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Introduction

The spinel-type ferrite materials attract the attention of researchers due to their unique structural and magnetic properties [1]. Thus, due to the complex nature of redistribution of magnetic cations between different crystallographic positions in the spinel crystal structure these compounds show unusual types of magnetic ordering, the spine-glass states, incommensurate and canted magnetic structures [2-4]. Besides, those materials also have found different applications in industry and technologies [5-7] as transformer cores, radio frequency circuits, antennas, data storage devices, magnetic nanostructures, and etс.

The formation of unique magnetic properties in spinel ferrites is mainly due to redistribution of magnetic ions between two non-equivalent crystallographic positions in the face-centered cubic structure with the space group Fd: crystallographic position A with tetragonal oxygen environment and position B with octahedral coordination one [8, 9]. It is accepted that all magnetic interactions in spinel ferrites are divided into three main groups: magnetic interactions between ions in position A (magnetic exchange interaction JAA), magnetic interactions JBB between cations in position B and exchange interactions between magnetic cations in different crystal positions – JAB [9, 10]. It is believed that the magnetic interaction of JAB is much stronger than the interactions of JAA and JBB, which leads to the stabilization of the ferrimagnetic state in mixed spinel types [10]. As, an example, for tetragonal ferrite, ZnFe2O4 is characterized by the filling of the iron ions in the octahedral positions only [11]. On the other hand, in the ferrite MnFe2O4, Fe3+ ions sits in both positions [12]. The changes in the doping ratio of  Mn3+ and Zn3+ ions of the initial spinel compound leads to significant transformations in the magnetic properties of such compounds.

Another interesting ferrite is CoFe2O4 [13, 14]. In this ferrite compound, cobalt ions Co3+ fill both A and B crystallographic positions and the relative distribution could depend on the synthesis conditions or the size effect of granules [15] or nanoparticles [16]. The relative distribution of cobalt cations between different crystallographic positions, as well as the features of the magnetic structure of ferrite materials, can be successfully studied by means of the neutron diffraction method [15, 17, 18]. On the other hand, doping with non-magnetic ions with large ionic radius can be applied to targeted control the occupation of different cations in certain crystallographic positions [19]. Thus, such large ions mainly occupy the oxygen octahedrа in cubic spinel structure, which leads to the redistribution of magnetic cations in the tetragonal crystallographic position [20] and as a result the changes in the magnetic structure of ferrites [21]. In our work, we had perform detailed studies of the crystal and magnetic structure of doped cobalt ferrites CoFe2-xCexO4 for cerium concentration range 0-0.1 due to the further insight of structure-magnetic properties relationships in spinel ferrites. 

Experimental techniques

The samples CoCexFe2-xO4, (x= 0.0, 0.03, 0.05, 0.1), prepared by chemical auto-combustion method [22]. The starting materials are the nitrates of Cobalt, Iron and Cerium. A stoichiometric ratio of citric acid with formula (C6H6O7) used as an organic fuel to achieve the required temperature of reaction. The mixture of nitrates and fuel were dissolved in a small amounts of doubly distilled water, thereafter stirred for 2 h and heated to a temperature of (80 ⁰C). The PH value of the solution is mandatory to be adjusted to 7–8 during the time of heating and stirring.  By the end of the previous process the water evaporated, and a dry viscous gel is formed. Therefore, the burned gel converted to fluffy powder, which was collected and ground in an agate mortar to obtain a fine powder. X-ray diffraction (XRD) performed by Rigaku diffractometer with Cu Kα-radiation (λ=1.5406 Å). (VSM) measurements obtained by using- Lake Shore Model 7410 (USA), at a temperature of 100 K and by Appling magnetic field up to 20 kOe. Neutron powder diffraction experiments at ambient conditions were performed with the DN-6 diffractometer [23] at the IBR-2 high-flux pulsed reactor (Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russia). Diffraction patterns were measured at a scattering angle of 2q= 90° with the resolution Dd/d=0.022 at d=2 Å. The typical exposure time of one neutron diffraction pattern was – 20 min. The analysis of neutron diffraction data was performed by the Rietveld method using the FullProf software package [24].

Results and discussion

X-ray diffraction

X-ray diffraction of the nano-ferrite samples CoCexFe2-xO4, (x= 0.0, 0.03, 0.05, 0.1) synthesized by chemical auto-combustion method shown in Figure 1. The results of XRD, published in our previous work [22], confirm the formation of the samples in nano-scale with a single phase cubic structure. The grain size (D) decreases with substitution ratio of Ce3+ in Co-ferrite system [22].

Low temperature (VSM) measurements

Magnetic hysteresis M-H loops obtained at 100 K by applying an external magnetic field of ±20 kG for CoFe2-xCexO4, (x= 0.0, 0.03, 0.05, 0.1) samples are shown in Figure 2. The M-H results will be discussed based on: 1- the concentration of paramagnetic Ce3+ ions, which have no magnetization contributions in the spinel lattice [25-28]. 2- the ionic radius of cerium (1.03Å) is relatively larger than that of Fe3+ (0.64 Å). This indicates that Ce3+ substitutes Fe3+ only in octahedral B-site, which has radius larger than that of the tetrahedral A-site. Therefore, the magnetic moment of B-site gradually reduces by further addition of Ce3+. Consequently, the net magnetic moment of the lattice decreases according to the equation: M = [MB - MA], where MA and MB represents the magnetic moments of A and B sites, respectively [29-32]. These results confirmed with the neutron diffraction data obtained in section 3.3. Besides, the disparity in ionic radii between Ce3+ and Fe3+ can causes a disturbance in the structure by producing strain and disorder in the electronic state. For all the samples in the series CoFe2-xCexO4, the hysteresis is clearly observed Figure 2. The magnetic parameters; Ms, Hc, Mr  calculated from M-H loops at 100 K listed in Table 1, are found to be larger than their values estimated at room temperature (RT) [22]. One of the reasons for increasing such parameters at low temperature is that the magnetic moments are thermally fluctuated and reduced. The Hc values ranging between 6434 and 8682 G, while Ms and Mr values were 45.6-120 and 33.2-95.5 (emu/g) respectively. These values obtained at 100 K are indication of the ferrimagnetic nature (FM) of the Ce3+ substituted Co-ferrite [25]. Moreover, the substitution of RE in CoFe2O4 increases the degree of anisotropy and the spin orbit coupling in B-site. One the other hand, except for the sample with (x=0.1) the values of Ms decrease by further addition of Ce3+ Figure 3. Similar behavior obtained for the remanence values Mr Table 1. Pervious works reported that the magnetic parameters for nanoparticles can be changed due to the effect of grain size, strain and values of magnetic moments. The spin coupling interaction between magnetic ions through the 3d electrons is the main reason for the magnetic properties of ferrites. In case of rare earth addition the RE3+-Fe3+ interaction happens by the 3d–4f coupling, which reduces the magnetic interaction through limitation of the charges exchange in the A- and B-sites. Moreover, the RE3+–RE3+ interactions are negligible and consequently the magnetization are reduced [33, 34]. The squareness factor Mr/Ms, Table 1 with values > 0.5 confirms the existence of cubic magnetocrystalline anisotropy, which is an indication of the single domain structure [29, 35, 36]. When the major hysteresis loops is closed Figure 2, it is also another signature of the formation of a single domain, while all the irreversible hysteresis processes are completed [37].

Neutron diffraction (ND)

The neutron diffraction patterns of the studied CoFe2-xCexO4 ferrites with different cerium content are shown in Figure 4. All neutron patterns correspond to the cubic structure with the space group Fdm [8]. The obtained structural parameters of studied compounds are listed in Table 2. When cerium concentration increases, the lattice parameter of cubic structure grows (Figure 5a). The crystal structure of CoFe2-xCexO4 ferrites contains oxygen octahedra with Fe/CoB-O and tetrahedral units with Fe/CoA-O (Figure 4b). The calculated from experimental data the bond lengths as a function of cerium concentration are shown in Figure 6.

It is possible to calculate the distribution of cations between tetragonal and octahedral crystallographic positions from neutron diffraction data. The refined chemical compositions of studied ferrites including the distribution of the different crystallographic positions are listed in Table 2.

The concentration dependence of the bond lengths Fe/Co-O for octahedral and tetrahedral positions for ferrites CoFe2-xCexO4 is shown in Figure 5b. We calculate the changes in the volumes of octahedral B and tetrahedral A crystallography units under variation of cerium content. The corresponding data is shown in Figure 6. The increase of the Fe/CoB-O bond length and the volume of the octahedra unit indicates the fact that cerium ions with a large ion radius embed in the octahedral units. It should be noted that the corresponding Fe/CoA-O bond length of tetragonal oxygen units and its volume does not change under the cerium doping. Under cerium increasing the bond angle Fe/CoA-O-Fe/CoB decrease from 123.5(4)o to 121.8(3)o.

It is known that the decrease in the valence angle means an increase in the structural disordering, which leads to a decrease in the magnetic moment of iron and cobalt in the appropriate crystallographic positions. The determined values of the average magnetic moments MA and MB of cobalt and iron magnetic ions in tetrahedral and octahedral crystallographic positions, respectively, were listed in Table 2. The magnetic moments MA and MB as a function of cerium concentration is presented in Figure 7. It is obvious that the increase of the cerium concentration leads to a decrease in the average magnetic moment not only in the octahedral position B where the cerium is embedded, but also in the tetragonal one. This is due to not only the change of weak magnetic interaction of JBB but also changes in the dominant magnetic exchange JAB [9, 10].

Conclusion

A mixture of pure CoFe2O4 and Co-ferrite doped Ce3+ ions have been prepared and studied in this study. The results of XRD confirm the formation of the samples in nano-scale with a single-phase cubic structure. VSM data shows that Ce3+ substitutes Fe3+ only in octahedral B-site, which indicates that the magnetic moment of B-site gradually reduces by further addition of Ce3+. The disparity in ionic radii between Ce3+ and Fe3+ can causes a disturbance in the structure by producing strain and disorder in the electronic state. A closed hysteresis loops is obtained, which is a signature of the formation of a single domain and all the irreversible hysteresis processes are completed. The effect of Ce cerium concentration for CoFe2-xCexO4 ferrite on their crystal and magnetic structure by neutron diffraction was investigated. The obtained values of the lengths of interatomic bonds and secondary of the magnetic moments in different crystallographic positions allow to identify structural mechanisms of formation of magnetic properties of ferrite CoFe2-xCexO4 at different x.