New Nanosized (Gd3+, Sm3+) Co-doped Zinc Ferrite for Telecommunication Applications. Magnetic and Structural Properties.

Highly crystalline ZnFe 1.98 Sm 0.01 Gd 0.01 O 4 nanoferrites were prepared by co-precipitation method for the first time. The nanoparticles were characterized using thermogravimetric and differential scanning calorimetry analysis (TGA and DSC), which shows the thermal behavior of the reagents mixture. XRD analysis confirms the formation of nanocrystalline ferrite phase with Fd 3̅ m space group, and the particle size was observed to be 11 nm . The FTIR reveals two based bands of absorption characterize the formation of the spinel structure. An exhaustive study of the magnetic properties, morphology, crystallinity and effects of co-doping Gd 3 + and Sm 3 + was presented in detail. The average crystallites size was observed to decrease for Gd 3+ and Sm 3+ co-doping. Magnetic measurements reveal weak ferrimagnetic behavior at low temperature and superparamagnetic at high temperature with a blocking temperature at 55 K.


Introduction
In recent years, nanotechnology has metamorphosed into a global technology, playing a crucial role not only in materials science, but also in several areas such as telecommunications and information technology, microelectronics, electronics and others. Nanoscience's are developing at an extraordinarily fast pace and rapid progress is being made in this field. With the advent of nanoscience's and nanotechnologies, new devices are appearing and thanks to nanotechnologies, obsolete devices are being replaced. Quantum mechanics has permitted a vertiginous understanding of physical and electronic properties at the nanometric scale, so physicists are naturally taking the lead in exploiting this brand new field of science for the benefit of human development. Magnetism, or more particularly nanomagnetic materials, will certainly play a crucial role in the implementation of new and more sophisticated applications using nanotechnologies. It should be noted that with magnetism and nanotechnology, devices based on new properties and functionalities will ineluctably emerge. The nanoferrite have been used in wide technological applications such as, nano-antennae, radio frequency circuits, transformer cores and read and write heads for high speed digital tapes. Thus, good control of the theoretical formalism of the role of magnetism and magnetic material properties in telecommunication systems and devices, is a great challenge for the advancement of device design and performance. Nanoferrites have been widely studied and applied in antennas [1]- [4] , circulators [5]- [7], insulators [8]- [10] and inductors [11]- [14].
Due to their low power losses over a large range of frequencies, Zn-Mn ferrites are beneficial as the base materials for inductors and transformers [15] . Also important for spinel-structured Zn-Mg ferrites are their high resistivity, low Foucault currents, magnetic and dielectric losses [16] . One of the key parameters in determining the performance and applications of magnetic materials are dielectric and magnetic power losses. However, the main cause that influenced dielectric and magnetic power losses was the contribution of total losses such as current losses of Foucault, hysteresis and other losses [17], [18] . Zn-Ni ferrites are the best and most versatile ferrites and have been extensively studied because of their many applications such as transducers, filters, memory devices, sensors, transformers, loading coils, various electronic devices and resonators, high-frequency microwave applications and devices [19], [20]. These three versatile mixed ferrites allow a wide range of applications in the frequency range from low to very high microwave frequencies.
Interestingly, with the development of technology and miniaturization, research and development has focused on new antenna technology and new substrates, adaptive network configuration, dynamic structure, sustainable performance, low cost and energy efficient use, etc. Zn 0.8 Mn 0.2 Fe 2 O 4 zinc-manganese ferrite with low loss properties (loss tangent 0<0.03) is used as an antenna substrate to introduce a new dielectric substrate for compact 5G antenna mounting [21]. Provided that the nanoferrites Zn-Mg, Zn-Mn and MgSm x Gd y Fe 2-x-y O 4 [22] , have given very good results, for the design of a micro-strip patch antenna, in the same sense our work will focus on ZnFe 1.98 0.01 Sm 0.01 O 4 .
It is well known that nanoferrite properties can be easily modified and optimized by integrating and properly adding divalent or trivalent cations into the spinel structure. To our knowledge and according to the literature, no published studies are available on the structure, morphology and magnetic properties of zinc ferrite co-doped by Gd 3+ and Sm 3+ . In the present work, we report on the synthesis of ZnFe 1.98 (GdSm) 0.01 O 4 nanoparticles . The effect of doping on the structural, morphological, solubility and magnetic properties is studied in detail.

Characterization
The sample synthesized was characterized using The Thermal analysis was carried out in TGA (Q500-TAInstruments). The X-ray diffraction analyses were carried out to determine the single phase. Measurements were made by an X-ray diffractometer (PANalytical, PW3050/60, XRD). The lattice parameter and crystallite sizes were calculated by the Rietveld refinement method and Debye-Scherrer formula respectively. Fourier Transform-Infrared spectra (FT-IR) of the samples were realized using an ABB Bomem FTLA 2000-102 spectrometer. Transmission electron microscopy (TEM) Tecnai G2 microscope were used to determine the particle morphology. The magnetic measurements were carried by Magnetic Property Measurement System (Quantum Design MPMS-XL-7AC SQUID) for study the magnetic behavior. .0% pure, Alfa Aesar) were dissolved stoichiometrically in deionized water, the entire mixture was stirred with a magnetic stirrer until the all compounds are completely dissolved at a temperature of 60°C for 15min . The prepared solution was co-precipitated at pH value of 10.5 using (3M) of Sodium hydroxide (NaOH) with two drops of oleic acid. The solution obtained is mixed at 80 ° C for 1h 15min and then abandoned to precipitate. The separation of the precipitates from solutions was done by micro-filter paper and washed several times using deionized water and subsequently dried into an oven at 100 ℃. The powder obtained were calcined at 700°C for 2h.

4.1.Thermal analysis
In order to study the formation process of ZnFe 1.98 Sm 0.01 Gd 0.01 O 4 powders, TGA and DSC analyses are used to determine the decomposition process of precursors and surfactant. The TGA and DSC curves are shown in Figure 1. Thermal decomposition takes place in three different stages, as can be seen on the TGA curves. Fig. 1 reveals two ramps of mass loss around the temperature range (100-160°C), followed by a prolonged loss of mass from 180 to 560 °C due to the combustion of the residual organic components and nitrates. The first weight loss of ~ 6% corresponds to loss of adsorbed water molecules present in the samples.
The second weight loss of ~ 3,8%, is due mainly to the decomposition of weakly bound functional group (-COOH) from oleic acid surfactant, and to which corresponds a strong endothermic peak in DSC. The total loss of weight corresponds to 9.8% of the starting weight.
The TGA curve pattern is linear from 560 to 700°C and after it no more weight loss took place which reflects the formation of nanocrystalline spinel ferrite.  To further reveal the detailed structural parameters, Rietveld refinement was carried out on XRD data of the sample using FullProf software, see Fig.3. The fit was determined by the quality of the fit as well as the low values of the reliable factors (χ 2 < 1) . A very good fitting parameters is obtained by fitting the respective experimental data. All peaks have been indexed in the spinel structure with a space group Fd3 ̅ m indicating the precision of the results.
The obtained lattice parameter is a = 8.4341 Å for ZnFe 1.98 Gd 0.01 Sm 0.01 O 4 is in relatively good agreement with those found in the literature [23].
It is well known that the incorporation of rare earth elements in a spinel lattice can lead to a micro-strain of the lattice. In this case, the Williamson-Hall method was used to estimate the average size of the crystallites and the strain of the lattice. The average crystallite size reveal that for all prominent peaks and the best linear fit applied. Crystallite size was calculated from the intercept and lattice deformation was obtained from the slope of the linear function analysis [24]. The crystallite size and lattice micro-strain are given in Table 1.
As shown in the Table 1, The calculated value of average crystallites size (D), of samples codoped with Gd 3+ and Sm 3+ ions is smaller than that of the undoped zinc ferrite ZnFe 2 O 4 synthetized by Tatachuk et al [25], this is due to the fact that more energy is required to insert the RE = (Gd 3+ , Sm 3+ ) ions, because the binding energy is a part of the internal energy.
Indeed, RE 3+ ions have an empty or half or full 4f electron shell with a stable structure, so that the sample containing the RE 3+ ions has a high thermal stability. The bond strengths of Zn 2+ -O 2-, Fe 3+ -O 2-, Sm 3+ -O 2and Gd 3+ -O 2are 159 (kJ mol -1 ), 390 (kJ mol -1 ), 573 (kJ mol -1 ) and 715 (kJ mol -1 ), respectively. As a result, zinc ferrites co-doped Gd 3+ and Sm 3+ exhibit greater thermal stability than pure zinc ferrites. Samples of zinc ferrites co-doped Gd 3+ and Sm 3+ therefore require more energy to boost crystal growth. It should be noted that a typically similar behavior with respect to the different rare earth dopants has been reported in the literature [26], [27].
For micro-strain it is clear that the value of is negative as there is compression in the lattice [28]. this can be explained by the exchange interaction force in the system due to the presence of the doping elements Gd 3+ and Sm 3+ having a high magnetic moment of spin. The details of this compression will be discussed in the magnetic discussion section.
Theoretical density − is calculate using the following relation: where M is the molecular weight of the sample, N is the Avogadro's number and a is the lattice parameter.
The calculated value of the X-ray density of ZnFe 1.98 Gd 0.01 Sm 0.01 O 4 is larger, this is due to the increase in the molecular weight of the sample by doping with Gd 3+ and Sm 3+ . Table 1. lattice parameter (a), Crystallite size ( − ), micro-strain, x-ray density ( − ) and the oxygen position parameter u for ZnFe1.98Gd0.01Sm0.01O4 nanoparticles. respectively.
Knowing that we work at the nanometric scale and that we dope with rare earths Sm and Gd much larger than Zn and Fe, and taking into account the result of Kolekar et al. [39] which showed that the probability of rare earth ions occupying tetrahedral sites can be excluded, since these sites are too small to be occupied by large rare earth ions, hence the distribution of cations in this case can be written as follows : Where is the degree of inversion, which reflects the percentage of Zn 2+ and Fe 3+ at the tetrahedral and octahedral sites. It is well known that the mean ionic radii of ions at tetrahedral site r tet and octahedral site r oct , in terms of their concentrations can be written as: Where, 3+ , 2+ , 3+ 3+ are radius of Fe 3+ , Zn 2+ , Sm 3+ and Gd 3+ ions respectively.
The theoretical lattice parameter can be calculated theoretically by the following equation: where is the radius of oxygen ion ( = 1.32 Å), and and are the radii of the tetrahedral and octahedral sites, respectively.
The oxygen position parameter or the anionic parameter u, which is the distance between the oxygen ion and the face of the edge along the cube diagonal of the spinel lattice is calculated by [40]: (for the unit-cell origin at 43m on an A-site cation) Where, r A ionic radius of A-site, R 0 is ionic radius of oxygen ion.
Considering the proposed cationic distribution formula, a computer program has been developed to adjust and find a better agreement between the theoretical values and the experimental data, of the magnetic moment and the lattice constant, optimizing the value of  To confirm the complete reaction and formation of the single ferrite phase after annealing.
The FTIR spectra of the annealed ferrite sample was recorded in the range of 2000-350 cm -1 . Fig.4 shows the FTIR spectra of sample.
In the FTIR spectra of spinel ferrites there are two main characteristic absorption peaks, which are related to intrinsic vibrations of oxygen bonds with metal cations at sites A and B [41].Where the first band is located at 408,87 cm −1 corresponds to the stretching vibrations  [42] as shown in Table 3. Table 3. Attribution of the vibration bands observed on the FT-IR spectra of ZnFe 1.98 (GdSm) 0.01 O 4 obtained by co-precipitation.
From the FTIR spectra, the results also showed that distortion occurs in the tetrahedral and octahedral sites after doping by Gd and Sm. The presence of the two characteristics peaks, and the absence of peaks associated to secondary phases or impurities, confirm the single phase formation of the investigated co-doped ferrites. These results are in perfect agreement with those determined by X-ray diffraction, which prove that a pure phase is obtained where Gd 3+ and Sm 3+ are totally soluble. In order further characterize the particle size and morphology of the sample, the TEM image of ZnFe 1.98 0.01 Sm 0.01 O 4 nanoparticle was presented in Fig 5 (a) .The average particle sizes of sample were estimated by a statistical analysis using Image J software, which reveals that the particle size to be 16~24 nm, as shown in Fig. 5(b), The average particle size values are in good agreement with XRD pattern values. The TEM image confirms that the nanoparticle has spherical shape and agglomerated due to magnetic dipole interactions between the nanoparticle. These agglomerates can be able to increase the magnetic interaction, Fine particle size and high magnetism of Gd 3+ and Sm 3+ ions substituted zinc ferrite leads agglomeration of ZnFe 1.98 0.01 Sm 0.01 O 4 nanoparticles .

Magnetic analysis
The Magnetic Property Measurement System (MPMS), was used to study the magnetic properties of sample, the figure. 6 shows the magnetic measurement of the hysteresis cycle at temperature 5k , 80k and 300k , under the external field applied ∓50 kOe. The Figure. Table.4 All values obtained by magnetic measurements The value of remanent magnetization and coercivity at room temperature and at 80 K are both zero, which proves that we are in the presence of superparamagnetic behavior. At 5 K a hysteresis cycle is observed, the M s , M r and H c increase, in addition M s and H c become more pronounced, which proves a transition to a ferrimagnetic behavior, which originates from the cationic distribution, generated by the occupation of specific sites and the distribution between octahedral and tetrahedral sites and also from the particle size [44]. The increase of H c at 5 K can be interpreted also by the non-compensation of exchange interactions between the three sub-lattices that make up the structure, and therefore the rotational magnetization mechanism is present. The appearance of superparamagnetism at 80 K and 300 K indicates that magnetocrystalline anisotropy, which is important for maintaining magnetic ions in certain directions, is very low compared to the thermal energy. Zn 2+ is diamagnetic in nature and have no unpaired electron. The only contribution to magneto-crystalline anisotropy comes from Fe 3+ , Gd 3+ and Sm 3+ and may be insufficient to maintain the magnetic order in some directions. The presence of superparamagnetic also indicates that the thermal energy may have exceeded the blocking temperature, this part will be more clearly elucidated later.   [41] hydrolysis in a polyol medium 6 37.0 -- [42] Ultrasound-assisted emulsion 12 25 -- [43] and 38 nm, with M S values between 0.72 to 3.4 emu/g, at an applied magnetic field 0.8 T [47], and that obtained by Ball milling method have crystallite sizes between 11 and 14 nm , with M S values between 10 and 7.5 emu/g, at an applied magnetic field 0.7 T [48] . and that obtained by coprecipitation method have crystallite sizes between 11 and 37 nm with M S values between 2.60 and 20.34 emu/g. The saturation magnetization varies closely with the particle size, the increase of which is manifested by a reduced displacement of the domain walls in the multi-domain range. This suggests that the increase in the Ms value with increasing particle size is significantly correlated with surface effects [49]. When temperature increases, The local structure of the particles, in term of cation distribution toward the tetrahedral and octahedral site of the spinel lattice. As a matter of fact, the partial migration of Fe 3+ from sites B to A and conversely that of Zn 2+ from sites A to B can lead to a decrease in magnetization in accordance with the ferrimagnetic Neel theory. It is also noted that magnetization decreases despite the presence of the paramagnetic ions Gd and Sm, this phenomenon can be explained by the fact that at high temperature, these ions attenuate the exchange interactions between Fe 3+ -Fe 3+ in the two sublattices. Gd 3+ and Sm 3+ ions are highly paramagnetic, thus by replacing Fe 3+ , the super exchange strength decreases at the detriment of the paramagnetic ions. The magnetic behavior of spinel-type antiferromagnetic materials is largely governed by the negative Fe 3+ -Fe 3+ interaction (3d electron spin coupling). The RE 3+ -Fe 3+ interaction (4f-3d coupling) and the RE 3+ -RE 3+ one interaction (4f-5d-4f indirect electron spin coupling) exist, but are very weak [50]. In the literature it has been reported that 4f electrons from rare earths generally remain very localized in the solid and form the magnetic electrons [51]- [53] , all of which influence the bonding angles and distances.
in order to study the effect of exchange interactions in our sample a theoretical analysis was carried out. It is known that the magnetic interactions vary according to the bond angles and inversely proportional to the bond lengths, for these reasons, the distances and angles, cationcation and cation-anion, were determined using the formulas presented in the Table 9. Table 9. Expressions for determining the cation-cation and cation-anion distances, and the bond angles From and Sm 3+ , which is large for the tetrahedral site and therefore Gd 3+ and Sm 3+ ions are compelled to occupy octahedral sites.
The calculated values of bond angles have been listed in Table 11. It has been found that θ 1 , θ 2 and θ 5 decrease while θ 3 and θ 4 increase compared with the result found in the literature [54]. magnetic moment compared to that of Fe 3+ (5µ B ) [55], [56].
to understand the correlation of magnetic properties with the characteristics of nanoparticles.
The variation of magnetization as a function of temperature provided us with this information.
The blocking temperature T B , which reflects the transition from the superparamagnetic state to the blocked state, is determined from the position of the MZFC peak, whose widening provides information on the degree of particle size distribution, since blocking temperatures are closely associated with the variation of nanoparticle sizes [57] . It should be noted that information on the structural disorder of nanoparticles can also be obtained from the temperature corresponding to the convergence of the MZFC and MFC curves. i.e. the irreversible temperature (T irr ), and its distance from T B [32] .    The work of Klemens Rumpf et al [61] has been very significant, showing that the decrease in the concentration of the particle solution results in a weakening of the magnetic coupling between the particles, which leads to a shift of the blocking temperature towards lower values, and that the decrease in particle size also leads to a decrease of the blocking temperature. According to two sublattice models of Neel's theory [65], and using the cation distribution:

. ( ) . ]
Therefore, the theoretic magnetic moment per formula unit in µ B , ( ), is described as : ( ) = − = . + ∑ = . + . + + . + (10) The net magnetic moment, ( ) has been calculated using the equation interactions. In addition, R is less than 0.50, the phenomenon can be attributed to surface spin disorder effects. The particles are smaller and then exhibit a greater surface contribution.

Conclusion
Gd 3+ , Sm 3+ co-doped Zinc ferrite nanoparticles with a single-phase cubic spinel structure were successfully prepared by coprecipitation method. Rietveld refinement of the XRD patterns indicated that the lattice parameter is in relatively good agreement with those found in the

Conflicts of interest
There are no conflicts to declare. Figure 1 Thermal analysis of the polymeric and nitrate precursors  The TEM analysis and particles size distribution of the nanoparticle ZnFe_1.98 Gd_0.01 Sm_0.01 O_4 Figure 6 Hysteresis loops of sample ZnFe_1.98 Gd_0.01 Sm_0.01 O_4 Figure 7 Zero eld cooled and eld cooled magnetization vs. temperature recorded in an external eld of 100 Oe