Impact of Tm3+ and Tb3+ Rare Earth Cations Substitution on the Structure and Magnetic Parameters of Co-Ni Nanospinel Ferrite

Tm-Tb co-substituted Co-Ni nanospinel ferrites (NSFs) as (Co0.5Ni0.5) [TmxTbxFe2−2x]O4 (x = 0.00–0.05) NSFs were attained via the ultrasound irradiation technique. The phase identification and morphologies of the NSFs were explored using X-rays diffraction (XRD), selected area electron diffraction (SAED), and transmission and scanning electronic microscopes (TEM and SEM). The magnetization measurements against the applied magnetic field (M-H) were made at 300 and 10 K with a vibrating sample magnetometer (VSM). The various prepared nanoparticles revealed a ferrimagnetic character at both 300 and 10 K. The saturation magnetization (Ms), the remanence (Mr), and magneton number (nB) were found to decrease upon the Tb-Tm substitution effect. On the other hand, the coercivity (Hc) was found to diminish with increasing x up to 0.03 and then begins to increase with further rising Tb-Tm content. The Hc values are in the range of 346.7–441.7 Oe at 300 K to 4044.4–5378.7 Oe at 10 K. The variations in magnetic parameters were described based on redistribution of cations, crystallites and/or grains size, canting effects, surface spins effects, super-exchange interaction strength, etc. The observed magnetic results indicated that the synthesized (Co0.5Ni0.5)[TmxTbxFe2−x]O4 NSFs could be considered as promising candidates to be used for room temperature magnetic applications and magnetic recording media.


Introduction
The complex oxides of transition metals are attractive both from a practical application [1][2][3] and from the point of view of studying the fundamental physical phenomena [4][5][6]. Close attention to these compounds appeared due to the interconnection of structural, charge, and spin interactions [7]. Multiferroics are the most relevant for research in the physics and chemistry of condensed matter [8][9][10]. Ferrites stand out among the most promising multiferroics [11][12][13].
The broad field of science and technology of spinel ferrite materials has been established [14][15][16]. Certainly, magnetic nanocrystal ferrites have the potentials for use as raw material for various technological industries processes, such as in non-volatile memory devices, spintronics, and energy storage devices [17][18][19], and also in bio-implementations, such as medical imaging, nano-drug delivery, and sensing [20,21]. The structure of spinel cubic ferrite contains a divalent cation (often transition metals) in addition to ferric ion, represented as Me 2+ Fe 2 3+ O 4 , where metals are bound by oxygen to form a face-centered cubic closed packing. Each of the cations resides either at tetrahedral A or an octahedral B lattice site [22]. Ferrites and derivatives are known for their broad ferromagnetic resonance linewidth, moreover, owing to their exceptionally high magnetic and dielectric loss, these crystals are regarded as crucial particularly in the area of electromagnetic interference and low observable technology (LOT) [23][24][25]. Typically, a candidate material for use as an electromagnetic resonance absorber should have (i) broad magnetic resonance bandwidth, large values of (ii) permeability, and (iii) permittivity [23,25]. NiCoFe 3 O 4 nanomaterials are reported to have a low coercivity (1.20 Oe) and high values of saturation magnetic flux density (2.1 T) [26] and Curie temperature (~527 • C), high permeability and permittivity, and low value of magnetocrystalline anisotropy and appreciable resistivity (~10 5 -10 4 ohm/cm). In addition, it is well known that both Co-and Ni are inverse spinels, that exhibit homogeneous distribution in the A and B lattice sites; thus, their magnetic features are attributed to antiferromagnetic coupling amongst the tetrahedral and octahedral sublattices [27,28]. Furthermore, nickel substituted cobalt ferrites demonstrate good chemical stability and thus found applications as a binder and as magnetic filler in electromagnetic shielding nanocomposites [29][30][31]. Moreover, it is generally anticipated that rare-earth substituted spinel ferrites, in many cases, would show a superior electric and magnetic character when compared with the pristine spinel counterpart [32].
The bottom-up chemical synthesis routes commonly employed to prepare magnetic nano ferrites include co-precipitation, thermal decomposition, microemulsion, hydrothermal, and polyol methods [33][34][35][36]. Although these techniques yield materials with a narrow size distribution, precise control of the structural morphology, surface area, and size/size distribution during the chemical reaction is challenging [37]. Additionally, large scale production of uniformly sized magnetic nanoparticles is crucial since many advanced technological applications are sensitive not only to nano-sized crystals but a material with crystals size consistency [38]. For instance, studies have shown that size/size distribution is a major factor that determines the mechanical and thermal stability of magnetic nanofluid that are used as heat transfer media [39]. Fortunately, a strict size control can be achieved through the sonochemical approach. This technique follows the acoustic cavitation phenomenon [37], where the reaction mixture is subjected to ultrasound treatment at high temperature and pressure. Consequently, the reaction is quenched by rapid cooling followed by the application of strong shock waves and microjets [37,40]. This process hinders secondary nucleation and offers excellent size/size distribution. In addition, the sonochemical method is inexpensive, environmentally benign, effective, and most importantly, produces magnetic nanocrystal with a better magnetic response.
Spinel ferrites substituted with rare-earth ions have been reported by numerous research groups. Biasi and co-workers investigated the magnetocrystalline anisotropy of NiCo x Fe 2−x O 4 . The report shows that, except for pristine NiFe 2 O 4 , all the samples had a positive value of magnetocrystalline anisotropy, which increases monotonically as more Co is introduced, the material, and thus, may have a practical application as magnetic material [41]. Zhang et al. [42] considered the magnetic properties of La x NiCoFe 2−x O 4 (x = 0.025-0.125) synthesized via a sol-gel method, the substitution of La 3+ effectively decreases the coercivity and increases the magnetization. On the other hand, Srinivasamurthy et al. [32] explored the phase and magnetic features of Ce-Sm doped Co-Ni nano spinel ferrite. They found that the magnetic measurements increased with increasing the dopant due to the improved superexchange interaction of A-B. Moreover, Hossain et al. [43] reported magnetic characteristics of Ni 0.7 Zn 0.2 Co 0.1 Fe 2−x Gd x O 4 (x = 0.00-0.12). Their findings showed that the saturation magnetization reduced while coercivity improved with adding Gd. Almessiere et al. implemented a research on magnetic merits of CoTm x Fe 2−x O 4 (0.0 ≤ x ≤ 0.08) and CoTb x Fe 2−x O 4 (x ≤ 0.10) NPs. Influence of synthesis method on structure and microstructural analysis was observed for nanosized substituted spinels [44]. The outcome of these studies demonstrated a strong influence of Tm and Tb individually on magnetic features of Co ferrites [45].
Although Tm and Tb are reported to influence the magnetic behaviors of ferrites solids [44,45], no clear trend of physicochemical properties due to substitution can be found thus far. Moreover, a bimetallic substitution into NiCoFe 2 O 4 is scarcely explored. Herein, we introduced a rare earth Tb 3+ and Tm 3+ as (Co 0.5 Ni 0.5 )[Tm x Tb x Fe 2−2x ]O 4 via ultrasonic technique. The material is characterized and studied the magnetic behavior as a function of the concentration of rare-earth dopants.

Materials and Methods
Ultrasound irradiation was employed to produce (Co 0. 5  solution was gradually adding to the nitrate solution, and the resultants solution stirred at room temperature. The pH was adjusted to 11 using an ammonia solution. The precursor mixture was undergoing ultrasound irradiation by ultrasonic homogenizer for 40 min and 20 kHz. The solid product was purified by washing using distilled water several times until a neutral pH is achieved. The solid is finally dried at 60 • C overnight to obtain NSFs [46,47]. The XRD Benchtop Rigaku Miniflex (Cu Kα line) was applied to identify the structure of the NSFs. The morphology and composition of the samples were analyzed using FEI Titan ST SEM and TEM equipped with an EDX spectrometer. Quantum Design PPMS DynaCool-9 coupled with VSM head was applied to study the magnetic properties of the products. In addition, the Rietveld refinement revealed the absence of any trace rare earth oxides, suggesting the purity of the synthesized NSFs. It can be observed that, that the most intense peak at 2θ = 34.96 • (x = 0.01-0.05) with a crystal plane (311) is shifted to a higher diffraction angle while x is increasing. Moreover, this peak becomes slightly broaden when increasing the ratio of the substituted ion; this is a characteristic of crystals with small particle size. Hence, the introduction of more Tm and Tb into the solid solution of the spinel ferrites hinders the crystal growth. A similar observation has been reported, where substitution using Gm 3+ , Sm 3+ and Eu 3+ resulted in a crystallite size reduction of Ni-Co ferrite [48]. On the other hand, cell parameters, cell volume, crystallite sizes, goodness fit (χ 2 ), and R-factors have been evaluated via refinement through Match3 and a Full Proof program of X-ray experimental data as included in Table 1-lattice parameter (a), volume of unit cell (V), and average crystal size determined from XRD patterns (D XRD ). A decrease in cell parameters and cell volume was observed when increasing the content of Tm 3+ and Tb 3+ (x = 0.0-0.05), this could be due to the deformation in spinel crystal by larger r Tm3+ (0.88 Å) and r Tb3+ (0.92 Å) in comparison with r Fe3+ (0.64 Å) which caused depositary in the grain boundary and hinders the cell parameters growth [49]. The crystal sizes were computed with the Debye-Scherer formula by considering the maximum peak (311) and found in the range of 11-13 nm.   Bertaut method applied to investigate cation occupancy of Co0.5Ni0.5TmxTbxFe2−2xO4 NSFs based on XRD data as following [50].

Structure
where I Obs. hkl and I Calc. hkl are the practical and calculated intensities, respectively, for reflection (hkl). The ratio of XRD lines, I 220 /I 440 , and I 422 /I 400 were used for calculating the cation distribution with the planes that sensitive to the cation distribution [50,51]. It is well-known that Spinel ferrites contain a crystallographic site, specifically Octahedral (B) and Tetrahedral (A). Table 1 listed the Nanomaterials 2020, 10, 2384 5 of 15 cation distribution of Co 0.5 Ni 0.5 Tm x Tb x Fe 2−2x O 4 system. The results revealed that for each value of x, the Fe 3+ , Ni 2+, and Co 2+ ions occupied the A-site and B-site. Both Tm 3+ and Tb 3+ cations are found that they occupied B-site only due to their higher ionic radii [52].

Surface Morphology
The morphological examination was conducted using SEM and the images for (Co 0.5 Ni 0.5 ) [Tm x Tb x Fe 2−2x ]O 4 (x = 0.00, 0.01, 0.03 and 0.05) NSFs were depicted in Figure 2. The crystals exhibited spherical shape morphology with an agglomerated appearance obviously due to ferrimagnetic character. Overall, the sample displayed an appreciable distribution of particle size, in the range 15 nm that agreed with the XRD analysis. Of note, the sample with the highest Tb 3+ and Tm 3+ doping (x = 0.5) contains some irregularly shaped nanocrystals, these crystals agglomerates and produce a secondary grain with a size range of 200-500 nm. The elemental weight percentage of (Co 0.5 Ni 0.5 )[Tm x Tb x Fe 2−2x ]O 4 (x = 0.02 and 0.05) NSFs were evaluated using EDX elemental and mapping as shown in Figure 3. The EDX spectrum of all samples have verified the occurrence of Co, Ni, Tm, Tb, O and Fe elements in products. This also indicated the efficiency of the ultrasound synthesis method. Calc hkl I are the practical and calculated intensities, respectively, for reflection (hkl). The ratio of XRD lines, I220/I440, and I422/I400 were used for calculating the cation distribution with the planes that sensitive to the cation distribution [50,51]. It is well-known that Spinel ferrites contain a crystallographic site, specifically Octahedral (B) and Tetrahedral (A). Table 1 listed the cation distribution of Co0.5Ni0.5TmxTbxFe2−2xO4 system. The results revealed that for each value of x, the Fe 3+ , Ni 2+, and Co 2+ ions occupied the A-site and B-site. Both Tm 3+ and Tb 3+ cations are found that they occupied B-site only due to their higher ionic radii [52].

Surface Morphology
The morphological examination was conducted using SEM and the images for (Co0.5Ni0.5)[TmxTbxFe2−2x]O4 (x = 0.00, 0.01, 0.03 and 0.05) NSFs were depicted in Figure 2. The crystals exhibited spherical shape morphology with an agglomerated appearance obviously due to ferrimagnetic character. Overall, the sample displayed an appreciable distribution of particle size, in the range 15 nm that agreed with the XRD analysis. Of note, the sample with the highest Tb 3+ and Tm 3+ doping (x = 0.5) contains some irregularly shaped nanocrystals, these crystals agglomerates and produce a secondary grain with a size range of 200-500 nm. The elemental weight percentage of (Co0.5Ni0.5)[TmxTbxFe2−2x]O4 (x = 0.02 and 0.05) NSFs were evaluated using EDX elemental and mapping as shown in Figure 3. The EDX spectrum of all samples have verified the occurrence of Co, Ni, Tm, Tb, O and Fe elements in products. This also indicated the efficiency of the ultrasound synthesis method.  To further study the structure, morphology, and particle size, TEM and SAED were employed on Co0.5Ni0.5)[TmxTbxFe2−2x]O4 (x = 0.02 and 0.05) NSFs as seen in Figure 4. The TEM images disclosed the aggregation of cubic and spherical particles. Thus, observation of TEM images confirmed the uniformity of the particles. The particle size distribution histogram were calculated via Image J software and found that DXRD of products have been within the range of 9-15 nm (Figure 4). The SAED showed a spotty bright ring with different intensities that confirmed the purity of the spinel NSFs ferrites structure. Accordingly, the index planes are consented with the XRD results. To further study the structure, morphology, and particle size, TEM and SAED were employed on Co 0.5 Ni 0.5 )[Tm x Tb x Fe 2−2x ]O 4 (x = 0.02 and 0.05) NSFs as seen in Figure 4. The TEM images disclosed the aggregation of cubic and spherical particles. Thus, observation of TEM images confirmed the uniformity of the particles. The particle size distribution histogram were calculated via Image J software and found that D XRD of products have been within the range of 9-15 nm (Figure 4). The SAED showed a spotty bright ring with different intensities that confirmed the purity of the spinel NSFs ferrites structure. Accordingly, the index planes are consented with the XRD results.

Magnetic Properties
The experiments of magnetization versus the implemented magnetic field, M-H, were made at two selected temperatures (300 and 10 K). M-H hysteresis loops of unsubstituted and Tb/Tmsubstituted Co-Ni spinel ferrites are existing in Figures 5 and 6, respectively. The insets in Figure 5 show magnified regions near the origin (H = 0 kOe) so that the coercivity will be more visible. At both measurement temperatures, the different produced products displayed an opened M-H hysteresis loops with a clear and large coercivity, which reveal the ferrimagnetic (FM) behavior of various samples at 300 and 10 K. It is slightly obvious in various M-H hysteresis loops that the magnetization was not saturated easily even if the applied field is high. This observation is largely ascribed to the disordered or canted spins at the surface of NSFs, which are hard to be aligned along the direction of the field, which in turn will cause a non-saturated magnetization in the nanoparticles. In the following discussions, we referred to the magnetization at the maximum applied field as the saturation magnetization. Furthermore, Figure 6 showed a clear distortion in the region close to H = 0 kOe of M-H hysteresis loops performed at a lower temperature. Such distortion in M-H hysteresis loops is associated with a phenomenon of spins freezing, owing to the considerable time dependency of the remanent magnetization [53].

Magnetic Properties
The experiments of magnetization versus the implemented magnetic field, M-H, were made at two selected temperatures (300 and 10 K). M-H hysteresis loops of unsubstituted and Tb/Tm-substituted Co-Ni spinel ferrites are existing in Figures 5 and 6, respectively. The insets in Figure 5 show magnified regions near the origin (H = 0 kOe) so that the coercivity will be more visible. At both measurement temperatures, the different produced products displayed an opened M-H hysteresis loops with a clear and large coercivity, which reveal the ferrimagnetic (FM) behavior of various samples at 300 and 10 K. It is slightly obvious in various M-H hysteresis loops that the magnetization was not saturated easily even if the applied field is high. This observation is largely ascribed to the disordered or canted spins at the surface of NSFs, which are hard to be aligned along the direction of the field, which in turn will cause a non-saturated magnetization in the nanoparticles. In the following discussions, we referred to the magnetization at the maximum applied field as the saturation magnetization. Furthermore, Figure 6 showed a clear distortion in the region close to H = 0 kOe of M-H hysteresis loops performed at a lower temperature. Such distortion in M-H hysteresis loops is associated with a phenomenon of spins freezing, owing to the considerable time dependency of the remanent magnetization [53].  The several magnetic parameters are concluded from the performed M-H measurements and are offered in Figure 7. The variations of the saturation magnetization (Ms) with respect to Tm-Tb amounts at 300 and 10 K are displayed in Figure 7a. It is clear that Ms value enhances with the reduction in the temperature of nanoparticles from 300 K down to 10 K. Generally, Ms below the Curie temperature (Tc) obeys the Bloch's law (Equation (2)) for bulky ferrimagnetic/ferromagnetic systems [54]: where M s (0) is the Ms value at = 0 K, (1 0 ⁄ ) is the Bloch's constant, is the Bloch's exponent, and 0 is the temperature at which M s = 0. In line with this equation, when the temperature is decreasing, the magnetization will increase. Accordingly, the improvement in Ms values at lower temperatures compared to those at 300 K has essentially resulted from the reduction in the thermal fluctuations at lower temperatures [55,56]. Furthermore, the improvement in magnetization is  The several magnetic parameters are concluded from the performed M-H measurements and are offered in Figure 7. The variations of the saturation magnetization (Ms) with respect to Tm-Tb amounts at 300 and 10 K are displayed in Figure 7a. It is clear that Ms value enhances with the reduction in the temperature of nanoparticles from 300 K down to 10 K. Generally, Ms below the Curie temperature (Tc) obeys the Bloch's law (Equation (2)) for bulky ferrimagnetic/ferromagnetic systems [54]: where M s (0) is the Ms value at = 0 K, (1 0 ⁄ ) is the Bloch's constant, is the Bloch's exponent, and 0 is the temperature at which M s = 0. In line with this equation, when the temperature is decreasing, the magnetization will increase. Accordingly, the improvement in Ms values at lower temperatures compared to those at 300 K has essentially resulted from the reduction in the thermal fluctuations at lower temperatures [55,56]. Furthermore, the improvement in magnetization is The several magnetic parameters are concluded from the performed M-H measurements and are offered in Figure 7. The variations of the saturation magnetization (M s ) with respect to Tm-Tb amounts at 300 and 10 K are displayed in Figure 7a. It is clear that M s value enhances with the reduction in the temperature of nanoparticles from 300 K down to 10 K. Generally, M s below the Curie temperature (T c ) obeys the Bloch's law (Equation (2)) for bulky ferrimagnetic/ferromagnetic systems [54]: where M s (0) is the M s value at T = 0 K, (1/T 0 ) α is the Bloch's constant, α is the Bloch's exponent, and T 0 is the temperature at which M s = 0. In line with this equation, when the temperature is decreasing, the magnetization will increase. Accordingly, the improvement in M s values at lower temperatures compared to those at 300 K has essentially resulted from the reduction in the thermal fluctuations at lower temperatures [55,56]. Furthermore, the improvement in magnetization is accredited to the enhancement of spins order at the surface of Tb-Tm substituted Co 0.5 Ni 0.5 Fe 2 O 4 nanoparticles [57]. Indeed, the spins moment of shells could additionally contribute to the resultant magnetization at lower temperatures, thus improving the total magnetization of NSFs [57].
Nanomaterials 2020, 10, 2384 9 of 16 accredited to the enhancement of spins order at the surface of Tb-Tm substituted Co0.5Ni0.5Fe2O4 nanoparticles [57]. Indeed, the spins moment of shells could additionally contribute to the resultant magnetization at lower temperatures, thus improving the total magnetization of NSFs [57]. The non-substituted sample (i.e., Co0.5Ni0.5Fe2O4) displayed Ms values of about ~42.3 and ~52.8 emu/g at T = 300 and 10 K, correspondingly. These registered values are lower than those attained in bulk Co0.5Ni0.5Fe2O4 system. These lower Ms values can be ascribed to the structural distortions in the surface such as dead surface layers and random spins canting in comparison to the bulk for which it can diminish the number of contributing moments [58][59][60]. Furthermore, the difference in the site occupancy of different cations in nanoparticulate and bulky systems is responsible for the dissimilarity in Ms values [61]. In fact, Co0.5Ni0.5Fe2O4 NPs do not exhibit an inverse spinel structure type like in bulk compounds, but they have a mixed spinel structure type. Consequently, this leads The non-substituted sample (i.e., Co 0.5 Ni 0.5 Fe 2 O 4 ) displayed M s values of about~42.3 and 52.8 emu/g at T = 300 and 10 K, correspondingly. These registered values are lower than those attained in bulk Co 0.5 Ni 0.5 Fe 2 O 4 system. These lower M s values can be ascribed to the structural distortions in the surface such as dead surface layers and random spins canting in comparison to the bulk for which it can diminish the number of contributing moments [58][59][60]. Furthermore, the difference in the site occupancy of different cations in nanoparticulate and bulky systems is responsible for the dissimilarity in M s values [61]. In fact, Co 0.5 Ni 0.5 Fe 2 O 4 NPs do not exhibit an inverse spinel structure type like in bulk compounds, but they have a mixed spinel structure type. Consequently, this leads to the observed decrease in the M s value. Nevertheless, the M s values observed in our samples are larger than those found in Co-Ni spinel ferrite NSFs produced via sol-gel auto-combustion approach [62,63] and mechanochemical technique [64]. Almost near M s values are observed in Co-Ni spinel ferrite NSFs generated through a one-pot modified-solvothermal approach [30].
M s decreases at both 300 and 10 K as a function of Tm-Tb contents. M s value decreases from~42.3 to~20.4 emu/g at 300 K and from~52.8 to~26.4 emu/g at 10 K. The minimum M s values of~20.4 and 26.4 emu/g, respectively, at 300 and 10 K are belonging to the composition with x = 0.05. Generally, the magnetic properties of spinel ferrite nanoparticles are significantly influenced by the microstructure, the composition, the crystallites size, and the distribution of cations between the B-and A-sites in spinel structure [65][66][67]. Firstly, it was found that M s decreases at both 300 and 10 K as a function of grains/crystallites size. The variation in M s value could be also described based on the experimental values of the magneton number (n B ) per formula unit in Bohr magneton (µ B ). The expression of n B is given as following [68]: The determined n B values are presented in Figure 7c. It is obvious that n B , at both measurement temperatures 300 and 10 K, decreases with the rise in Tb 3+ and Tm 3+ contents, which reflect that the A-B superexchange interactions are weakened due to co-substitution effect. As evident from Figure 7a,c, the values of M s and n B exposed similar tendencies as a function of Tb 3+ and Tm 3+ content.
The coercive fields (H c ) deduced from M-H loops are presented in Figure 7e. One can remarkably observe an increase in the coercivity of all prepared nanoparticles with the diminution in the temperature from 300 down to 10 K, which indicates that the prepared nanoparticles become magnetically harder at very low temperatures. The H c values for various synthesized products improve from 346.7-441.7 Oe at 300 K to 4044.4-5378.7 Oe at 10 K. The coercivity is a sensitive characteristic to the temperature of a product. In fact, additional magnetic moments are frozen within anisotropic directions at very low temperatures. Hence, the observed increment trend in H c values is generally assigned to the effects of thermal fluctuations of the blocked moments across the anisotropy barriers. The effect of spins freezing is predominant at lower temperatures mainly below the blocking temperature (T B ). This could develop because of the exchange coupling among the spins of the core and the surface. The coercive field (H c ), for an assemblage of non-interacting three-dimensional single domain magnetic (SDM) NSFs and in a temperature interval lower than T B , can be expressed as follow [69,70]: This expression is well-known as the Kneller's law. It is a simple model form of thermal activation of the moments of nanoparticles across the anisotropy barriers. In Equation (4), the constant H 0 is the value of H c at T = 0 K. It is evident from this equation that H c value increases with the decrease in the temperature below T B . This indicates that the effects of thermal activation of the nanoparticle moments across the anisotropy barriers are prominent at lower temperatures. Nevertheless, one should also take into account that the anisotropy effect could have a great influence when one is investigating the nanoparticles at lower temperatures. Hence, other factors (in addition to the improvement of anisotropy), such as the intrinsic structural characteristics of NSFs comprising the volume distribution, the interactions between particles, and the random anisotropy, could also affect the thermal dependency of H c in the case of NSFs [71].
In the current investigation, the variation of H c values at both 300 and 10 K could be explained based on the cations redistribution at the octahedral and tetrahedral sites and on the change of grains/crystallites size [47,65]. The non-substituted Co 0. 5 [73]. The variations of the M r value and the squareness ratio (SQR = M r /M s ) against Tm-Tb contents are displayed in Figure 7b,d. It is observed that both M r and SQR values for different samples increase with reducing the temperature from 300 down to 10 K, which indicates that the strength of the magnetic anisotropy intensifies at lower temperatures [74]. The M r values are around~12.6 and~31.8 emu/g, respectively, at 300 and 10 K for un-substituted sample (x = 0.00). As observed in Figure 7a,b, the variations in M r and M s values exposed similar tendency versus Tb 3+ and Tm 3+ contents. Indeed, M r values are maximum for the non-substituted Co 0.5 Ni 0.5 Fe 2 O 4 NPs and then decreased upon Tb-Tm co-substitution. As shown via the morphological observations, the densities of grains of the diverse prepared products are very close. Therefore, the decline in M r values is largely dependent on the evolution of M s and the net alignment of grains magnetization induced by weak exchange interactions between particles. According to the Stoner-Wohlfarth concept for non-interacting particles with randomly oriented easy axes, SQR is around~0.8 for cubic anisotropy and~0.5 for uniaxial anisotropy [74]. Furthermore, a SQR value lower than 0.5 reflects that a multi-magnetic domain (MMD) structure is formed in which the motion of domain walls permits for an easier change in the orientation with the applied field, whereas, SQR value ≥0.5 implies that the system is around the single magnetic domain (SMD) size [75,76]. As shown in Figure 7d, SQR values for the synthesized products are in the interval of 0.298-0.441 (i.e., lower than 0.5) at T = 300 K, indicating that these products display a MMD structure with uniaxial anisotropy. However, SQR values are exceeding the value of 0.5 at 10 K but are still lower than 0.8, which implies that these products have a virtually SMD structure with the coexistence of cubic and uniaxial anisotropy.

Conclusions
The interdependence of Tm-Tb on the phase and magnetic features of Co-Ni NSFs as a new study has been presented. (Co 0.5 Ni 0.5 )[Tm x Tb x Fe 2−2x ]O 4 (x = 0.00-0.05) NSFs. NSFs were produced via ultrasound irradiation procedure. X-ray diffraction presented a single-phase formation of NSFs. It was found that the cell parameters decrease with the rise in the content of substitution ions. The morphology and grain size were estimated by SEM and TEM. The M-H hysteresis loops of various prepared nanoparticles showed a ferrimagnetic behavior at both measurement temperatures 300 and 10K. It was found that M s , M r , n B decreased as a function of Tb-Tm content. H c values decreased with the increase of x content up to 0.03 and then increased with the further rise of Tb-Tm content. The variations in these magnetic parameters are successfully described based on the redistribution of cations, variations crystallites and/or grains size, canting effects, surface spins effects, super-exchange interaction strength, etc. The obtained magnetic results are found to be encouraging for the possible use of these products in room temperature magnetic applications and magnetic recording media.