Effect of Ho³⁺ substitution on the cation distribution, crystal structure and magnetocrystalline anisotropy of nanocrystalline cobalt ferrite

Abstract

Ho³⁺ ion-substituted nanocrystalline cobalt ferrite materials with the chemical formula CoFe_{2− x} Ho _x O₄ for x = 0.0, 0.025, 0.05, 0.075 and 0.1 have been synthesised by standard citrate precursor method. Crystal structure and phase purity have been studied by powder X-ray diffraction (XRD) method by employing Rietveld refinement technique. The distribution of cations between the tetrahedral site (A-site) and octahedral site (B-site) has been estimated by Rietveld analysis. The refinement result shows that Ho³⁺ ion has a strong preference for octahedral sites (B-sites). The lattice constants decrease with the Ho³⁺ concentration up to x = 0.05. Crystallite size decreases with the Ho³⁺ concentration. The magnetic hysteresis loop measurements have been carried out at room temperature using a vibrating sample magnetometer (VSM) over a field range of ±2 T. The magnetisations in saturation have been analysed by employing the ‘law of approach (LA)’ technique. The magnetocrystalline anisotropy constant and saturation magnetisation are found to decrease with the Ho³⁺ concentration up to x = 0.05. The coercivity decreases with the Ho³⁺ concentration. The vibrational modes of the octahedral and tetrahedral metal complex in the sample have been carried out using Fourier transform infrared spectroscopy (FT-IR). The FT-IR spectra of the samples have been analysed in the wave number range of 350–1000 cm⁻¹. We have observed two prominent absorption bands which are assigned to tetrahedral and octahedral metal complexes. The elemental analysis has been carried out using energy dispersive spectroscopy (EDS) with the help of field emission scanning electron microscope (FE-SEM) and the results reveal that, elements are as per the stoichiometric ratio in all the samples.

Keywords:

• spinel
• ferrite
• nanocrystalline
• Rietveld
• magnetocrystalline anisotropy

1. Introduction

Ferrimagnetic spinel ferrites having general molecular formula (M)²⁺[Fe₂]³⁺O₄: M = Co²⁺, Fe²⁺, Ni²⁺, etc.) are important classes of magnetic ceramics which crystallise to a cubic closed-pack structure of oxygen ions with space group. In spinel ferrite, the unit cell consists of eight formula units, i.e. 56 ions, in which 32 divalent oxygen ions are in direct contact to one another forming interstitial sites called tetrahedral (A-sites) and octahedral (B-sites) sites. The unit cell consists of 64 tetrahedral and 32 octahedral sites, out of which eight tetrahedral and 16 octahedral sites are occupied by divalent and trivalent metal cations, respectively 1. In general, simple single-magnetic cation spinel ferrites have limited technological applications but mixed spinel ferrites are widely used because they exhibit wide variety of physical properties. In mixed spinel ferrites, the magnetic properties depend on several factors such as, method of preparation, chemical composition, annealing temperature and distribution of cations among the tetrahedral (A) and octahedral (B) sites 1. However, understanding the cation distribution in these mixed spinel ferrites and their effect on the magnetic properties is still a challenging problem. Among the mixed spinel ferrites, cobalt ferrite (CoFe₂O₄) has drawn considerable attention due to its high coercivity, moderate saturation magnetisation along with good mechanical hardness and chemical stability 2. It is a hard ferrimagnetic material with a high-magnetic ordering temperature around ∼520°C and it is represented as ()[]O₄, where cations inside the round and square brackets occupy A-sites and B-sites, respectively, and x depends on the thermal history and preparation conditions 3. This material is a versatile magnetic material for technological applications such as, magnetic resonance imaging contrast agents, data storage devices, transformer cores, ferrofluid technology, magneto caloric refrigeration, etc. 4–6.

The cubic CoFe₂O₄ has large magnetocrystalline anisotropy energy (MAE) with positive anisotropy constant and it has six easy directions along the cubic edges of the crystal represented as ⟨100⟩, four hard directions across the body diagonals denoted as ⟨111⟩ and 12 saddle points across the face diagonals which lead to large and positive magnetocrystalline anisotropy constant (K ₁) 7–9. The large magnetocrystalline anisotropy of pure cobalt ferrite (CoFe₂O₄) is primarily due to a strong spin(S)–orbit (L) coupling in Co²⁺ ions at the octahedral sites. The crystal field (trigonal field) is not capable of removing the orbital degeneracy of Co²⁺ at the octahedral sites so that the orbital magnetic moment is not quenched and therefore there is strong L–S coupling which produces large MAE 10. Thus large multiaxial positive K ₁ makes it hard magnetic material. The reported values of K ₁ of bulk CoFe₂O₄ at room temperature range from 2.1 × 10⁶ to 3.9 × 10⁶erg/cm³ depending on the stoichiometry of the material and heat treatment 11,12. The K ₁ of nanocrystalline cobalt ferrite are found to depend on synthesis method as well as annealing temperature 13. The K ₁ of nanocrystalline cobalt ferrite synthesised by citrate precursor method and annealed at 400°C (crystallite size about ∼12 nm) is found to be 0.843 × 10⁶erg/cm³ and increase with the crystallite size 13. The K ₁ of CoFe₂O₄ particles of size about ∼3.3 nm is found to be 3.15 × 10⁷erg/cm³ 14. This magnetocrystalline anisotropy is a very important parameter for the characterisation of the magnetic materials, which decides whether the magnetic material is magnetically soft or hard material and, it can be tuned by replacing A site and/or B site by different transition and non-transition elements. The recent investigations of the substitution at the Fe sites of CoFe₂O₄ by various cations like Ga, Mn, Al, Cr, etc., have revealed the change in atomic level magnetic interaction, which has modified the K ₁ and magnetic properties 15–18.

The magnetic properties in mixed spinel cobalt ferrite are largely governed by various superexchange interactions (i.e. Fe³⁺(B)–O–Fe³⁺(B), Fe³⁺(B)–O–Co²⁺(B), Fe³⁺(B)–O–Fe³⁺(A), Co²⁺(B)–O–Fe³⁺(A) and Co²⁺(A)–O–Fe³⁺(B). Hence, the magnetic behaviour is largely governed by the spin coupling of the unpaired transition metal 3 d electrons present at the A- and B-sites 19. The RE³⁺ (RE ≈ Rare Earth) ions possess a variety of magnetic properties such as, their magnetic moment vary from 0 (La³⁺) to 10.64 µ_B (Dy³⁺) 20–23. If there is substitution of small amount of RE cations (RE³⁺, i.e. the 4f elements series) in place of Fe ions, one can expect an appearance of spin coupling of 3 d-4f electrons, which will modify the magnetic properties such as change of magnetic moment, K ₁, etc. Several authors have reported the synthesis of RE³⁺ substituted nanocrystalline spinel ferrites using solid-state route. However, it suffers from lot of drawbacks like phase segregation such as orthoferrites (REFeO₃) 24–28, hematite (α-Fe₂O₃) 29,30 and metal monoxides 31 even for very low RE³⁺ concentration. However, there are few reports available, which have mentioned the synthesis of RE³⁺ substituted nanocrystalline spinel ferrites in single-phase form using different chemical routes despite having big difference in ionic radius of RE³⁺ and Fe³⁺ ions. For instance, using micellar route, Zhao et al. 23 have prepared the pure and chemically homogeneous CoFe_{2− x} Nd _x O₄ up to x = 0.2. Also CoFe_{2− x} RE _x O₄ with RE = Ce, Sm, Eu, Gd, DY and Er up to x = 0.12 have been prepared by Kahn et al. 20 using the same micellar route. Kim et al. 32 have successfully synthesised pure and homogeneous CoFe_1.9RE_0.1O₄ nanocrystals with RE = Y, La, Nd and Gd. Panda et al. 21 have prepared CoFe_{2− x} RE _x O₄ with RE = Gd and Pr in single phase without any chemical heterogeneities up to x = 0.2. Tahar et al. 33 have successfully synthesised CoFe_1.9RE_0.1O₄ (RE = La, Ce, Nd, Sm, Eu, Gd, Tb and Ho) in single phase using polyol method. Here, we have used citrate precursor method to synthesise the Ho³⁺ substituted cobalt ferrite samples and observed that, the samples are in crystalline state and single-phase form even at low annealing temperature despite having large difference in ionic radius of Ho³⁺ and Fe³⁺.

The carriers of magnetism in RE elements are the 4f electrons. The holonium (Ho³⁺) has 4f electrons 10 and it has very high magnetic moment (10.60 µ_B for Ho³⁺). Hence, due to its magnetic nature, substituting Ho³⁺ ion in the place of Fe³⁺ in cobalt ferrite, it gives rise to 3 d–4f electron coupling. Therefore, one can expect to modify the structural and magnetic properties. The structural and magnetic properties of Ho³⁺ substituted nanocrystalline cobalt ferrite have been reported by various groups. Muthuselvam et al. 34 have synthesised CoFe_1.95Ho_0.05O₄ spinel ferrite nanomaterial using mechanical alloying method and, results revealed that samples show soft ferromagnetic character. Tahar et al. 33 have prepared CoFe_1.9Ho_0.1O₄ nanoparticles by polyol method and found that particles are superparamagnetic at room temperature. Even though there are a few reports on Ho³⁺ doped CoFe₂O₄, according to our knowledge there are no detailed studies on crystal structure of nanocrystalline CoFe_{2− x} Ho _x O₄. Also, there are inadequate information on magnetic properties and magnetocrystalline anisotropy of Ho³⁺ doped cobalt ferrite. Hence in this report, we have studied detailed crystal structure and size-dependent K ₁ at room temperature of CoFe_{2− x} Ho _x O₄ (x = 0.0, 0.025, 0.05, 0.075 and 0.1) nanocrystalline materials.

2. Experimental

Nanocrystalline powders of CoFe_{2− x} Ho _x O₄ for x = 0.0, 0.025, 0.05, 0.075 and 0.1 were prepared by the citrate precursor method. Cobalt nitrate (Co(NO₃)₂ · 6H₂O), iron nitrate (Fe(NO₃)₃ · 9H₂O), holonium oxide (Ho₂O₃) and Citric acid (C₆H₈O₇ · H₂O) with 99.9% purity were used as starting materials. The molar ratio of metal nitrates to citric acid was taken as 1 : 3. The metal nitrates were dissolved in a deionised water (milli Q grade) to get a solution. An aqueous solution of citric acid was mixed with metal nitrates solution. The mixed solution was heated at 80°C with constant stirring using hot plate. The solution became viscous and finally forming brown gel. The gel was dried overnight using an oven at 80°C in order to remove excess water. During the process of drying, the gel swells into the fluffy mass and eventually broke into brittle flakes. The resulting materials were heat treated in air atmosphere at 200°C and 600°C for 2 h at each temperature. The crystalline phase of the annealed samples was identified by the powder XRD method (Rigaku Miniflex) using Cu-Kα radiation. The magnetic hysteresis loops were recorded at room temperature (300 K = 27°C) by using a LakeShore (Model No. 7410) VSM. The maximum field used was ±2 T. FT-IR was recorded with a Perkin Elmer (Model Spectrum 400) within the wave number range of 325–1000 cm⁻¹. The compositions of all the samples were studied by EDS using Hitachi S4800 FE-SEM.

3. Results and discussions

3.1. Structural analysis

Typical XRD pattern of the sample CoFe_1.9Ho_0.1O₄ annealed at 200°C is shown in Figure 1. The XRD pattern shows broader peaks and incomplete crystallisation. It reveals that, due to large difference in ionic radius of Ho³⁺ (0.90 Å) and Fe³⁺ (0.64 Å) cations, thermal energy for 200°C annealed samples is not sufficient for the complete incorporation of the Ho³⁺ ions into the spinel lattice. Therefore, more energy is needed to make Ho³⁺ ions enter into the spinel lattice to improve the crystallisation. So, we have annealed the samples at 600°C for 2 h and the XRD patterns are shown in Figure 2. The XRD patterns show an improvement in the sharpness of the peaks and reduction in the peak broadening compared to 200°C annealed samples. It reveals that the growth of crystal take place with increasing heat treatment. All the samples are essentially in single-phase form. We have not observed any trace of impurity peaks which confirms that Ho³⁺ ions have been incorporated into the spinel lattice. All the XRD peaks could be indexed to space group with cubic symmetry. We have observed that, the XRD peaks for the samples annealed at 600°C appear to be broadened with increasing Ho³⁺ concentration (x = 0.1), as a result of incorporation of the Ho³⁺ ion into the spinel lattice. With the gradual increase in Ho³⁺ concentration for x>0.1, crystallisation of the samples become more difficult and some sort of amorphous-like phases (figure not shown) prevail because more dopant concentration leads to a higher potential barrier that Ho³⁺ ion has to overcome for entering the spinel crystal lattice. The segregation of different phases may have started x< 0.1 due to which we have observed anomaly in physical properties (magnetic, lattice parameters, etc.) with Ho³⁺ concentration for x > 0.05 (discussed later). However, we have not observed any phase segregation by our present XRD study. It requires more detailed study by other techniques to resolve the issue which is beyond the scope of this article.

Figure 1. XRD patterns of the sample CoFe_1.9Ho_0.1O₄ annealed at 200°C.

Figure 2. XRD patterns of the samples CoFe_{2− x} Ho _x O₄ (x = 0.0, 0.025, 0.05, 0.075 and 0.1) annealed at 600°C.

We tried to increase the crystallinity of high Ho³⁺ doped samples (x ≤ 0.1) by annealing above 600°C (i.e. 1000°C). However, we have observed that in addition to spinel phase, there is also another phase which has segregated as HoFeO₃ (figure not shown). So we conclude that, the RE³⁺ ions (Ho³⁺ ion) which have a higher ionic radius than Fe³⁺ ion can be substituted for Fe³⁺, when the samples are in nanocrystalline form. In the nanocrystalline form, due to large surface to volume atoms reduces the symmetry of the crystals as well as crystal anisotropy, whereas in the bulk materials, crystals are highly anisotropic and have a high degree of symmetry which leads to phase segregation. Hence, in this report we have studied in detail for 600°C annealed nanocrystalline sample.

All XRD patterns were analysed employing Rietveld technique 35 with the help of Fullprof Suite 2009 release programme. The patterns for all the samples could be refined using the space group. Typical XRD patterns along with Rietveld refinement are shown in Figure 3 for the sample CoFe_1.95Ho_0.05O₄ annealed at 600°C. Here the experimental data are shown as open circles and calculated intensities are shown as solid line. The bottom line represents the difference between measured and calculated intensities. The allowed Braggs positions for the space group are marked as vertical lines. All the observed peaks are allowed at Bragg 2θ positions. The typical fractional atomic positions and isothermal parameters of the atoms for the sample CoFe_1.95Ho_0.05O₄ annealed at 600°C are given in Table 1. The oxygen positions (x = y = z) were taken as free parameters, however all other atomic fractional positions were taken as fixed. Other parameters, such as, lattice constants, isothermal parameters, occupancies, scale factors and shape parameters were taken as free parameters. Background was refined by using pseudo voigt function.

Figure 3. Rietveld refined XRD pattern for the sample CoFe_1.95Ho_0.05O₄ annealed at 600°C. The circles represent experimental points and the solid line represents Rietveld refined data. The bottom line shows the difference between the experimental and refined data. The marked 2θ positions are the allowed Bragg peaks.

Table 1. Atomic coordinates and isothermal parameters for CoFe_1.95Ho_0.05O₄ composition.

Atoms	x	y	z	B iso
Co/Fe/Ho	0.1250	0.1250	0.1250	0.1199
Fe/Co/Ho	0.5000	0.5000	0.5000	0.8292
O	0.2442	0.2442	0.2442	1.0000

The R _p (profile factor) and refined lattice parameters for all the samples annealed at 600°C are listed in Table 2. The R _p factors are found to be large. A similar R _p factor has been observed by the other research group for nanocrystalline samples 36. It could be due to the low signal-to-noise ratio of XRD patterns for nanocrystalline materials. However, we have observed a low value of χ ² (goodness of fit) which justifies the goodness of refinement. In the diffraction pattern of nanocrystalline materials, diffuse scattering is dominant than in those of bulk crystalline materials due to large ratio of surface to volume atoms. The diffuse scattering becomes significant at the nanoscale while Bragg scattering gets diminished which leads to decline in crystallinity 37. Hence large reliability factors are observed.

Table 2. Parameters obtained from Rietveld analysis of XRD patterns for the sample CoFe_{2− x} Ho _x O₄ (x = 0.0, 0.025, 0.05, 0.075 and 0.1) annealed at 600°C. Errors of the lattice parameters are shown in brackets.

Sample	R p	Χ ^2	a = b = c (Å)	D (nm)
CoFe2O4	16.6	0.79	8.378(22)	35.12
CoFe1.975Ho0.025O4	19.3	0.67	8.370(12)	15.37
CoFe1.95Ho0.05O4	19.1	0.75	8.365(14)	13.41
CoFe1.925Ho0.075O4	19.5	0.68	8.375(16)	11.16
CoFe1.9Ho0.1O4	20.1	0.84	8.374(18)	9.89
Notes: R p = profile factor, χ^2= goodness fit factor, a = lattice parameter (Å), D = average crystallite size in nm.

The analysis of the crystallite size has been carried out using the broadening of the XRD peaks. Peak broadening comes from several sources such as instrumental effect, finite crystallite size and strain effect within the crystal lattice. The crystallite size of the samples have been obtained using Rietveld method because in Rietveld method all the instrumental factors are taken into account for the correction of peak broadening. A complete expression used in Rietveld method 35 is defined as,

where U, V and W are the usual peak shape parameters, IG is a measure of the isotropic size effect and D _ST = coefficient related to strain. The value of the crystallite size for the samples annealed at 600°C is listed in Table 2. We have observed that the average crystallite sizes of the samples (annealed at 600°C) decreases with the increase of Ho³⁺ concentration. It reveals that when Ho³⁺ ion is substituted in the place of Fe³⁺ ion, it may induce a crystalline anisotropy and this crystalline anisotropy increases with Ho³⁺ concentration. Apart from this with increasing Ho³⁺ concentration, volume strain inside the material will also increase. Therefore, for a system to remain in stable equilibrium, crystal anisotropy and volume strain should balance each other. In order to relax the volume strain, the crystallite size decreases with the increase of Ho³⁺ ions.

The cation distributions among the tetrahedral and octahedral interstitial sites were estimated by the Rietveld refinement of the occupancy values. The estimated cation distributions from Rietveld analysis for the samples annealed at 600°C are listed in Table 3. One can observe that Ho³⁺ ions are within the error in the A-site. Hence, Ho³⁺ ions show a strong preference for octahedral sites. The valency of Ho atom is +3 only. The crystal field stabilisation energy of Ho³⁺ is high and element having high crystal field stabilisation energy have a strong affinity to the B-sites. Hence, the strong preference of Ho³⁺ ion for the B-sites may be due to its high crystal field stabilisation energy 38. In spinel lattice, the radius of the octahedral site is larger than the tetrahedral site. The ionic radius of the Ho³⁺ ion is larger than Fe ions. One can assume that when small amount of Ho³⁺ cation is substituted for Fe³⁺ cation, it enter into the octahedral sites and induces rearrangement of cations between the tetrahedral and octahedral sites to minimise the free energy of the system. By increasing the Ho³⁺ concentration, it induces partial migration of Co²⁺ ions (0.74 Å) from B to A sites accompanied by an opposite transfer of an equivalent number of Fe³⁺ ions (0.64 Å) from A to B sites in order to relax the strain at the B-sites. The migration of cations from tetrahedral sites to octahedral sites and vice-versa could produce a significant effect on the lattice constant.

Table 3. Site occupancies of cations for the samples CoFe_{2− x} Ho _x O₄ (x = 0.0, 0.025, 0.05, 0.075 and 0.1) annealed at 600°C.

Sample	A-site	B-site
CoFe2O4	Co0.110Fe0.890	Co0.890Fe1.100
CoFe1.975Ho0.025O4	Co0.175Fe0.824Ho0.001	Co0.825Fe1.151Ho0.024
CoFe1.95Ho0.05O4	Co0.187Fe0.810Ho0.003	Co0.813Fe1.140Ho0.047
CoFe1.925Ho0.075O4	Co0.219Fe0.780Ho0.001	Co0.781Fe1.145Ho0.074
CoFe1.9Ho0.1O4	Co0.299Fe0.699Ho0.002	Co0.701Fe1.201Ho0.098

The values of lattice constants for all the samples annealed at 600°C are listed in Table 2. We have observed that the lattice constant decreases with the Ho³⁺ concentration up to x = 0.05. Similar decrease in lattice parameters have been observed for RE³⁺ ions substituted cobalt ferrite nanocrystals 39,40. The observed decrease of lattice constant could be explained on the basis of rearrangement of cations between the A-site and B-site in order to relax the lattice strain (discussed in the above section). For x > 0.05, there is inconsistency in the variation of lattice constant. It appears that, there might exist some other phase (secondary phase) in a very small amount in addition to Co–Ho ferrite. This small amount of extra phase might induce some distortion in the spinel lattice corresponding to some expansion of the spinel lattice with the result of increasing lattice parameter. But the XRD pattern could not show the evidence of extra phase. This might be due to small Ho³⁺ doping concentration in the sample, the extra phase is below the detection limit of X-ray spectrum. It requires a more detailed study. In this regard, we have planned for high power X-ray radiation and Mösbauer spectroscopy study to understand these samples.

3.2. Spectral measurement

The FT-IR spectra for the sample CoFe_{2− x} Ho _x O₄ annealed at 600°C with x = 0.0 and 0.025 are shown in Figure 4. The spectra indicate the presence of two strong absorption bands in the range of 350–600 cm⁻¹ which is a common feature of the spinel ferrite 41. For undoped sample (x = 0.0), the spectra show two prominent absorption bands with peaks at 502 (ν ₁) and 435 (ν ₂) cm⁻¹. The band positions are found to be in agreement with the characteristic infrared absorption bands of cobalt ferrite nanocrystals 42. The band ν ₁ is assigned to the vibration of the bond between the oxygen ion and the tetrahedral metal ion (O–M_Tet) and the band ν ₂ is assigned to the vibration of the bond between the oxygen ion and the octahedral metal ion (O–M_Oct) 43. When Ho³⁺ ion is substituted for Fe ion (for x = 0.025), we observed that the absorption bands (ν ₁) and (ν ₂) slightly shift with peaks at 494 and 412 cm⁻¹, which indicates that Ho³⁺ ion has been incorporated into the spinel lattice which supports the XRD analysis.

Figure 4. FT-IR spectra of the samples CoFe_{2− x} Ho _x O₄ with x = 0.0 and 0.025 annealed at 600°C.

3.3. Elemental analysis

Typical FE-SEM image of the sample CoFe_1.975Ho_0.025O₄ annealed at 600°C is shown in Figure 5. The image shows that the particles have an almost homogeneous distribution. The composition of the samples CoFe_{2− x} Ho _x O₄ is determined using the EDS analysis. The compositional analysis for all the samples was found to be close to stoichiometry. The typical EDS pattern of sample CoFe_1.975Ho_0.025O₄ annealed at 600°C is shown in Figure 6. The EDS pattern reveals the presence of Co, Fe, Ho, Au and O elements in the sample. One cansee that except the extra Au peak; no any other peaks have been traced. The gold peak appears due to the thin coating on the sample surface to make it conducting. It reveals that there is no contamination in the sample.

Figure 5. FE-SEM image of the sample CoFe_1.975Ho_0.025O₄ annealed at 600°C.

Figure 6. The EDS pattern of the sample CoFe_1.975Ho_0.025O₄ annealed at 600°C. Au (gold) peaks are due to thin coating on the sample.

3.4. Magnetic studies

Magnetic hysteresis loops for CoFe_{2− x} Ho _x O₄ samples annealed at 600°C are shown in Figure 7. The saturation magnetisations M _S for the samples CoFe_{2− x} Ho _x O₄ were estimated from a fit over the high field data using the ‘LA to Saturation’ equation (discussed in the next section). The values of saturation magnetisation for all the samples are listed in Table 4. We have observed that saturation magnetisation decreases with the Ho³⁺ concentration up to x = 0.05 composition. The observed behaviour could be explained as follows: (1) the surface effect becomes prominent in nanocrystalline material due to large ratio of surface to volume atoms. At the surface, structure is distorted and atoms are under the effect of strain which leads to vacancies, variety of interatomic spacing and low coordination number. All of these factors induce a broken exchange bonds for the surface atoms, which leads to spin disorder 44. The disordered spins at the surface may exhibit low magnetisation. (2) The strength of superexchange interaction are expected to be modified in RE³⁺(rare earth) ion doped cobalt ferrite due to the appearance RE³⁺–Fe³⁺/Co²⁺ interaction which is a weak interaction relative to Fe³⁺–Fe³⁺/Co²⁺ interaction 45, hence affects the saturation magnetisation. For x > 0.05, there is unusual behaviour of saturation magnetisation with Ho³⁺ concentration.

Figure 7. Hysteresis loops for the samples CoFe_{2− x} Ho _x O₄ (x = 0.0, 0.025, 0.05, 0.075 and 0.1) annealed at 600°C.

Table 4. Coercivity, saturation magnetisation (M _S), and anisotropic constant (K ₁) of the samples CoFe_{2− x} Ho _x O₄ (x = 0, 0.025, 0.05, 0.075 and 0.1) annealed at 600°C.

Sample	Coercivity (kOe)	M S (emu g^−1)	K 1 (erg cm^−3)
CoFe2O4	1.394	50.00	2.27 × 10^6
CoFe1.975Ho0.025O4	1.347	12.21	0.77 × 10^6
CoFe1.95Ho0.05O4	1.158	07.62	0.40 × 10^6
CoFe1.925Ho0.075O4	1.096	36.64	2.75 × 10^6
CoFe1.9Ho0.1O4	0.847	17.02	1.42 × 10^6

The values of coercivity for all the samples are listed in Table 4. We have observed that the coercivity decreases with the Ho³⁺ concentration. In a single domain region the variation of coercivity with the crystallite size is expressed as 19,

where g and h are constants. The size of the crystallite decreases with the Ho³⁺ concentration. In the single domain region, as the crystallite size decreases the coercivity decreases, because of thermal effects. It appears that the crystallite sizes of the Ho substituted samples are within the range of single domain size limit.

In order to extract the anisotropy information of the samples CoFe_{2− x} Ho _x O₄ annealed at 600°C, the ‘LA’ to saturation was employed to analyse the data in saturation region. LA describes the dependence of magnetisation M on the applied magnetic field for H ≫ H _c. The magnetisation near the saturation M _S can be written as 10,

where M is the magnetisation, H is the applied magnetic field, M _S is the saturation magnetisation, μ _o is the permeability of the free space, K ₁ is the cubic anisotropy constant. The numerical coefficient 8/105 applies to cubic anisotropy of random polycrystalline samples. Therefore M _S and K ₁ are the only fitting parameters in Equation (3). In the present series, the experimental data [M–H curve] above than 1 T (high field parts) is fitted to Equation (3). Typical fitting curve to LA is shown in Figure 8 for the sample CoFe_1.95Ho_0.05O₄ annealed at 600°C. The values of M _S and b are obtained from fitting and, K ₁ was calculated using the equation

Figure 8. Fit to LA for the sample CoFe_1.95Ho_0.05O₄ annealed at 600°C.

The values of K ₁ for all the samples are listed in Table 4. Our result of magnetocrystalline anisotropy for undoped sample (CoFe₂O₄) is comparable to the earlier reports 46. We have observed that the K ₁ decreases with the Ho³⁺ concentration up to x = 0.05 composition. The origin of the magnetocrystalline anisotropy in the spinel ferrite is the L–S coupling at the crystal lattices and in nanocrystalline material it strongly depends on the crystallinity 47. Increasing Ho³⁺ ion in the place of Fe ion leads to decrease of crystallite size and enhancement of surface area in the sample. At the surface of the samples, surface strain is dominant, i.e. crystal lattice are not in well-defined order which may perturb the crystal symmetry at the surface and affects the L–S coupling, i.e. magnetocrystalline anisotropy. It reveals that for nanocrystalline material, surface effects play a dominant role rather than cation distribution for the determination of magnetic anisotropy, which we have planned to carry out by high-power XRD (Synchrotron radiation and Mossbauer spectroscopy). Coercivity, M _S and K ₁ are not consistent with the increase of Ho³⁺ concentration for x > 0.05. It could be due to phase segregation which has been discussed in the previous section (XRD analysis). Hence, the materials for x > 0.05 are under investigation.

4. Conclusions

Nanocrystalline Ho³⁺ substituted cobalt ferrite CoFe_{2− x} Ho _x O₄ (x = 0.0, 0.025 and 0.05) have been synthesised successfully by citrate precursor method. The lattice constant strongly depends on the Ho³⁺ concentration. FT-IR spectra show two significant absorption bands which confirm the incorporation of the Ho³⁺ ion into the spinel lattice. The magnetic properties are strongly affected by surface effect rather than cation distribution. The samples with a low concentration of Ho³⁺ reveal that there is tendency of the material to show soft ferrimagnetic character. For higher concentration of Ho³⁺ (x > 0.05), it is difficult to control the physical parameters.

Acknowledgement

The authors are thankful to the Centre of Instrumentation facility (CIF), Indian Institute of Technology Guwahati, Guwahati – 781039, for extending the VSM facilities. The authors gratefully acknowledge Department of Atomic Energy, Government of India (Sanction No. 2011/20/37 P/03/BRNS/0076) for the financial support.