Structural, optical and magnetic properties of nickel–copper ferrite NixCu1−x Fe 2O4

Nickel-copper ferrite nanoparticles NixCu1-x Fe2O4 with values x = 0.3, 0.5,0.7 fabricated by combustion method. X-ray diffraction (XRD) analyzes confirmed the formation of the ferrite structure. The average size of crystals was estimated to range from 39 to 44 nm. The particle morphology was detected and interpreted by the FSEM scanning microscope and the porosity characteristic of the ferrite structure based on the combustion method was observed. The FTIR analysis was performed to investigate the bonds in which the tensile vibrational mode of the tetrahedral site in the range of the wavelength of 500–600 cm−1.The magnetic properties of nanoparticles were investigated using VSM analysis and the effect of increasing of copper ion on MS saturation magnetization and HC coercivity force was investigated. With respect to the saturation magnetization values for the synthesized samples, it was observed that by increasing the Cu content from x = .3 to x = .5 the saturation magnetization decreased and then increasing with increasing Cu content such that at x = .5, we had the lowest saturation magnetism. Reduction of saturation magnetization Copper ions occupy ferric ions in tetrahedral sites and iron ions are transferred to octahedral sites. The results of UV–Vis indicate to complete absorption in the samples. The linearity of the edge of the absorption spectrum relates to a direct energy band gap and the effect of increasing copper ions on ferrite conductivity was investigated.


Introduction
Soft ferrite is widely used for many types of magnetic devices such as high frequency transformers, inductors, magnetic heads and microwave or high frequency absorber applications (Singh et al. 2016Kaur et al. 2019;Joshi et al. 2017;Nandotaria et al. 2018); because, they have higher electrical resistance compared to soft magnetic alloys. Various replacements have been taken into consideration in order to achieve the desirable electrical and magnetic properties. Useful range of ferrite frequency is limited to the beginning of resonance phenomenon within which permeability in critical frequency would be reduced. Therefore, information related to dependency of frequency to initial permeability is required. Many cases of research have been performed on magnetic spectrum of different types of ferrites within wide range of frequency (Rado et al. 1950;Rado 1953;Smit and Wijn 1954;Miles et al. 1957;Snoek 1948;Hoque et al. 2002;Yang et al. 2020;Narang and Arora 2019). Those groups of magnetic materials main component of which being ferric oxide and having ferrimagnetic properties are called ferrite; also, from among main characteristics of them can be made to desirable magnetic parameters such as magnetic permeability coefficient, saturated induction and high specific electrical resistance (about 1012 Ω). Ferrite nanocrystals doped with different divalent metals like chrome, copper, manganese, and zinc are highly used due to improvement made in some of their electrical properties (Gubbala et al. 2004;Saafan et al. 2010;Singhal and Chandra 2007); and, copper or zinc-substituted nickel ferrite shows more improvement as a soft magnetic material (Qiu et al. 2004).
Soft magnetic ferrites are usually produced through solid-state method due to simplicity of process (Mathew and Juang 2007); however, these methods are seriously limited in producing fine-grained powders in nano size (Patil et al. 2008). New methods like combustion synthesis have been developed to overcome above limitations. Glycine-nitrate process in which glycine is used as fuel and nitrate as an oxidant is a quick and low cost method done with few numbers of equipment so that homogeneous nanoparticles with high crystallinity percentage would be produced (Chick et al. 1990). Combustion method is based on combustion of an aqueous solution including desirable metallic salts (usually nitrates) and some amounts of organic fuels. Considerable aspect of combustion method concerns very good and homogeneous mixture of reaction components through usage made of one fuel and proper complexing agent (citric acid, urea, glycine, and etc.); and, using an aqueous solvent as a reaction intermediate, exothermic reaction between fuel and oxidant material will take place. In general, a good fuel has to react without being volatile; and, it has to produce non-toxic gases and be able to act as a complexing agent for metal cations (Chikazumi 2009).
Instability factors of Nano-ferrites are affected by interplay of their crystal and magnetic structures. Studying the behavior and above inter-mutual properties shows high sensitivity to fabrication method of magnetic nanoparticles and their size in nano-scale magnetic fields. In the research and after making nickel-copper ferrites (Ni x Cu 1x Fe 2 O 4 ) through combustion method with different weight percentages; their structural, optical and magnetic properties have been studied. In Sect. 2, the experiment method is presented, followed by the results and analyses in Sect. 3. and glycine (C 2 H 5 NO 2 ), all of which purchased from Merck Co. have been used. Required amounts of zinc, copper, and iron nitrates have been weighted by gravimetric calculations, using digital scale; then, they have been poured in the beaker. Considering selection of fuel ratio to nitrate being equal to 0.5, glycine amount has been calculated and weighted; then, it has been poured in the beaker. Proper amount of water (40 cc) has been poured in the beaker; then, the beaker containing these materials has been put Page 3 of 13 697 on heater. Primarily water inside the beaker has been vaporized and after almost 25 min averagely calculated for three samples, spontaneous combustion has been occurred. Within a few seconds, a dark brown porous fragile material would be produced which is the same ferrite concerned. Images related to the aforementioned spontaneous combustion and fabricated ferrite is presented in Fig. 1. High gas pressure at time of exit causes porosity to be created; so, final product includes micro particles with very low particle accumulation. This lack of accumulation will lead to large site occupied by particles. Therefore, using mortar we make particles to occupy less space.

Experiment method
In gravimetric calculations, molar mass of each of these chemical compounds has been used. To fabricate nickel-copper ferrite, 2 to 1 relationship of iron nitrate and total amounts of nickel and copper nitrates have been dissolved in distilled water with consideration of molar mass of each as well as x value. In order for prepared material to be enough for various tests, 0.2 mol of Iron nitrate (4.04gr) and 0.01 mol nickel and copper nitrate (0.532gr) have been considered; while, nickel and copper amounts have been weighted with consideration of x value. That is 0.02 × 3 + 0.01 × 2 = 0.08 mol nitrate. Considering glycine-nitrate ratio (G/N = 0.5), glycine weight has been calculated; and, 0.04 mol glycine would be equal to 3.0028gr. For example, in preparing Ni .7 Cu .3 Fe 2 O 4 and with consideration of the method explained, 0.007 mol nickel nitrate, 0.003 mol copper nitrate and 0.02 mol iron nitrate have been weighted and poured into the beaker.
X-ray diffraction pattern of samples has been analyzed by Philips X-ray diffractometer under radiation of CuKα on 1.54 A° wavelength. Morphological study of powders has been performed through FESEM images (Hitachi S4160). Magnetic properties have been studied by VSM device under 25 Hz frequency. FTIR analysis has been performed by infrared spectroscopy (VERTEX 70) and UV-Vis spectroscopy has been done by double beam spectrophotometry (Hitachi U-3501).

Results and analyses
To study phases available in nanopowder fabricated from samples, XRD analysis within the range of 10-85° has been used. Figure 2 shows that clear peaks of X-ray diffraction corresponding to main reflection planes (220), (311), (400), (422), (511), and (440) are indicative of cubic spinel structure with Fd3m site group; and, availability of lattice sub planes (331), (222), and (111) is well matched with cubic spinel JCPDS diffraction file( JCPDS card number:74-2399). Also, XRD analysis shows that main phase formed in the samples is Ferrite phase and line broadening shows nanometric structure of samples. Using Scherrer equation: and peak (311), average size of crystallites(D) can be estimated, where, radiated wavelength is 1.54 Å (Cu-Kα radiation), 1∕2 is half of the peak width (rad) and is diffraction angel. With consideration of peaks (511) and (440) and using distance of planes as well as corresponding (hkl) Miller indices, lattice constant will be obtained from following equation: Considering the point that upon increase, error in the lattice constant would be reduced, mean of the two lattice constants related to bigger angels has been obtained; and, the related results are provided in Table.1. According to the values provided in the table, it is observed that lattice constants related to three samples of synthesized nickel-copper ferrites which can be considered as copper doped nickel ferrite are compatible with values of nickel and copper ferrites lattice constants provided in the reference (Chavana et al. 2010).
(1) In the table, crystallite size, lattice constant, lattice strain, and percentage of crystallization are reported as well.
Size of obtained particles with consideration of XRD results are from 39 to 44 nm. So, formation of nanoparticles with size of particles or crystallites is confirmed. It is also shown in Table.1 that increase of copper ion and decrease of nickel ion would be resulted in changes and contrast between particle size and magnetic energy. In second sample, balance would be made between the above changes so that order and stability of structure would be resulted in it. In second sample, maximum crystallite size is observed; and, observing the column strain values cited in it, lowest lattice strain value is also related to the second sample. This is correct and confirmed with consideration of inverse dependence between strain and crystallite size. Considering V = a 3 (V is volume and a is lattice constant) the sample with lower volume is more stable; and, this is consistent with previous analyses performed in relation to the second sample. In general, it can be suggested that higher order in the lattice is related to higher crystallite size and lower lattice constant observed in the second sample. Upon increase of copper, lattice constant would be increased which can be related to Ni 2+ (0.69 Å) having smaller radius being replaced with Cu 2+ (0.72 Å) ions with bigger radius. This is consistent with references (Jadhav et al. 2009;Dionne 1970;Dimri et al. 2006;Zaki 2012). Also upon increase of Cu in the samples, it is observed that XRD angles of diffraction peak (311) will show tendency towards lower values which can be due to the point that in increasing trend, Cu value in lattice constant would be also increased. The reason is that, changes in particle size and magnetic energy which is observed upon Cu increase here will lead to replacement of particles and changes of angles. High crystallinity of samples is indicative of structural durability and stability of samples.
To study size, shape of particles and distribution of synthesized particles, FESEM (field emission scanning electron microscope) has been applied. The images in Fig. 3 show that the clusters are composed of fine particles. As far as no distributor has been used; formation of agglomeration is due to magnetic interaction and high reactivity expected in nanoparticles. This characteristic has been observed in all of the nanoparticles (Upadhyay et al. 2004). Samples on the surface are highly porous which can be attributed to quick exit of high volume of gases produced during combustion. Availability of porous lattice is one of characteristics of producing nanoparticles by combustion method. This porosity can be observed in nano and also bulk scales respectively with consideration of left and right images in Fig. 3. Particle size with consideration of images is within 30-60 nm range which is consistent with the results from crystallites in XRD analysis (Table.1). FTIR transmission spectra are shown in Fig. 4 to study chemical bonds and to specify type of functional groups available in the compound. The bands in wavenumber about 548-560 cm −1 are related to vibrating-stretching mode of Fe ions located in tetrahedral site of the lattice with oxygen. Absorption band about 400-500 cm −1 is related to stretching fluctuation of Fe in octahedral site which cannot be observed due to device limitations; and, this is indicative of spinel phase formed in nickel-copper ferrite. Stretching/bending fluctuation mode of nitrate group NO 3 − within the wavenumber range of 1380 cm −1 and also within the wavenumber range of 1569-1653 cm −1 is related to carboxyl group COO − ; and, within the wavenumber range of 2331-2348 cm −1 and 3410-3446 cm −1 , it is related to bond stretching of water molecule as well as fluctuations of hydroxyl functional group (O-H) (Yan et al. 2008;Tawfik and Hemeda 2002;Raghavender et al. 2011). Changes of wavenumber of sites are dependent on cationic mass related to oxygen-cation distance and bonding force between magnetic ions located in sub lattices. Considering changes of  Table.1, increase of copper ion in compound will lead to wavenumber displacement towards lower frequencies. Since changes of wavenumber has inverse relation with bond length; through increase of unit cell and bond length of Fe 3+ -O 2− in tetrahedral sites, displacement towards less wavenumbers can be justified (Singh et al. 2011).For magnetization measurement of samples at room temperature, an AGFM device (maximum 10kOe) has been used.
The hysteresis loop of samples at room temperature have been shown in Fig. 5. The saturation magnetization values of the samples were determined by fitting the high-field ( 1 H → 0) data using the following function (Abouzir et al. 2020): where is a fitting constant and H is the applied magnetic field. Also, changes of coercivity(H c ), retentivity(M r ) and saturation magnetization(M s ) with changes in copper substitution amount in ferrite nanoparticles are provided in Table.2. Based on theory of Neel ferrimagnetism in spinel structure, cations are located in two different tetrahedral (A) and octahedral (B) sub lattices; and, magnetic moments of ions in each sub lattice are in parallel orientation; while, they are antiparallel in relation to each other. Considering the theory and knowing that magnetic moments of Fe +3 , Ni +2 , and Cu +2 are respectively equal to 7.1, 5, and 3.2 μs (Raghavender et al. 2011), magnetic behavior of samples can be justified. One the hand, Ni +2 has strong dependence on octahedral site B and usually occupies the site. Cu +2 also prefers octahedral site; however, tetrahedral site A is shown to be occupied by it. Fe +3 also exists in both sites (Azadmanjiri et al. 2007). Considering values cited in saturated magnetization column in Table.2 for synthesized samples it is seen that when Cu increase from x = 0.3 to x = 0.5, saturated magnetization would be reduced. In continuation, through increase of Cu, the value would be increased i.e. in x = 0.5 minimum the saturated magnetization will be observed. In relation to reduction of saturated magnetization from x = 0.3 to 0.5 it can be suggested that upon increase of Cu, Cu +2 ions in tetrahedral sites A will be substituted Fe +3 ions. This way, Fe +3 ions will go from tetrahedral site A to octahedral site. Therefore, magnetic moment in site A as well as superexchange interaction between two sub lattices A and B would be reduced, reaching its minimum value in x = 0.5. Also, due to concentration increase in Fe +3 in octahedral sites B, number of Fe +3 and Fe +2 pairs will be increased which by itself will lead to anion vacancies in the lattice. These vacancies will lead to reduction of superexchange interaction and reduction of saturated magnetization, as a result. As for the samples, saturated magnetization will be increased from x = 0.5 to 0.7. This way, it can be suggested that in ferrites and through increase of one ion with lower magnet in one position, spin canting in opposite position will be created (Dionne 1970). Considering reduction of magnetic moment of tetrahedral site A, due to increase of copper ion in this position and transfer of Fe +3 to octahedral site B, spin canting will happen. That is, spins in position A can no longer keep spins in position B powerfully in antiparallel form. As a result, moments in both sites will be no more parallel  and spin canting will be observed in site B. Therefore, magnetization B will be reduced and considering the point that total saturated magnetization will be resulted from difference of saturated magnetization of octahedral site B and tetrahedral site A (Dimri et al. 2006), total saturated magnetization will be increased upon reduction of saturated magnetization. When particle size changes to nanoscale, cation distribution in both A and B positions would be changed as well. There are several of superexchange interactions among positions A and B including J AA , J BB , and J AB . Competition between these interactions is determinant of magnetization level of material. When particle size becomes close to nanoscale, quantum tunneling, cation redistribution and surface spin canting will be effective on physical characteristics of ferrite more than ever. In addition, grain size affected the value of saturation magnetization and coercivity. By comparing the results obtained from Tables 1 and 2 in samples between grain size, saturation magnetization and coercivity, it becomes clear that the M s and M c values were found to increase in single-domain grains until it reaches a maximum value and inversely proportional to the grain size for multi-domain grains. The behavior of these two quantities is consistent with the results published in the reference (Hajalilou & Mazlan 2016;Cherigui et al. 2008).
Comparing bulk and nano scales, when particle size becomes close to nanoscale, surface spin canting will lead to reduction of saturated magnetization in the samples. Also, disordered nanoparticle spins on surface prevent more internal spins to be oriented completely; and, they will lead to reduction of saturated magnetization in nanoparticles. On the other hand, when particle size is reduced, number of domains will be reduced to a certain size in which the particle has been created only from one domain. Upon reduction particle size, coercive force in material will be increased to its maximum value; because, force required for change of spin orientation in single domain is much bigger than that required for movement of walls. Coercive force is affected by different factors such as defects, surface effects, pressures, non-magnetic atoms, and etc. On the other hand, growth of particles and substitution of less magnetic copper ion with iron in the compound will lead to reduction of interaction between magnetic particles as well as reduction of resistance in domains walls. Therefore, coercive force will be reduced (Zaki 2012;Upadhyay et al. 2004).
UV-Vis absorbance spectra and absorbance coefficient of ferrite nanoparticles with three different weight percentages are shown in Fig. 6. As observed, the optical absorbance which shows complete absorption at low wavelengths in samples. Sudden change Fig. 6 a Optical absorbance UV of samples, b absorbance coefficient of samples in one certain wavelength confirms presence of energy band; and, as far as the graph is linear at absorption limit, energy gap is direct (Cherigui et al. 2008).
Direct and indirect optical gap can be calculated through Eq. 4, where, hν is photon energy, E g is gap energy, n depends on nature of transfer and theoretically is equal to 1 and 1/2. α 0 is a fixed absorbance coefficient resulted from analysis of UV-Vis absorbance spectra. It has to be noted that absorbance coefficient and absorbance are linear proportionate and different in one constant value.
Considering Eq. 5, ( ( ) h ) 1∕n ∕h will be drawn based on hν and in accordance with the results from UV-Vis spectra, graph of which is provided in Fig. 6b.
Then Eq. 5 will be equalized to zero and/or the intercept to the tangent line of linear part of graph with horizontal axis will be obtained as values of gap energy. Values of direct gap energy n = 1/2 for nickel-copper ferrite particles with 0.7, 0.5, and 0.3 Percentages are respectively equal to 4.12, 3.91, and 3.60 eV. Values of gap energy are affected by different factors such as crystallite size, structural parameters, and presence of impurity. It is observed that upon increase of Cu, gap energy would be reduced. As referred to before, Ni +2 is highly dependent on site of octahedral B and usually occupies the position. Upon increase of Cu, Cu +2 ions will substitute Fe +3 ions in tetrahedral A site. Fe +3 ions will go from site of tetrahedral A to site of octahedral B. This will lead to increase of Fe +3 concentration in site B. As a result; while, numbers of Fe +3 and Fe +2 pairs will be increased which by itself causes creation of anion vacancies in the lattice. Conduction mechanism in ferrite is considerably affected by transfer of electron holes between Fe +3 and Fe +2 at octahedral B site. Here, it is observed that upon increase of Cu, gap energy would be reduced i.e. conduction will be increased.

Conclusions
Ferrite nanoparticles Ni x Cu 1-x Fe 2 O 4 (x = 0.3,0.5, 0.7) were fabricated by combustion method with glycine fuel. Presence of clear X-ray diffraction peaks corresponding to the main reflection planes in XRD patterns of samples confirmed the formation of nanoparticle with cubic spinel structure. The formation of ferrite phase based on FTIR results related to presence vibration mode Fe ions located at lattice tetrahedral site with Oxygen is also verifiable. Combustion materials are very porous and therefore have a large surface area, which can be clearly seen in FESEM images, which is due to the release of large volumes of gases during the process. The results of calculating the particle size synthesized using both SEM and XRD analysis are in agreement with each other. The results of VSM show that the magnetic behavior of nanoparticles depends on the effect of increasing copper ions and decreasing the amount of nickel. By increasing the value of Cu from x = 0.3 to x = 0.5, the amount of saturation magnetization decreases and then with increasing the amount of Cu, this value increases so that at x = 0 0.5 we see the lowest saturation magnetization. These changes were explained by the placement of copper and nickel ions in the tetrahedral and octahedral sites and in terms of the exchange interactions between the sites and also the spin canting. The direct gap energy was calculated using the UV result. The rate of (4) ( ) = 0 (h − E g ) n ∕h (5) ( ( ) h ) 1∕n = 0 (h − E g ) copper dopant on conduction was studied so that the energy gap increases, the conduction decreases by increasing the amount of copper which is well compatible with the conduction mechanism.