Investigation on the structural, dielectric and impedance analysis of manganese substituted cobalt ferrite i.e., Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4)

Abstract

Manganese substituted cobalt ferrites, i.e., Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) were prepared by a solid state reaction method. XRD analysis confirmed the formation of a single-phase cubic spinel structure for all of the synthesized compositions, whereas an SEM study revealed that Mn substitution changes the microstructure. ⁵⁷Fe Mössbauer spectroscopy measurements suggested that Fe³⁺ cations progressively migrate with Mn addition from tetrahedral (A) sites to octahedral (B) sites which have a relatively smaller covalency. Therefore, the distribution of cations between the A- and B-sites changed with increasing x. Moreover, interestingly, the Fe²⁺/Fe³⁺ cation ratio remains zero and high spin Fe³⁺ is the only oxidation state observed at both sites for all of the synthesized compositions. In order to explore the effects of observed variations in the microstructure and cation distribution on the dielectric and resistive properties, the prepared samples were subjected to impedance spectroscopic experiments in a wide frequency range at room temperature. Mn substitution is found to improve the resistive properties by about two orders of magnitude. This increase in the resistive properties is explained in terms of the variations in the microstructure and decrease in the mobility of the charge carriers associated with the cations redistribution. Similarly, the variation in the dielectric permittivity is also conferred in terms of the change in microstructure and cation redistribution.

---

Introduction

Spinel ferrites have been extensively studied in recent years because of their significant structural, magnetic, electrical and magnetoelectric properties, which can be utilized in a wide range of applications like transformer cores, magnetic resonance imaging, microwave devices and data storage devices.^1–3 Among the spinel ferrites, cobalt ferrite CoFe₂O₄ is a well-known ferrimagnetic material which reveals exceptional properties such as high magnetocrystalline anisotropy, moderate saturation magnetization, a high coercive field, significant mechanical hardness, high resistivity and low loss behaviour.⁴ Since, the physical properties of ferrites are found to be dependent on the synthesis conditions, e.g., compaction pressure, sintering time, and temperature, morphology and cation distribution.⁵ Therefore, in recent years, cobalt ferrite and/or cobalt ferrite substituted with other metal ions at Co or Fe sites have been extensively investigated in order to modify the structural, electrical, magnetic, and dielectric properties in controlled manner.^6–8

Currently, interest has been shifted to manganese substituted cobalt ferrites, i.e., CoFe_2−xMn_xO₄, due to their enhanced magnetomechanical effect and stress sensitivity, which makes these materials attractive for stress sensing applications.⁹ It has been found that substitution of Mn for Fe in cobalt ferrite leads to structural distortion due to migration of Co from B-sites to A-sites which in turn affect the magnetic and magnetomechanical properties of CoFe_2−xMn_xO₄ system.¹⁰ However in our recent study,¹¹ higher magnetostriction and strain sensitivity is obtained for the substitution of Mn for Co instead of Fe in the cobalt ferrite, i.e., Co_1−xMn_xFe₂O₄, which describes the significance of Mn substitution for Co instead of Fe in tuning the magnetoelastic response of cobalt ferrite. Similar to magnetic and/or magnetostrictive properties, the electrical properties of cobalt ferrite also depend on the substitution of Mn ions at Co or Fe sites. Ramana et al.¹² reported the effect of Mn substitution on the structural, magnetic and dielectric properties of CoFe₂O₄ and established a correlation between the structure–magnetic–dielectric properties in CoFe_2−xMn_xO₄ system. According to them, the hopping of holes from Co²⁺ to Co³⁺ and electron from Fe²⁺ to Fe³⁺, and Mn²⁺ to Mn³⁺ govern their dielectric properties. Later on, Kolekar et al.¹³ investigated the temperature dependent dielectric constant, ac electrical conductivity and impedance analysis of CoFe_2−xMn_xO₄. They explained the observed behaviour on the basis of two-layer model containing the low-resistive grains separated from each other by high-resistive grain boundaries. However, there are few reports found in literature on the dielectric and impedance properties of Mn substitution for Co instead of Fe in cobalt ferrite, i.e., Co_1−xMn_xFe₂O₄, to the best of our knowledge. Recently, Reddy et al.¹⁴ reported the variation in the dielectric properties on the basis of nonzero Fe²⁺/Fe³⁺ ratio for different Mn content in Co_1−xMn_xFe₂O₄. Similarly, Yadav et al.¹⁵ investigated the effects of Mn content on the magnetic and dielectric properties of Co_1−xMn_xFe₂O₄ and explained the change in the dielectric properties on the basis of charge hoping between Mn³⁺, Mn²⁺, Fe³⁺ and Fe²⁺ and the change in these cations concentration with doping. However, the reported data showed irregular pattern of the electrical and magnetic results with Mn content and were discussed without incorporating the role of single phase and defect chemistry along with any possible correlation. Moreover, none of the above mentioned reports discussing the effects of cation distribution and morphology on the dielectric properties. Although the effects of these cation distribution and morphology on the magnetic properties of Co_xMn_1−xFe₂O₄ have been reported much,^16–18 however, their effects on the dielectric properties need attention. The current study is aimed at the investigation of cation distributions, and their effects on the electrical conduction and the dielectric relaxation in Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4).

Experimental

A series of manganese substituted cobalt ferrite samples with compositions of Co_1−xMn_xFe₂O₄ (x = 0.0, 0.1, 0.2, 0.3 and 0.4) were prepared by solid state reaction method. Starting materials were iron oxide (Fe₂O₃), cobalt oxide (Co₃O₄) and manganese oxide (MnO₂). Stoichiometric amounts of these powders were mixed and wet grounded for 2 h in an agate mortar and pestle and then calcined at 900 °C for 2 h. The samples were then re-ground further for 2 h and pressed in to disk shape of 13 mm diameter and thickness of 1 mm under compaction pressure of 167 MPa. Finally, these disks were sintered in air at 1300 °C for 12 h and were subsequently furnace cooled to room temperature. The intensities were recorded from 15° < 2θ < 75° with a scan step size of 0.02° with a time of 1 second per step. The phase analysis of the prepared materials were examined by X-ray diffractometer (Panalytical X'pert Pro) with Cu Kα radiation (λ = 1.54 Å). Collected data were refined using the Rietveld package TOPAS (Bruker AXS Topas V 2.1) based on the fundamental parameter approach, with diffractometer parameters and wavelength settings adjusted using a LaB6 standard. Scanning Electron Microscope (FE-SEM; Hitachi S4800) was used in order to investigate the morphology of the prepared samples. For SEM analysis, the fractured inner surfaces of the sintered pellets were directly stuck to the aluminium sample holder by a carbon tape. Surface imaging analysis was performed using probe electron beam operating at 20 kV. For room temperature ⁵⁷Fe Mössbauer measurements, the sintered pellets of all samples were properly ground. ⁵⁷Co (Rh-matrix) source was used in transmission mode. α-Fe foil was used for the Mössbauer spectrometer calibration. Data were analyzed using the MOS-90 computer program by assuming all peaks as Lorentzian in shape.

Impedance spectroscopy on the sintered pellets of Co_1−xMn_xFe₂O₄ was performed in the frequency range of 0.1 Hz to 10⁷ Hz at room temperature, using an Alpha-N Analyser (Novocontrol, Germany). The surfaces on both sides of the pellets were cleaned properly and contacts were made by silver paint on opposite sides of the pellets, which were cured at 150 °C for 3 h. Before the impedance experiments, the dispersive behaviour of the leads was carefully checked which ensured the absence of any extraneous inductive and capacitive coupling in the experimental frequency range. The ac signal amplitude used for all of these studies was 0.2 V. WINDETA software was used for data acquisition, which was fully automated by interfacing the analyzer with a computer. ZVIEW software was used for the fitting of the measured results.

Results & discussion

X-ray diffraction patterns of Mn substituted cobalt ferrite samples (i.e. Co_1−xMn_xFe₂O₄) are shown in Fig. 1. All XRD patterns were analysed by employing Rietveld refinement based on the fundamental parameter approach. XRD analysis indicates that all samples were crystallized in single phase spinel structure corresponding to the Fd3̄m space group. The lattice parameter a for Co_1−xMn_xFe₂O₄, determined from XRD data, was found to increase with increasing Mn content from 8.379 Å to 8.418 Å (see Table 1). However, in our case, the observed change in the lattice parameter with Mn content might be due to the presence of Mn²⁺ as well as Mn³⁺ in the prepared samples. A similar variation in lattice parameter with Mn content is also observed by other groups.^19–21 Therefore, the variation of the lattice parameter for Co_1−xMn_xFe₂O₄ samples can be understood by comparing the ionic radius of Mn²⁺ (0.83 Å) and Mn³⁺ (0.74 Å) ions with that of Co²⁺ (0.78 Å) ions.

Fig. 1 Rietveld refined X-ray diffraction patterns for Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples. The open circles indicate experimental data and solid line represents Rietveld refined data.

Table 1 Structural (a, D_x, D, P) and impedance fitting (R_g, C_g, R_gb, C_gb, R_o, C_o) parameters for the Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples

Sample (x)	a (Å)	Dx (g cm^−3)	D (g cm^−3)	P (%)	Rg (Ω)	Cg (F)	Rgb (Ω)	Cgb (F)	Ro (Ω)	Co (F)
0.0	8.379	5.296	5.130	3.13	—	—	6075	9.5 × 10^−10	—	—
0.1	8.391	5.273	5.016	4.88	8337	2.1 × 10^−12	212 810	2.6 × 10^−10	—	—
0.2	8.394	5.268	4.838	8.16	7758	6.7 × 10^−12	179 260	1.9 × 10^−10	96 174	5.6 × 10^−9
0.3	8.411	5.236	4.658	11.04	20 962	8.6 × 10^−12	250 520	9.9 × 10^−10	189 360	1.2 × 10^−8
0.4	8.418	5.223	4.517	13.52	151 810	3.8 × 10^−12	512 190	8.7 × 10^−9	202 320	1.4 × 10^−9

---

The variations in the X-ray density (D_x) and bulk density (D) with Mn content (x) are shown in Table 1. The X-ray density for each Mn content (x) was calculated according to the equation:

where 8 represents the number of molecules in a unit cell of spinel lattice, ‘M’ is the molecular weight of the synthesized composition, ‘N’ is Avogadro's number and ‘a’ is the lattice parameter. The bulk density of the un-substituted sample was about 97% of the corresponding X-ray density (see Table 1). It is revealed that both densities decreases with increasing Mn content (x); however, a difference is seen between the values of D_x and D attributing to the porosity of the prepared samples. The present result of porosity (%) is also given in Table 1 indicating an increase in the porosity of the samples with increasing Mn content (x). A decreasing trend in density and increasing trend in porosity on Mn substitution at Co site is in accordance with the reported results,¹⁵ however, the relatively smaller values of the porosity in our case can be attributed to high compaction pressure and sintering temperature. Fig. 2 shows the scanning electron micrograph (SEM) for a few representatives Mn substituted samples. It reveals that the un-substituted (x = 0.0) sample gives a uniform microstructure and the particles themselves are practically free of pores; however with increasing Mn content (i.e., x = 0.2 & 0.4) the samples shows non-uniformity in the grain size. As a result, the porosity is found to increase, accompanied by a reduction in grain size and a subsequent decrease in the samples density with increasing Mn content (x), which is in agreement with the above discussed results.

Fig. 2 SEM micrographs of Co_1−xMn_xFe₂O₄ samples with (a) x = 0.0, (b) x = 0.2 and (c) x = 0.4.

⁵⁷Fe Mössbauer spectroscopy was conducted to confirm the cation distribution and oxidation state of iron (Fe) in the Mn substituted cobalt ferrite samples. ⁵⁷Fe Mössbauer spectra of the Co_1−xMn_xFe₂O₄ samples with x = 0.0, 0.1, 0.2, 0.3 and 0.4 recorded at room temperature are shown in Fig. 3, whereas the extracted parameters obtained from the fitting of Mössbauer spectra are summarized in Table 2. For all samples, the Mössbauer spectra shows the presence of two distinct magnetic sextets, representing two different types of ferromagnetic Fe atoms located in the tetrahedral (A) and octahedral (B) sites within the spinel structure. With increasing Mn content, the line width (Γ) of the spectra representing B-site of iron becomes broader than the A-site due to hyperfine field distribution at the B-sites.²² The value of quadrupole splitting (Δ) of all samples is found to be negligibly small (i.e. almost zero) showing the overall cubic symmetry in all samples. The observed value of isomer shift (δ) for both sites shows the presence of only trivalent state of iron (i.e., Fe³⁺) in the prepared samples. However, the observed smaller value of A-site isomer shift compared to B-site is due to a large covalency at the A-site.²³ Moreover, the value of hyperfine magnetic field (H_eff) decreases with increasing Mn content; however, it is found that the observed decrease in the H_eff at B-site is considerable as compared to A-site. This behaviour is attributed to the migration of Fe³⁺ ions from A- to B-sites, as Mn²⁺ ions has preference for A-site.¹⁸ The continuous migration of the Fe³⁺ cations from A-site to B-site with the increase in Mn content and preference of Mn cations for the A-site are also evident from the observed progressive increase in the percentage spectral area associated with the B-site Fe³⁺ cations.

Fig. 3 Mössbauer spectra of Co_1−xMn_xFe₂O₄ samples for (a) x = 0.0, (b) x = 0.1, (c) x = 0.2, (d) x = 0.3 and (e) x = 0.4 recorded at room temperature.

Table 2 Mössbauer parameters for the Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples

Sample (x)	Site	Heff (kOe)	Δ (mm s^−1)	δ (mm s^−1)	Γ (mm s^−1)	Relative area (%)
0.0	A	495 (±3)	0.00 (±0.003)	0.23 (±0.005)	0.40 (±0.02)	41
	B	510 (±4)	0.00 (±0.001)	0.40 (±0.006)	0.87 (±0.04)	59
0.1	A	497 (±2)	0.01 (±0.000)	0.22 (±0.005)	0.38 (±0.01)	38
	B	506 (±4)	0.00 (±0.000)	0.39 (±0.003)	0.80 (±0.02)	62
0.2	A	493 (±1)	0.00 (±0.001)	0.20 (±0.003)	0.35 (±0.03)	34
	B	497 (±2)	0.00 (±0.002)	0.40 (±0.008)	0.80 (±0.04)	66
0.3	A	491 (±1)	0.01 (±0.007)	0.21(±0.008)	0.30 (±0.00)	31
	B	490 (±2)	−0.04 (±0.003)	0.40 (±0.00)	0.91 (±0.01)	69
0.4	A	492 (±1)	0.05 (±0.005)	0.23 (±0.003)	0.35 (±0.04)	30
	B	482 (±3)	−0.07 (±0.003)	0.38 (±0.004)	0.98 (±0.08)	70

---

The information about the cation distributions between the A- and B-sites can be obtained from the relative peak area (RA) and the ratio of A-site sextet intensity to that of B-site. It is found that Mössbauer fitting for x = 0.0 sample gave us direct calculation of Fe³⁺ at the A- and B-sites and on the basis of these numbers (maintaining spinel stoichiometry) Co cation distribution is estimated and written in Table 3. Now keeping in mind the conventional approach for Mn in spinel ferrite, i.e., 80% of Mn²⁺ has to occupy tetrahedral A-site and the remaining 20% of Mn²⁺ will occupy octahedral B-site.²⁴ Using this approach, we may estimate the cation distribution of Mn and Co on the basis of Fe distribution among the A- and B-sites which show that cations are randomly distributed over the A- and B-sites (see Table 3) indicating mixed spinel structure in all samples. These results are also in accordance with the previous reports of Mn substitution on Co site in cobalt ferrite.^25,26

Table 3 Cation distribution in the spinel structure as estimated by Mössbauer spectroscopy for the Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples

Sample (x)	A-site	B-site
0.0	Co0.18Fe0.82	Co0.82Fe1.18
0.1	Co0.16Mn0.08Fe0.76	Co0.74Mn0.02Fe1.24
0.2	Co0.14Mn0.16Fe0.7	Co0.66Mn0.04Fe1.3
0.3	Co0.12Mn0.24Fe0.63	Co0.58Mn0.06Fe1.34
0.4	Co0.1Mn0.32Fe0.58	Co0.5Mn0.08Fe1.42

---

Impedance spectroscopy is a well-known and powerful technique for investigating the electrical properties such as conductivity, dielectric behaviour and relaxation characteristic of the electro-ceramic materials.²⁷ The impedance analysis allows one to determine the contributions of various processes such as bulk effects and the grain boundaries. Fig. 4 shows the complex impedance plane plots (Z′ vs. Z′′) of the Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples measured at room temperature, whereas the arrow shows the direction of the increase in frequency. The impedance plane plots of the polycrystalline materials is generally characterized by the appearance of one or more semicircles depending upon the number of relaxation effects present in the system. The diameter of the each semicircle at Z′ axis shows the individual resistance of the corresponding relaxation effect, whereas, the total resistance of the sample is equal to intercept of the curve on Z′ axis at low frequencies. Generally in ceramic materials the grain boundaries are more resistive owing to the presence of higher density of structural and chemical defects when compared to the grain interiors.²⁷ Consequently, the charge carriers feel it harder to follow the variations in the applied ac signal and relax at lower frequencies when compared to those inside the grains. On these basis, the semicircle with smaller diameter (smaller resistance) at higher frequencies is attributed to the grain interiors and the semicircle with larger diameter (larger resistance) can be attributed to the more resistive grain boundaries. It can be seen that a single semicircular arc is present for the un-substituted sample (i.e., x = 0.0) indicating a single relaxation phenomenon at room temperature. However, with the addition of Mn content in cobalt ferrite, emergence of new semicircular arc can also be seen representing another type of conduction process in the substituted samples. Thus, the appearance of two semicircular arcs in impedance plane plots at each Mn substituted samples indicated the presence of two types of relaxation phenomena with sufficiently different relaxation times (τ = RC), where τ, R and C are the relaxation time, resistance and capacitance of the charge carriers, respectively, associated with each relaxation. Whereas, the diameters of both semicircular arcs axis increased with increasing Mn content indicating a change in its electrical properties.

Fig. 4 Complex impedance plane plots (Z′ vs. Z′′) of the Co_1−xMn_xFe₂O₄ samples with (a) x = 0.0, (b) x = 0.1, (c) x = 0.2, (d) x = 0.3, (e) x = 0.4, and (f) complex modulus spectra of the prepared samples with different Mn content.

To assign different electro-active regions in the impedance plane plots, an equivalent circuit model is employed to fit the measured experimental data. The impedance data were fitted using the following combinations of equivalent circuits consisting of parallel RQ elements connected in series as: (i) R_gbQ_gb; (ii) (R_gQ_g)(R_gbQ_gb); (iii) (R_gQ_g)(R_gbQ_gb)(R_oQ_o), where ‘R’ and ‘Q’ are the resistance and constant phase element. The constant phase element is used to address the deviation of capacitance from ideal behaviour and C = R^1−n/nQ^1/n, where the parameter ‘n’ estimates the non-ideal behaviour having a value of zero for pure resistive behaviour and is unity for capacitive behaviour.²⁸ Here, the subscript ‘g’, ‘gb’ and ‘o’ stand for grain interiors (Gs), grain boundary (GBs) and oxidation effects discussed below, respectively, according to their geometrical capacitance.²⁹ Fig. 4(a) shows only one semicircle in impedance plane plot of the un-substituted sample i.e., x = 0.0 which is best fitted by the single RQ equivalent circuit. The points in the impedance plane plot are observed impedance data, while continuous line shows the fitted results. The values of the fitted equivalent circuit parameters are listed in Table 1. The obtained values of resistance and capacitance for x = 0.0 sample at room temperature are 6075 Ω and 9.5 × 10⁻¹⁰ F, respectively. Here, the obtained value of capacitance corresponds to the geometrical capacitance of GBs; therefore, the presence of one semicircle indicating that the GBs effects dominate the conduction process, while the contribution from Gs is too weak to separate. However, when Mn is substituted in cobalt ferrite with x = 0.1, the impedance plane plot is fitted with two parallel RQ equivalent circuits i.e., (R_gQ_g)(R_gbQ_gb). The calculated values of capacitance are 2.8 × 10⁻¹² F and 2.6 × 10⁻¹⁰ F; which corresponds to the geometrical capacitance of Gs and GBs, respectively. The arc on the low frequency side is due to the GBs conduction and that on the high frequency side is due to the Gs conduction (see Fig. 4(b)). Furthermore, with increasing Mn content, the diameter of these semi-circular arcs changes systematically which is an indication of the relative contributions from GBs resistance and Gs resistance. With further substitution of Mn in cobalt ferrite (i.e., x = 0.2–0.4), the impedance plane plot is fitted with three parallel RQ equivalent circuits i.e., (R_gQ_g)(R_gbQ_gb)(R_oQ_o). The obtained values of capacitance lies in the range of Gs and GBs (see Table 1); however, conventionally third relaxation in impedance spectroscopy is treated as electrode effect. To clarify this point, the complex modulus plot (M′ vs. M′′) of the prepared samples with different Mn content is carefully inspected. It is clear from Fig. 4(f) that the modulus data does not fit into complete semicircles in the studied frequency range. The large semicircle is believed to be induced by the grain effect, due to the smaller capacitance value dominated in the electric modulus spectra, while the small semicircle is attributed to the grain boundary effect. It is well known that the complex modulus analysis is suitable when materials have nearly similar resistance but different capacitance.³⁰ Also, the advantage of adopting complex electric modulus spectra is that it can discriminate against electrode polarization and grain boundary conduction processes. Here, it is clearly visible that at low frequency the curve is passing through the origin (see Fig. 4(f)); moreover the low value of modulus also ruled out any possibility of electrode effect in the present frequency domain. Therefore, the emergence of third relaxation phenomenon with Mn content (i.e., x ≥ 0.2) is might be attributed to the non-homogenous distribution of oxygen and most probably oxidation of Mn²⁺ ions. To understand this assumption, one can expect that during sintering when the sample is fired at 1300 °C, oxygen enters the materials from external surfaces, travel through pores and GBs networks and occupy interstitial positions. As a result, the excess of oxygen may results in the oxidization of manganese ions i.e., change of Mn²⁺ to Mn³⁺. This is also in accordance with the XRD results which suggest the existence of mixed valence Mn ions.

In an impedance plane plot, the low frequency intercept at the Z′ axis gives the total resistance of the system under investigation. It can be seen from Fig. 4(a)–(e) that the total resistance increases with increasing Mn content. It is discussed above that with the substitution of Mn, the number of Mn²⁺–O–Mn³⁺ hoping pair's increases and is expected to decrease the resistive properties. Similar kinds of results are also reported in literature for substituted cobalt ferrites.^31–33 However, in the present work, not only the total resistance but also R_g and R_gb too have increasing trend with the increase in Mn content. It is found that the total resistance of the Mn substituted samples increases by two orders of magnitude as compare to un-substituted sample. This significant increase in the total and grain boundary resistance on Mn substitution can be understood on the basis of following reasons. Firstly, since the particle size decreases and the porosity of the system increases with the increase in Mn content. As a consequence, the surface area (grain boundary region) with highly resistive nature increases along with poor contact between the neighbouring grains overcoming the decrease in resistance associated with the increase in Mn²⁺–O–Mn³⁺ hoping pairs. Secondly, it is believed that the conduction in Co_1−xMn_xFe₂O₄ is due to the hoping of the electrons between the divalent Co/Mn with trivalent Fe. Recalling the results of Mössbauer spectroscopy where it is observed that the Fe³⁺ cations progressively shift towards the octahedral B-sites which have relatively a smaller covalency. As a consequence of the smaller covalency of the Fe³⁺–O²⁻ bond at the B-site results in the formation of superexchange Fe³⁺–O–Fe³⁺ network which localized the mobility of charge carriers. Similarly, with the oxidation of Mn²⁺ to Mn³⁺ (as discussed above for x ≥ 0.2), the formation of Fe³⁺–O–Mn³⁺ network is also enhancing the above mentioned localized mechanism which results in significant increase in the overall resistance of the prepared samples. Since, Fe³⁺–O–Fe³⁺ network is thermodynamically more stable as compared to Fe³⁺–O–M²⁺ linkages, therefore, the charge sharing or the hoping of the electrons through Fe³⁺–O–M²⁺ network becomes difficult, which results in the decrease of hoping mobility and hence the overall conductivity decreases due to more localization.

Fig. 5 shows the frequency dependence of the imaginary part of the impedance at room temperature for Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples. Here, the Z′′ plots are normalized against the maximum value Z′′_max and exhibit some important features such as (i) appearance of one or more peaks at particular frequencies, known as associated mean relaxation frequencies (f_r), and (ii) shift in the peak frequency toward lower frequency with increasing Mn content in Co_1−xMn_xFe₂O₄ system. The appearance of two peaks with the substitution of Mn in cobalt ferrite can be attributed to the impedance of the grain interiors and grain boundaries (as discussed above) at higher and lower frequencies, respectively. It can be seen that there is a shifting of the peak frequencies, both at grain interiors and at grain boundaries, towards the lower frequency side with Mn content. It is emphasized here that the charge carriers with higher value of the mobility will follow the variations in the ac electric field up to higher frequencies and hence show the higher relaxation frequency when compared to the charge carriers with lower mobility.³⁴ Therefore shift of the mean relaxation frequency towards lower frequencies indicates a decrease in the mobility of the conduction carriers both inside the grains and at grain boundaries with the increase in Mn content. As discussed above, the decrease in the mobility of the charge carriers at grain boundaries can be attributed to the increase in porosity and surface area and hence larger number of defects impeding the carrier motion. At the same time, the decrease in the mobility of charge carriers at grain interiors can also be interpreted on the basis of possible contributions from the two effects; (i) shift of the charge carriers from the tetrahedral to octahedral sites as discussed above, and (ii) decrease in particle size as follows. It has been found in the literature that the specific resistance of the grains increases with a decrease in grain size.^35,36 Grain boundaries generally consist of a positively/negatively charged core structure surrounded by an oppositely charged space charge layer extending into the grain interiors in the adjacent grains. The density of charge in the space charge layer is a function of distance from the grain boundary core. As a consequence, a potential difference exists between the core and the space charge layer (ψ_c) and between the space charge layer and the grain interior (ψ_s).³⁷ This ψ_s is expected to decrease the ease of carrier motion in the region of grains adjacent to the space charge layer. Due to smaller particle size, the space charge region penetrates the area relatively deeper into the grains and hence a relatively larger grain resistance is expected.

Fig. 5 Frequency dependence of imaginary part of impedance for Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples measured at room temperature.

Fig. 6 shows the bode plots for the imaginary parts of the electrical impedance Z′′ and modulus M′′ for some selected compositions. These two quantities are selected with the aim that the Z′′ bode plot is effective in augmenting the effects from the more resistive grain boundaries in the system whereas the M′′ bode plots are effective in resolving the effects from the less capacitive grain interiors.²⁷ The Z′′ bode plot in Fig. 6(a) for CoFe₂O₄ shows only a single relaxation peak at about 20 kHz corresponding to the grain boundary effect. Whereas M′′ bode plot for CoFe₂O₄ shows a stronger additional effect associated with the grain interiors which is only partially visible on the high frequency side. The above results can be interpreted on the basis of sufficiently high mobility of the relaxation charge carriers with the relaxation frequency beyond the current measured range. As a consequence, the impedance plane plot shows a single semicircle for CoFe₂O₄. However, on substituting Mn, the carrier mobility decreases and the relaxation frequency of the carriers shift back in the measured frequency range, resulting in the appearance of the second semicircle corresponding to the grain interiors. Furthermore, the combined plot of Z′′ and M′′ versus frequency is able to distinguish whether the short-range or long-range movement of charge carries is dominant in a relaxation process. The separation of peak frequencies between Z′′ and M′′ indicates that the relaxation process is dominated by the short-range movement of charge carriers and departs from an ideal Debye-type behaviour while the frequencies coincidence suggests that long range movement of charge carriers is dominant.^38,39 However, the mismatch between the peak frequency of the normalized Z′′ and M′′ plot for all samples (see Fig. 6) indicates that the carriers are localized and departs from an ideal Debye-type behaviour, whereas the relaxation process is dominated by the short-range conduction of charge carriers.

Fig. 6 Normalized imaginary parts of the impedance and modulus vs. the frequency for Co_1−xMn_xFe₂O₄ samples with (a) x = 0.0 and (b) x = 0.4 measured at room temperature.

The frequency dependence of dielectric permittivity (ε′) for Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples measured at room temperature in the frequency range of 0.1–10⁷ Hz is shown in Fig. 7. It is found that for all samples ε′ decreases as frequency increases and remains constant at higher frequencies, indicating the usual dielectric dispersion. The larger value of dielectric permittivity at lower frequencies is mainly due to the contribution from the interfacial polarization. Whereas, the observed decrease in dielectric permittivity at higher frequencies is attributed to the only ionic and orientation polarizations. It is also well known that the polarization in ferrite is through a mechanism similar to the conduction process in which electron exchange takes place between cations of different valence state.⁴⁰ For ferrite materials several reports are available which correlated the electron hopping and hole hopping between the 2+ and 3+ cations at octahedral [B] sites with n-type and p-type of conductivities, respectively.^41–43 However, hopping probabilities between Fe³⁺ and Fe²⁺ ions play a decisive role in the overall conduction process in the ferrites. In the present Co_1−xMn_xFe₂O₄ system, only one valence state of Fe cation i.e., Fe³⁺ is found to exist in the prepared sample as deduced from the Mössbauer measurements. Therefore, the charge sharing or the orientation of the dipoles in the current systems is possible through the Fe³⁺–O²⁻–M²⁺ (M is Co or Mn) and Mn²⁺–O–Mn³⁺ exchange paths (as discussed above). However, it can be seen in Fig. 7 that with the substitution of Mn in cobalt ferrite the dielectric permittivity plot exhibit two distinct features.

Fig. 7 Variation of dielectric constant with frequency for Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples measured at room temperature. Inset shows enlarge view at higher frequency.

It can be seen that the magnitude of ε′ increases at low frequencies; whereas at higher frequencies the value of ε′ decreases (see inset of Fig. 7) on increasing Mn concentration. The decrease in the dielectric constant in the high frequency regime corresponding to the grain interiors is expected. Since, with Mn substitution, the carrier mobility decreases and hence probability of dipole orientations decreases with the applied variations in the ac electric field. Consequently, the polarization and hence the dielectric permittivity decreases with the increase in Mn content in Co_1−xMn_xFe₂O₄. Although, the mobility of the dipoles at grain boundaries also decreases with the increase in Mn content and hence a decrease in the dielectric constant is expected. However, on Mn substitution, increase in the dielectric constant in the low frequency regime which is associated with the grain boundary effect or interfacial polarization, can be associated with the increase in surface area linked with the decrease in particle size. The capacitance C_gb in frequency range associated with the effects from the grain boundaries is calculated as: where ‘A’ and ‘d’ are the area and thickness of the grain boundary layer, respectively. It can be seen that even when the intrinsic dielectric constant ε_gb at grain boundaries remains unchanged, an increase in the interfacial area ‘A’ results in the increase in the capacitance and hence in an apparent increase in ε′ in the grain boundary region of frequency. This shows that the apparently increased value of the dielectric constant in the grain boundary region is an extrinsic effect rather than the intrinsic change in dielectric constant.

In order to understand the conduction behaviour and to determine the parameters that may control the conduction processes in the Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples, the AC conductivity data were collected at room temperature in the frequency range from 0.1 Hz to 10 MHz as shown in Fig. 8. For all samples, the conductivity value is seen to increase with increasing frequency. Since hopping conduction is related to the presence of hopping channels; therefore, an increase in frequency facilitates the conductive channels to become more active by promoting the hopping of charge carriers. Moreover, it is observed that with the addition of Mn content three distinct regions are visible in the conductivity spectra of all substituted samples. In region I, conductivity curve is nearly frequency independent. In region II, conductivity curve is increased with increasing frequency. Whereas, the increase of conductivity curve is slower in region III showing a different type of response of bound charge carriers at higher frequencies in comparison with region II. However, there is a shift of regions I, II and III of conductivity curve towards the lower frequencies with increasing Mn content in cobalt ferrite. To understand AC conductivity dynamics, the total conductivity of the localized charge carriers is explained by the Jonscher power law:⁴⁴

σ_ω = σ_o + Aωⁿ (2)

Fig. 8 Variation of ac conductivity as a function of frequency for Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) samples measured at room temperature. Inset shows variation of the slope parameter (n) with Mn content (x) at different frequencies.

The first term on right side of eqn (1) is the frequency-independent conductivity at low frequencies and is considered as dc conductivity. The interesting feature is that the limit of dc conductivity decreases with the addition of Mn content which indicates that conduction process in the substituted sample is different from the un-substituted sample. Whereas, the second term of eqn (1) is frequency-dependent conductivity which is related to the dielectric relaxation caused by the localized charge carriers. Here, ω is the angular frequency (2πf), A is a constant and the exponent n is the slope of the frequency dependent region, 0 ≤ n ≤ 1. Fitting of the experimental data yields a value of n whose dependence on Mn content is a function of the conduction mechanism. Inset of Fig. 8 shows the variation of the slope parameter (n) with different Mn content. For region I (0.1–10 Hz), there is no change in n with Mn content due to a non-equilibrium occupancy of the trap charges. Whereas, the value of n for region II (10⁴ to 10⁵ Hz) and region III (10⁶ to 10⁷ Hz) is found to vary between 0.12–0.46 and 0.36–0.81, respectively. The observed modulation in the value of n with respect to Mn content shows peak maxima in region II whereas peak minima in region III, respectively, at x = 0.1 as shown in the inset of figure. Hence, the conduction arises in region II and III is due to the short-range translation hopping assisted by both small polaron and large polaron hopping mechanisms.

Conclusions

We have investigated the effect of Mn substitution on the structural, dielectric and impedance properties of Co_1−xMn_xFe₂O₄ (0.0 ≤ x ≤ 0.4) ferrites prepared by ball milling solid state reaction method. X-ray diffraction analysis reveals that all of the samples crystallize in a cubic spinel structure with the Fd3̄m space group. The lattice parameter increases whereas the X-ray density, bulk density and average grain size are found to decrease with increasing Mn content (x). Mössbauer results showed that Co, Fe and Mn ions are randomly distributed over the A- and B-sites for the prepared samples. Significant increase in the total resistance and the resistance at grain interiors and grain boundaries is obtained with increasing Mn content which is mediated by the variations in the cation distributions and microstructure. Similarly, the dielectric properties are also strongly affected by the cation redistributions and the change in morphology associated with the increase in Mn content. The obtained results demonstrate that the structural and electrical properties can be tailored by substituting the Mn ion content in the cobalt ferrite. However, the enhanced values of resistance for the prepared samples make them attractive for their potential use in high-frequency applications.

References

1. B. H. Liu, J. Ding, Z. L. Dong, C. B. Boothroyd, J. H. Yin and J. B. Yi, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 184427.
2. N. Ponpandian, P. Balaya and A. Narayanasamy, J. Phys.: Condens. Matter, 2002, 14, 3221.
3. M. Kumar, S. Shankar, O. P. Thakur and A. K. Ghosh, Mater. Lett., 2015, 143, 241.
4. A. Muhammad, R. Sato Turtelli, M. Kriegisch, R. Grössinger, F. Kubel and T. Konegger, J. Appl. Phys., 2012, 111, 013918.
5. I. C. Nlebedim, J. E. Snyder, A. J. Moses and D. C. Jiles, J. Magn. Magn. Mater., 2010, 322, 3938.
6. S. D. Bhame and P. A. Joy, J. Appl. Phys., 2006, 99, 073901.
7. R. C. Kambale, P. A. Shaikh, C. H. Bhosale, K. Y. Rajpure and Y. D. Kolekar, Smart Mater. Struct., 2009, 18, 115028.
8. R. Sato Turtelli, M. Atif, N. Mehmood, F. Kubel, K. Biernacka, W. Linert, R. Grössinger, C. Kapusta and M. Sikora, Mater. Chem. Phys., 2012, 132, 832.
9. J. A. Paulsen, C. C. H. Lo, J. E. Snyder, A. P. Ring, L. L. Jones and D. C. Jile, J. Appl. Phys., 2005, 97, 044502.
10. J. A. Paulsen, C. C. H. Lo, J. E. Snyder, A. P. Ring, L. L. Jones and D. C. Jiles, IEEE Trans. Magn., 2003, 39, 3316.
11. M. Atif, R. Sato Turtelli, R. Grossinger and F. Kubel, J. Appl. Phys., 2013, 113, 153902.
12. C. V. Ramana, Y. D. Kolekar, K. K. Bharathi, B. Sinha and K. Ghosh, J. Appl. Phys., 2013, 114, 183907.
13. Y. D. Kolekar, L. J. Sanchez and C. V. Ramana, J. Appl. Phys., 2014, 115, 144106.
14. M. P. Reddy, X. Zhou, A. Yann, S. Du, Q. Huang, A. Adel and M. Amer, Superlattices Microstruct., 2015, 81, 233.
15. S. P. Yadav, S. S. Shinde, A. A. Kadam and K. Y. Rajpure, J. Alloys Compd., 2013, 555, 330.
16. S. R. Naik, A. V. Salker, S. M. Yusuf and S. S. Meena, J. Alloys Compd., 2013, 566, 54.
17. K. Krieble, T. Schaeffer, J. A. Paulsen, A. P. Ring and C. C. H. Lo, J. Appl. Phys., 2005, 97, 10F101.
18. D. H. Lee, H. S. Kim, C. H. Yo, K. Ahn and K. H. Kim, Mater. Chem. Phys., 1998, 57, 169.
19. K. J. Standley, Oxide Magnetic Materials, Clarendon Press, Oxford, 1972.
20. S. D. Bhame and P. A. Joy, J. Appl. Phys., 2006, 100, 113911.
21. M. Atif, R. Sato Turtelli, R. Grössinger, M. Siddique and M. Nadeem, Ceram. Int., 2014, 40, 471.
22. M. Siddique, R. T. Ali Khan and M. Shafi, J. Radioanal. Nucl. Chem., 2008, 277, 531.
23. K. P. Thummer, M. C. Chhantbar, K. B. Modi, G. J. Baldha and H. H. Joshi, Mater. Lett., 2004, 58, 2248.
24. V. A. M. Brabers, Handbook of Magnetic Materials, Elsevier, New York, 1995, vol. 8, p. 189.
25. G. A. Sawatzky, F. Van Der Woude and A. H. Morish, Phys. Rev., 1969, 187, 747.
26. V. K. Singh, N. K. Khatri and S. Lokanathan, Pramana, 1981, 16, 273.
27. M. Idrees, M. Nadeem, M. Atif, M. Siddique, M. Mehmood and M. M. Hassan, Acta Mater., 2011, 59, 1338.
28. J. Stankiewicz, J. Sese, J. Garcia, J. Blasko and C. Rillo, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 61, 11236.
29. M. Atif and M. Nadeem, J. Sol-Gel Sci. Technol., 2014, 72, 615.
30. J. Suchanicz, J. Mater. Sci. Eng. B, 1998, 55, 114.
31. C. Murugesan and G. Chandrasekaran, RSC Adv., 2015, 5, 73714.
32. T. M. Rahman, M. Vargas and C. V. Ramana, J. Alloys Compd., 2014, 617, 547.
33. R. Pandit, K. K. Sharma, P. Kaur and R. Kumar, Mater. Chem. Phys., 2014, 148, 988.
34. M. Idrees, M. Nadeem, M. Mehmood, M. Atif, K. H. Chae and M. M. Hassan, J. Phys. D: Appl. Phys., 2011, 44, 105401.
35. J. Topfer, H. Kahnt, P. Nauber, S. Senz and D. Hesse, J. Eur. Ceram. Soc., 2005, 25, 3045.
36. A. V. Shlyakhtina, S. N. Savvin, A. V. Levchenko, A. V. Knotko, P. Fedtke, A. Busch, T. Barfels, M. Wienecke and L. G. Shcherbakova, J. Electroceram., 2010, 24, 300.
37. R. Waser and R. Hagenbeck, Acta Mater., 2000, 48, 797.
38. W. Li and R. W. Schwartz, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 75, 012104.
39. M. Atif and M. Nadeem, J. Alloys Compd., 2015, 623, 447.
40. L. T. Rabinkin and Z. I. Novikova, Ferrites 146 I2V, Acad. Nauk. USSR, Minsk, 1960.
41. M. Younas, M. Atif, M. Nadeem, M. Siddique, M. Idrees and R. Grossinger, J. Phys. D: Appl. Phys., 2011, 44, 345402.
42. K. M. Batoo and M. S. Ansari, Nanoscale Res. Lett., 2012, 7, 112.
43. M. Atif, M. Nadeem, R. Grossinger and R. Sato Turtelli, J. Alloys Compd., 2011, 509, 5720.
44. A. K. Jonscher, Nature, 1977, 264, 673.

---