Ferrimagnetic garnets are isomorphic with the naturally occurring garnet Ca₃Fe₂(SiO₄)₃. Specifically, Yttrium iron garnet (Y₃Fe₅O₁₂, YIG) was discovered in 1956, and demonstrated suitability for high frequency microwave applications.^[1–3] The discovery of YIG led to a revolution in the technological advancement of passive microwave devices including tunable filters, circulators, and gyrators, as well as magnetic-bubble-domain-type digital memory devices and other applications.^[4–6]

The unit cell which has a cubic symmetry contains eight formula units of garnet, where the metal ions occupy three different interstitial sites. The Fe³⁺ ions occupy the 24d tetrahedrally coordinated sites and the 16a octahedrally coordinated sites, whereas the RE ions occupy the 24c dodecahedral sites. These latter sites are not all crystallographically equivalent, where six different c sites were reported.^[7]

Since Y³⁺ is a nonmagnetic ion, the magnetization of YIG arises from the superexchange interaction between the moments of Fe³⁺ ions at a and d sublattices, resulting in a net magnetization of per molecule at 0 K. When nonmagnetic Y³⁺ ions are substituted by heavy rare-earth (RE) ions from the series Gd³⁺ through Yb³⁺, however, the magnetization as a function of temperature exhibits a compensation temperature (T_comp) at which the magnetization vanishes.^[1,6] This is because these heavy RE elements are magnetic due to their unfilled 4f orbitals, introducing a third magnetic sublattice (c) which couples antiferromagnetically with the net magnetization of the Fe³⁺ sublattices due to the fact that the a–d superexchange interaction of Fe³⁺ ions is much stronger than the a–c or d–c interactions between Fe³⁺ and RE ions. Accordingly, such a substitution would facilitate the modifications of the magnetic properties of the garnet compounds, which renders these compounds attractive from the scientific and technological point of view. Further, the strong Fe–Fe interaction is responsible for the magnetic ordering of rare earth iron garnets (RIG), and the weak RE–Fe interactions make the Curie temperature of all rare-earth iron garnets nearly the same (∼550 K).^[8–10]

The effects of RE substitution for Y on the magnetic properties and hyperfine interactions in YIG garnets were investigated by several researchers. The saturation magnetization of Y_3−xDy_xFe₅O₁₂ nanoparticles prepared by the sol-gel method was found to decrease linearly with increasing Dy³⁺ concentration (x) in a range between , and increase with the increase of particle size.^[11,12] Also, room temperature ⁵⁷Fe Mössbauer spectroscopy study of rare earth iron garnets (R_xY_1−x)₃Fe₅O₁₂, where R is either Ho³⁺ or Gd³⁺, has shown that the hyperfine field at the iron nucleus in the octahedral and tetrahedral sites increase with rare earth substitution.^[13] On the other hand, room temperature Mössbauer spectroscopy indicated that Ho substitution for Y in YIG did not induce noticeable changes in the hyperfine fields of the octahedral site nor tetrahedral sites.^[14]

In this study, Y_3−xDy_xFe₅O₁₂ powders are prepared by the solid state reaction method with part of Y ions being substituted by Dy ions in the full range between 0.0 and 3.0 (x=0.0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0). The structural and magnetic properties of the prepared compounds are investigated by x-ray diffraction (XRD), Mössbauer spectroscopy, and vibrating sample magnetometry (VSM). Also, differential scanning calorimetry is employed to investigate the Curie temperature of the compound. The interpretation of the magnetic results is based on the structural data and on the thermal measurements. This work is a continuation of our project involving the investigation of rare-earth iron garnets by several techniques such as nuclear magnetic resonance (NMR) of holmium in different RIG hosts,^[10] Mössbauer spectroscopy,^[13,14] and magnetization measurements.^[8,9]

Y_3−xDy_xFe₅O₁₂ powders with x =0.0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 were prepared by the solid state reaction method. Metallic oxides Y₂O₃, Dy₂O₃, and Fe₂O₃ were used to fabricate Y_3−xDy_xFe₅O₁₂ powder samples. Stoichiometric ratios of the metallic oxides were loaded into a hardened stainless steel cup with a ball-to-powder ratio of 8:1. The milling process was carried out at 250 rpm for 16 h. The resulting precursor was annealed at 1300 °C for 2 h. The XRD patterns were collected using a Philips X’pert PRO X-ray diffractometer (PW3040/60) operating at (45 kV, 40 mA), with Cu– radiation (λ = 1.5405 Å). The samples were scanned over an angular range of with 0.02° scanning step and speed of 1°/min. The XRD patterns were analyzed using X’pert HighScore software to identify the phases present in each sample. Rietveld refinement of the XRD patterns for all fabricated samples was carried out using FullProf suite 2000 software to obtain the values of refined structural parameters.

Samples for Mössbauer spectroscopy studies were prepared by gently pressing a thin layer of the powdered sample between two circular Teflon disks with diameter 2 cm, which is small compared with the distance between the -ray source and the sample, in order to avoid the angular broadening of the spectrum. Room temperature (RT) Mössbauer spectra were collected using a standard constant acceleration Mössbauer spectrometer over 1024 channels. The -ray source was a 50-mCi ⁵⁷Co in a rhodium matrix. The spectra were then analyzed using fitting routines based on least-squares analysis.

The magnetic measurements were carried out using a vibrating sample magnetometer (VSM MicroMag 3900, Princeton Measurements Cooperation), providing a maximum applied magnetic field of 10 kOe (1 Oe =79.5775 A/m). The measurements were performed at room temperature.

Differential scanning calorimetry (DSC) was used to obtain quantitative and qualitative information about phase transitions involving endothermic or exothermic processes, or changes in the heat capacity of the sample under investigation. This technique was therefore employed to investigate the phase transitions and related critical temperatures of the prepared garnets using a NETZSCH–Gerätebau GmbH 204 F1 Phoenix calorimeter. The DSC measurements were performed in a temperature range from 30 °C to 350 °C at a heating rate of 5 °C per minute.

The structural characteristics of all Y_3−xDy_xFe₅O₁₂ samples are investigated using XRD measurements. Rietveld analysis of the diffraction patterns (shown in Fig. 1) is carried out to obtain the refined structural parameters of crystalline phases in the samples, and the refined structural results are summarized in Table 1. Figure 1 indicates that all samples reveal the presence of a single garnet phase, crystallizing in a body-centered cubic (BCC) structure with space group. The lattice parameter a of the two end compounds (Y₃Fe₅O₁₂ and Dy₃Fe₅O₁₂) is in very good agreement with previously reported values^[6] and the low values of χ₂ obtained from the Rietveld analysis indicate good agreement between the theoretical pattern (black continuous line) and the experimental data (red dots), where the line in blue representing the residual difference between the observed and calculated patterns, was a straight horizontal line with small ripples for all samples. Moreover, the enlarged views of the patterns of the two end compounds (Fig. 2) reveal that the two samples are crystallographically identical, indicating a complete substitution of Dy³⁺ ions at the Y³⁺ sites.

Fig. 1.

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	Fig. 1. (color online) Refined XRD patterns for Y3−xDyxFe5O12 samples.

Fig. 2.

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	Fig. 2. (color online) Refined XRD patterns for samples Y3−xDyxFe5O12 with x = 0 and x =3, with residual difference between the experimental and calculated data given in the lower part of the plots (blue line).

Table 1.

Table 1.

Table 1. Lattice constant a, unit cell volume V, χ 2, and x-ray density of Y3−xDyxFe5O12 garnets. . Composition x χ2 a/Å V/Å3 ρx/(g/cm3) (±0.01) Y3Fe5O12 1.81 12.373(4) 1894.4 5.18 Dy0.5Y2.5Fe5O12 1.90 12.376(9) 1896.0 5.43 Dy1.0Y2.0Fe5O12 1.67 12.383(8) 1899.2 5.68 Dy1.5Y1.5Fe5O12 1.56 12.390(5) 1902.3 5.92 Dy2.0Y1.0Fe5O12 1.68 12.394(7) 1904.2 6.18 Dy2.5Y0.5Fe5O12 1.15 12.409(1) 1910.8 6.41 Dy3Fe5O12 2.63 12.400(9) 1907.0 6.68

Table 1. Lattice constant a, unit cell volume V, χ 2, and x-ray density of Y3−xDyxFe5O12 garnets. .

The data in Table 1 reveal that the lattice parameter a and the cell volume increase with the Dy³⁺ substitution increasing, which can be attributed to the fact that the ionic radius of Dy³⁺ (1.027 Å) is greater than that of Y³⁺ (1.019 Å) at dodecahedral sites.^[15] The monotonic increase of the x-ray density with increasing x, however, is opposite to what is expected based on the increase of the cell volume. This behavior can be associated with the increase of the molecular weight of the compound with Dy³⁺ substitution level increasing. The x-ray density is defined as

Fig. 3.

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	Fig. 3. (color online) Linear increase of the product of the x-ray density and cell volume with x value increasing.

Figure 4 shows Mössbauer absorption spectra of all Y_3−xDy_xFe₅O₁₂ samples, and the hyperfine parameters are listed in Table 2. These parameters are obtained by fitting Mössbauer spectra with three magnetic sextets, two of which correspond to Fe³⁺ ions at two non-equivalent octahedral (16a) sites, and one corresponds to Fe³⁺ ions at the tetrahedral (24d) site. The intensity ratio of the components associated with the octahedral sites to that with the tetrahedral site does not deviate from the value of ∼37:63 for each of all compounds, which is in good agreement with the theoretical ratio of 2:3. The hyperfine fields of the Dy³⁺ substituted compounds do not deviate appreciably from the value of B_hf = 497 kOe nor 487 kOe nor B_hf= 401 kOe for the pure YIG. This is an indication that the a–d superexchange interactions between Fe³⁺ ions at the octahedral and tetrahedral site are much stronger than ca or cd interactions between Fe³⁺ and rare-earth ions.^[1] The difference in hyperfine field between the two sublattices is due to the difference in the number of O²⁻ ions coordinated with Fe⁺³ ions in the octahedral sites and tetrahedral site of the iron garnet crystal lattice. In addition, the values of the center shifts (isomer shifts) are nearly the same for all samples. In view of the fact that the center shift is dependent on the s-electronic density at the nucleus,^[16] the constancy of the center shifts for the octahedral sublattice (0.38 ±0.02 mm/s) and tetrahedral sublattice (0.15 ±0.02 mm/s) is an indication that the substitution of Y³⁺ ions by Dy³⁺ ions does not perturb the wave function of the Fe³⁺ ions, which is a further indication of the weak c–a and c–d coupling. This conclusion is also supported by the fact that the observed average hyperfine field of the octahedral sites (∼492 kOe) and that of the tetrahedral site (∼401 kOe) are practically equal to those of 492 kOe–495 kOe and 397 kOe–399 kOe, respectively, for Ho-substituted YIG.^[14]

Fig. 4.

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	Fig. 4. (color online) Mössbauer spectra for Y3−xDyxFe5O12 samples (solid circles) together with theoretical spectra obtained from fitting software (red solid curves). Components corresponding to octahedral sites are represented by blue curves, while the component corresponding to tetrahedral sites is represented by green curves.

Table 2.

Table 2.

Table 2. Hyperfine parameters and percentage relative intensity (I) values obtained at room temperature for the Y3−xDyxFe5O12 samples. . Site Bhf/kOe (±5) CS/(mm/s) (±002) Width/(mm/s) (±003) I/% (±2) x=0 Octahedral(s) 497 0.38 0.35 27 487 0.38 0.39 10 Tetrahedral 401 0.15 0.50 63 x=0.5 Octahedral(s) 497 0.38 0.35 27 487 0.38 0.39 10 Tetrahedral 401 0.15 0.54 63 x=1.0 Octahedral(s) 496 0.38 0.29 27 488 0.38 0.30 10 Tetrahedral 400 0.16 0.55 63 x=1.5 Octahedral(s) 497 0.38 0.32 27 485 0.38 0.34 10 Tetrahedral 401 0.16 0.57 63 x=2.0 Octahedral(s) 497 0.38 0.35 27 488 0.38 0.32 10 Tetrahedral 402 0.16 0.58 63 x=2.5 Octahedral(s) 497 0.38 0.34 27 489 0.37 0.34 10 Tetrahedral 403 0.16 0.58 63 x=3.0 Octahedral(s) 492 0.39 0.35 26 484 0.37 0.38 10 Tetrahedral 398 0.16 0.62 64

Table 2. Hyperfine parameters and percentage relative intensity (I) values obtained at room temperature for the Y3−xDyxFe5O12 samples. .

The hysteresis loops (Fig. 5) indicate that all samples of Y_3−xDy_xFe₅O₁₂ are soft magnetic materials each with a very small coercivity. Also, the loops indicate that the saturation magnetization decreases monotonically with Dy³⁺ concentration increasing. As a consequence of the a–d superexchange interaction between Fe³⁺ ions being much stronger than the superexchange interaction between the Fe³⁺ ion and the magnetic rare-earth ion,^[1,6] the net magnetization of the iron sublattices couples antiferromagnetically with the c sublattice containing the rare earth ions, and the net magnetization of the compound is given by^[6]

Fig. 5.

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	Fig. 5. (color online) Hysteresis loops for Y3−xDyxFe5O12 samples.

Assuming phase separation in the Dy-substituted compound into two separated garnets according to the formula:

Fig. 6.

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	Fig. 6. (color online) Illustration of saturation magnetization behavior with Dy concentration (x) increasing.

The initial magnetization curves (Fig. 7) of the samples of Y_3−xDy_xFe₅O₁₂ show that both the initial magnetic susceptibility χ_in and saturation magnetization M_s decrease with rare earth substitution increasing. Figure 8 shows a plot of the observed M_s [in units (emu/g)] and χ_in [in units () as a function of dysprosium concentration x. The saturation magnetization exhibits nearly a linear decrease with x increasing, which is in agreement with the reported behavior of the saturation magnetization of Y_3−xDy_xFe₅O₁₂() prepared by the sol–gel method.^[11] On the other hand, χ_in shows a sharp decrease with x increasing from x = 0 to x =1, and a slow decreasing tendency with fluctuations for x greater than 1.0. The weakening of the magnetic parameters with Dy substitution is a consequence of the weak antiferromagnetic coupling between the RE magnetic sublattice and the net magnetization of the Fe sublattices, which leads to a sharper drop of the RE-sublattice magnetization (in comparison with the decrease of the magnetization of the Fe sublattices) as the temperature increases toward room temperature.^[19]

Fig. 7.

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	Fig. 7. (color online) Initial magnetization curves of Y3−xDyxFe5O12 garnets.

Fig. 8.

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	Fig. 8. (color online) Saturation magnetization Ms and initial magnetic susceptibility χin as a function of x for Y3−xDyxFe5O12 garnets.

Differential scanning calorimetry (DSC) measurements are performed on all samples and the results are illustrated in Fig. 9. The thermal curves of all samples are almost smooth with small kinks (marked by arrows) in a temperature range of . Since abrupt changes in the thermal curves are usually associated with structural phase transitions or changes of the specific heat of the material under investigation, the positions of the small kinks in the thermal curves can be associated with temperatures at which the samples must have passed through transitions between phases with slightly different specific heats. In view of the fact that the magnetic contribution to the specific heat is rather small as reported for other magnetic oxides,^[20] the observed kink in the thermal curve is associated with the Curie temperature at which ferrimagnetic–paramagnetic phase transition takes place.

Fig. 9.

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	Fig. 9. (color online) DSC versus T curves of Y3−xDyxFe5O12 garnets.

The T_c values for Y₃Fe₅O₁₂ and Dy₃Fe₅O₁₂ (276.0 °C and 278.3 °C, respectively) are in good agreement with previous experimental results on rare earth iron garnets.^[6] Further, T_c does not seem to change appreciably with Dy concentration, and did not differ from the values found previously for Gd_3−xEr_xFe₅O₁₂ either,^[21] indicating that T_c is independent of rare-earth substitution and is determined only by the strong superexchange interaction between the two iron sublattices. If, however, we believe the small increase of T_c (from 276.0 °C to 278.3 °C) with x increasing, this increase could then be attributed to the slight strengthening of the superexchange interactions as a result of the additional weak interaction between the RE and Fe sublattices.

Dy-substituted YIG garnets are successfully synthesized by using the conventional solid state reaction method, where XRD patterns reveal the presence of a single garnet phase in each sample with no secondary phases. The lattice constant a and cell volume V increase with increasing Dy³⁺ substitution for Y³⁺ due to the larger ionic radius of Dy³⁺, whereas the increase of the molecular mass is responsible for the observed increase of the x-ray density of the substituted compound. RT Mössbauer spectra indicate that the substitution of Dy³⁺ for Y³⁺ at the dodecahedral c site does not perturb the Fe³⁺ wave function appreciably, keeping the hyperfine parameters practically unchanged. The saturation magnetization decreases almost linearly with Dy³⁺ substitution increasing, which is explained in terms of a simple magnetic dilution model. The Curie temperature determined from the DSC measurements is found to be nearly the same for all Dy substituted compounds.

The authors Mahdi Lataifeh and Ibrahim Abu-Aljarayesh would like to thank the Deanship of Research and Graduate Studies of Yarmouk University under Garnet No. 33/2015 used to execute part of the measurements (XRD and the thermal differential scanning calorimetry measurements) at Jordan University of Science and Technology.