Investigation of Crystal Structure, Electrical and Magnetic Properties of Spinel Mn-Cd Ferrite Nanoparticles

Cd1 − xMnxFe2O4 (x = 0, 0.25, 0.5, 0.75, 1) spinel ferrite nanoparticle samples were synthesized using a flash auto-combustion technique and analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier-transform infrared spectroscopy (FTIR). The inspection of dielectric and magnetic properties of the prepared ferrites was carried out by using broadband dielectric spectroscopy (BDS) and vibration sample magnetometer (VSM) measurements, respectively. X-ray diffraction analysis verified the formation of the main cubic phase with space group Fd3m and a decrease in lattice constants with the increase in Mn-content. FTIR study revealed the two characteristic absorption bands of spinel ferrites and their dependence on Mn-content was investigated and explained. Elastic moduli, bulk modulus, rigidity modulus, Young modulus, and calculated Debye temperature have been studied and found to decrease with the increase in Mn-content. SEM analysis revealed nanoparticles agglomeration of uniform grains with increasing in the average grain size as Mn-content increased. The VSM measurements showed an increase in saturation magnetization accompanied by a decrease in coercivity as Mn-content increased. Dielectric investigations showed very high values of permittivity and dielectric loss at lower frequencies (between 105 and 106 @ 0.1 Hz according to the manganese content) reflecting the combination of exchange of electrons between ferrous and ferric ions and ions’ transport. The ac-conductivity showed a plateau that yields the dc-conductivity at lower frequencies followed by a characteristic frequency at which it tends out to follow a power law. The relation between these two parameters confirms the empirical BNN-relation.


Introduction
In the last few years several researches are carried out on magnetic nanoparticles to increase the potential of applications in this field by improving their physical properties for several industrial and technological applications. Between these, soft ferromagnetic materials are commonly used in both DC and AC applications such as electromagnets, relays, transformers, motors, generators, inductors, antenna rods, microwave isolators, phase shifters and filters [1][2][3].
Nanosized magnetic particles have properties which are definitely unlike that of the relating bulk materials because of their reduced size and the consequent impact of magnetic interactions between particles. Spinel ferrite nanoparticles have the common formula AFe 2 O 4 (A: divalent metal cation) where a face-centered cubic lattice is formed by oxygen ions and A ions located at tetrahedral and/or octahedral sublattice sites [4,5]. The unpaired electrons of transition metal cations positioned at tetrahedral and octahedral sites are responsible for magnetization in spinel ferrites due to variations in their spin magnetic moments. The substituted cations may be linked into the lattice of the host ferrites which successively changes the whole distribution of the cations in the system [6][7][8][9]. Due to their unique dielectric and magnetic properties, the spinel ferrites nanoparticles became promising in the microwave absorbing field of applications. In addition, the ferrites under consideration here have many fields of applications in magnetic recording and information storage.
The chemical composition and method of preparation can effectively control the cation distribution in the ferrites. Nano-ferrites are prepared by employing several methods listed and reviewed by Ref. [10][11][12][13][14][15][16]. Among these methods is the citrate-gel auto-combustion method that was employed to synthesize the present work. This preparation technique has the advantage of not only producing nano-sized spinel ferrites with high-grade quality in terms of homogeneity and control of stoichiometry, but also simplicity related with preparation temperature and time.
Yadav et al. [17] reported that introducing Mn 2+ in system of cobalt ferrite with a ratio of 0.3 increased the value of saturation magnetization by 31.2%. Mixed Cd-ferrite has significant technical applications as these ferrites are characterized by high resistivity, high permeability and low magnetic losses. Conjugation of various divalent metallic ions in chemical structure of ferrites might increase their distinctive features. The addition of cobalt ions to ferrites improved coercivity by increasing the magneto-crystalline anisotropy caused by the interaction of cobalt and iron ion's spins [18,19].
In the present work, the authors aim to synthesize spinel ferrite nanoparticles with auto combustion method; one of the best and simplest reported techniques that gives better homogeneity, requires no high temperatures, short preparation time… etc. The target is to enhance Cd-based spinel ferrites through Mn substitution that is expected to improve structural, electrical and magnetic properties of prepared (Cd-Mn)F 2 O 4 ferrites. Another objective is to present a detailed structural study (XRD, SEM, EDX, FTIR) of spinel ferrite nanoparticles with more precise identification of FTIR characteristic peaks and engaging it to calculate the elastic properties of prepared ferrites.

Samples Preparation
Nano-sized Cd 1 − x Mn x Fe 2 O 4 ferrites with x = 0.00, 0.25, 0.50, 0.75 and 1.00 were synthesized by using a flash autocombustion method as illustrated in Fig. 1  starting materials. At room temperature, small amount of distilled water was used to dissolve stoichiometric concentrations of the listed nitrates and citric acid (C 6 H 8 O 7 , (99%) (LOBA CHEMIE) was operated as a fuel. Mixing of the resultant solution took place by using hotplate magnetic stirrer at 70 °C to ensure homogeneity and ammonia was employed to fine-tune the solution pH value. To evaporate residual water; the mixture was heated at about 95 °C under regular stirring. The obtained brown gel was spontaneously ignited at ambient air which resulted in the formation light brown ash powder. Using a mortar and pestle, the porous ash samples were crushed into fine powder and annealed at 300 °C for 6 h. Then, these powders were subjected to a second cycle of grinding to be ready for various investigations.

Samples Characterization
Powder X-ray diffraction (XRD) measurements were employed to study the structure and phase purity of the samples by using Bruker D8 Advance diffractometer with Cu K α radiation. The obtained XRD patterns were examined by Rietveld method along with Fullprof software. The images for the analyzed samples were obtained with a scanning electron microscope (Quanta 250 FEG) attached to an EDX unit. Image J software was used to examine the SEM images.
The infrared spectrometer Perkin-Elmer 1430, Germany, was used to perform FTIR spectra on all studied samples in the wavenumber range of 200-4000/cm. The vibrating sample magnetometer (VSM) was used to investigate magnetic hysteresis characteristics in magnetic fields with intensities up to 25 kOe at room temperature.
Dielectric investigations of samples were performed using a Novocontrol high-resolution alpha analyzer in the frequency range 10 -1 -10 7 Hz at room temperature. The investigated samples with a thicknesses of 1-2 mm were sandwiched between two freshly polished brass electrodes with a top electrode diameter of 10 mm to form a parallel-plate capacitor cell. The complex permittivity (ε* = ε′-−iε′′) was measured using a sinusoidal voltage of 1 V amplitude over 10 −1 -10 7 Hz frequency range. For complex dielectric spectroscopy, the investigated composites can be characterized by any of the complex parameters that are related to each other by the following Eq.   [20]. Among the different quantitative methods for studying materials from powder XRD data; Rietveld method [21] is widely employed as it presents whole-pattern fitting approach rather than single-peak analysis. The Rietveld refinement of diffraction patterns for samples with x = 0, 0.5 and 1.0 was performed as shown in Fig. 3. As seen, the figure confirmed that the samples with x = 0 and x = 0.5 contain two phases; cubic spinel phase with space group Fd3m and hemitate hexagonal phase α-Fe 2 O 3 with space group R-3c. The volume fraction of the hemitate hexagonal phase α-Fe 2 O 3 was found to decrease with incrasing of Mn-content.
The XRD spectra of the cubic spinel phase revealed a shift in the noticeable (311) peak towards higher 2θ angle  Table 1. It is obviously realized that the lattice parameters decreased with increasing of Mn concentration. This could be attributed to the difference in ionic radii of Cd 2+ (0.97 Å) and Mn 2+ (0.80 Å) [22] and confirms the Mn 2+ ions substitution of Cd 2+ ions in these ferrites.
Using the Scherrer formula (Eq. 2) [23], the average crystallite sizes of the samples were approximately calculated based on the X-ray Miller indices (220), (311), (222), (400), (422) and (440) whereas: where D is the average crystallite size, k is Scherrer's constant with a value of 0.94 for spherical crystals with cubic symmetry, λ is the wavelength of X-ray radiation, β is the full width at half-maximum and θ is the angle of diffraction. It can be observed that the crystallite size increases with increasing of Mn content as listed in Table 1.
The theoretical X-ray density (ρ x ) was estimated by means of Eq. (3) [24]: where M is molecular mass, N A is Avogadro's number, Z = 8 and signifies the number of molecules per spinel unit cell and a is the lattice constant. Table 1 lists variation of calculated theoretical density with Mn-content (x). The observed decrease in x with x is referred to the decrease in the molecular weight of prepared samples due to the difference in atomic weight and density of Mn and Cd.
The variation of distances between magnetic ions [hopping length of tetrahedral site (L A ) and hopping length of octahedral site (L B )] were calculated by applying Eqns. (4 and 5) [25]: Hoping lengths were found to decrease with increasing manganese content, see Table 1. This may be ascribed to the decrease in lattice parameter of all the samples by increasing Mn 2+ ions. XRD data may be used to determine the cation distribution in spinel ferrites using reflections (220), (440), and (400). In Cd 1 − x Mn x Fe 2 O 4 ferrites, ions of cadmium favor to inhabit the tetrahedral sites whereas ions of manganese favor octahedral sites [26]. However, ferric ions are expected to occupy both tetrahedral and octahedral positions [27]. Therefore, when a substantial number of Mn 2+ ions substitutes Cd 2+ , ferric ions are expected to migrate from octahedral sites into tetrahedral sites.

SEM and EDX Analysis
Surface morphological properties of the cadmium-manganese ferrite samples were investigated by using scanning electron microscopy (SEM). Figure 4a shows SEM micrographs of Cd 1 − x Mn x Fe 2 O 4 spinel ferrite samples with x = 0.0, 0.5 and 1.0. These Micrographs reveal that the samples contain nanoparticles agglomeration of uniform grains due to their mutual magnetic interactions and high surface energy. Also, SEM images shows an increase in particle size with increasing of Mn-content (x), Fig. 4b, which is in harmony with particle size calculations based on XRD analysis. The increasing of crystallite size may be attributed to the difference in ionic radii of Fe 2+ ions, Cd 2+ ions and Mn ions (0.80 Å) [22]. Figure 5 reveals energy-dispersive X-ray spectroscopy (EDX) charts of Cd 1 − x Mn x Fe 2 O 4 ferrites with x = 0.0, 0.5 and 1.0 samples. The undoped sample, x = 0, displays no trace of impurities or Mn element. As observed, increasing of Mn-content (x) is reflected in increasing of its intensity and real weight percent as tabulated in Table 2.  [28,29]. The band around 1636/cm is assigned to bending vibration of water molecules [30,31], whereas the band at 1377/cm to trapped nitrates in prepared ferrites [32]. The absorption bands in the range 400-750/ cm reflect the fundamental lattice vibrations of the crystal lattice. The bands in the range 560-590/cm and 468-477/cm are assigned to tetrahedral (ν t ) and octahedral (ν o ) stretching vibrations of metal ion and oxygen (M-O) complex.
The higher values of ν t as compared to ν o is referred to the short bond length of tetrahedral coordination as compared to octahedral one. The presence of these two fundamental peaks confirms the spinel structure of prepared ferrites [33] as revealed by XRD analysis. Figure 7 shows deconvolution of absorption spectra in the range 400-800/cm. For x = 0.0 (CdFe 2 O 4 ), the peak at 453/ cm is assigned to α-Fe 2 O 3 impurity phase [34,35], whereas ν t and ν o are observed at 560 and 477/cm, respectively. As observed, the increase in Mn-content (x) causes a decrease in the intensity of α-Fe 2 O 3 peak and vanished for x = 1.0 sample (MnFe 2 O 4 ) in consonance with XRD results. The observed shoulders of tetrahedral bands were clarified by deconvolution and ascribed to Jahn-Teller distortion due to bonding of oxygen ions with divalent Cd, Mn, and Fe ions [36]. Figure 8 depicts the variation of ν t and ν o with the increase in Mn-content (x). It has been reported [37,38] that the nonmagnetic divalent Cd 2+ ions prefers to occupy the tetrahedral sites and forces Fe ions to inhabit the octahedral sites forming normal CdFe 2 O 4 spinel ferrite for x = 0.0. As the magnetic divalent Mn 2+ increases with the increase in x; inverse spinel ferrites are developed with   [39]. Therefore, the decrease in Cd 2+ content upon the increase in x is compensated by the transfer of Fe 3+ ions from octahedral to tetrahedral sites. This resulted not only in the increase in ν t with the increase in x, but the decrease in ν o with the increase in x, as well. This could be attributed to the fact that the ionic radius of Fe 3+ is smaller than that of Cd 2+ which causes a decrease in Fe-O bond length and consequently a shift in ν t towards higher energy [40].
On the other hand, this migrated Fe 3+ ions from octahedral sites are replaced by Mn 2+ ions with ionic radius greater than that of Fe 3+ and consequently a shift towards lower energy is observed in ν o with the increase in Mn-content. Finally, the strong variation of ν t with x as compared to ν o could be attributed to the large difference between ionic radii of Fe 3+ and Cd 2+ as compared to that of Mn 2+ and Fe 3+ radii. Table 3 lists band positions of ν t and ν o stretching vibrations, corresponding force constants k t and k o and mean force constant k m . These force constants were  where M t and M o are molecular weights of tetrahedral and octahedral cations, respectively. The variation of force constants with Mn-content is listed in Table 3. It worth to mention that even though tetrahedral vibrations (ν t ) increased with the increase in x, the corresponding force constant k t decreased which is attributed to the large difference of molecular weight of Cd as compared to Mn and Fe. Therefore, the listed decrease in mean force constant k m upon replacing Cd ions by Mn ions (Table 3) suggests weakening of interatomic binding as a result of altering both bond lengths and molecular weight of these cations. Investigating elastic properties of ferrites is not only important for application purposes but enhances our understanding of the nature of interatomic and interionic forces in these material, as as well. The elastic constants of a material are of much importance in determination of its response/deformation to an applied force. Spinel ferrites are considered as homogenous and isotropic solids and identifying its reduced elastic constants are important for engineering applications. Since spinel ferrites are isotropic and homogenous materials with cubic symmetry, the components of elasticity tensor C 11 and C 12 are almost equal. The longitudinal elastic wave velocity (V l ), transverse elastic waves velocity (V t ), mean elastic wave velocity ( V m ), bulk modulus ( B), rigidity modulus (G), Young modulus (E), Poisson ratio (σ) and Debye temperature (θ D ) were calculated using the following relations (8,9,10,11,12,13,14,15,16) [41][42][43][44][45][46].
where k m is mean force constant, a is lattice parameter, x is x-ray density, h is Planck's constant, k B is Boltzmann's constant, N A is Avogadro's number and V A is mean atomic volume. Table 4 shows the calculated elastic parameters for different Mn-content. Longitudinal, transverse and mean elastic wave velocities ( V l , V t V m ) (Fig. 9), B, G, E (Fig. 10) and θ D

Magnetic Properties
Magnetic hysteresis loop displays the history of magnetization in magnetic materials and gives unique criteria for determining spin ordering. The M-H hysteresis loops of Cd 1-x Mn x Fe 2 O 4 samples (x = 0.0, 0.25, 0.5, 0.75, 1.0) are illustrated in Fig. 11. The magnetic properties such as saturation magnetization (M s ), magnetic moment (η B ), Coercivity (H c ), retentivity (M r ) and anisotropy constant (K) are given in Table 5. Saturation magnetization (M s ) was found to increase with increasing Mn 2+ content up to x = 1.0, as shown in Fig. 12. The increasing trend of M s might be ascribed to many factors. The first one is attributed to substitution of small magnetic moment of Cd 2+ (d 10 ) ions by large magnetic moment of Mn 2+ (d 5 ) ions [49]. The second factor is the particle size which was found to increase (see XRD and SEM analysis) with increasing of Mn-content. It can be clarified on the basis of changes in exchange   interactions between tetrahedral and octahedral sub-lattices [50,51]. For instance, sample with x = 1.0 with larger particle size showed higher M s as compared to other samples, see Table 1. Another important factor is the difference in saturation magnetization of specimens with variable Mn 2+ concentration (x) is largely determined by cation distribution and super-exchange process that occurs between Fe-ions and Mn-ions at tetrahedral (A) and octahedral (B) sites. Since the cation distribution revealed that Mn 2+ ions occupied the B-sites, some Fe ions from these sites migrates to A-sites upon the increase in Mn-content. As the concentration of Fe ions at A-sites grows; its magnetic moment rises and magnetic moment of B-sites declines. As a result, magnetization of the A sub-lattice decreases resulting in an increase in the net magnetization M = M B − M A . The coercivity (H c ) is the intensity of magnetic field necessary to decrease the magnetization of samples to zero. As seen in Fig. 12, the H c decreases with increasing of Mncontent; coercivity is inversely proportional to saturation magnetization as stated by Eqn. (17) [26]: where K is the anisotropy constant, μ B is the universal constant of permeability at free space and M s is the saturation magnetization.
Using the following relation (18) [52], the magnetic moment per formula unit in Bohr magnetron (B) was computed: where M w is the molecular weight of the sample and M s is the saturation magnetization in the electromagnetic unit. Table 5 shows the variation in magnetic moment with Mn concentration. Due to the increase in saturation magnetization, the magnetic moment of samples rises with Mn-content in Cd-Mn ferrites.

Dielectric and Electrical Investigations
The dielectric and electrical measurements of the samples Cd 1-x Mn x Fe 2 O 4 with x = 0.0, 0.25, 0.5, 0.75, 1.0 were carried out on a broad frequency range. Figure 13 represents the frequency dependence of dielectric constant of the asprepared Cd 1 − x Mn x Fe 2 O 4 ferrite nanoparticles. The figure reflects a superposition of polarization of the dipoles originated from the charge transfer among the di-valent and trivalent cations inside the spinel structure and the contribution of charge carriers' transport. Important information such as polarization mechanism and localized electric charge carriers in ferrites can be deduced from dielectric spectra. The frequency dependence of permittivity undergoes a gradual decrease throughout the frequency range in three distinguished trends. The first trend, a sharp decrease with frequency up to 100 Hz, followed by a warp-like behavior and then slow decrease accompanied by a collapse in all samples under investigation. The permittivity increases, generally, with the increase of Mn 2+ concentration. This is accompanied by a remarkable attenuation of the secondary phases however, the number of Fe 3+ ions at B-sites increases with the increase of grain size. Transport of Fe 3+ under the effect of the external electric field results in the growth of Fe 2+ ↔ Fe 3+ ion-pairs at B-sites and hence the interfacial polarization rises through the increase of grain size. Similar interpretation was discussed very recently by Dubey and Lahiri [53]. This confirms the tendency of ferromagnetic behavior to switch to paramagnetic as a result of Fe 3+ migration with the growth of grain size of Cd 1 − x Mn x Fe 2 O 4 ferrite nanoparticles. Additionally, at higher frequencies, exchange of electrons between Fe 2+ and Fe 3+ ions cannot follow the applied AC electric field reflecting in the attenuation of dielectric constant.
Similar behavior is noticed for the dielectric loss (ε′′), confirming the fact that both parts of the complex dielectric function (ε′ and ε′′) are not independent. The splitting out of the dielectric parameters of the different samples with sharp decrease as frequency increases is due to conductivity contribution. This confirms the governing equation that describes the relationship between the complex conductivity and dielectric functions.
The observed bend at the intermediate frequency range is attributed to the space-charge polarization at the grain boundaries. This generates a potential barrier, and therefore, the charge carriers accumulate at the grain boundary. The space charge polarization can be explained by Maxwell-Wagner-Siller (MWS-type) polarization processes usually found in inhomogeneous medium containing of conducting grains separated by grain boundaries of high electrical resistivity [54][55][56][57]. At the region of high-frequency, the space charge polarization consequence is decreased, and the hopping rate of charge carriers lags behind that of the applied electric field. This explains the close-in addition to the reduction-of ε′ values for all the five investigated samples. The extremely high values of ε′ and ε′′ at lower frequencies (typically 10 -5 -10 6 at 0.1 Hz) reflecting the high effect of dc-conductivity on the dielectric parameters as frequency decreases. This confirms the relationship between complex permittivity and conductivity as stated before.
The dependence of the real part of complex conductivity (σ′) on frequency for the as-prepared Cd 1 − x Mn x Fe 2 O 4 ferrites at room temperature is illustrated in Fig. 14. The frequency dependence of σ′ follows the following empirical Jonscher Eq. (19) [58], as was recently found in many conductive glasses as well as polymeric systems [57,59,60], At lower frequencies, the actual component of conductivity appears to be smaller or even develops a separate frequency trajectory. This plateau yields directly the dc-conductivity (σ dc ) and the characteristic frequency (ν c ) at which the dispersion of σ′ sets in and turns into a power law at higher frequencies. Three fitting parameters are illustrated graphically against Mn concentration in Fig. 15. It is obvious from the figure that, to some extent, ν c and σ dc behave in similar manner as a function of Mncontent. This can be explained by considering that the characteristic frequency is related directly to the reciprocal of the hopping time that characterizes the transport of charge carriers. Therefore, it is reasonable to observe a gradual increase of dc-conductivity with the characteristic frequency which confirms the well-known Barton-Nakajima-Namikawa (BNN) relation expressed as: where p is a numerical constant of order 1, o the permittivity of vacuum and ∆ε the relaxation strength. This can also be expressed as: dc ∼ c .
The inset of Fig. 15 depicts the Mn concentration dependence of the exponential parameter n. As seen, it decreases linearly as Mn concentration increases that explain why the curves became close to each other as the frequency increases.

Conclusion
Cd 1 − x Mn x Fe 2 O 4 spinel ferrite nanoparticles were prepared by using flash auto-combustion method. X-ray diffraction study confirmed the synthesis of the main cubic phase. The substitution of manganese caused a compression in the crystal lattice and an enlargement of the particle size. FTIR analysis showed the presence of the two fundamental tetrahedral and octahedral stretching vibrations of metal ion-oxygen bands in the range 560-590/cm and 468-477/cm, confirming spinel structure of prepared ferrites. The dependence of the fundamental vibrations on Mn-content was studied and explained in terms of Fe3+ ions migration from octahedral to tetrahedral sites. FTIR was employed to calculate wave velocities, elastic moduli and Debye temperature and their behavior with Mn concentration was examined. Magnetic measurements revealed an increase in both saturation magnetization and magnetic moment with increasing of Mn-content, whereas coercivity demonstrated an inverse dependence on x. The electrical properties was investigated over a broad range of frequencies from 10 -1 up to 10 7 Hz. The substitution of Cd by Mn resulted generally in remarkable increase of permittivity and electrical conductivity, especially at lower frequencies. The variation of electrical properties with Mn-content was explained in terms of variation in grain size and electron exchange between Fe 2+ and Fe 3+ ions. The frequency dependence of real part of complex conductivity was examined and its variation with hopping time at lower frequencies was investigated and found to agree with theoretical work.