**3.7 Magnetic properties of MFe2O4 nanocrystal obtained VSM**

The room temperature (300 K) magnetic properties of the prepared precursors and MFe2O4 nanoparticles calcined at different temperatures were investigated by the VSM technique in the range of approximately –15 to +15 kOe. Except for the precursors which were nonmagnetic material, the calcined samples exhibited different magnetic behaviors. The room temperature magnetic behaviors of metal ferrite nanoparticles which fabricated by thermal treatment method, can be explained as the results of the four important factors: cationic distribution in spinel structure, the heating rate of calcinations, impurity phase of α-Fe2O3, and the surface spin structure of nanoparticles. Although all of these factors can be effective in magnetic behaviors but, their effects on the ferrite nanoparticles with different structures are not similar. We will have a discussion on this matter in next subsections.

#### **3.7.1 Znic ferrite nanoparticles**

Figure 25 shows the magnetization curves of precursor and ZnFe2O4 nanoparticles at (a) 723 (b) 773 (c) 823 and (d) 873 K. Their coercivity fields (Hc) are almost negligible, and all of them exhibit super-paramagnetic behaviours. Table 4 provides the values of saturation magnetization (Ms) of the calcined samples, along with calcinations temperatures and particle sizes. These data make it clear that different parameters were responsible for the saturation magnetization decreasing from 4.49 to 0.74 emu/g when the particle size increased from 17 to 31 nm. Cation inversion is one of the most important parameters that can be effective in the variation of the magnetic properties of zinc ferrite nanoparticles from the properties of the bulk form of the same material. In bulk form, zinc ferrite has an normal spinel structure in which all Zn2+ ions are in A sites and Fe3+ ions are distributed in B sites [47]. However, in bulk, zinc ferrite only occurs in intra-sub-lattice (B-B) exchange

Fig. 24. TEM images of nickel ferrite nanoparticles calcined at (a) 723 (b) 773 (c) 823 (d) 873 K.

The room temperature (300 K) magnetic properties of the prepared precursors and MFe2O4 nanoparticles calcined at different temperatures were investigated by the VSM technique in the range of approximately –15 to +15 kOe. Except for the precursors which were nonmagnetic material, the calcined samples exhibited different magnetic behaviors. The room temperature magnetic behaviors of metal ferrite nanoparticles which fabricated by thermal treatment method, can be explained as the results of the four important factors: cationic distribution in spinel structure, the heating rate of calcinations, impurity phase of α-Fe2O3, and the surface spin structure of nanoparticles. Although all of these factors can be effective in magnetic behaviors but, their effects on the ferrite nanoparticles with different structures

Figure 25 shows the magnetization curves of precursor and ZnFe2O4 nanoparticles at (a) 723 (b) 773 (c) 823 and (d) 873 K. Their coercivity fields (Hc) are almost negligible, and all of them exhibit super-paramagnetic behaviours. Table 4 provides the values of saturation magnetization (Ms) of the calcined samples, along with calcinations temperatures and particle sizes. These data make it clear that different parameters were responsible for the saturation magnetization decreasing from 4.49 to 0.74 emu/g when the particle size increased from 17 to 31 nm. Cation inversion is one of the most important parameters that can be effective in the variation of the magnetic properties of zinc ferrite nanoparticles from the properties of the bulk form of the same material. In bulk form, zinc ferrite has an normal spinel structure in which all Zn2+ ions are in A sites and Fe3+ ions are distributed in B sites [47]. However, in bulk, zinc ferrite only occurs in intra-sub-lattice (B-B) exchange

**3.7 Magnetic properties of MFe2O4 nanocrystal obtained VSM** 

are not similar. We will have a discussion on this matter in next subsections.

**3.7.1 Znic ferrite nanoparticles** 

interactions, and it does not have intra-sub-lattice (A-A) exchange interactions or inter-sublattice (A-B) super-exchange interactions [48]. Inter-sub-lattice (A-B) super-exchange interactions of the cations are much stronger than the (A-A) and (B-B) interactions [18].Due to the cation inversion, which originates from thermal and mechanical treatment [40], the structure of ZnFe2O4 transfers from a normal spinel structure to a mixed spinel structure [48]. This cation inversion causes the zinc ferrite nanoparticles to experience inter-sub-lattice (A-B) super-exchange interactions and intra-sub-lattice (A-A) exchange interactions in addition to intra-sub-lattice (B-B) exchange interactions. But, due to the degree of inversion, which is large for smaller size particles, inter-sub-lattice (A-B) super-exchange interactions in smaller size particles occur to a greater extent than in larger size particles. Hence, saturation magnetization increases for smaller size particles [49], using Mossbauer's experiment, showed that the degree of inversion is large in the case of smaller size particles. Also, an impure α-Fe2O3 phase was detected by XRD (Figure20a), the heating rate of calcinations and the surface spin structure can be an influence that increases the saturation magnetization in smaller size particles [37].

Fig. 25. Magnetization curves at room temperature for precursor and zinc ferrite nanoparticles calcined at (a) 723 (b) 773 (c) 823 (d) 873 K.

#### **3.7.2 Manganese ferrite nanoparticles**

Figure 26 shows the curves of magnetization of precursor and MnFe2O4 nanoparticles which exhibited a typical super-paramagnetic behavior. Table 4 depicts the values of saturation magnetization (Ms) of different samples. When the calcination temperature increased from 723 K to 873 K, the saturation magnetization increased from 3.06 to 15.78 emu/g. This can be attributed to spin canting and surface spin disorder that occurred in these nanoparticles [50].The interactions between the A and B sub-lattices in the spinel lattice system (AB2O4) consist of inter-sub-lattice (A-B) super-exchange interactions and intra-sub-lattice (A-A) and (B-B) exchange interactions. Inter-sub-lattice super-exchange interactions of the cations on the

Crystalization in Spinel Ferrite Nanoparticles 375

As listed in Table 4, the values of Ms for the nickel ferrite nanoparticles were observed to increase with increasing temperature [58, 59]. The largest saturation magnetization was 34.19 emu/g for the sample calcined at 873 K, which is lower than that reported for the multi-domain, bulk nickel ferrite (55emu/g) [60].The decrease in saturation magnetization of these samples, compared to that of bulk material, depends on four factors explained in section 2.15. It seems that in inversed spinel ferrite nanoparticles such as nickel ferrite or cobalt ferrite nanoparticles which fabricated by thermal treatment method, the heating rate of calcination is more important than other parameters that can effectively increase or decrease the saturation magnetization.[35,61]. In our experiments, the heating rate of calcination was 10 K/min for nickel, zinc and manganese ferrite nanoparticles calcined at 723, 773, 823, and 873 K, which was a medium heating rate (Table 3). Therefore, it is possible that calcination at a slower heating rate would allow crystallization to be more complete and the magnetic phase could also increase, resulting in larger saturation magnetization. Sangmanee *et al*. [36] showed that saturation magnetization increases from 9.7 to 56.5 emu/g with decreasing the heating rate of calcination from 20 K/min to 5 K/min in cobalt ferrite nanostructures calcined at 773 K and fabricated by electrospinning. In addition, the appearance of the weakly-magnetic, impure phase of α-Fe2O3 (shown in Figure20c) can reduce the saturation magnetization [37].Variations of saturation magnetization with particle size for nickel ferrite nanoparticles are listed in Table 4. The saturation magnetization values of the calcined samples increase with increasing particle size, which may be attributed to the surface effects in these nanoparticles. The surface of the nanoparticles seems to be composed of some distorted or slanted spins that repel the core spins to align the field direction. Consequently, the saturation magnetization decreases for smaller sizes [62-64]. Furthermore, the surface is likely to behave as an inactive and dead layer with inconsiderable magnetization [56, 57]. The variation in the value of the saturation magnetization with particle size also can be resulted from the cation redistribution (interchanging of Ni and Fe ions of the tetrahedral and octahedral sites). This cation redistribution, causes that the structure of NiFe2O4 transfers from an inverse spinel structure

Fig. 27. (left) The magnetization curves of precursor and the nickel ferrite nanoparticles calcined at (a) 723 (b) 773 (c) 823 and (d) 873 K which measured at room temperature in the range of approximately −15 to +15 kOe. Figure27. (right) the expanded field region around the origin for clear visibility of the readers, in the range of approximately −400 to +400 Oe.

(A-B) are much stronger than the (A-A) and (B-B) intra-sub-lattice exchange interactions [18, 51].As discussed earlier (Figure20b), by increasing the calcination temperature of the MnFe2O4 nanoparticles, Fe3+ ions transferred from B site to A site, so, consequently, the accumulation of Fe3+ ions increased in A site; however, the FeA3+- FeB3+ super-exchange interactions increased (FeA3+- FeB3+ interactions were twice as strong as the MnA2+- FeB3+ interactions), and this can lead to an increase in saturation magnetization in MnFe2O4 nanoparticles [52]. Aslibeiki *et al*. [53] showed that saturation magnetization increases with increasing temperature and particle size in MnFe2O4 nanoparticles.It has been reported [54] that the spin disorder may occur on the surface of the nanoparticles as well as within the cores of the nanoparticles due to vacant sublattice disorder sites (FeA3+) and poor crystal structure. The other point that is understood from Table 4 is that the values of saturation magnetization are expressively lower than those reported for the bulk MnFe2O4 (80 emu/g) [55]. The decrease in saturation magnetization of all the samples compared to that of the bulk is ascribed to the surface effects in these nanoparticles. The existence of an inactive magnetic layer or a disordered layer on the surfaces of the nanoparticles and the heating rate of calcinations can be due to the decrease of saturation magnetization compared to the bulk value [56, 57].

Fig. 26. Magnetization curves at room temperature for precursor and manganese ferrite nanoparticles calcined at (a) 723 (b) 773 (c) 823 (d) 873 K.

#### **3.7.3 Nickel ferrite nanoparticles**

Figure 27 (left) exhibits the hysteresis curves of precursor and NiFe2O4 nanoparticles which exhibited a typical ferromagnetic behavior. It can be seen from this figure that the magnetic properties of nanoparticles depended on the calcinations temperature. Saturation magnetization (Ms) values of 21.37, 26.67, 29.05 and 34.19 emu/g are observed for the nickel ferrite nanoparticles calcined at 723, 773, 823, and 873 K, respectively. There is a clear tendency of Ms increase with the enhancement of crystallinity of the NiFe2O4 nanoparticles.

(A-B) are much stronger than the (A-A) and (B-B) intra-sub-lattice exchange interactions [18, 51].As discussed earlier (Figure20b), by increasing the calcination temperature of the MnFe2O4 nanoparticles, Fe3+ ions transferred from B site to A site, so, consequently, the accumulation of Fe3+ ions increased in A site; however, the FeA3+- FeB3+ super-exchange interactions increased (FeA3+- FeB3+ interactions were twice as strong as the MnA2+- FeB3+ interactions), and this can lead to an increase in saturation magnetization in MnFe2O4 nanoparticles [52]. Aslibeiki *et al*. [53] showed that saturation magnetization increases with increasing temperature and particle size in MnFe2O4 nanoparticles.It has been reported [54] that the spin disorder may occur on the surface of the nanoparticles as well as within the cores of the nanoparticles due to vacant sublattice disorder sites (FeA3+) and poor crystal structure. The other point that is understood from Table 4 is that the values of saturation magnetization are expressively lower than those reported for the bulk MnFe2O4 (80 emu/g) [55]. The decrease in saturation magnetization of all the samples compared to that of the bulk is ascribed to the surface effects in these nanoparticles. The existence of an inactive magnetic layer or a disordered layer on the surfaces of the nanoparticles and the heating rate of calcinations can be due to the decrease of

Fig. 26. Magnetization curves at room temperature for precursor and manganese ferrite

Figure 27 (left) exhibits the hysteresis curves of precursor and NiFe2O4 nanoparticles which exhibited a typical ferromagnetic behavior. It can be seen from this figure that the magnetic properties of nanoparticles depended on the calcinations temperature. Saturation magnetization (Ms) values of 21.37, 26.67, 29.05 and 34.19 emu/g are observed for the nickel ferrite nanoparticles calcined at 723, 773, 823, and 873 K, respectively. There is a clear tendency of Ms increase with the enhancement of crystallinity of the NiFe2O4 nanoparticles.

saturation magnetization compared to the bulk value [56, 57].

nanoparticles calcined at (a) 723 (b) 773 (c) 823 (d) 873 K.

**3.7.3 Nickel ferrite nanoparticles** 

As listed in Table 4, the values of Ms for the nickel ferrite nanoparticles were observed to increase with increasing temperature [58, 59]. The largest saturation magnetization was 34.19 emu/g for the sample calcined at 873 K, which is lower than that reported for the multi-domain, bulk nickel ferrite (55emu/g) [60].The decrease in saturation magnetization of these samples, compared to that of bulk material, depends on four factors explained in section 2.15. It seems that in inversed spinel ferrite nanoparticles such as nickel ferrite or cobalt ferrite nanoparticles which fabricated by thermal treatment method, the heating rate of calcination is more important than other parameters that can effectively increase or decrease the saturation magnetization.[35,61]. In our experiments, the heating rate of calcination was 10 K/min for nickel, zinc and manganese ferrite nanoparticles calcined at 723, 773, 823, and 873 K, which was a medium heating rate (Table 3). Therefore, it is possible that calcination at a slower heating rate would allow crystallization to be more complete and the magnetic phase could also increase, resulting in larger saturation magnetization. Sangmanee *et al*. [36] showed that saturation magnetization increases from 9.7 to 56.5 emu/g with decreasing the heating rate of calcination from 20 K/min to 5 K/min in cobalt ferrite nanostructures calcined at 773 K and fabricated by electrospinning. In addition, the appearance of the weakly-magnetic, impure phase of α-Fe2O3 (shown in Figure20c) can reduce the saturation magnetization [37].Variations of saturation magnetization with particle size for nickel ferrite nanoparticles are listed in Table 4. The saturation magnetization values of the calcined samples increase with increasing particle size, which may be attributed to the surface effects in these nanoparticles. The surface of the nanoparticles seems to be composed of some distorted or slanted spins that repel the core spins to align the field direction. Consequently, the saturation magnetization decreases for smaller sizes [62-64]. Furthermore, the surface is likely to behave as an inactive and dead layer with inconsiderable magnetization [56, 57]. The variation in the value of the saturation magnetization with particle size also can be resulted from the cation redistribution (interchanging of Ni and Fe ions of the tetrahedral and octahedral sites). This cation redistribution, causes that the structure of NiFe2O4 transfers from an inverse spinel structure

Fig. 27. (left) The magnetization curves of precursor and the nickel ferrite nanoparticles calcined at (a) 723 (b) 773 (c) 823 and (d) 873 K which measured at room temperature in the range of approximately −15 to +15 kOe. Figure27. (right) the expanded field region around the origin for clear visibility of the readers, in the range of approximately −400 to +400 Oe.

Crystalization in Spinel Ferrite Nanoparticles 377

study also substantiated that, in ferrites, the values of the quantities that were acquired by VSM, such as saturation magnetization and coercivity field, are primarily dependent on the methods of preparation of the ferrites. This simple method, which is cost-effective and environmentally friendly, produces no toxic byproducts and can be used to fabricate pure,

Furthermore, this method can be extended to the synthesis of other spinel ferrite

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**5. References** 

to a mixed spinel structure [65].Figure 27 (right) shows the expanded coercivity field (Hc) of region around of origin for clear visibility at room temperature in the range of approximately –400 to +400 Oe. The coercivity field values are listed in Table 4. These variations are not similar with saturation magnetization because, when the particle size increases from 15 to 69 nm, the coercivity field decreases from 150 to 32 Oe at room temperature. Variations of the coercivity field with particle size of nickel ferrite nanoparticles can be elucidated on the basis of domain structure, critical size, and the anisotropy of the crystal [16, 66-67].

Finaly, It is worth noting that the magnetic properties of similar ferrite nanoparticles of the same particle size differ depending on the preparation method used. Table 5 shows some literature values of Ms and Hc that were measured at similar conditions for some spinel ferrite nanoparticles. The data show that the pairs of similar spinel ferrite nanoparticles of the same particle size have different saturation magnetization values and coercivity fields. The results indicate that, in fact, the magnetic properties of ferrites are related primarily to the methods used to prepare them.


Table 5. Magnetic properties of some spinel ferrite nanoparticles reported in the literatures which were measured at room temperature in range of approximately −10 to +10 kOe.
