Zn2+ substituted superparamagnetic MgFe2O4 spinel-ferrites: Investigations on structural and spin-interactions

Nano-magnetic ferrites with composition Mg1−xZnxFe2O4 (x = 0.3, 0.4, 0.5, 0.6, and 0.7) have been prepared by coprecipitation method. X-ray diffraction (XRD) studies showed that the lattice parameter was found to increase from 8.402 to 8.424 Å with Zn2+ ion content from 0.3 to 0.7. Fourier transform infrared (FTIR) spectra revealed two prominent peaks corresponding to tetrahedral and octahedral at around 560 and 430 cm−1 respectively that confirmed the spinel phase of the samples. Transmission electron microscopy (TEM) images showed that the particle size was noted to increase from 18 to 24 nm with an increase in Zn content from x = 0.3 to 0.7. The magnetic properties were studied by vibrating sample magnetometer (VSM) and electron paramagnetic resonance (EPR) which ascertained the superparamagnetic behavior of the samples and contribution of superexchange interactions. The maximum magnetization was found to vary from 23.80 to 32.78 emu/g that increased till x = 0.5 and decreased thereafter. Further, X-ray photoelectron spectroscopy (XPS) was employed to investigate the chemical composition and substantiate their oxidation states.


Introduction 
Nano-spinel ferrites have drawn considerable attention of researchers owing to their fascinating and noticeably distinguishing characteristics than their corresponding bulk part. They have a wide range of applications in diverse fields like memory storage devices, high-density magnetic recording discs, ferrofluids, magnetocaloric refrigeration, hyperthermia, drug delivery, and many other biomedical applications [1][2][3][4][5][6]. A cubic spinel ferrite, having a variety of applications like catalysis, humidity sensing, magnetic technology, and biomedicine [7,8]. Mg 1-x Zn x Fe 2 O 4 has been reported as a promising candidate for hyperthermia therapy in cancer treatment owing to their appropriate heating effects in response to the alternating magnetic field, chemical stability, biocompatibility, and superparamagnetic properties [9,10]. Moreover, magnesium and zinc are eco-friendly and nontoxic elements, and are essential vital elements found in the human body [11]. Liu et al. [12] synthesized Mg 1-x Zn x Fe 2 O 4 nanoparticles by coprecipitation method and studied their structural, magnetic, and thermal properties. They revealed that the AC magnetic field induced heating properties in these materials facilitates their application in hyperthermia treatment. Reyes-Rodríguez et al. [13] also developed Mg 1-x Zn x Fe 2 O 4 nanoparticles by sol-gel method and confirmed that nanoparticles can raise the temperature of medium up to 42 ℃ in 10 min. Kassabova-Zhetcheva et al. [14] studied the superparamagnetic properties of Mg x Zn 1−x Fe 2 O 4 and their potential application in hyperthermia treatment; however, their heating ability was not estimated. Mg 1-x Zn x Fe 2 O 4 is a high frequency soft magnetic ferrite which is simple and cost-effective. Besides, it is well known that as the substitution of zinc increases and Curie temperature decreases. So, many researchers have emphasized the need for a detailed study of nano-size Mg-Zn ferrites, their superparamagnetic behavior, and the spin-exchange interactions occurring in these materials by which we can well explain the compositional and size dependence of their structural and magnetic properties [15,16].
In the current communication, a detailed investigation has been carried out on the synthesis of superparamagnetic Mn 1-x Zn x Fe 2 O 4 ferrite nanoparticles (NPs) and their characterization for structural and magnetic properties. Their properties are well explained based on results obtained by using analytical techniques viz. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM), vibrating sample magnetometer (VSM), and electron paramagnetic resonance (EPR).

1 Synthesis
Mg 1-x Zn x Fe 2 O 4 (x = 0.3, 0.4, 0.5, 0.6, and 0.7) NPs were synthesized by co-precipitation method using chemical reagents of analytical grade (Sigma Aldrich). Stoichiometric ratio of Mg(NO 3 ) 2 ·6H 2 O, Zn(NO 3 ) 2 ·9H 2 O, and Fe(NO 3 ) 3 ·9H 2 O was mixed in distilled water individually to get a clear homogenous solution. These solutions were mixed and heated at 60 ℃ under constant stirring. Then, oleic acid was added dropwise to the solution to avoid atmospheric oxidation and agglomeration of particles. With constant heating at 80 ℃ and stirring, the analytical grade ammonia solution was added for the formation of precipitates until the pH was adjusted to 11-12. To transform hydroxides into ferrites, a constant temperature of 85 ℃ was maintained for approximately 1 h. They were then washed with distilled water several times and dried to get NPs.

2 Characterization
XRD measurements were carried out by Rigaku Ultima IV Powder XRD with Cu Kα radiations (λ = 1.5406 Å) in 2θ range of 20°-70° with scanning speed of 2 (º)/min. FTIR spectroscopy measurements were done using Perkin Elmer Frontier infrared spectrophotometer by KBr pallet technique in wavenumber range of 4000-400 cm -1 . Morphology, size, and shape of the samples were analyzed using a cryo-TEM Thermo Scientific Model Talos by dispersing the powder on carboncoated copper grids. Magnetic properties were investigated by employing Microsense EZ9 VSM at room temperature (RT) in the field range of ±10,000 G. Omicron X-ray photoelectron spectroscopy (XPS) was used to probe the electronic and chemical composition of the samples. EPR spectra were recorded at RT using Bruker Biospin Make, Model A300 at a frequency of 9.85 GHz and modulation frequency of 100 kHz.

1 XRD analysis
XRD pattern for Mg 1-x Zn x Fe 2 O 4 (0.3, 0.4, 0.5, 0.6, and 0.7) powder confirmed spinel cubic structure for all the samples as shown in Fig. 1. The major peaks corresponded to planes (220), (311), (400), (422), (511), and (440) that matched well with the JCPDS file 00-008-0234 [17]. The crystallite size (D) was calculated about the plane (311) corresponding to the peak having maximum intensity using the Scherrer's formula [18]: and experimental lattice parameter (a exp ) was evaluated using the following equation: where k = 0.9 is shape factor, d is interplanar spacing, λ is the wavelength of Cu Kα radiations (1.5406 Å), β and θ 311 are full width half maxima (FWHM) and Bragg's angle, respectively, corresponding to the plane (311). Table 1 shows the cation distribution, values of a exp and D for all the samples. It is seen that Zn 2+ ions exclusively occupy A sites, Mg 2+ predominantly occupy B sites, a few Mg 2+ ions migrate to A sites whereas Fe 3+ ions are distributed over A and B sites. The cation distribution given in Table 1 which is used for the theoretical calculations is obtained based on the Mossbauer study by Mohammed et al. [19] while the experimental calculations are made using the XRD pattern obtained in Fig. 1. It is observed that as Zn 2+ substitution increases from 0.3 to 0.7, a exp values increase from 8.402 to 8.424 Å. This can be explained based on cation radii of ions; Zn 2+ ions (0.74 Å) have larger ionic radii than Mg 2+ (0.66 Å) and Fe 3+ ions   [20,21]. Using the cation distribution given in Table 1, the average cationic radius at A (r A ) and B (r B ) sites can be given using Eqs. (3) and (4) where C A is ionic concentration for A site and C B for B sites, respectively, r Fe 3+ , r Mg 2+ , and r Zn 2+ are radii of Fe 3+ , Mg 2+ , and Zn 2+ ions, respectively. Table 2 shows that upon increasing the Zn content, r A and r B both increase which can be due to larger Zn 2+ replacing smaller Fe 3+ ions at A sites and Mg 2+ substituted by larger Fe 3+ ions at B sites as explained above. Theoretical lattice parameter (a th ) can be calculated by using an oxygen ion radius (R O = 1.32 Å) using Eq. (5) [23]: It is noted that both a exp and a th show an increasing trend with Zn concentration increasing. It is observed that a th shows a more linear trend with increasing Zn content. The difference in the values of a exp and a th can be due to the theoretical calculations considering a closely packed spinel structure. However, each lattice is distorted due to the larger size of cations compared to the tetrahedral and octahedral sites.
Oxygen positional parameter (U), which gives the qualitative measurement of displacement of oxygen It is observed from Table 2 that values of U and δ increase with substitution of Zn 2+ ions. In this case, as the x value increases, larger Zn 2+ ions occupy A sites and replace smaller Mg 2+ and Fe 3+ ions. This expansion in A sites leads to movement of adjacent oxygen ions, this leads to an increase in U. The deviation of U from U ideal is a measure of the effect of trigonal distortion at B sites due to the displacement of oxygen ions. So, an increase in deviation in the present case indicates increasing trigonal distortion at B sites.
Distance between cation-anion at A sites (R A ) and B sites (R B ) also known as bond lengths can be calculated using Eqs. (8) and (9) [25]: Table 3 shows the variation in values of bond lengths R A and R B with Zn substitution. It is noted that R A values increase while R B values decrease with increasing x. The observed variation can be due to the substitution process: The substitution of Zn 2+ ions with larger ionic radius causes expansion at A sites, and hence the R A increases. This displacement in oxygen ions away from A sites (towards B sites) results in shrinkage of B sites. Hence, R B decreases [19]. Further, values of R A are higher than R B which can be explained as the covalent bonding of Fe 3+ ions at B sites is more than at A sites. Hence, the results are in good agreement with the explanation that relates to the increase in covalent bonding with a decrease in bond length [26].
The tetrahedral edge length (R X ), shared octahedral edge length ( X R ), and unshared octahedral edge length ( X R ) are calculated using Eqs. (10)-(12) [19]:  It is clear that as Zn concentration increased, R X and X R values increased due to their dependence on lattice parameter. However, the decrease in X R values with x can be due to distortion of B sites symmetry as a result of variation in U that causes anions to come close to the edge and hence reducing the B shared edge length [27].
The distance between cation-anion (p, q, r, and s), cation-cation (b, c, d, e, and f), and the angle between them in spinel ferrites are shown in Fig. 2 and evaluated using Eqs. (13)-(21) [28]. Table 4 shows that all cation-anion and cationcation distances (except p) show an increasing trend with Zn doping as the values of these parameters depend on the experimental lattice parameter and oxygen positional parameter [19]. These interionic distances The variation in the values of bond angles with Zn 2+ ion content is shown in Table 5. The increasing angle values refer to the strengthening of corresponding cation-cation or cation-anion interaction decrease indicate weakening of the concerned interactions. It is observed that the angles θ 3 and θ 4 increased while θ 1 , θ 2 , and θ 5 decreased with increasing x in Mg 1-x Zn x Fe 2 O 4 (x = 0.3, 0.4, 0.5, 0.6, and 0.7) indicating strong A-B interactions, and weak B-B interactions, respectively [27].

2 FTIR spectroscopy analysis
FTIR is a remarkable spectroscopic technique that helps to estimate the formation of cubic spinel phase and probe the various functional groups present in the samples. Waldron [30] asserted that ferrites can be characterized by vibrational frequencies referred to as ν 1 , ν 2 , ν 3 , and ν 4 . Frequencies ν 1 and ν 2 correspond to the intrinsic stretching vibrations of Fe 3+ -O 2at A sites around 600-500 cm -1 and B sites 450-350 cm -1 , respectively. Moreover, ν 3 and ν 4 occur at small frequencies and attributed to the metal ions vibrations at A sites or B sites. Figure 3 shows the FTIR spectrum for Mg 1-x    where c is the speed of light (3×10 10 cm/s), ν is the vibrational frequency at A and B sites, and m is the reduced mass of Fe 3+ and O 2-(2.601×10 -23 g). Values of force constants K T and K O are summarized in Table 6. It is noted that K T values decrease with an increase in Zn content. This is understood as: If the substituted ion has a larger ionic radius than the replaced one then cation-oxygen bond lengths at that site increase and consequently force constant decreases. Since, lesser energy is required to break the longer bonds. On the other hand, K O values increase as Zn content increases due to the movement of O 2ions towards Fe 3+ ions at B sites as a result of charge imbalance caused by the migration of Fe 3+ ions from A sites to B sites. This movement leads to a decrease in bond length and hence, an increase in force constant K O [33]. The broad absorption band observed in the range of 3250-3591 cm -1 was assigned to the presence of adsorbed water on the surface of NPs [34,35]. Band at 2927 cm -1 refers to the presence of C-H stretching vibrations in all the samples due to the use of KBr while making pallets [36]. Bands at approximately 1696-1391 and 1091-826 cm -1 correspond to in-plane and out-plane of O-H vibrations, respectively [37]. Figure 4 shows the TEM images of Mg 1-x Zn x Fe 2 O 4 (x = 0.3, 0.5, and 0.7) NPs. It has been observed that most of the particles are spherical and agglomerated. Further, it is also noted that the particle size increases as 18, 22, and 24 nm with Zn concentration 0.3, 0.5, and 0.7, respectively, owing to the larger size of the Zn ions than replaced smaller Mg ions.  where MW is molecular weight, and 5585 is magnetic factor. It is observed that M Max value increases to x = 0.5 and then starts to decrease. The reason for such variation in M Max value can be due to the cation redistribution over A and B sites. In Mg 1-x Zn x Fe 2 O 4 , both Mg 2+ and Zn 2+ are diamagnetic and hence, non-magnetic. So, their net magnetization depends upon the distribution of Fe 3+ ions over A and B sites. The resultant magnetization for oppositely magnetized A and B sublattices is given by

4 VSM analysis
where M S stands for saturation magnetization, M B and M A denote the magnetic moments at A and B sites, respectively. MgFe 2 O 4 (x = 0) is an inverse spinel ferrite with Mg 2+ ions on B sites and Fe 3+ ions on A and B sites. However, there can be a possibility of a small number of "x" Mg 2+ ions migrating to A sites [39]. The cation distribution may be given as www.springer.com/journal/40145 where the curved brackets represent A sublattices and square bracket B sublattices, respectively. With the substitution of "y" Zn 2+ for Mg 2+ ions, where Zn 2+ ions have a strong preference for A site, Fe 3+ ions are pushed from A to B sites. This causes the magnetization of A sites to decrease due to a reduction in Fe 3+ ions and the magnetization of B site increases. Therefore, the net magnetization increases till x = 0.5. The cation distribution can be modified as Further, when the content of Zn 2+ increased more than x = 0.5, the net magnetization starts to decrease because then, the fewer Fe 3+ ions on A site are not anymore able to align the magnetic moments of ions on B site antiparallel to themselves due to negative B-B interactions [40].
In addition, S is a characteristic parameter for magnetic materials that determines whether intergrain exchange interaction exists between NPs or not. Stoner and Wohlfarth [41] asserted that S = 0.5 refers to non-interacting randomly oriented NPs whereas S < 0.5 to magnetostatic interaction between the particles. It can be clearly seen from Table 7 that S is less than 0.5 for all the compositions. The decrease in coercivity with Zn content can be attributed to the conversion of a single domain to multidomain as the particle size increases [17,42]. However, in parallel to the role of particle size, anisotropy also plays an important role in the value of coercivity and for the sample with x = 0.7, the shape anisotropy is higher, due to which these particles have higher values of coercivity [43].

5 EPR analysis
EPR is an outstanding spectroscopic technique to examine the dynamical magnetic properties at higher frequencies. Magnetic parameters like super-exchange interactions, magnetic anisotropy, spin-spin relaxation, and dipolar interactions govern the magnetic behavior  0.3, 0.4, 0.5, 0.6, and 0.7 of NPs which are in turn explained by studying the Lande's g-factor, resonance field (H r ), and linewidth (∆H PP ) [44][45][46]. The EPR spectrum measurements for Mg 1-x Zn x Fe 2 O 4 ferrite NPs were made at a constant microwave frequency of 9.8 GHz in the field range of 0-10,000 G at RT. Figure 6 shows the first derivate of intensity (I) versus field (H). It is observed that all samples exhibit a symmetrical broad single resonance signal indicating that Mg 2+ , Zn 2+ , and Fe 3+ ions coexist. The values of g-factor, relaxation time (T 2 ), and spin concentration ( S N ) have been calculated using H r and ∆H PP in the following Eqs. (34)-(37): where h is the Plank's constant (6.626 × 10 -34 J·s),  is the electromagnetic radiation frequency, B  is the Bohr magneton (9.27 × 10 -24 J/T)， and ΔH 1/2 is the linewidth corresponding to height half of absorption peak. Table 8 summarizes the estimated values of various EPR parameters. The g-factor values are observed to   Fig. 6. According to the equation modified by Schlomann [47,48], field contributing to the line broadening can arise from various factors such as anisotropy (H a ), porosity (H p ), eddy currents (H e ), and inhomogeneous demagnetization (H id ): Srivastava and Patin [49] also investigated the linewidth contribution from the aforementioned factors on Ni-Zn and Mg-Mn ferrites and noted that M S plays an important role in influencing the linewidth and H r . H r is a fundamental intrinsic property that depends on the internal field, which is further influenced by cation distribution, dipolar interactions, and superexchange interactions. Further, the variation in values of ∆H PP and g-factor is due to the influence of magnetic dipolar interactions and superexchange interactions between the particles. Since, the magnetization is noted to increase with Zn 2+ ions due to the strengthening of superexchange interactions between sublattices A and B via O 2ions. Consequently, the first term in Eq. (38) becomes very small, and the second term dominates. At x = 0.5, magnetization has the maximum value and hence, ∆H PP and g-factor are the maximum. On further increase of Zn substitution, M Max decreases, and anisotropy term dominates resulting in lowering of ∆H PP values. Priyadarshini et al. [35] reported a similar increase in linewidth with saturation magnetization for Ni-Zn ferrites. Moreover, the linewidth is also considered to be a measure of field inhomogeneity in the material, and a decrease in ∆H PP values after x = 0.5 can be due to the improved magnetic homogeneity in the particles [36,44]. Table 8 shows the experimental values of the magnetic moment (μ B ) and noted to increase with Zn substitution till x = 0.5. Thus, the addition of Zn 2+ ions causes strengthening of superexchange interactions that contribute to the enhancement in the internal field and consequently decrease in H r . Spin relaxation is a process of transfer of energy difference (∆E) to adjacent electrons and the variance of T 2 that determines the relaxation process and rate of absorption of energy [36]. T 2 for all the compositions is mentioned in Table 8 and plays a vital role in restricting the linewidth. Moreover, the trend of T 2 is observed to be inverse to that of ∆H PP .

6 XPS analysis
XPS is a versatile technique that is helpful in probing the elemental composition and their chemical/oxidation states. A survey scan of synthesized Mg 0.5 Zn 0.5 Fe 2 O 4 samples was obtained that confirmed the presence of Mg, Zn, Fe, and O species. High-resolution scan for Fe 2p, O 1s, Mg 2p, and Zn 2p was performed for further analysis (Table 9). Carbon correction has been done using binding energy (284.6 eV) of C 1s before examining the data.
Fe 2p spectra in Fig. 7 have been deconvolved in five peaks of Fe 2p 3/2 and Fe 2p 1/2 . Fe 2p 3/2 peak intensity is higher than that of Fe 2p 1/2 due to spin-orbit coupling (j-j). A satellite peak is present at 715.38 eV separating Fe 2p 3/2 and Fe 2p 1/2 peaks that confirm the  presence of Fe 3+ ions corroborating well with XRD results [50]. Deconvolution of Fe 2p 3/2 peak in Fe 3+ (B) and Fe 3+ (A) peaks revealed the existence of Fe 3+ ions at B and A sites respectively as a result of partial-inversion of the spinel structure [51,52]. O 1s spectra deconvolved in two peaks at 530.8 and 529.46 eV that show the contribution of oxygen in different environments. The peak at 529.46 eV appears due to metal-oxygen bonding and the peak at 530.8 eV can be ascribed to oxygen vacancies or metal-hydroxyl bonds at the surface. Mg 2p signal reveals that the spectrum is composed of two bands located at 49.3 and 54.5 eV. The peak at lower binding energy corresponds to Mg 2+ ions at A site that shows the presence of a very small fraction of Mg 2+ ions. The intense peak at 54.5 eV ascribed the presence of Mg 2+ ions at B site in a large amount. The fitting of Zn 2p spectra in two signals corresponds to Zn 2p 1/2 (1044.45 eV) and Zn 2p 3/2 (1021.39 eV). The spin-orbit splitting energy is found to be 23.06 eV which is in good agreement with some previous results [53,54].

Conclusions
Mg 1-x Zn x Fe 2 O 4 (x = 0.3, 0.4, 0.5, 0.6, and 0.7) NPs have been successfully synthesized by co-precipitation method. XRD analysis confirmed the spinel cubic structure for all the samples. Effects of Zn content on the various structural parameters like lattice parameter, crystallite size, bond length, and angle have been investigated based on the proposed cation distribution and compared with the theoretically predicted ones.
Lattice parameter was found to increase from 8.402 to 8.424 Å with the substitution of Zn 2+ ions owing to the larger ionic radius of Zn 2+ ions than Mg 2+ and Fe 3+ ions. FTIR studies revealed the stretching vibrational bands at A and B sites and their corresponding force constants. The observed behavior/trend was explained based on bond length (metal-oxygen) and charge imbalance at respective sites. TEM images showed that particle size increased from 18 to 24 nm with Zn substitution which corroborates well with XRD results. Magnetic studies by VSM revealed that the maximum magnetization and magnetic moment increases up to x = 0.5 and decreases thereafter with the addition of Zn 2+ ions. The values of H C and M R were observed to be negligibly small indicating the superparamagnetic behavior of the synthesized NPs. EPR spectra revealed that the variation in values of g-factor and ∆H PP was attributed to the contribution of superexchange and dipolar interactions and was found to match well with the VSM results. XPS analysis was used to study the chemical composition and their oxidation states.