrical resistivity ρ_dc at specific temperatures. From the slope of the Arrhenius plot, the activation energy data were obtained as follows13 (1) where ρ_T is the electrical resistivity at a particular temperature T, ρ₀ is the resistivity at room temperature, k_B (8·616 eV K⁻¹) is Boltzmann's constant, T is the absolute temperature and ΔE is the activation energy.

Drift mobility μ_d was calculated using the standard relationship in accordance to equation (2)14 (2) where e is the charge on an electron, ρ is the resistivity at a particular temperature and concentration of charge carriers and η is calculated from equation (3)15 (3) where M is the molar mass, N_A is Avogadro's number, ρ_m is the measured density and N_Fe is the number of iron atoms in the chemical formula of the ferrites.

The dielectric constants ϵ′ were measured at room temperature in the frequency range of 0·1–5·0 MHz using an LCR Meter Bridge (model HP 4284 A) in accordance with the relation described in equation (4). For this purpose, circular discs from the powder of the prepared nanoferrites were made, and then a silver coating on the adjacent faces was applied to obtain the parallel plate capacitor geometry with the sample materials as the dielectric medium (4) where C is the capacitance (Faraday) of the parallel plate capacitor, d is the thickness (m) of the disc, A is the cross-sectional area (m²) of a flat surface of the pellet sample and ϵ₀ is the permittivity of free space, equal to 8·854×10⁻¹² F m⁻¹.

The dielectric loss tangent tan δ as a function of frequency was studied at room temperature, i.e. 373 K. The dielectric loss tangent tan δ values were obtained from the standard relation given in equation (5)11, 12 (5) where δ is the loss angle, f is the frequency, R_p is the equivalent parallel resistance and C_p is the equivalent parallel capacitance.

Using the dielectric constant ϵ′ and the dielectric loss tangent tan δ values, the ac conductivity σ_ac of the prepared samples was calculated at an angular frequency ω in accordance to relation (6)16 (6)

Results and discussion

The electrical and dielectric properties of the prepared ferrites of Mn_1−xNi_xFe₂O₄ (x = 0·00, 0·25, 0·50, 0·75 and 1·00) have been investigated, and the results are summarised in Table 1 and discussed below.

Table 1

Summary of results of electrical and dielectric properties of nanoparticles of Mn_1−xNi_xFe₂O₄ ferrites for Ni concentrations x = 0·00, 0·25, 0·50, 0·75 and 1·00*

Composition	MnFe₂O₄	Mn_0·75Ni_0·25Fe₂O₄	Mn_0·50Ni_0·50Fe₂O₄	Mn_0·25Ni_0·75Fe₂O₄	NiFe₂O₄
x value	x = 0·00	x = 0·25	x = 0·50	x = 0·75	x = 1·00
Parameter
t_ave/nm	25·00	23·52	21·78	19·62	13·50
ρ_dc at 373 K/Ω cm	4·97×10⁶	4·60×10⁶	2·40×10⁶	1·58×10⁶	1·38×10⁶
ρ_dc at 573 K/Ω cm	6·40×10⁵	6·90×10⁴	3·42×10³	2·90×10³	1·70×10²
ΔE at 373 K/eV	0·63	0·57	0·51	0·49	0·43
R	0·998	0·998	0·998	0·998	0·998
μ_d at 373 K/cm² V⁻¹ s⁻¹	1·63×10⁻⁹	1·76×10⁻⁹	3·3×10⁻⁸	3·89×10⁻⁸	6·63×10⁻⁸
ϵ′ at 0·10 MHz	2·55×10⁴	7·05×10⁴	2·21×10⁴	1·91×10⁴	8·21×10⁴
ϵ′ at 0·50 MHz	1·98×10⁴	3·44×10⁴	1·42×10⁴	1·69×10⁴	4·8×10⁴
ϵ′ at 1·00 MHz	1·77×10⁴	2·90×10⁴	1·31×10⁴	1·61×10⁴	3·97×10⁴
tan δ at 0·10 MHz	0·29	0·92	0·68	0·15	0·59
tan δ at 1·00 MHz	0·22	0·36	0·19	0·10	0·36

*Values of various parameters are given such as dc electrical resistivity ρ_dc, activation energy ΔE, correlation coefficient R, drift mobility μ_d, dielectric constant ϵ′ and tangent loss factor tan δ. Values of average particles size t_ave are also summarised for various compositions of prepared Mn–Ni nanoferrites.4

Electrical properties

Direct current electrical resistivity

In general, an increase in temperature results in an increment in the resistivity of metals, while the semiconductor exhibits the opposite behaviour with temperature. The prepared nanoferrites of Mn_1−xNi_xFe₂O₄ are insulators to exhibit semiconductor-like characteristics with the increase in temperature. The resistivity behaviour is investigated in the temperature range of 373–573 K considering the influence of Ni concentrations x = 0·00, 0·25, 0·50, 0·75 and 1·00 in the nanoferrites of Mn_1−xNi_xFe₂O₄. Table 1 summarises the electrical properties of the nanoferrites of Mn_1−xNi_xFe₂O₄. The electrical resistivity behaviour of the prepared nanoferrites of Mn_1−xNi_xFe₂O₄ with varying nickel concentrations x was observed to follow the Arrhenius relation in accordance with equation (1), as presented in Fig. 1.

Figure 1

Linear dependence of temperature on electrical resistivity ln ρ_dc in accordance to Arrhenius plot for nanoferrites of Mn_1−xNi_xFe₂O₄ (x = 0·00, 0·25, 0·50, 0·75 and 1·00): straight lines are best fit to equation (1); inset graph shows resistivity as function of temperature at various Ni concentrations x

It is well known that the electrical resistivity ρ_dc of ferrite decreases with an increase in temperature, thus confirming the semiconductor nature of the prepared nanoferrites in the present work.17, 18 This observation is attributed to the increase in the thermally activated drift mobility μ_d of charge carriers in accordance with the conduction mechanism of the hopping of electron.19 In the hopping conduction mechanism, the charge carrier's mobility is temperature dependent, and the band gap between the conduction band minima and the valence band maxima can be tuned by an appropriate choice of a dopant. The latter characteristics are clearly exhibited by incorporating Ni in the prepared nanoferrites and are indicated by the decrease in resistivity as the x content is increased. The observed extent of variation in ρ_dc in the current work was also found to be highly dependent on temperature. The variation in resistivity of the prepared ferrites is in agreement with related studies on ferrites, which indicated that the addition of Mn resulted in the enhancement of resistivity.20^–22 The above mentioned observations regarding ρ_dc in the prepared nanoferrites can be explained by considering the Verwey mechanism due to electron hopping between the Fe²⁺ tetrahedral site (A site) and the Fe³⁺ octahedral site (B site),23, 24 i.e. cations that are capable of promoting the increment in this transition, thus resulting in increases in the conduction. Therefore, the observed decrease in dc resistivity ρ_dc with the increase in Ni may be attributed to the presence of relatively higher electron hopping between Fe²⁺ ions in A sites and Fe³⁺ ions in B sites. Improvements in the resistivity upon increment in Mn contents appeared to be the replacement of the Fe²⁺–Fe³⁺ conduction mechanisms by a more complex conduction mechanism. Presumably, replacing Fe and/or Ni ions with the addition of Mn ions seems to eliminate the easy conduction paths otherwise provided by the former ions.

By taking the inverse of the experimentally determined values of ρ_dc, it is convenient to calculate dc electrical conductivity σ_dc using the σ_dc = 1/ρ_dc relationship. In order to illustrate the temperature dependence of σ_dc, a representative example is presented in Fig. 2 for Mn_0·50Ni_0·5Fe₂O₄. As indicated, it seems that there are two straight lines that suggest two different activation energies for Mn–Ni ferrites. The line changes its slope at the temperature of ∼452 K, which is known as the Curie temperature T_c. It was reported that a change in the gradient of the straight line must take place on passing through the Curie point. The magnitude of this gradient effect depends on the ions’ exchange interaction, which then subsequently determines the Curie point T_c.25, 26 The activation energies ΔE for electrical conduction are calculated from the slopes of lines on both sides of T_c and in the low temperature found to be within the range of 0·466–0·544 eV and in the high temperature regions between 0·707 and 0·884 eV.

Figure 2

Representation of dc conductivity against temperature for Mn–Ni nanoferrites of Mn_0·50Ni_0·5Fe₂O₄

Activation energy ΔE

Activation energy is needed to release an electron from the ion for a jump to a neighbouring ion, hence giving rise to the electrical conductivity. In the current work, ΔE values were also determined using equation (1) from the slopes of the Arrhenius relationship in the linear plots of ln ρ_dc against 1/k_BT given in Fig. 1, and the values are summarised in Table 1. The ΔE values were found to decrease approximately linearly as the Ni concentrations x increase in Mn_1−xNi_xFe₂O₄ and therefore resulted in an enhancement of conductivity or a decrease in resistivity. This observation is presented in Fig. 3 as a function of Ni concentration x along with dc resistivity. The values of ΔE decreased from 0·63 to 0·43 eV, corresponding to a ∼47% change as the Ni concentration increased from 0·0 to 1·0. This shift in ΔE is attributed to the above mentioned discussion of the decrease in ρ_dc with the increase in Ni concentration because the activation energy behaves in the same way as that of resistivity. In ferrites, the activation energy is not dependent on the concentration of charges but is associated with the variation in the charge carrier's mobility localised at the ions or vacant sites to give electrical energy to overcome the barrier experienced by the electrons during the process of conduction via the hopping mechanism.19 Since, in the prepared ferrites, ΔE values were found to be >0·4 eV, this observation therefore suggests that the conduction is due to polaron hopping.27

Figure 3

Effect of Ni concentrations x = 0·00, 0·25, 0·50, 0·75 and 1·00 on dc resistivity ρ_dc and activation energy ΔE (eV) of nanoferrites of Mn_1−xNi_xFe₂O₄

Drift mobility μ_d

The drift mobility μ_d is a proportionality factor between the drift velocities of charge carriers in a semiconductor and electric field. Figure 4 represents the effect of temperature on the drift mobility μ_d for various Ni concentrations x in Mn_1−xNi_xFe₂O₄. It is evident that nanoferrites having higher resistivity are exhibiting higher drift mobility μ_d for various compositions. In accordance with the hopping model, the electron–photon interaction induces strong localisation of electron on the cations.28 The increase in μ_d with temperature may be due to the enhancement of charge carriers, which start hopping from one site to another site by the increase in temperature, as explained above for the dc electrical resistivity.

Figure 4

Effect of temperature on drift mobility μ_d in prepared nanoferrites of Mn_1−xNi_xFe₂O₄ for various Ni concentrations of x = 0·00, 0·25, 0·50, 0·75 and 1·00

Dielectric characteristics

In the current work, the dielectric characteristics of the prepared ferrites of Mn_1−xNi_xFe₂O₄ with varying applied frequency f and Ni concentrations x = 0·00, 0·25, 0·50, 0·75 and 1·00 have been investigated. The results are summarised in Table 1 and discussed below.

Dielectric constant ϵ′

The dielectric behaviour of ferrites is one of the most important characteristics of the type of electrical insulator that may be polarised in the presence of an applied electric field. Under such condition, electric charges slightly shift from their average equilibrium positions to induce dielectric polarisation rather than flow through the material as in the case of a conductor. Considering this, the term ‘insulator’ refers to the electrical conduction of a low degree, while the term ‘dielectric’ is generally used to describe the behaviour of the material with a high polarisability expressed by a number called the dielectric constant ϵ′. In the current work, dielectric constant ϵ′ measurements were carried out in the frequency range from 0·1 to 5·0 MHz at room temperature, i.e. 373 K. The dielectric constant values ϵ′ have been obtained from the standard relation given in equation (4), and the results obtained are summarised in Table 1 and presented in Fig. 5.

Figure 5

Effect of frequency on dielectric constant ϵ′ for various Ni concentrations in prepared nanoferrites of Mn_1−xNi_xFe₂O₄ (x = 0·00, 0·25, 0·50, 0·75 and 1·00)

Figure 5 indicates several interesting observations to represent the dielectric dispersion in ferrites. It is evident that the values of ϵ′ are much higher at lower frequencies. Further, the ϵ′ values continue to decrease with the increase in frequency and decreased steeply at lower frequency, while at high frequencies, their values become smaller, exhibiting an independent behaviour for all the compositions investigated. These observations are in good agreement with the usual dielectric behaviour of ferrites and suggest complex contributions of compositional, structural and morphological factors. The dispersion in frequency dependence of ϵ′ can be explained on the basis of the Maxwell–Wagner interfacial type polarisation,29 which is in agreement with Koop's phenomenological theory.30 According to this theory, the conductivity of grain boundaries is higher at lower frequencies to contribute more towards the dielectric value due to the predominance of species such as Fe²⁺ ions, vacancies, grain boundary and interfacial dislocation pile-ups.29 The decrease in ϵ′ values with the increase in frequency for the prepared nanoferrites is observed because any species contributing to polarisability seem to lag behind the applied field at higher frequencies.31 On the other hand, in the lower frequency regimen, there is dispersion in ϵ′ values due to interfacial polarisation as electronic and atomic polarisations remain approximately constant at such applied frequencies. Furthermore, the dielectric polarisation in ferrites is similar with the conduction hopping mechanism.23, 24 Hopping between Fe²⁺ and Fe³⁺ produces the local displacement of electrons in the direction of the applied field, and these electrons then determine the polarisation. It is greatly influenced by the frequency as well as the structural arrangements in the spinel ferrites, such as the electron exchange between Fe²⁺ Fe³⁺ ions in between tetrahedral and octahedral sites. This variation in the concentration of Fe²⁺ ions results in local displacement of electrons in the direction of the electric field to influence electric polarisation in spinel ferrites, and hence, both polarisation and ϵ′ are expected to increase with the concentration of Fe²⁺. As the applied frequency increases, polarisation decreases and then reaches a constant value because; beyond certain higher frequencies of the external field, the electron exchange between Fe²⁺ Fe³⁺ cannot follow the alternating field, and thus, it exhibits the approximately constant values of ϵ′.32

Dielectric loss factor tan δ

The dielectric loss factor or tangent loss factor tan δ as a function of frequency was studied at room temperature, i.e. 373 K. The tan δ values were obtained from the standard relation given in equation (5). Figure 6 represents the variation of tan δ at room temperature as a function of applied field frequency. It is evident that, for each composition, tan δ values are found to decrease with an increase in applied frequency. All the samples exhibit dispersion due to the Maxwell–Wagner interfacial type polarisation, in agreement with Koop's phenomenological theory, as discussed above.30 The decrease in tan δ takes place when the jumping rate of charge carriers lags behind the alternating electric field beyond a certain critical frequency. The change in tan δ is greater at low frequencies and smaller at high frequencies for the investigated samples. There is a strong correlation between the dielectric behaviour and the conduction mechanism in ferrites. As discussed earlier, conduction in ferrites is considered to be due to the hopping of electron between Fe ions in different valence states +2 and +3 over the octahedral sites. From these considerations, one can see that the behaviour of tan δ with frequency is showing the expected decrease in its value with the increase in the applied frequency. Similarly, the dielectric loss ϵ‘’ values were calculated from the relation ϵ″ = ϵ′tan δ. The dielectric loss of the prepared nanoferrites was observed to follow the typical ferrites’ behaviour and was found to decrease with the applied frequency, as presented in Fig. 7. Dielectric loss is an important part of the total core loss in ferrites, and therefore, low dielectric losses and electric polarisation are highly desirable.33 The dielectric loss increases with the increment of local displacement of hopping of electrons in the direction of the applied electric field and generally reflected in the conductivity measurements as the materials with high losses also exhibit high conductivity and vice versa.

Figure 6

Effect of frequency on dielectric loss factor tan δ for various Ni concentrations in prepared nanoferrites of Mn_1−xNi_xFe₂O₄ (x = 0·00, 0·25, 0·50, 0·75 and 1·00)

Figure 7

Effect of frequency on dielectric loss ϵ′′ for various Ni concentrations x = 0·00, 0·25, 0·50, 0·75 and 1·00 in prepared nanoferrites of Mn_1−xNi_xFe₂O₄

Alternating current conductivity σ_ac

To understand the conduction mechanism in the prepared nanoferrites of Mn_1−xNi_xFe₂O₄, the ac conductivity σ_ac was also studied as a function of frequency f. Figure 8 shows the variation in σ_ac versus ln f. The plots are approximately linear to indicate that the σ_ac values increase with the increase in frequency and thus exhibit a similar trend as other ferrites do.34 The observed results again can be explained by considering the electrical conduction mechanism in terms of the electron and polaron hopping model. In the current work, the plots are approximately linear, suggesting conduction with a small polaron type as it is known to be valid for ionic solids. With the increase in applied frequency hopping, conduction also increases to induce a gradual increase in conductivity since there are more electron hopping between two adjacent octahedral sites (B sites) and transition between Fe²⁺ and Fe³⁺ ions in the lattice structure. As discussed earlier, the frequency dependent conduction is mainly attributed to a small polaron type hopping mechanism, and the present study also supports that, because of the linear response of σ_ac to the frequency, the conduction mechanism in the nanoparticles of Mn_1−xNi_xFe₂O₄ spinel ferrite is of a small polaron type.

Figure 8

Effect of frequency on ac conductivity for various Ni concentrations x = 0·00, 0·25, 0·50, 0·75 and 1·00 in prepared nanoferrites of Mn_1−xNi_xFe₂O₄

Conclusion

It can be concluded that the substitution of Ni in Mn_1−xNi_xFe₂O₄ (x = 0·00, 0·25, 0·50, 0·75 and 1·00) spinel ferrites produced significant changes in their electrical and dielectric properties. The dc electrical resistivity ρ_dc of the prepared nanoferrites with sizes between 13 and 25 nm was measured, and other electrical parameters such as activation energy ΔE and drift mobility μ_d were also obtained. The dc electrical resistivity was measured in the temperature range of 373–573 K and was found to increase with the increase in the concentration of Mn in the ferrites. This observation is attributed to the hoping conduction mechanism model of electron and polarisation. In addition, the dc electrical resistivity was found to decrease with the increase in temperature and follow the Arrhenius relation observed normally in ferrites to confirm the semiconductor characteristics of the prepared nanoferrites. Activation energy ΔE and drift mobility μ_d of the prepared nanoferrites were found to decrease with the increase in Ni concentration x. The drift mobility exhibited linear dependence on temperature, while the activation energy showed an inverse dependence on resistivity. The decrease in dielectric constant ϵ‘ and loss tangent tan δ with frequency in the range of 1–5 MHz shows dielectric dispersion in the lower frequency region. The ac conductivity of the samples observed to increase with an increase in applied frequency supports the conduction mechanism of small polaron hopping type.

The study of the electrical and dielectric properties of the prepared Mn_1−xNi_xFe₂O₄ spinel nanoferrites has important prospective applications for various electronic devices. The results obtained indicate that, with an increase in the Ni ion concentration, electrical properties can be tuned to control the electrical resistivity of the synthesised ferrites and thus have important practical applications. For example, an increase in the Ni ion concentration results in the enhancement of the conductivity and is therefore capable to cause a decrease in the electric power losses in various electronic circuitries in devices such as those of computers and transformer coils. On the other hand, however, this factor can affect the capability of charge storage in the capacitors. This is because the materials with a small Ni extent can possess higher polarization density and the capacitor would polarize in short amount of time. Therefore, the higher conducting ferrite materials with more Ni contents can cause degradation of the charge storing capabilities of capacitors, but higher contents of Mn in a capacitor can result in an improvement in its charge storing capabilities.

Footnotes

Acknowledgements

The authors thank Z. Iqbal, S. Ameer, N. Ahmed, S. Ahmed and A. Ahmed from the School of Chemical and Materials Engineering, National University of Sciences and Technology, for their support in carrying out the characterisation of the samples.

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Electrical and dielectric characteristics of magnetic ceramics of Mn 1−x Ni x Fe 2 O 4 spinel nanoferrites

Abstract

Keywords

Introduction

Experimental

Results and discussion

Electrical properties

Direct current electrical resistivity

Activation energy ΔE

Drift mobility μd

Dielectric characteristics

Dielectric constant ϵ′

Dielectric loss factor tan δ

Alternating current conductivity σac

Conclusion

Footnotes

Acknowledgements

References

Drift mobility μ_d

Alternating current conductivity σ_ac