The series of five nanoferrites Cu_XCo_1-XFe₂O₄ (X = 0, 0.25, 0.5, 0.75, 1) has been synthesized by the sol-gel self-combustion route [1Mishra, S.; Karak, N.; Kundu, T.K.; Das, D.; Maity, N.; Chkravorty, D. Nanocrystalline nickel ferrites prepared by doping with niobium ions. Mater. Lett., 2006, 60, 1111-1115.
[http://dx.doi.org/10.1016/j.matlet.2005.10.085] ] using suitable stoichiometric amounts of the following starting reactants: Fe(NO₃)₃.9H₂O(Sigma Aldrich, 98%), Cu(NO₃)₂.6H₂O(Sigma Aldrich, 98%), Co(NO₃)₂.6H₂O(Sigma Aldrich, 99%) and citric acid(C₆H₈O₇, Sigma Aldrich, 99.5%), which have been dissolved in a minimum quantity of distilled water under magnetic stirring. Citric acid was taken in a 1:1 molar ratio to the metal cations and has also been used as a chelating agent and auto combustion fuel.

The obtained aqueous solutions of each explored composition X were heated at 80 °C under stirring, and at the same time, the pH was adjusted to 7 with an appropriate amount of concentrated ammonia solution leading to the formation of viscous black gels. The gels were slowly dried again by increasing the temperature to below 250 °C until reaching their corresponding autocombustion temperatures at which the dried gels ignited to form fractal loose precursor powders, which were slightly ground and then calcined at 900 °C for 2 hours leading to the formation of the five synthesized nanoferrites which are as follows:

S1M1(X = 0): (CoFe₂O₄);

S1M2(X = 0.25): (Cu_0.25Co_0.75Fe₂O₄);

S1M3(X = 0.5): (Cu_0.5Co_0.5Fe₂O₄);

S1M4(X = 0.75): (Cu_0.75Co_0.25Fe₂O₄);

S1M5(X = 1): (CuFe₂O₄).

The structural characterizations by X-ray powder diffraction of the five calcined autocombusted powders at 900 °C during 2 h have been performed at 25 °C by using Philips X’Pert X-ray powder diffractometer (PANalytical, France), operating at the wavelength Cu-Kα radiation in the 2θ diffraction angle range 10-99 ° with the scan step of 0.02 ° and the counting time of 0.16 s. The Fourier transform infrared spectra for recording data were determined using NICOLET IR 200 FTIR spectrometer (Thermo Fisher Scientific, France), in the field of sweeping range 400-4000 cm^-1. The surface morphology and elemental composition analysis of the five studied nanoferrites have been analyzed by using MERLIN field emission scanning electron microscopy (Carl-Zeiss, France), coupled to the energy-dispersive X-ray spectroscopy, with a high resolution (0.8 nm and 1.4 nm at 15 kV and 1 kV, respectively). The electrical conductivity properties have been studied by complex impedance spectroscopy using the SI 1260 Impedance/Gain-Phase analyzer (Solartron Analytical, UK), with data acquisition frequency range of 10 Hz-32 MHz at intervals of 10 points per decade and under 100 mV applied voltage. The vacuum evaporation technique has been used for the gold electrode deposition on the two faces of each cylindrical pellet with a diameter of 13 mm, obtained by uniaxial compaction at a pressure of 120 MPa and sintered at 1173 K for 24 h. The electrical measurements have been carried out in the temperature range of 293-373 K with a 20 K increment. The magnetic measurement recording of both hysteresis loops, at 10 and 300 K, and ZFC-FC magnetization curves, in the temperature range of 10-300 K and under 500 Oe applied magnetic field, was performed by using MPMS SQUID magnetometer (Quantum Design, UK).

The five recorded X-ray powder diffractograms of the synthesized ferrites, Fig. (1), have similar profiles and clearly show only the single-phase corresponding to the five explored copper substituted cobalt ferrite nanoparticles: S1M1(X = 0.0); S1M2(X = 0.25); S1M3(X=0.5), S1M4(X=0.75) and S1M5(X=1). Indeed, the XRPD patterns have been indexed on the basis of the spinel face-centered cubic system with Fd3-m space group according to the JCPDS card file N° 00-022-1086 of CoFe₂O₄ and without any detection of additional phase peaks such as: CuO(JCPDS N° 99-200-4198, 99-200-3986); CoO(JCPDS N° 99-101-0211); FeO(JCPDS N° 99-200-3990, 99-200-3961, 99-200-2015); CuFeO₂(JCPDS N°99-200-2901, 99-100-0016) or Fe₂O₃(JCPDS N° 99-200-4059, 99-200-4032,99-200-2092, 99-200-0140). Consequently, the derived results from the XRPD acquisition data confirmed well that the five compositions are formed by a pure poly oriented nanocrystal with a single phase cubic spinel structure and suggested that the basic lattice stability of the five elaborated spinel ferrite nanoparticles did not chang during the substitution process of cobalt by copper within the parent cobalt ferrite basic structure when X composition increased from 0 to 1 [15Raju, K.; Venkataiah, G.; Yoon, D.H. Effect of Zn substitution on the structural and magnetic properties of Ni–Co ferrites. Ceram. Int., 2014, 40, 9337-9344.
[http://dx.doi.org/10.1016/j.ceramint.2014.01.157] ]. Moreover, the lattice parameter determinations were performed by the least square fit refinement program, CELREFF [16Altermatt, U.D.; Brown, I.D. A real-space computer-based symmetry algebra. Acta Crystallogr. A, 1987, 34, 125.
[http://dx.doi.org/10.1107/S0108767387099756] ], using the hkl and 2θ(°) values derived from the XRPD acquisition data.The crystallographic parameters of the unit cell of the five studied nanoferrites are listed in Table 1 .

Fig. (1) XRP diffractograms of nanoferrites S1M1-5.

Table 1
Refined lattice parameters and crystallite size calculations of nanoferrites S1M1-5

In addition, during the substitution procedure, the increase of Cu content from 0 to 1 caused a slight displacement of XRPD peaks toward lower 2θ diffraction angles compared to those of the parent ferrite CoFe₂O₄. In particular, as clearly shown in the upper right inset of Fig. (1), the observed 2θ low shift, from 2θ[CoFe₂O₄(X=0)] = 35.49 ° to 2θ[CuFe₂O₄(X=1)] = 35.42 °, in case of the Bragg reflection (1 1 3), is due to the slight increase in the unit cell parameter, from a[CoFe₂O₄] = 8.389(3) Ǻ to a[CuFe₂O₄] = 8.405(5) Ǻ, Table 1 , which is induced by the low difference between cationic radius values of cobalt and copper: r(Co²⁺) = 0.72 Ǻ; r(Cu²⁺) = 0.73 Ǻ.

Moreover, the crystallite size value D was calculated using Scherrer equation [17Liu, C.; Rondinone, A.J.; Zhang, Z.J. Synthesis of magnetic spinel ferrite CoFe₂O₄ nanoparticles from ferric salt and characterization of the size-dependent superparamagnetic properties. Pure Appl. Chem., 2000, 72, 37-45.
[http://dx.doi.org/10.1351/pac200072010037] ]:

Where λ is the wavelength of the CuKα (1.54187 Å), ∆(2θ) is the full width at the half maximum (FWHM) of the (1 1 3) diffraction peak in radian, and θ is the Bragg's angle.

The crystallite size calculation values illustrated in Table 1 , prove well the nanocrystallinity of the five explored ferrites and seem to be increased with X composition from D_XRPD[CoFe₂O₄] = 19.96 nm to D_XRPD[CuFe₂O₄]= 24.94 nm.

On the other hand, in case of Cu_XCo_1-XFe₂O₄ (X = 0, 0.3, 0.5, 0.7, 1) series, a similar work synthesized by the coprecipitation technique [13Samavati, A.; Ismail, A.F. Antibacterial properties of copper-substituted cobalt ferrite nanoparticles synthesized by co-precipitation method. Particuology, 2017, 30, 158-163.
[http://dx.doi.org/10.1016/j.partic.2016.06.003] ], the investigators mentioned that during the substitution process, when X copper content increased from 0 to 1, both the calculated unit cell parameter and the estimated crystallite size via Scherrer equation decreased mutually as follows: from a[CoFe₂O₄(X =0)] = 8.354(2) Ǻ to a[CuFe₂O₄(X =1)] = 8.311(2) Ǻ and from D[CoFe₂O₄] = 30 nm to D[CuFe₂O₄] = 18 nm, respectively. This declared that the slow linear decreasing trend in the unit cell parameters is attributed to the replacement of the larger ionic radius of Co²⁺ by the smaller ionic radius of Cu²⁺ in the host system. Moreover, the latest rendition seems to be in contradiction with the ionic radius values of Co²⁺(0.70 Å) and Cu²⁺(0.73Å), cited previously in the same work [13Samavati, A.; Ismail, A.F. Antibacterial properties of copper-substituted cobalt ferrite nanoparticles synthesized by co-precipitation method. Particuology, 2017, 30, 158-163.
[http://dx.doi.org/10.1016/j.partic.2016.06.003] ], because logically, the refined lattice parameter value should increase with X Cu²⁺ content increase, which has the larger cationic radius compared to that of Co²⁺ cation and consequently, such interpretation is in coherence with the XRPD results reported herein.

In order to further investigate the crystal structure, vibrational FTIR spectroscopy measurements have been performed. However, the FTIR spectra of the five studied nanoferrites, Fig. (2), show the presence of two main absorption bands centered at the following frequency values: 410 cm^-1 and 595 cm^-1, characteristic of the typical vibrational modes of monophasic cubic spinel structure and thus can be attributed to the intrinsic vibration modes of octahedral (16d special position) and tetrahedral (8a special position) sites, respectively within the ferrite crystal network [18Labde, B.; Sable, M.C.; Shamkuwar, N. Structural and infra-red studies of Ni_1+xPb_xFe_2−2xO₄ system. Mater. Lett., 2003, 57, 1651-1655.
[http://dx.doi.org/10.1016/S0167-577X(02)01046-7] , 19Waldron, R.D. Infrared spectra of ferrites. Phys. Rev., 1955, 99, 1727-1735.
[http://dx.doi.org/10.1103/PhysRev.99.1727] ]. Moreover, the average values of these previous two absorption bands are coherent with those reported in a similar work using the coprecipitation method as the synthesis technique [13Samavati, A.; Ismail, A.F. Antibacterial properties of copper-substituted cobalt ferrite nanoparticles synthesized by co-precipitation method. Particuology, 2017, 30, 158-163.
[http://dx.doi.org/10.1016/j.partic.2016.06.003] -19Waldron, R.D. Infrared spectra of ferrites. Phys. Rev., 1955, 99, 1727-1735.
[http://dx.doi.org/10.1103/PhysRev.99.1727] ]. In addition, it can be deduced that the FTIR study results are in good agreement with those of XRPD, which confirm well that the five synthesized nanoferrites are pure single phases with cubic spinel crystal network.

The FESEM micrographs Fig. (3) have allowed to conclude that the observed morphologies of the five explored nanoferrites are roughly similar and are composed of a uniform grain size distribution with angular shapes, correlating the one observed in the CoFe₂O₄ FESEM micrograph [20Sanpo, N.; Berndt, C.C.; Wen, C.; Wang, J. Transition metal-substituted cobalt ferrite nanoparticles for biomedical applications. Acta Biomater., 2013, 9(3), 5830-5837.
[http://dx.doi.org/10.1016/j.actbio.2012.10.037] [PMID: 23137676] ]. The average grain sizes vary between D_FESEM(S1M1) = 22.05 nm and D_FESEM(S1M5) = 27.17 nm, whose values seem to be relatively higher than those calculated by Scherrer equation, D_XRPD, and Langevin function fitting, D_LFF, using XRPD and SQUID magnetic data, respectively. However, the presence of dead magnetic layers on the particle surfaces within the five studied nanostructures could explain the origin of the observed grain size difference between D_FESEM and D_LFF [21Dhiman, M.; Singhal, S. Enhanced catalytic properties of rare-earth substituted cobalt ferritesfabricated by sol-gel auto-combustion route. Mater. Today: Proceedings, 2019, 14, 435-444.]. Moreover, as shown in the lower-left inset of Fig. (3) (S1M1 and S1M5), the EDX spectra of elementary qualitative analysis indicate the presence of constituent elements of CoFe₂O₄ and CuFe₂O₄, respectively. The analysis results of elemental compositions of the five Cu-substituted cobalt ferrite nanoparticles listed in Table 2 are in good agreement with the nominal formula of each nanoferrite.

In addition, the information derived from the XRPD, FTIR and FESEM-EDX data allow concluding that the used sol-gel autocombusted process is the promising synthesis technique which leads to the elaboration of pure fine powders and the cubic spinel basic host lattice has been integrally preserved during the substitution procedure which is due to the slight cationic radius difference between Cu²⁺ and Co²⁺.

Table 2
EDX elemental composition of nanoferrites S1M1-5.

Fig. (2) FTIR spectra of nanoferrites S1M1-5.

Fig. (3) FESEM micrographs of nanoferrites S1M1-5.

The Nyquist diagrams of the five explored copper substituted cobalt ferrites, in the temperature range 293-373 K, have similar profiles. As shown in Fig. (4a) the presence of a single semicircular arc in the recorded impedance diagram of CoFe₂O₄[X=0] is an indication that the electrical conduction behavior is mainly due to the corresponding bulk resistance with the absence of the grain boundary effect [20Sanpo, N.; Berndt, C.C.; Wen, C.; Wang, J. Transition metal-substituted cobalt ferrite nanoparticles for biomedical applications. Acta Biomater., 2013, 9(3), 5830-5837.
[http://dx.doi.org/10.1016/j.actbio.2012.10.037] [PMID: 23137676] -22Macdonald, J.R. Impedance Spectroscopy-Emphasizing Solid Materials and Synthesis., (3rd ed. ), 1987, ]. However, in this case, the direct current conductivity value has been calculated by the following equation: , where E and S are the thickness and the surface of the used pellet respectively, R_DC is the bulk resistance value determined at the five selected experimental temperatures from the semicircle intercept on the real axis in the corresponding Nyquist diagram plots. In addition, the representative curves of ln(σ_DC) versus of the selected nanoferrites, Fig. (4b), show a linear trend and well fit the Arrhenius equation σ_Tot = σ₀exp(-E_a/K_BT), where σ₀ is the preexponential factor, E_a is the activation energy of electrical conduction, K_B is the Boltzmann constant and T is the absolute temperature. Moreover, the increased electrical conductivity observed with temperature increase shows that the conducting behavior is an activated thermally process and as a result, allows to calculate the activation energy value from the corresponding plot slope obtained from fitting data of each studied nanoferrite. Based on the electrical property results derived from Table 3 , which are in good agreement with those reported in the bibliographic data [23Belam, W.; Essoumhi, A.; Satre, P. Synthesis and Physico-Chemical Characterizations of the Lithium-Substituted NASICONS Series with General Formula Li_2.8Zr_2−ySi_1.8−4yP_1.2+4yO₁₂ where (0 ≤ y ≤ 0.45). Z. Phys. Chem., 2007, 221, 225-234.
[http://dx.doi.org/10.1524/zpch.2007.221.2.225] -27Belam, W. Sol–gel chemistry synthesis and DTA–TGA, XRPD, SIC and ⁷Li, ³¹P, ²⁹Si MAS–NMR studies on the Li-NASICON Li₃Zr_2−ySi_2−4yP_1+4yO₁₂ (0 ⩽ y ⩽ 0.5) system. J. Alloys Compd., 2013, 551, 267-273.
[http://dx.doi.org/10.1016/j.jallcom.2012.10.005] ], the DC electric conductivity of the five explored nanoferrites is found to increase with increasing temperature from 293 K to 373 K and at fixed X composition. Indeed, in case of CoFe₂O₄[X=0], the DC conductivity value increases up to twenty orders of magnitude, whereas in case of CuFe₂O₄[X=1], the conductivity increase reaches ten orders only. The best DC electrical conductivity value σ_DC(373K) = 27.03x10^-3S.cm^-1 has been observed at 373 K for CuFe₂O₄[X = 1] nanoferrite with an associated lower activation energy of 0.269 eV. The observed phenomenon could be attributed to the increased electrical charge carrier drift mobility and also indicates the presence of semiconductor like behavior. On the other hand, at a fixed temperature, the DC electrical conductivity raises six and three orders of magnitude at 293 K and 373 K, respectively. In addition, the mentioned previous electrical conductivity growth with X composition increase from 0 to 1 could be originated from the difference between the elementary electrical conductivity of both transition metals Co(0.172 S.cm^-1) and Cu(0.294 S.cm^-1), showing an improvement in the conductivity value by an increase of charge carrier concentration when copper content increases from 0 to 1, and consequently, leading to the activation energy value decrease from E_a(S1M1) = 0.345 eV to E_a(S1M5) = 0.269 eV. Furthermore, in order to identify the electrical conduction mechanism within the five explored nanoferrite frameworks, the study of alternating current conductivity σ_AC variation has been carried out in the experimental frequency range. However, in case of S1M5 nanoferrite, the graphical representation of ln(σ_AC) as a function of ln(f), Fig. (5a), shows the linear portion in the curve in the lower frequency range, followed directly by a plot exponential increase with frequency in the higher frequency domain which suggests that the mentioned AC electrical conduction mechanism in the host system follows the Jonsher’s universal power law equation:σ_AC =σ_DC + Pωⁿ

Wherein n, ω and P are the dimensionless angular frequency exponent, angular frequency and temperature-dependent constant, respectively [28Jonscher, A.K. The ‘universal’ dielectric response. Nature, 1977, 267, 267-679.
[http://dx.doi.org/10.1038/267673a0] ]. In addition, the numeric values of n = 2, P(373 K) = 4.405x10^-16 S.cm^-1.rad^-1 and σ_DC(373 K) = 0.0277 S.cm^-1, have been determined by using the second order polynomial fitted curve of σ_AC(373 K) versus frequency of S1M5 nanoferrite, Fig. (5b), which has the highest electrical conductivity value at 373 K, with an R-square value equal to 0.9999. Furthermore, the previous fitted value of σ_DC (373 K) = 0.0277 S.cm^-1 is very close to that derived from S1M5 impedance diagram recorded at 373 K, whose value is equal to 0.0270 S.cm^-1. Consequently, the charge carrier transport occurs according to the electron hopping exchange between ferrous Fe²⁺ and ferric Fe³⁺ cations which are located at randomly equivalent crystallographic sites in the applied electrical field direction [29Andoulsi, R.; Horchani-Naifer, K.; Férid, M. Structural and electrical properties of calcium substituted lanthanum ferrite powders. Powder Technol., 2012, 230, 183-187.
[http://dx.doi.org/10.1016/j.powtec.2012.07.026] -31Belam, W. Sol-gel chemistry autocombustion synthesis and physicochemical characterizations of the series of Li–Cu cobalt ferrite nanoparticles LiCu_(1-2Y)Co_(1–Y)Fe_(1+2Y)O₄. J. Mol. Struct., 2020, 1209127937
[http://dx.doi.org/10.1016/j.molstruc.2020.127937] ].

Fig. (4) (a) Impedance diagram of the nanoferrite S1M1 in the temperature range 293-373 K. (b) Arrhenius plot of nanoferrites S1M1-5.

Fig. (5) (a) Graphic representation of Ln(σAC) versus Ln(f) of nanoferrite S1M5. (b) Second order polynomial fitted curve of σAC(373 K) versus frequency of nanoferrite S1M5.

As shown in Fig. (6a), the recorded ZFC-FC magnetization curves in the temperature range 10-300 K and under 500 Oe applied magnetic field have allowed determining the blocking temperature of each studied nanoferrite, T_B, which is situated at the first intersection special point between ZFC and FC curves. However, the deduced blocking temperature values from their corresponding ZFC-FC curves: T_B(S1M1) = 285.15 K, T_B(S1M2) = 280.93 K, T_B(S1M3) = 277.24 K, T_B(S1M4) = 273.81 K, T_B(S1M5) = 270.57 K, seem to be decrease with the increase of X copper composition. Indeed, in case of CoFe₂O₄[X=0] cubic spinel basic structure, Fe³⁺ metallic cations with 3d⁵ electronic configurations create high spin states and their orbital angular moments are trapped in a weak ligand field. As a result, the magnetic magnitude anisotropy contribution should be mainly determined from the strong L-S coupling strength of Co²⁺ metallic cations with 3d⁷ electronic configurations at the octahedral sites, which generate a large magnetocrystalline anisotropy constant and consequently lead to the high magnetocrystalline anisotropy energy barrier value. Moreover, the observed decrease of anisotropy constant value from K[S1M1(X=0)] = 5.08 erg.cm^-3 to K[S1M5(X=1)] = 1.63 erg.cm^-3, with X copper incorporation increase from 0 to1, is mainly due to the lower Cu²⁺ L-S coupling contribution compared to that of Co²⁺ and thus, that leads to the previously mentioned decrease in the blocking temperature value, which also seems to decrease with the increase in particle size. However, such interpreted results are in coherence with the equation , which is derived from the magnetocrystalline anisotropy constant K reported hereafter.

Moreover, the presence of bifurcation between ZFC and FC curves proves well that the five explored nanoferrites which are initially ferrimagnetic at the blocked regime transit to the superparamagnetic regime above the blocking temperature T_B which is characterized by the dominance of magnetic single domains. Within these domains, the magnetic anisotropy energy barrier value, KV, becomes smaller than the thermal energy value, K_BT, leading to the deblocking of magnetic moment switchability to the applied field which caused the transition to the superparamagnetic state, obeying to the Curie-Weiss law [32Jacob, J.; Khader, M. Investigation of mixed spinel structure of nanostructured nickel ferrite. J. Appl. Phys., 2010, 107, 114310-114320.
[http://dx.doi.org/10.1063/1.3429202] , 33Singh, M.; Ulbrich, P.; Prokopec, V.; Svoboda, P.; Santava, E.; Stepanek, F. Vapour phase approach for iron oxide nanoparticle synthesis from solid precursors. J. Solid State Chem., 2013, 200, 150-156.
[http://dx.doi.org/10.1016/j.jssc.2013.01.037] ]. In addition, the five ZFC profiles exhibit a linear region starting from 10 K which corresponds to the tendency to saturation accompanied directly by a large increase in the magnetization magnitude up to the blocking temperature, while a trend to the saturation has been observed in the five ZF magnetization curves, which confirms the presence of strong A-B dominant dipolar interactions [34Thampi, A.; Babu, K.; Verma, S. Large scale solvothermal synthesis and a strategy to obtain stable Langmuir–Blodgett film of CoFe₂O₄ nanoparticles. J. Alloys Compd., 2013, 564, 143-150.
[http://dx.doi.org/10.1016/j.jallcom.2013.02.139] ]. The previously mentioned typical superparamagnetic behavior has been observed in a similar work devoted to the cobalt ferrite nanoparticles [34Thampi, A.; Babu, K.; Verma, S. Large scale solvothermal synthesis and a strategy to obtain stable Langmuir–Blodgett film of CoFe₂O₄ nanoparticles. J. Alloys Compd., 2013, 564, 143-150.
[http://dx.doi.org/10.1016/j.jallcom.2013.02.139] ].

As can be seen from the 10 K magnetic hysteresis loops in Fig. (6b) the five studied copper-substituted cobalt ferrite nanoparticles are in blocked regime which obeys to the Stoner-Wolhfarth law [35Ribeiro, A.L. Characterization of soft magnetic materials using a modified Stoner-Wohlfarth model. J. Magn. Magn. Mater., 1994, 133, 97-100.
[http://dx.doi.org/10.1016/0304-8853(94)90499-5] ]. However, the absence of hysteresis in the 300 K M-H curves, as shown in Fig. (7a), is an indication of superparamagnetic behavior and as a result, the five explored nanoferrites can be considered as magnetic single domains. In addition, the observed increase in saturation magnetization values M_S at 10 K compared to those at 300 K could be originated from the magnetic moments under the applied field direction which is strongly influenced by the mutual competition state between the magnetocrystalline anisotropy energy and the thermal energy as a function of temperature. In fact, the random orientation of magnetic moments becomes dominant above the blocking temperature at which the thermal energy value overcomes that of anisotropy energy. Moreover, the 300 K saturation magnetization value 55.97 emu/g, Table 4, is very close to that cited in the case of CoFe₂O₄ nanocrystals, 56.7 emu/g, but is less than that of the bulk counterpart value 80 emu/g [35Ribeiro, A.L. Characterization of soft magnetic materials using a modified Stoner-Wohlfarth model. J. Magn. Magn. Mater., 1994, 133, 97-100.
[http://dx.doi.org/10.1016/0304-8853(94)90499-5] ]. In fact, the presence of surface spin canting orientation, forming a core and shell within the magnetic ferrite nanoparticle structure, is essentially due to the surface spin disordering and magnetic dead layers at the surfaces, which are generally considered to be responsible for the reduced saturation magnetization magnitude of the five studied nanoferrite crystal lattices with respect to their bulk parent basic structure.

Fig. (6) (a) The ZFC-FC magnetization curves of the nanoferrites S1M1-5 recorded in the temperature range 10-300 K and under 500 Oe magnetic field. (b) The 10 K hysteresis loops of the nanoferrites S1M1-5.

Fig. (7) (a) The 300 K hysteresis loops of the nanoferrites S1M1-5. (b) Langevin function fitted superparamagnetic M-H curves of the nanoferrites S1M1-5.

Table 3
Electric properties of nanoferrites S1M1-5.

Table 4
Magnetic properties measured at 10 K and 300 K of nanoferrites S1M1-5

On the other hand, in case of the cubic spiel ferrite structure AB₂O₄, Neel [36Neel, L. Propriétés magnétiques des ferrites: ferrimagnétisme et antiferromagnétisme. Ann. Phys., 1948, 3, 137-198.
[http://dx.doi.org/10.1051/anphys/194812030137] ] has reported that the magnetic properties seem to be strongly sensitive to the metallic cation nature and the distribution method into the A(8a) tetrahedral and B(16d) octahedral crystallographic sites which result in predominant A-B dipolar interactions between A and B metallic cations which are generated by the orientation in opposite directions of the magnetic moments of A and B sublattice whose resultant magnitude value determines the net magnetic moment intensity value of the lattice which is equal to M_L = ∑M_B - ∑M_A. However, both M-H curves of the five explored nanoferrites, recorded on SQUID at 10 and 300 K, show the decrease of saturation magnetization with the increased Cu²⁺ content from 0 to 1, which is mainly influenced by the electron magnetic dipole moment magnitude that depends on the metallic cation nature inside the two A and B sublattice sites. Indeed, within the cubic inverse spinel ferrite basic framework CoFe₂O₄[X = 0], the Fe³⁺(5 μ_B) cations are distributed evenly between A and B sublattice sites, while the Co²⁺(3 μ_B) cations occupy only B sublattice sites. Furthermore, the latest substitution derivative CuFe₂O₄[X = 1], has been identified as a cubic inverse spinel structure within which the Cu²⁺(1 μ_B) cations have a strong specific affinity to occupy the B octahedral sublattice sites imposed by the crystal field stabilization energy of metallic cation occupation in spinel sublattice sites [37Deraz, N.M. Size and crystallinity-dependent magnetic properties of copper ferrite nanoparticles. J. Alloys Compd., 2010, 501, 317-325.
[http://dx.doi.org/10.1016/j.jallcom.2010.04.096] ]. However, the net magnetic moment calculation values M_L of the five studied nanoferrites: S1M1(3μ_B per molecule); S1M2(2.5μ_B per molecule); S1M3(2μ_B per molecule); S1M4(1.5μ_B per molecule) and S1M5(1μ_B per molecule), seem to be decreased with the increase of Cu²⁺ content from 0 to 1, which leads to the observed magnitude reduction of saturation magnetization M_S.

According to the magnetic theory, the magnetic behavior can be subdivided on the basis of particle size into four domains: superparamagnetic domain (SPMD), single domain (SD), pseudo-single domain (PSD) and the multidomain (MD). The specific transition from the MD state to the SD one occurs when the particle reaches the magnetic single domain critical size D_c(LFF), which strongly depends on magnetocrystalline energy magnitude. Likewise, the transition from the MD state to the SPMD one is reached below the supercritical threshold size called the superparamagnetic particle diameter D(LFF). Thus, in case of SPMD state, particles are in SD and consequently, both remanence and coercivity values are close to zero. However, the magnetization magnitude M versus both magnetic field H and absolute T obeys to the following mathematic equation: M = M_s.L(x)

Where L(x) is the Langevin function, x = M_s is the saturation magnetization, μ_p is the particle magnetic moment, μ_B is the Bhor magneton, N_P is the number of particles per unit mass contributing to the magnetization and K_B is the Boltzmann constant.

The magnetic anisotropy constant value K can be determined by the following expression:

Where T_B and V are the blocking temperature of the sample and the volume of the single particle, respectively.

In case of MD-SD spherical nanoparticle transition, the critical diameter value D_c of the magnetic single domain can be calculated by the following relation [38Néel, L. Théorie du traînage magnétique des ferromagnétiques en grains fins avec applications aux terres cuites. Ann. Geophys., 1949, 5, 99-136.]:

Wherein A is the stiffness constant.

In order to further investigate magnetic features, Langevin function fitting on the 300 K superparamagnetic M-H data of the five explored nanoferrites, Fig. (7b), has been used to calculate the following superparamagnetic parameters: M_s(LFF), μ_p, D(LFF), K, N_P and D_c(LFF) which are summarised in Table 5.

Table 5
Fit parameters values of M_s(LFF), D(LFF), D_C(LFF), μ_p, K and N_P, with the corresponding R² fit goodness factors of nanoferrites S1M1-5.

In addition, it can be deduced from the theoretical calculation results illustrated in Table 5 that the calculated values of M_s(LFF) and D(LFF) by Langevin function fitting, (LFF), are in good agreement with those determined from the experimental data: M_s(300 K) and D(XRPD), and the large values of magnetocrystalline anisotropy constants are basically due to the presence of strong L-S couplings between Cu²⁺(1 μ_B), Co²⁺(3 μ_B) and Fe³⁺(5 μ_B) cations which are distributed over the tetrahedral and octahedral of the inverse spinel structure, whose value seems to decrease with the increase of X Cu²⁺ composition from K[S1M1(X = 0)] = 5.08x10⁵ erg.cm^-3 to K[S1M5(X = 1)] = 1.63x10⁵ erg.cm^-3. Moreover, the increase of D_C(LFF) value with the decrease of M_S could be due to the magnetic moment difference between Cu²⁺(1 μ_B) and Co²⁺(3 μ_B) cations. Indeed, during the substitution procedure when Cu²⁺ composition increases from 0 to 1, at the same time Co²⁺(3 μ_B), composition decreases from 1 to 0 and hence, the induced decrease in M_S magnitude leads to the increase in D_C(LFF) value which enhances the SD state size within the basic framework. Moreover, the calculated D_C(LFF) values of the five studied nanoferrites: D_C[S1M1(X = 0)] = 3.174 μm; D_C[S1M2(X = 0.25)] = 4.206 μm; D_C[S1M3(X = 0.5)] = 5.930 μm and D_C[S1M4(X = 0.75)] = 9.122 μm], are lower than that of the hematite SD-MD transition particle size D_C = 15 μm, whose value is slightly lower than that of S1M5: D_C[S1M5(X = 1)] = 17.092 μm.