Abstract

A series of praseodymium-doped Zn_0.5Mg_0.5Pr_xFe_2-xO₄ (x= 0.0, 0.02, 0.06 and 0.10) ferrites were synthesized by solid-state reaction method to study the impact of doping Pr³⁺ ions on the structural and magnetic properties of Zn_0.5Mg_0.5Pr_xFe_2-xO₄ ferrite compositions. The powdered x-ray diffraction studies revealed the presence of peaks corresponding to tetrahedral and octahedral positions, confirming cubic spinel structure in all samples. Vibratory sample magnetometer study revealed changes in microscopic magnetic properties. The net magnetization increased while the coercivity decreased with increase in concentration of Pr³⁺ substitution. ⁵⁷Fe Mössbauer studies were used to obtain the chemical state of iron and its occupancy to tetrahedral/octahedral site and to estimate the cation distribution of tetrahedral site and octahedral site in all synthesized ferrite compositions. Using the cation distribution of tetrahedral site and octahedral site, an attempt is made to understand the magnetic properties of Pr doped Zn-Mg ferrites.

1. Introduction

Spinel system with general formula MFe₂O₄; M = Fe²⁺, Zn²⁺, Co²⁺, Mg²⁺, Mn²⁺ etc. are named as magnetic spinel ferrites. Spinel ferrites are fundamentally important in the study of super paramagnetism by altering the chemical composition ¹. The spinel structure allows substitution of different metal ions resulting into changes in its electric and magnetic properties ². The substitution of metal ions can affect the occupancy of Fe³⁺ ions to be either in tetrahedral site A or in octahedral site B and causes a marked difference in the hyperfine fields at ⁵⁷Fe nuclei present in site A and site B of spinel structure. ⁵⁷Fe Mössbauer spectroscopy can be used to study the environment surrounding the iron nuclei in spinel ferrite structures ^{3, 4, 5, 6, 7}. In Mössbauer spectroscopy, the precession and the transition between the precession states is faster in comparison to the experimental time scale and hence an average value of magnetic hyperfine field is obtained. This experimental time scale is of the order of nuclear larmor precession time (nano second) ⁸.

In the study of magnetic properties, the super paramagnetic blocking temperature T_B is considered as a significant parameter ⁹. T_B is the temperature at which the relaxation time is equal to the time scale of the experimental technique is below T_B, the Mössbauer spectra are magnetically split and exhibit magnetic hyperfine splitting pattern consisting of six line components (sextet) for each iron site in the material. Above T_B, the Mössbauer spectra contain only singlets or doublets. In a broad temperature range, the spectra of magnetic nano particle can also show the superposition of sextets and doublets or singlets due to the distribution of anisotropy energy various (kV).

The relaxation time is given as

Where K is anisotropy constant, kB is Boltzmann constant, T is temperature and V is the crystallite volume.

In case of very small sized crystallites, the relaxation time is less than the larmor precession time and leads to super paramagnetic relaxation. In spinel ferrites of nano-sized crystallites this super paramagnetic relaxation can occurs. Due to super paramagnetic relaxation, the spinels do not exhibit magnetic hyperfine splitting and instead of magnetic sextet only doublets are expected to be obtained in its Mössbauer spectrum.

In present study, the Pr³⁺ substituted Zn-Mg ferrites were prepared by solid state reaction method and finally were sintered at 1180°C. The structural parameters were determined from the Rietvield fitments of x-ray diffraction pattern in all samples. The ⁵⁷Fe Mössbauer spectroscopic study was carried out to obtain the chemical state of iron in each composition by determining the local environment of Fe atom. For all samples, the cation distribution of tetrahedral and octahedral sites was estimated from relative amount of iron in tetrahedral and octahedral sites in spinel structure. The estimated cation distribution was then used to study the magnetic interactions in Pr³⁺ substituted Zn_0.5Mg_0.Pr_xFe₂O₄ ferrites.

2. Experimental

The solid state reaction method was used to synthesize the as prepared Zn-Mg ferrite ¹⁰ and Pr substituted series of Zn_0.5Mg_0.5Pr_xFe₂O₄ (x= 0.0, 0.02, 0.06 and 0.10) ferrite compositions. All prepared samples were sintered at 1180°C. The x-ray diffraction studies were carried out at room temperature by using PANalytical X’pert Pro MPD diffractometer of Cu-Kα radiation. The diffraction patterns were collected at 2⁰ per minute scanning rate from 10⁰ to 80⁰ range of 2θ. The indexing and refinement of peaks obtained in x-ray diffraction patterns was carried out by using “FullProf programme ¹¹ to calculate several x-ray parameters like lattice constant, crystallite size, x-ray density and lattice strain.

Mössbauer spectra were recorded at room temperature (300K) with a conventional constant acceleration spectrometer using a 10 mCi ⁵⁷CO source embedded in Rhodium matrix. Details of the experimental set-up were kept similar as reported earlier by Ram et. al. ¹². The Mössbauer absorbers were prepared by sandwiching a thin layer of fine powdered ferrite samples in between two paper discs and tightly covered with cello tape such that the thickness of absorber remains uniform. All spectra showing superposition of quadrupole doublets were computer fitted to resolve them using a least square routine computer program written by Meerwall ¹³ by assuming each spectrum to be sum of Lorentzians functions. During the curve fitting, the width and intensity of the two halves of a quadrupole doublet were constrained to be equal. The quality of the fit was judged from the value of ² which was obtained close to 1.0 per degree of freedom in most of the cases. However, a deviation in the value of ² has been accepted in some occasion when iterations did not improve the value of ². The isomer shift (IS) value is reported with respect to the spectrum of standard iron foil of 25 μm thickness. Solid lines in the spectra reported here represent computer fitted curve and dots represent the experimental points.

The magnetic properties of prepared samples were investigated by recording the variation of magnetizing intensity with applied magnetic field by using Vibrating Sample Magnetometer. The magnetic field was applied in the range of -15 kOe to +15 kOe. The microscopic magnetic parameters like saturation magnetization, coercivity, retentivity, etc. have been calculated to understand the magnetic nature of prepared Pr-substituted Zn_0.5Mg_0.5Pr_xFe_2-xO₄ ferrites.

3. Results and Discussion

The x-ray diffraction patterns obtained for all synthesized Pr-substituted Zn-Mg ferrites compositions ¹⁴ with chemical formula Zn_0.5Mg_0.5Pr_xFe_2-xO₄ (x=0.0, 0.02, 0.06 and 0.10) are displayed in Figure 1. The absence of additional peak corresponding to impurity phase Fe₂O₃ confirms the formation of single phase cubic spinel structure in all synthesized ferrite compositions. The broadening of diffraction peaks is attributed to the formation of nano sized particles in all samples. The calculated values of lattice constant, crystallite size, x-ray density and lattice strain are listed in Table 1. The lattice constant ‘a’ was calculated by using the relation here (h,k,l) is the index of the XRD reflection peak and ‘d’ is the inter-planar spacing ¹⁵. The x-ray density () in all samples has been calculated by using the formula ρ_x = where M is relative molecular mass, N_A is Avogadro number and ‘a’ is lattice constant ¹⁵. The lattice constant obtained in all Pr-substituted samples is less than the lattice constant obtained in pure sample (x=0). The variations of lattice constant and crystallite size with increasing Pr concentration in Zn_0.5Mg_0.5Pr_xFe_2-xO₄ ferrites are displayed in Figure 2. From Figure 2, it is seen that in sample for x=0.02, the calculated value of lattice constant is 8.3762 Å which is the smallest value among all samples in present study. This decrease in lattice constant with inclusion of Pr³⁺ ions is obvious because the larger ionic radii Pr³⁺ ion (1.13 Å) has preferential occupancy to octahedral site by replacing Fe³⁺/Mg²⁺ ions from octahedral to tetrahedral site. This results into decrease of lattice constant. However, for higher concentration of Pr-substitution, the minor increase in lattice constant from 8.3762 Å (x=0.02) to 8.3997 Å (x=0.10) can be explained in context to the linear vibration of crystallography parameters when larger sized Pr³⁺ ions incorporates in lattice structure because of all the samples were synthesized at constant temperature and nature of bonding was also same ¹⁶.

From Table 1, it can be seen that the x-ray density also increases with increase in the concentrations of Pr substitution. The increase in x-ray density is obvious due to the larger atomic weight of Pr (140.90), which results into an increase in relative molecular mass with increase in concentration of Pr substitution. The crystallite size in all samples was calculated using the Scherer’s formula ¹⁵. The calculated average crystallite size has been observed in the range 53.2 nm to 41.7 nm corresponding to the formation of nano-sized crystallites. This decrease in crystallite size with increasing concentration of Pr Substitutions is due to the Pr³⁺ ions which are distributed over the grain boundary and can obstruct the crystal growth ¹⁷. For sample (x=0.10) the crystallite size is obtained to be very small (41.7 nm) in comparison to pure sample (53.2 nm). The sharp decrease in crystallite size with increasing concentration of Pr substitution can be attributed to the larger ionic radii of Pr³⁺ ion due to which the Pr³⁺ ion may reside partially at the grain boundary and cause pressure on the grain resulting in to obstruction of the growth of crystal ¹⁸. When Pr³⁺ ions enter the lattice of spinel, the changing lattice parameters also leads to change in lattice strains. From Table 1, it can be seen that lattice strain ‘η’ increases with increasing concentration of Pr substitution.

The Mössbauer spectra of all synthesized sample recorded at room temperature are displayed in Figure 3. The concentration of Pr³⁺ substitutions is mentioned in the figure itself. The Mössbauer parameters obtained by the least square fitting of Lorentzians lines are given in Table 2. The isomer shift (IS) value is reported with respect to the spectrum of standard iron foil of 25 μm thickness. In present study, the Isomer shift values are obtained ranging from 0.1 mm/s to 0.4 mm/s which are attributed to iron in Fe³⁺ state ^{19, 20}. The assignment of iron in Fe³⁺state occupying either tetrahedral site or octahedral site is done in accordance with earlier reported work ^{7, 21, 22}. The doublet with higher value of isomer shift is assigned to iron in Fe³⁺ state occupying tetrahedral site-A while the doublet with smaller value of isomer shift is assigned as iron in Fe³⁺ state occupying octahedral site-B.

From Table 2, it can be seen that in pure sample (x=0.0) the isomer shift value for site-A is greater than that of site-B. In a similar type of study on Zn-Mn ferrites, Ram and Singh ⁷ and Wang et. Al. ²⁰ has already reported this trend of larger value of isomer shift for Fe³⁺ iron in site-A. The samples with x=0.06 and x=0.10 exhibits only one central doublet attributing to the magnetically isolated Fe³⁺ ion which does not show magnetic ordering due to surrounding non magnetic particles ²³.

The amount of iron in Fe³⁺ state occupying the tetrahedral site-A and octahedral site-B was estimated by the relative area of the quadruple doublet(s) ²⁴. In pure sample (x=0.0), the distribution of Fe³⁺ ions into site-A and site-B clearly indicate the formation of mixed inverse spinel structure. This formation of inverse spinel Zn-Mg ferrite (x=0) is obvious due to the tendency of divalent ions Zn²⁺ which has preferential occupancy to A-site while Mg²⁺ has preferential occupancy to B-site ^{25, 26}.

From Table 2, it can be seen that with increasing concentration of Pr substitution, the relative amount of iron in tetrahedral site reduces and it increases in octahedral site. This clearly reflects the migration of Fe³⁺ ions into octahedral site. The Fe³⁺ ions migrated from tetrahedral site to octahedral site has replaced only Mg²⁺ ions present in octahedral site. It is because Pr³⁺ ions due to their larger ionic radii (1.13 Å) preferentially occupies only octahedral site.

The Mössbauer spectra of samples (x=0.06, 0.10) exhibit only one central doublet corresponding to Fe³⁺ iron in B-site only. It shows the complete migration of Fe³⁺ from tetrahedral to octahedral site by replacement of Mg²⁺ from octahedral site. The tetrahedral site now has only divalent ions Zn²⁺ and Mg²⁺ while the octahedral site has only trivalent ions Fe³⁺ and Pr³⁺_. The cation distribution of tetrahedral site and octahedral site is estimated from Mössbauer spectra in keeping with the earlier reported study by Ram and Singh ⁷, Singh S. ¹⁴ and Mohammed et. al. ²⁷ and is given in Table 3.

Using the cation distribution given in Table 3, the average ionic radii at the tetrahedral site (r_A) and at octahedral sites (r_B) in all samples can be calculated by following relations ²⁸

(1)

(2)

Where C^A and C^B are the ionic concentration in A-site and B-sites respectively, and are the radii of Zn²⁺, Mg²⁺, Pr³⁺ and Fe³⁺ respectively.

Using the values of radii of tetrahedral site-A (r_A) and radii of octahedral site-B (r_B), the theoretical values of lattice constant a_th in all samples can be obtained by the relation ²⁹

(3)

here R₀ is the radius of oxygen ion (R₀ = 1.32 Å)

The calculated values of mean ionic radii of tetrahedral site-A (r_A), mean ionic radii of octahedral site-B ( r_B) and calculated value of lattice constant ‘ a_th’ are listed in Table 4.

It can be seen from Table 4, that the mean ionic radii of r_A and r_B both increases with increase in the concentration of Pr substitution. However, the increase in r_A is very small in comparison to the increase in r_B. The variation in r_A and r_B arise due to difference in the ionic radii of ions present in a particular site ^{30, 31}. The increase in the value of octahedral site mean ionic radii r_B is attributed to the substitution of larger ionic radii Pr³⁺ ion (1.13 Å) at octahedral site-B by replacing smaller ionic radii Fe³⁺ ions (0.67 Å). On the other hand, at tetrahedral site-A the Zn²⁺ ions with ionic radii (0.74 Å) are accompanied either by Mg²⁺ ions having ionic radii 0.66 Å or by Fe³⁺ ions of ionic radii 0.67 Å. At the tetrahedral site-A, due to small difference between the ionic radii of incumbent Fe³⁺ and Mg²⁺ ions, the increase in tetrahedral site mean ionic radii r_A is in small proportion.

From Table 4, it can also be seen that the theoretical value a_th and experimental value a_exp of lattice constant are nearly same for pure sample (x=0) indicating the formation of spinel ferrite with less distortion from cubic structure. However, the difference between a_th and a_exp values probably incorporates because in the theoretical calculations a closely packed structure of spinel ferrite is considered. In the samples containing Pr substitution, an increase in a_th is observed and it further increases with increasing Pr concentration. This larger variation in a_th and a_exp for higher concentration of Pr substitution is attributed to the distortion from cubic structure which is obvious as the substitution of Pr³⁺ ions with ionic radii (1.13 Å) larger than the ionic radii of Fe³⁺ ions (0.67 Å) will exert an internal stress which can cause the distortion from cubic structure.

In present study, the extent of distortion from cubic symmetry has been estimated by calculating the oxygen positional parameter (u) which describe the displacement of oxygen ions considering origin at site-A and assuming centre of symmetry at (3/8, 3/8, 3/8). The deviation of (u) from its standard value (u_ideal = 0.375) is given by inversion parameter (δ). The oxygen positional parameter (u) and inversion parameter (δ) for all samples was calculated by using the relations ³² and listed in Table 4.

(4)

(5)

In an ideal FCC structure, the origin from site-A to site-B is convertible by using the relation ³³

From Table 4, it is seen that the oxygen positional parameter (u) is slightly larger than the ideal value but show a decreasing trend as the concentration of Pr³⁺ substitution in increased. The displacement of oxygen ions in spinel structures is also related to the ratio of largest divalent ion to the smallest trivalent ion ³³. A larger value of this ratio favours larger displacement of oxygen ions and hence larger value of (u) is expected. In present study, the largest divalent ion is Zn²⁺ ion and the smallest trivalent ion is Fe³⁺ ion. The ratio is obtained to be larger favouring larger value of (u). The deviation of (u) from its standard value is an indicator of the trigonal distortion at site-B. It is observed in Table 4 that the trigonal distortion at site-B decreases with increasing concentration of Pr substitution. The decrease in the value of inversion parameter (δ) with increasing Pr³⁺ concentration is attributed to the expansion of octahedral interstices to accommodate the Pr³⁺ ions having larger ionic radii. The increasing value of mean ionic radii of octahedral B-site (r_B) is due to this expansion of octahedral interstices. The Pr³⁺ ions have preferential occupancy to octahedral site which already has larger interstices in comparison to tetrahedral site. The larger ionic radii Pr³⁺ ions will cause the increase in bond length at octahedral site. The increase in bond length is an indicator of weakening of super exchange interactions.

The M-H curve obtained in all synthesized samples of Zn_0.5Mg_0.5Pr_xFe_2-xO₄ ferrites, recorded at room temperature in the applied magnetic field range ±15kOe are shown in Figure 4. The calculated magnetic parameters in Zn_0.5Mg_0.5Pr_xFe_2-xO₄ ferrites are listed in Table 5.

The magnetization in all samples showed an increase with increasing magnetic field and attained maximum value at around 15kOe. None of the produced ferrites has attained saturation magnetization. The maximum magnetization also showed an increase with increasing Pr content. A remarkable increase in total magnetization is observed in x=0.06 and x=0.10 samples. This increase in maximum magnetization can be explained on the basis of cation distribution of tetrahedral site-A and octahedral site-B due to which the magnetization at site-A and site-B is effective.

For nano-sized ferrites, the total magnetization is given as M_s= M_B-M_A ^{19, 34}.

Where M_B is magnetization of sub lattice-B and M_A is magnetization of sub lattice-A.

From Table 3, it is evident that in sample (x=0) the iron is present in Fe³⁺ state and occupy site-A as well as site-B resulting into net magnetization, the same is also observable in Figure 4. In sample (x=0.02) due to the partial migration of Fe³⁺ ions from site-A to site-B, an increase in magnetization at site-B and simultaneous decrease in magnetization at site-A has resulted in to an increase in net magnetization. In samples (x=0.06 and x=0.10) the increase in total magnetization is obvious because the cation distribution indicates the occupancy of Fe³⁺ ions only in site-B. The non occupancy of Fe³⁺ ions in site-A results into zero magnetization in site-A because the other divalent ions Zn²⁺ and Mg²⁺ present in site-A exhibits zero magnetic moment. This rise in maximum magnetization in samples (x=0.06 and 0.10) can be also seen in Figure 4.

The increase in net magnetization can also be explained on the basis of decrease in crystallite size (Table 1) with increasing concentrations of Pr substitution. The smaller grain size leads to larger surface/volume ratio which does not support random canting for particle surface spins and hence reduces anti-ferromagnetic exchange interaction ³⁵. The larger ionic radii Pr³⁺ ion does not enter the tetrahedral site because the inter planer spaces in tetrahedral site-A is small in comparison to the inter planer spaces in octahedral site-B. The Pr³⁺ ions enter octahedral site by replacing Fe³⁺ ions. The cation distribution of tetrahedral and octahedral sites with increasing Pr-substitution (Table 3) reveals the migration of Fe³⁺ ions to octahedral site-B and Mg²⁺ ions to tetrahedral site-A. It points out that Pr³⁺ ions replaces Fe³⁺ ions at octahedral site and meanwhile Fe³⁺ ions of both tetrahedral and octahedral sites replaces Mg²⁺ ions from octahedral site. The presence of Fe³⁺ ion only in octahedral site will reduce anti-ferromagnetic B-B exchange interaction leading to reduction in spin canting in site-B, hence the increase in magnetic moment of sub lattice-B leads to an increase in net magnetization ³⁶. The variation of oxygen positional parameter (u) with increasing concentration of Pr-substitution is also indicating the expansion of octahedral interstices to cause weakening of A-B interaction. The variation of saturation magnetization (M_s) obtained in all synthesized Pr-substituted ferrite samples are displayed in Figure 5. The saturation magnetization (M_s) is found to increase with increasing concentration of Pr-substitution. From Table 3, it can be seen that for larger concentration of Pr-substitution, the occupancy of octahedral site by Fe³⁺ ion increases. In samples x=0.06 and x=0.10 along with Pr³⁺ ions, the Fe³⁺ ions are present only in octahedral site. Since Pr³⁺ ion of larger ionic radii (1.13Å) has preferred occupancy of octahedral site and accommodates only in octahedral site, the interaction of Fe³⁺ ion with Pr³⁺ ions in the spin down state (4e, 4f₁ and 4f₂) can enhance the net magnetization ³⁷. Hence the larger values of net magnetization for increasing Pr concentration indicate that the Fe³⁺ ions in the spin down states have interacted with Pr³⁺ ions. This leads to an increase in net magnetization in upward spin, the magnetic moment also increase resulting into an increase in net magnetization.

The coercivity of as prepared Zn-Mg ferrite sample (x=0) is 28.893. The smaller value of coercivity less than 100 Oe indicates that it is a soft magnetic material. From Figure 5, it is seen that coercivity of Pr-substituted samples is obtained to be less than that of pure sample (x=0). With increasing Pr-content, the coercivity in sample x=0.02 is 21.186 and increases in small proportion with increasing Pr-content and reaches to 24.773 in sample x=0.10. Irrespective of the decrease in crystallite size in Pr-substituted samples, the decrease in coercivity in sample x=0.02, can be attributed to the larger ionic radii of Pr³⁺ ions due to which it is distributed over the boundary of grain and cause an increase in surface disorder. For further increasing the Pr concentration, the surface disorder also increases and hence rise in coercivity is expected. In an earlier work, Yuping et. al. ³⁸ and Shirsath et. al. ³⁹ has also reported the increase in coercivity with rare earth doping.

4. Conclusions

Rare earth Pr³⁺ ions substituted Zn_0.5Mg_0.5Pr_xFe_2-xO₄ (x=0.0, 0.02, 0.06 and 0.10) ferrites were successfully synthesized by solid state reaction method. Various structural parameter studied by using x-ray diffraction patterns confirmed the formation of single phase cubic structure in all samples. The Lattice constant as well as x-ray density increased with substitution of Pr³⁺ ions in Zn-Mg ferrites. The crystallite size was obtained in decreasing trend i.e from 53.2 nm (x=0) to 41.7 nm (x=1.0), attributing to the formation of nano-sized crystallites. ⁵⁷Fe Mössbauer spectra of all sample reflected super paramagnetic nature attributing to the formation of nano structured spinel ferrites. The super paramagnetic behavior points towards the non magnetic ordering by Fe³⁺ ions surrounded by non metallic particles. The synthesized nano-sized ferrites with increasing concentration of Pr³⁺ ions exhibit enhanced net magnetization and smaller value of coercivity indicating the soft magnetic behavior of all samples.

Acknowledgments

Authors are thankful to Department of Physics Jai Narain Vyas University Jodhpur for providing the research facilities. One of the authors Shailndra Singh is thankful to University Grants Commission (UGC), New Delhi for providing the UGC-BSR doctoral fellowship.

Declaration

The manuscript has been prepared through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors declare that they have no conflicts of interest.

References