Cation trivalent tune of crystalline structure and magnetic properties in coprecipitated cobalt ferrite nanoparticles

CoFe2O4, CoBi0.1Fe1.9O4, CoLa0.1Fe1.9O4, and CoAl0.1Fe1.9O4 nanoparticles were successfully synthesized by the coprecipitation method. After annealing at 700 °C for 5 h, the x-ray Diffractometer results confirm that a single phase of cobalt ferrite-based nanoparticles is obtained, which is suitable for ICDD 22-1086. The addition of Bi3+, La3+ and Al3+ ions to the cobalt ferrite nanoparticles modified the crystallite size and lattice constant. Trivalent metal cation substitution tunes the crystallite size which has also been confirmed by measuring the grains with Scanning Electron Microscope images. In the Far Transform Infra-Red curve, the addition of metal ions (Bi3+, La3+, and Al3+) to cobalt ferrite nanoparticles resulted in absorption peaks at the tetrahedral and octahedral sites without any additional absorption peaks. The VSM results showed that saturation magnetization decreased drastically in the presence of trivalent non-magnetic cations, which confirms the replacement of Fe3+ by trivalent non-magnetic cations. The kOe order of the coercive field was obtained in this experiment. The largest coercive field of the cobalt ferrite nanoparticles was obtained with the addition of La3+ ions, i.e. 3.67 kOe suggest to support both Jahn-Teller effect and strain-induced magnetism.

Among the ferrite-based nanoparticles, cobalt ferrites are one of the popular classes that has an inverse spinel structure with Co 2+ ions filling the octahedral sites and Fe 3+ being in both the tetrahedral and octahedral sites [8,18,19]. The tunable magnetic properties via the cations redistribution in tetrahedral and octahedral sites are the advantages of this class. Moreover, the substitution of other metal ions into the cobalt ferrite structure also changes these properties [11,12,20], as well as variations in the synthesis [21,22], and annealing temperature [19,23]. These modifications are carried out to attain specific magnetic properties according to the desired  [13]. This is also confirmed in figure 2 which is the result of Rietveld refined patterns of CoFe 2 O 4 , CoBi 0.1 Fe 1.9 O 4 , CoLa 0.1 Fe 1.9 O 4 , and CoAl 0.1 Fe 1.9 O 4 nanoparticles, respectively. XRD patterns were analyzed using the Rietveld refinement technique using Fullprof TM software indexed in cubic symmetry with the space group Fd-3m, refinement parameters are tabulated in table 1. The results show that the magnitude of χ 2 (goodness of fit) is close to 1 which justifies the goodness of refinement [10,16,53,54]. The absence of an impurity peak that appears confirms that the synthesis of cobalt ferrite with trivalent ion substitution still maintains the spinel crystal structure [55]. The whole calculation result of the crystalline parameter for trivalent ion-substituted cobalt ferrite is summarized in table 1.

Result and disscusion
The lattice constant (a R ) obtained from refinement are 8.3998 Å for CoBi 0.1 Fe 1.9 O 4 and 8.3987 Å for CoAl 0.1 Fe 1.9 O 4 , which is slightly higher than CoFe 2 O 4 (8.3825 Å). This increase indicates that Bi 3+ and Al 3+ ions have a strong site preference for octahedral sites. Therefore, the replacement of Fe 3+ with Bi 3+ or Al 3+ can result in the expansion of the unit cell [36]. Meanwhile, CoLa 0.1 Fe 1.9 O 4 has a value of 8.3819 Å which is slightly lower than the CoFe 2 O 4 . A similar decrease in lattice constant and shrinkage in unit cell volume was observed in the previously studied RE 3+ doped cobalt ferrite [53,56]. Kumar and Kar [56] reported a decrease in the lattice constant from 8.360 to 8.358Å, and Channagoudra et al [53] reported this decrease from 8.384 to 8.383Å in the La 3+ substitution. Lattice constants generally increase when larger RE 3+ ions displace Fe 3+ . However, the decrease in lattice constants is explained due to the redistribution of cations in the spinel structure [42,56]. In general, in spinel structures, the radius of the octahedral sites (0.9 Å) is larger than that of the tetrahedral sites (0.58 Å). When a small amount of the Fe 3+ cation is substituted by the larger ionic radius RE 3+ cation, it preferentially enters the large radius octahedral site by rearranging the cations between the tetrahedral and octahedral sites, thereby minimizing the free energy of the system. Meanwhile, the Co 2+ cation (0.74 Å) initially occupies the octahedral site, due to the substitution of RE 3+ ions, some migrate to the tetrahedral site and an equivalent amount of Fe 3+ cations (0.64 Å) migrate in the opposite direction from the tetrahedral to the octahedral site, to relax the strain at octahedral sites and hence, instead of increasing, the lattice constants partially decrease when Fe 3+ is replaced by larger La 3+ ions [53]. Figure 3 shows the shifts of the hkl peak (    constants, resulting in changes in the particle size [57]. The highest peak hkl (311) was used to calculate the crystallite size using the Debye-Scherrer formula for all nanoparticles [13], where l is the wavelength of Cu-Kα radiation, b is the full width at half maximum (FWHM), and q is the Bragg angle. Here, the atomic radii of trivalent support the change of crystallite size. The presence of the Jahn-Teller effect should attribute to the change of the crystallites size [45,46]. The lattice constants (a) of all the nanoparticles were calculated using the following equation: where d is the interplanar distance and (h,k,l) is the Miller index of the nanoparticles. The obtained cobalt ferrite lattice constant a, decreased with the addition of Bi 3+ and Al 3+ ions, whereas the a increased with the addition of La 3+ ions. The crystallite size and lattice constant decreased because of the difference in the ionic radii of Bi 3+ (0.74) and Al 3+ (0.51) compared to that of Fe 3+ (0.78). Therefore, the smaller Bi 3+ and Al 3+ ions completely replaced the Fe 3+ ions in the octahedral position [49,51]. The increase in crystallite size and lattice constant upon the addition of La 3+ ions was explained for two reasons. First, the difference in the ionic radii between La 3+ ions (1.03) and Fe 3+ ions (0.78) causes the lattice structure to be distorted [50]. Second, the rare Earth ion La 3+ enters the octahedral site and partially replaces Fe 3+ . Thus, vacancies of Fe 3+ ions were formed. Thus, the addition of La 3+ ions causes strain in the crystal lattice, inhibiting crystallization. Furthermore, to reduce the strain on the crystal lattice, the growth of crystal anisotropy causes the particle size to increase [57]. Furthermore, XRD data analysis can be used to obtain the density (dx) and strain (ε) of CoFe 2 O 4 , CoBi 0.1 Fe 1.9 O 4 , CoLa 0.1 Fe 1.9 O 4 , and CoAl 0.1 Fe 1.9 O 4 nanoparticles. The density of the nanoparticles can be obtained using the following equation: where M is the molecular weight of the nanoparticles, N is Avogadro's number (6.022 × 10 23 mol −1 ), and a 3 is the cell volume of the Calculation of the microstrain value can also be done using the Williamson-Hall equation, which is obtained from the b strain and b D magnitudes as follows [59]:  and La 3+ ions. Meanwhile, the microstrain magnitude with the addition of Al 3+ ions did not change significantly, which was equal to 0.768 × 10 3 . The induced Microstrain in nanoparticles was contributed by two sources (1) surface strain due to the reduction in particle size, and (2) local strain resulting from a large number of oxygen vacancies in the nanoparticle core [60].
The compressive microstrain obtained from the nanoparticles is due to the variation in distribution between the tetrahedral and octahedral sites. Another cause is the difference in the ionic size of the two metal cations. Using the magnitude of a and the oxygen position parameter (u) ∼ 0.381 Å, the tetrahedral bond length (d AX ) and the octahedral bond length (d BX ) can be calculated using the following equation [61], Furthermore, using the magnitude of a can also be used to calculate the hopping length at the tetrahedral (L A ) and octahedral (L B ) sites using the following equation [62], The d AX and d BX magnitudes for all nanoparticles are shown in table 2, where d AX is the shortest distance between the tetrahedral site cation and the oxygen ion, and d BX is the shortest distance between the octahedral site cation and the oxygen ion. The d AX and d BX magnitudes show a decrease with the addition of Bi 3+ and Al 3+ ions in the CoFe 2 O 4 nanoparticles. Meanwhile, d AX and d BX magnitudes showed an increase with the addition of La 3+ ions in the CoFe 2 O 4 nanoparticles. The lengths between the magnetic ions at the tetrahedral and octahedral sites known as L A and L B are also tabulated in table 2. The hopping lengths also have similar changes in magnitudes as in the bond lengths at both the tetrahedral and octahedral sites. This phenomenon can be associated with changes in crystallite size, lattice constants, and magnetic properties such as strain-induced magnetism and the Jahn-Teller effect [63].  [64]. This is evidenced by the SEM images, which show the incorporation of particles located in the nanometer region. The ferrite formed during the sintering of the pores between the particles is removed, and a strong bond is formed in the form of agglomeration. Thus, the interaction between grain boundaries and porosity is important for determining the grain-to-particle size [49]. In this study, it was also observed that the particle size had a similar trend with the calculated crystallite size magnitudes obtained from the XRD analysis (table 3) [19]. The result is that the particle size with bismuth and aluminum doping has an impact on reducing both the particle size and crystallite size [49,65]. The addition of lanthanum to CoFe 2 O 4 resulted in larger particle size [66].  the tetrahedral site, which was smaller than that at the octahedral site. The absorption band is known to have an inverse relationship with the bond length. Thus, the FTIR data obtained experienced a shift to a higher frequency after doping. This is explained by a decrease in the site radius, which increases the fundamental frequency; therefore, the center frequency must shift to a higher frequency side [49].
The force constants at the tetrahedral (Ft) and octahedral (Fo) sites of where M 1 and M 2 are the molecular weights of the cations at tetrahedral and octahedral sites, respectively. The calculated force constants at the tetrahedral and octahedral sites are listed in table 4. Furthermore, the FTIR results can also be used to calculate the magnitude of Young's modulus by taking into account the elastic stiffness constant and the average force constant with the following equation [69],   whereF is the average force constant, C 11 and C 12 are the stiffness constants, d P is the Poisson's ratio calculated using the equation d P = 0.324(1-1.043P) (P is the pore fraction) [70], and E is Young's modulus. Table 4 shows that the results of the average force constant of CoFe 2 O 4 increased significantly after being given the addition of Bi 3+ and La 3+ ions. While, the addition of Al 3+ ions experienced a very small decrease in the average force constant. This result resulted in a very large change in Young's modulus in the CoFe 2 O 4 nanoparticles after being given the addition of Bi 3+ and La 3+ ions, whereas the addition of Al 3+ ions did not change. A significant change in Young's modulus will result in a strain-induced magnetic anisotropy [61,71]. Figure 7 also indicates the presence of other absorptions. The absorption that appears is in the area around 3400 cm −1 , which indicates the presence of hydroxyl group stretching vibrations. Another absorption peak was observed at ∼2300 cm −1 indicating the presence of aliphatic and aromatic C-H bonds. The peak at approximately 1600 cm −1 can be attributed to the symmetrical and asymmetrical strain vibrations of the CO 2 group [72][73][74].      K calculation magnitude is one-tenth of the order smaller than the K 1 calculation. So, the contribution of the effective ansiotropy (K eff ) of magnetic nanoparticles is dominantly contributed by K 1 . The calculation of the anisotropic stress field magnitude ( s H ) as shown in  [48,71,75,76].
When, single-domain and multi-domain configuration is discussed if the M R /M S magnitude <0.5 then magnetization process is included in the multi-domain structure. Contrary if the M R /M S magnitude >0.5 indicates magnetization which is associated with the formation of a single-domain structure in the grain. Table 5 also shows that the M R /M S magnitudes were 0.56, 0.65, 0.62, and 0.52 for CoFe 2 O 4 , CoBi 0.1 Fe 1.9 O 4 , CoLa 0.1 Fe 1.9 O 4 , and CoAl 0.1 Fe 1.9 O 4 nanoparticles, respectively. The obtained results confirm that all nanoparticles magnetic have a single-domain structure which contribute to the high coercive field [53,77,78].
The H C and M S results shown in figure 8 were used to calculate the magnitude of the n B and K, as shown in table 4. by the following equation [15], Law, H is the applied field, and m 0 is permeability of the free space [80]. Meanwhile, the B value can also be used to calculate the effective magnetic anisotropy (K eff ). K eff follows the equation where the magnitude of h is a constant which is 4/15 for uniaxial anisotropy and 8/105 for cubic anisotropy. In where, K 1 is the magnetocrystalline anisotropic constant, | | l l = is the magnetostriction constant, and s is the internal compressive stress. The relationship between effective magnetic anisotropy and magnetocrystalline anisotropic constant is K eff = K 1 + s K where s K is magnetoelastic anisotropic constant (i.e., strain-induced magnetoelastic anisotropic constant). The magnitude of s K is obtained from the relationship of induced stress with Young's modulus and microstrain (s e = E ) along the c-direction as follows, where, l is obtained from the average magnetostriction constant ( ( ) ). CoFe 2 O 4 has two magnetostrictive strain coefficients, namely l 100 = -5.9 × 10 −4 and l 111 = 1.2 × 10 −4 along the crystallographic axes 〈100〉 and 〈111〉 [61]. Furthermore, the anisotropic stress field magnitude can also be obtained using the following equation, Meanwhile, the estimation of the static Jahn-Teller (J-T) splitting of e .g. and t 2g orbits can be calculated by the following equation [82], where, d e is the static Jahn-Teller (J-T) splitting of e g orbit, d JT is the static Jahn-Teller (J-T) stabilization of t 2g orbit, D c is the cubic crystal field energy ∼2 eV, c lat is elastic constant ∼2 × 10 12 dyne cm −2 , and d BX is the octahedral bond length [61].  [61,82].
From the calculation results, the trivalent metal cation substitution determines the magnitude of the microstrain. So, the two mechanism such as Jahn-Teller effect and strain-induced magnetism attribute to the changes of magnetic properties [42,44,45]. The highest H C of La 3+ substituted CoFe 2 O 4 has the potential to be used as an alternatively permanent magnet.

Conclusion
CoFe 2 O 4 , CoBi 0.1 Fe 1.9 O 4 , CoLa 0.1 Fe 1.9 O 4 , and CoAl 0.1 Fe 1.9 O 4 nanoparticles were successfully synthesized by the coprecipitation method. The addition of metal ions (Bi 3+ , La 3+ , and Al 3+ ) to CoFe 2 O 4 results in the formation of a cubic spinel structure in the XRD pattern. Although the crystal structure did not change, the shift in the peak of hkl (311) showed that each ion occupied a different crystal structure, both in octahedral and tetrahedral sites. The addition of Bi 3+ and Al 3+ ions to CoFe 2 O 4 reduced its crystallite size and lattice constant. The addition of La 3+ ions to CoFe 2 O 4 resulted in an increase in the crystallite size and lattice constant. This event was caused by the difference in the radii of the ions (Bi 3+ , La 3+ , and Al 3+ ) that replaced Fe 3+ . The change in crystallite size was confirmed by SEM images, which showed a decrease in grain size when Bi 3+ and Al 3+ ions were added to CoFe 2 O 4 and an increase when La 3+ ions were added to CoFe 2 O 4 . In the FTIR curve, the addition of metal ions (Bi 3+ , La 3+ , and Al 3+ ) to CoFe 2 O 4 produced absorption peaks at tetrahedral and octahedral sites. The absorption that appeared at the tetrahedral and octahedral sites was the effect of ion substitution on the CoFe 2 O 4 structure. The VSM curve shows that the kOe order of the coercive field is obtained for the whole nanoparticles magnetic samples. The realization of a large coercive field is contributed by the presence of a single domain configuration for the whole magnetic nanoparticle sample. In addition, the both Jahn-Teller effect and the strain-induced magnetism resulting in a high-stress field-anisotropy is also seen as another supporting factor for the presence of a large coercive field in this cobalt ferrite-based nanoparticle system. This shows that CoFe 2 O 4 after doping with Bi 3+ , La 3+ , and Al 3+ has the potential to be used as a permanent magnet.