Ferrimagnetic to paramagnetic transition and dielectric relaxation in Ni_1-xZn_xFe₂O₄ ferrites

Abstract

The spinel ferrite system Ni_1-xZn_xFe₂O₄ (x=0-0.7, Δx=0.1) was prepared by wet chemical co-precipitation method using sulfates of respective metal ions. The electrical resistivity and dielectric properties of the prepared samples have been studied as a function of temperature, frequency, and Zn content (x). The DC resistivity (ϱ) was measured in the temperature range of 300 to 800 K. The curves so plotted show two phases viz. ferrimagnetic and paramagnetic, wherein the transformation from former to later phase took place at the Curie temperature, T_C. The values of T_C were found to decrease with the increase in x. The values of activation energy (ΔE<0.2 eV) depicted the possibility of the hopping mechanism governing the conduction within the ferrites. The ferrite samples exhibited semiconducting behavior, where the electrical resistivity (ρ) decreased with the increasing temperature. The dielectric constant (ε’) and dielectric loss (ε”) were studied as a function of composition, temperature, and frequency.

Keywords:
wet chemical co-precipitation method; DC resistivity; ferrimagnetic phase; paramagnetic phase; Curie temperature; dielectric properties

INTRODUCTION

Ferrites, which are magnetic oxides, form a class of very good dielectric materials because of their high resistivity and low loss behavior. These properties have made them be utilized in technological applications over a wide range of frequencies. Ni-Zn ferrites are very important soft magnetic materials, having many applications in both low and high-frequency devices. Ni-Zn ferrites are also used in the fabrication of multilayer chip inductors (MLCI). Multilayer inductors are one of the groups of passive surface mounting devices (SMD), which is an important component for the latest electronic products such as cellular phones, notebook computers, video camera recorders, floppy drives, etc. ^{1), (2}. Ni-Zn ferrites also play a useful role in many technological applications because of their high resistivity, low dielectric loss, high Curie temperature, and chemical stability ^{3)- (5}. These features make them a suitable material for numerous applications like RF coils, transformer cores, and antenna rods.

The analysis of Raman spectra of Ni-Zn ferrites confirmed the displacement of Fe²⁺ ions due to substitution of Zn²⁺ ions; the displacement of ions leads to interesting physical properties of the ferrite ⁶. Recently Ni-Zn ferrites possessing interesting optical and electrical properties suitable for sensor applications were reported by Sankaranarayanan et al. ⁷. A long period for dielectric relaxation was reported for bulk Ni-Zn ferrite suggesting the ferrite as a promising candidate for future spintronic devices ⁸. Analysis of frequency-dependent dielectric properties of Ni-Zn ferrites shows the complex dielectric behavior of the ferrite due to the presence of different relaxation mechanisms within the 20 Hz to 20 MHz frequency band ⁹. The Curie temperature (T_C) study of Ni-Zn ferrites reports that the ferrites can be configured for a suitable value of T_C by varying the composition of the constituent elements; the ferrites possess high thermal stability owing to higher T_C¹⁰. The cation distribution study of Ni-Zn ferrites reported that the cations of the compositional elements are not specific about their occupancy at a sub-lattice site, suggesting the creation of a mixed spinel phase within the ferrite ¹¹. Due to this importance, we are presenting here a systematic study on the DC electrical resistivity and dielectric properties of nanocrystalline Ni-Zn ferrites prepared by a chemical co-precipitation method.

EXPERIMENTAL

The spinel ferrite system Ni_1-xZn_xFe₂O₄ with a variable composition (x=0.0-0.7, Δx=0.1) was prepared by air oxidation of an aqueous suspension containing Ni²⁺, Zn²⁺and Fe³⁺ cations in proper proportions. The starting solutions were prepared by mixing a 50 mL aqueous solution of FeSO₄.7H₂O, NiSO₄.7H₂O, and ZnSO₄.7H₂O in stoichiometric proportion. A 2 M solution of NaOH was prepared as a precipitant and added to the aqueous solution of sulfates to obtain the suspension (pH=11) containing dark-colored intermediate precipitant. The suspension was then heated at a constant temperature of 60 °C. The process of continuous stirring while heating, bubbled the oxygen into the suspension, promoting the oxidation reaction. The reaction continued till it yielded the brown-colored precipitate of the ferrite. The ferrite precipitate was filtered and washed several times by distilled water. The wet samples of the Ni-Zn system were annealed at 600 °C for 12 h. Details of this method of preparation are discussed in our previous publication ¹². DC electrical resistivity measurements of all the samples were carried out on a disc-shaped pellet of 10 mm diameter and 2 mm thickness. The measurements were carried out in the range of 300 to 800 K using the two-probe method. The dielectric constant (ε’) and dielectric loss (ε”) were measured as a function of frequency and temperature using an LCR-Q meter (HP 4284).

RESULTS AND DISCUSSION

The Rietveld refined XRD (X-ray diffraction) patterns of the Ni-Zn ferrite system for the typical samples with x= 0.1, 0.3, and 0.5 are shown in Fig. 1. All the peaks were indexed according to Bragg’s law ¹³, and those matched well with the peaks of NiFe₂O₄ in JCPDS file 44-1485 ¹⁴. The XRD analysis thus confirmed the formation of the single spinel phase in the ferrite crystal with space group Fd3m. The amounts of O, Fe, Ni, and Zn at tetrahedral and octahedral sites were quantified by using the Rietveld method. The obtained results of occupancy of the atoms are listed in Table I. It was clear that Zn had strong occupancy at the tetrahedral site only. However, Fe and Ni did not exhibit preference to a particular sub-lattice site. The refined XRD patterns were used for calculation of the particle size (t) from Scherer’s relation:

$t=\frac{0.9\lambda }{\beta \cos \theta }$ (A)

Figure 1:
XRD patterns of the typical Ni-Zn ferrites with x= 0.1, 0.3 and 0.5.

Table I
Values of occupancy of constituent elements of Ni_xZn_1-xFe₂O₄. The atoms showing occupancy at the octahedral site are shown by square brackets and those at the tetrahedral site are shown by parentheses.

Atom	x=0.0	x=0.1	x=0.2	x=0.3	x=0.4	x=0.5	x=0.6	x=0.7
O	4.00	4.00	4.00	4.00	4.00	4.00	4.00	4.00
[Ni]	0.98	0.87	0.76	0.65	0.54	0.43	0.32	0.21
[Fe]	1.02	1.13	1.24	1.35	1.46	1.57	1.68	1.79
(Ni)	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
(Zn)	0.00	0.10	0.20	0.30	0.40	0.50	0.60	0.70
(Fe)	0.98	0.87	0.76	0.65	0.54	0.43	0.32	0.21

where, λ is the wavelength of X-ray (=1.54 Å), β the full width at half maximum of the (311) peak, and θ the angle of diffraction. The obtained values are listed in Table II. The magnitude of t less than 100 nm indicated the formation of the ferrite nanoparticles.

Table II
Particle sizes (t), Curie temperatures (T_C) and activation energies (E_p, E_f and ΔE) for Ni_1-xZn_xFe₂O₄.

x	t (nm) (±5 nm)	TC (K) (±1 K)	Activation energy (eV) (± 0.001 eV)
			Ep	Ef	ΔE=Ep-Ef
0.1	90	862	0.763	0.587	0.176
0.2	85	840	0.638	0.506	0.132
0.3	79	820	0.625	0.497	0.128
0.4	91	797	0.594	0.478	0.116
0.5	85	733	0.555	0.464	0.091
0.6	90	704	0.545	0.451	0.094
0.7	87	671	0.531	0.443	0.088

DC electrical resistivity measurements were performed on the disc-shaped pellets by varying the temperature from 300 to 800 K for all the samples of the ferrite system. The variation of log(ρ) with 10³/T for all the compositions is shown in Fig. 2. DC electrical resistivity of the present system was found to decrease with the increase of Zn concentration. The decrease in ρ, on increasing Zn content, can be explained as follows. In the present Ni-Zn ferrites, the Zn ions preferred the occupation of tetrahedral (A) sites and Ni²⁺ ions preferred the occupation of octahedral [B] sites, while Fe³⁺ ions partially occupied the (A) and [B] sites. On increasing Zn²⁺ ion substitution at (A) sites, Ni²⁺ ion concentration at [B] sites decreased. This led to the migration of some Fe³⁺ ions from (A) site to the [B] site to substitute the reduction in Ni²⁺ ion concentration at B-sites. As a result, the numbers of ferrous and ferric ions at the [B] site (which are responsible for electrical conduction in ferrites) increased due to which, the resistivity decreased with Zn substitution in the ferrites. A similar trend, but with a different magnitude of resistivity has been reported by Ghazanfar et al. ¹⁵.

Figure 2:
Variation of DC resistivity (ρ) with reciprocal temperature (1/T).

The decrease in resistivity of the ferrites with increasing temperature depicted in Fig. 2 confirmed that the ferrites under investigation had semiconducting behavior. The variation of resistivity with the increase in temperature showed a perceptible kink near the transition temperature in all the cases. This transition temperature at which the slope of logarithm of resistivity versus reciprocal of temperature curve changed was identified as the Curie temperature (T_C). The derivatives of the curves (dρ/dT) are exhibited in Fig. 3 in which the 1/T_C values are clearly indicated by the arrows over the curve at the Curie point of the ferrite. These values of T_C obtained from curves of log(ρ) vs. 10³/T are listed in Table II. It was clear that the Curie temperature decreased with the increase in x. This was attributed to the decreasing A-B interaction resulting from the replacement of magnetic Fe³⁺ ions by non-magnetic Zn²⁺ ions. It can be noted from Figs. 2 and 3 that at the values of T_C, a kink in each phase occurred at the Curie point of the corresponding ferrite. Similar transitions near Curie temperature have also been observed in other ferrite systems ¹². It has been shown theoretically that on passing through the Curie point, a change must occur in the gradient of the straight line, and the magnitude of the effect depends upon the exchange interaction. The experimental observation of transition near the Curie point is thus in conformity with the theory developed by Irkin and Turov ¹⁶. The values of activation energies in the ferrimagnetic and paramagnetic regions were calculated from the slopes of log(ρ) vs. 1/T plots. The variation of resistivity with temperature obeys the Arrhenius relation:

$\rho ={\rho }_{0}exp\left[\frac{\Delta E}{k·T}\right]$ (B)

where ΔE is the activation energy in eV, ρ₀ is the resistivity at room temperature, k_B is the Boltzmann constant and T is the absolute temperature. The activation energy values corresponding to the two regions (before and after Curie temperature) were estimated using Eq. B for each sample and are presented in Table II. The decrease in the activation energy may be attributed to the creation of a small number of oxygen vacancies. It may also be justified due to the decrease in resistivity with the increase in Zn concentration because the activation energy behaves in the same way as that of the DC electrical resistivity ¹⁷. In the present Ni-Zn ferrite series, the preference of Ni²⁺ ions at octahedral [B] site and Fe³⁺ ions on tetrahedral (A) site as well as octahedral [B] site favored the following exchange interaction: $N{i}^{2+}+F{e}^{3+}\leftrightarrow N{i}^{3+}+F{e}^{2+}$. Thus, the conduction mechanism for the n-type semiconductor is predominantly due to the hopping of electrons from Fe²⁺ to Fe³⁺, while the conduction mechanism for the p-type semiconductor is due to the transfer from Ni³⁺ to Ni^{2+ (18}. It is clear from Table II that the activation energy for conduction in the ferrimagnetic region (E_f) was lower than that in the paramagnetic region (E_p). The activation energy (ΔE) of the ferrite sample is given by Eq. C. In the present series, the activation energy (ΔE) was found to be below 0.2 eV, therefore, the conduction in these ferrites might be due to the hopping of electrons.

$\Delta E=E_p-E_f$ (C)

Figure 3:
Variation of derivative of DC resistivity (dρ/dT) with reciprocal of temperature (1/T).

The variation of dielectric constant (ε’) with temperature is shown in Fig. 4a for all the values of x. It was evident that ε’ increased with the increase in temperature. Similar nature was observed in different cases for other ferrites ^{1), (19), (20}. Fig. 4b shows the variation of dielectric loss (ε”) as a function of temperature. It was evident that ε” also increased with the increase in temperature. The variation of ε’ and ε” can be explained on the basis of the polarization process. According to Rabkin and Novikova ²¹, the process of dielectric polarization in ferrites takes place through a mechanism similar to the conduction process by electron exchange $F{e}^{2+}\leftrightarrow F{e}^{3+}$ and $N{i}^{2+}\leftrightarrow N{i}^{3+}$ from which one obtains local displacement of the electrons in the direction of electrical field; these displacements determine the polarization. Both types of carriers i.e. ‘n’ and ‘p’ contribute to the polarization and their contribution depends on the temperature. Hence, the influence of temperature on the electronic exchange $F{e}^{2+}\leftrightarrow F{e}^{3+}$ and $N{i}^{2+}\leftrightarrow N{i}^{3+}$ is more pronounced than on the displacement of peak carriers, due to which ε’ and ε” increase rapidly with the increase in temperature.

Figure 4:
Variation with temperature (T) of: a) dielectric constant (ε’); and b) dielectric loss (ε”).

Fig. 5a shows the variation of dielectric constant with frequency for all the samples. It was seen that the dielectric constant ε’ decreased with the increase in frequency. The behavior of frequency dependence of ε’ for Ni_1-xZn_xFe₂O₄ is in good agreement with those of the Y³⁺ substituted Mg-Zn ferrites ²², for which ε’ continuously decreases with increasing frequency. More dielectric dispersion is observed in the low-frequency region, which may be due to the Maxwell-Wagner interfacial type of polarization ^{23), (24}, which is in good agreement with Koop’s phenomenological theory ²⁵. The decrease in polarization with the increase in frequency may be due to the fact that, beyond a certain frequency of the electric field, the electronic exchange between Fe²⁺ and Fe³⁺ cannot follow the alternating field; therefore, the dielectric constant decreases with increasing frequency. The variation of dielectric loss (ε”) with frequency at room temperature is depicted in Fig. 5b for the ferrite samples. All the samples showed a normal dielectric behavior with the frequency where the parameter ε” also decreased exponentially with the increase of frequency. A typical plot showing the variation of dielectric constant with x is shown in Fig. 6. It shows that ε’ increases with increasing Zn content. This may indicate the possibility of a decrease in the hopping interaction with the increasing addition of Zn²⁺ ions. In the present Ni-Zn ferrites, Zn²⁺ ions occupy tetrahedral (A) sites whereas Ni²⁺ ions prefer to go to the octahedral [B] sites. The Fe ions, which exist in 2+ as well as in 3+ states, occupy both (A) and [B] sites. When Zn²⁺ is added in place of Ni²⁺ ions, some of the Fe³⁺ ions are converted to Fe²⁺ ions to maintain charge neutrality. As a result, hopping between Fe³⁺ and Fe²⁺ ions increases leading to a decrease in grain resistance. This increases the probability of electrons reaching the grain boundary. Consequently, polarization and dielectric constant increase ²⁶.

Figure 5:
Variation with frequency (f) of: a) dielectric constant (ε’); and b) dielectric loss (ε”).

Figure 6:
Variation of dielectric constant (ε’) with Zn content (x) at a constant frequency (100 Hz).

CONCLUSIONS

The Zn-substituted NiFe₂O₄ nanoparticles were successfully prepared by a wet chemical co-precipitation method. The particle sizes calculated from the refined XRD patterns varied from 79 to 90 nm. The presence of a single spinel phase in the ferrites was confirmed from the Rietveld refinement of the XRD pattern. The occupancy of the elements obtained from the Rietveld method suggested that Zn showed a strong preference for the tetrahedral site while Ni and Fe showed their occupancy to both the sub-lattice (tetrahedral and octahedral) sites. DC electrical resistivity study showed the presence of ferrimagnetic and paramagnetic phases for the two different temperature regions in Ni-Zn ferrite. The values of Curie temperature of the ferrite (Ni_1-xZn_xFe₂O₄) samples decreased from 862 to 671 K with the increase in x, which may be due to a decrease in strength of A-B interaction with increasing x. The values of activation energy were less than 0.2 eV, which indicated that the hopping mechanism was governing the conduction in the ferrites. The dielectric polarization in the ferrites was strongly influenced by temperature, wherein more dispersion in values of dielectric constant (ε’) occurred for temperatures >700 K. The dielectric dispersion at low frequencies (<10 kHz) indicated the presence of Maxwell-Wagner interfacial polarization in the ferrite system. Increasing the concentration of Zn²⁺ in the Ni-Zn ferrite system increased its dielectric constant. The dielectric study suggested the suitability of Ni-Zn ferrite synthesized by wet chemical co-precipitation method for high-frequency applications.

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Publication Dates

• Publication in this collection
  17 May 2021
• Date of issue
  Apr-Jun 2021

History

• Received
  06 June 2020
• Reviewed
  11 Sept 2020
• Reviewed
  09 Nov 2020
• Accepted
  13 Nov 2020