Thermomagnetization characteristics and ferromagnetic resonance linewidth broadening mechanism for Ca-Sn Co-substituted YIG ferrites

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Thermomagnetization characteristics and ferromagnetic resonance linewidth broadening mechanism for Ca-Sn Co-substituted YIG ferrites ⁎

Yan Yanga, Zhong Yub, Qiguang Guob, Ke Sunb, , Rongdi Guob, Xiaona Jiangb, Yu Liub, Hai Liub, Guohua Wub, Zhongwen Lanb a b

Department of Electronic Engineering, Chengdu Technological University, Chengdu 611730, China School of Materials and Energy, University of Electronic Science and Technology of China, Chengdu 610054, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Yttrium iron garnet ferrites Ca-Sn co-substitution Brillouin function Curie temperature Ferromagnetic resonance linewidth Molecular-field coefficients

Yttrium iron garnet (YIG) ferrites own significant applications in microwave magnetic devices, such as circulators, isolators and filters. The excellent performance and reliability of these devices are strongly dependent on the saturation magnetization (Ms), ferromagnetic resonance (FMR) linewidth (ΔH), dielectric loss tangent (tan δε) and Curie temperature (Tc) of the garnet ferrites. Here, we fabricate Ca-Sn co-substituted Y3-xCaxFe5-xSnxO12 (x = 0.0, 0.1, 0.2, 0.3 and 0.4) ferrites using solid-state reaction method, and investigate the thermomagnetization characteristics of Brillouin function and FMR linewidth based on Néel model of ferrimagnetism and spin wave approach, respectively. This study clarifies the intrasublattice molecular-field coefficients ωaa, ωdd and intersublattice coefficients ωad = ωda. More importantly, we propose an accurate formula of Curie temperature Tc for garnet ferrites. Furthermore, Ca-Sn co-substitution can tailor the FMR linewidth based on the adjustment of anisotropy and the realization of densification. Finally, Y2.7Ca0.3Fe4.7Sn0.3O12 ferrite exhibits optimized magnetic property: 4πMs = 2073 Gs, ΔH = 42 Oe, Tc = 491 K.

1. Introduction With the rapid improvement of a great number of technological applications, ferrites have been applied to many aspects in variety of forms due to their extraordinary property [1–5]. Especially, the garnet ferrites have been extensively used in microwave magnetic devices such as circulators, isolators and filters [6–8], in virtue of its manipulated saturation magnetization Ms and Curie temperature Tc, low dielectric loss tangent (tan δε) and narrow ferromagnetic resonance (FMR) linewidth ΔH in microwave regions [9–11]. Fig. 1 exhibits the diagrammatic sketch of the Y3Fe5O12 (YIG) ferrite structure, which has bcc structure with eight formula units and three sublattices, tetrahedral d sites, octahedral a sites, and dodecahedral c sites. The dodecahedral c sites have been occupied by Y3+ ions, while the tetrahedral d sites and octahedral a sites have been occupied by Fe3+ ions in 2:3 ratios respectively. Because Y3+ ion is nonmagnetic, the contribution of magnetic moment arises from two Fe3+ ions in a sites and three Fe3+ in d sites which exhibits antiparallel alignment, leave a net moment from Fe3+ ions in d sites [12]. More importantly, the various crystallographic sites can make it probable to replace YIG ferrite with various cations, and these substitutions can adjust magnetic property. The required properties for specific applications have been

⁎

studied by manipulating the fabrication process or using the proper ions substitution. According to the existing researches, the property of YIG-based ferrites could be modified by introducing cations substitution, such as V5+, Gd3+, In3+, Bi3+, Sn4+ [13–15]. For instance, V5+ substitution can obviously decrease the densification temperature [16,17], but weaken both Ms and Tc [18,19]. Meanwhile, Gd3+ substitution can tune Ms of YIG ferrite and control its temperature stability owing to the compensation point of Ga3Fe5O12 ferrite is about room temperature [20]. In addition, the introduction of In3+ ions could effectively weaken the magnetocrystalline anisotropy constant K1 to reduce FMR linewidth ΔH [21,22]. Whereas, with increasingly rigorous demand of wide operating temperature range and low microwave loss of radar systems, the microwave devices and components require the YIG-based ferrites with high temperature stability and narrow ΔH. Thus, it is necessary to cognize the effect factors of Tc and the broadening mechanism of ΔH. Fortunately, the Néel molecular-field theory provides a valid approach to explore the relationship between magnetization and temperature. Furthermore, the spin wave approach offers a method to investigate the ΔH broadening mechanism. Both the Néel molecular-field theory and spin wave approach have successfully applied to thermomagnetic

Corresponding author. E-mail addresses: [email protected], [email protected] (K. Sun).

https://doi.org/10.1016/j.ceramint.2018.03.249 Received 10 February 2018; Received in revised form 24 March 2018; Accepted 28 March 2018 0272-8842/ © 2018 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Please cite this article as: Yang, Y., Ceramics International (2018), https://doi.org/10.1016/j.ceramint.2018.03.249

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Fig. 1. Diagrammatic sketch of garnet ferrite structure.

characteristics and ΔH for ferrites, particularly for the spinel [23–25] and garnet ferrites [26–29]. In term of thermomagnetic behavior, E.E. Anderson [26] has studied the molecular-field coefficients and exchange interactions. The Tc has been computed based on the assumption of a-a and d-d interactions are zero, which is discrepant with the real situation so that the results are unsound. Meanwhile, P. Röschmann and P. Hansen [27] have researched the cations distribution of substituted YIG ferrite and its molecular-field coefficients. However, the acquisition of molecular-field coefficients was based on the empirical considerations accompanying with lots of analytical calculations. Concerning ΔH, Xu [29] has investigated the influence of In-substitution on it, but the linewidth broadening mechanism has not been cognized deeply. In general, it is emphasized that the previous studies mainly focus on the magnetic property such as Ms and Hc. rather than the thermomagnetization characteristics and the broadening mechanism of ΔH for Ca-Sn co-substituted YIG ferrites [30,31]. So far, the molecular-field coefficients ωaa, ωdd and ωad have not been calculated completely and the formula of Tc has not been expanded to garnet ferrites. Moreover, neither the magnetocrystalline anisotropy constant K1 nor anisotropy linewidth (ΔHa) and porosity linewidth (ΔHp) yet have been investigated completely. Thus, this study would focus on solving these issues.

Fig. 2. XRD patterns of the Y3-xCaxFe5-xSnxO12 with different Ca-Sn co-substituted content x. d −d

(P), P = Xd b × 100%, was calculated through X-ray density dX and X bulk density db.

3. Results and discussion 3.1. Phase, microstructure, static magnetic property In Fig. 2, the XRD patterns of Y3-xCaxFe5-xSnxO12 with various Ca-Sn co-substituted content coincide well with the powder diffraction file of JCPDS No. 77-1998. XRD patterns confirm that all the samples are typical garnet structure with no tanglesome peaks, and the reflection peaks move towards small angle. Furthermore, the lattice constant a (shown in Table 1) gradually goes up with increasing Ca-Sn co-substituted content, the result is consistent with the skewing of reflection peaks. The radius of Sn4+ (0.71 Å) is bigger than Fe3+ (0.61 Å), and the radius of Ca2+ (1.12 Å) is larger than and Y3+ (1.01 Å), respectively. Consequently, the introduction of Sn4+ and Ca2+ accounts for the lattice expansion. Fig. 3 represents the SEM photographs of the samples. As can been seen, no obvious grain can be observed and the grain boundaries are ambiguous. It is clear that Bi2O3 additive would be a form of liquid phase during sintering that helps to promote the solid-state mass transfer and sintering. It is worth noting that the transfer mechanism contributes to eliminate porosity of samples, therefore the densification and homogeneity of samples can be improved. Low porosity of all the samples as shown in Table 1 also authenticate the improvement. Fig. 4 manifests the change of Ms and Hc as a function of Ca-Sn cosubstituted content. In view of Ms, it increases gradually due to the augment of net molecular M = |Md − Ma|, resulting from the reduction of Fe3+ substituted by nonmagnetic Sn4+ ions in octahedral a sites. The Hc is associated with K1 and stress [32], and in order to probe into its cause of this reduction, K1 is estimated by fitting the experimental M-H curve based on the empirical law of approach to saturation:

2. Experiment procedures Ca-Sn co-substituted polycrystalline Y3-xCaxFe5-xSnxO12 (x = 0.0, 0.1, 0.2, 0.3 and 0.4) ferrites were fabricated by the solid-state reaction method with high purity raw powders of Y2O3 (99.99%), CaCO3 (99.0%), SnO2 (99.8%), and Fe2O3 (99.9%). For the sake of ensuring the precise chemical composition, we used zirconia ball as ball milling medium. The raw powders were milled for 9 h. The dried powders were calcined at 1100 °C for 3 h. The calcined powders were mixed with Bi2O3 (0.2 wt%), and then milled for 9 h again. The dried powders were prepared into granular with 12 wt% polyvinyl alcohol and molded into toroids (Φ21 mm × Φ11 mm ×h5 mm) at 15 MPa. Then, the toroids were sintered at 1400 °C for 4 h in atmosphere and left to cool to room temperature inside a furnace. Then parts of sintered samples have been fabricated into small spheres with different diameters (Φ1.5 mm, Φ0.8 mm) for the measurement of specific Ms and ΔH. Ms was measured from 1.8 K to 400 K with an external magnetic field H of 1 T by superconductor quantum interfere device (SQUID). ΔH was measured in TE104 cavity at X-band (9.2 GHz) through IEC standard. Coercivity Hc was measured with the magnetic field of 2000 A/m and 1 kHz by B-H analyzer SY-8232. Density db was measured by Archimedes method. Fracture morphology was observed by scanning electron microscope (SEM) JEOL TSM-6490L. X-ray diffraction (XRD) patterns were carried out by the Philips diffractometer and the X-ray with a copper target was operated at 40 kV and 40 mA. The porosity

Table 1 The density db, lattice constant a, porosity P, anisotropy constant K1 and anisotropy field Ha of the Y3-xCaxFe5-xSnxO12 with various Ca-Sn co-substitution content x. x 3

db (g/cm ) a (Å) P (%) K1 (kJ/m3) Ha (kA/m)

2

0.0

0.1

0.2

0.3

0.4

5.02 12.376 2.95 0.645 6.92

5.06 12.389 1.88 0.576 5.73

5.06 12.404 1.74 0.559 5.49

5.05 12.426 1.58 0.547 5.25

5.06 12.430 1.59 0.534 5.09

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Fig. 3. The SEM photographs of the Y3-xCaxFe5-xSnxO12 with different Ca-Sn co-substituted content: (a) x = 0.0, (b) x = 0.1, (c) x = 0.2, (d) x = 0.3, (e) x = 0.4.

3.2. Thermomagnetization characteristics According to the ions distribution of garnet ferrite, which have three distinguishable sublattices, the resultant magnetic moment per mole can be given as: (3)

M (T ) = Mc (T ) − Md (T ) − Ma (T ) , 4+

3+

2+

substitutes Fe in octahedral a sites, Ca subwhereas, when Sn stitutes Y3+ in dodecahedral c sites to balance the valence. Considering the nonmagnetic ions Y3+ and Ca2+, the Mc(T) is always equal to zero, thus, the Eq. (3) could be simplified as: (4)

M (T ) = Md (T ) − Ma (T ),

Then, based on the Néel model of ferrimagnetism, with an assumption of orbit angular momentum freezes (J=S, where J and S are azimuthal quantum number and spin quantum number, respectively), the temperature relationship of the magnetic moment can be described by Brillouin function as:

Fig. 4. The 4πMs and Hc of the Y3-xCaxFe5-xSnxO12 with different Ca-Sn cosubstituted content x.

a b MH = Ms ⎛1 − − 2 − …⎞ + χp H H H ⎝ ⎠

b=

8 K12 105 μ02 Ms2

Mi (T ) = Mi (T ) B Ji (yi ), (1)

(5)

where the subscript i refers to the particular sublattice, Mi(0) is the molecular moment per mole at 0 K, and B Ji (yi) is the Brillouin function expressed as:

(2)

B Ji (yi ) =

where a and b refer to the resistance of technical magnetization, H means external magnetic field, χp is paramagnetic susceptibility and μ0 is vacuum permeability [23]. Hc is in direct proportion to K1 (shown in Table 1) and in inverse proportion to Ms, therefore, the increasing Ms and decreasing K1 result in the reduction of Hc. Simultaneously, Hc is in direct proportion to stress that has positive correlation with porosity (P). Therefore, both K1 and P can induce the decrease of Hc.

2Ji + 1 2J + 1 ⎞ 1 1 coth ⎛ i yi − coth ⎛ yi ⎞, 2Ji 2Ji ⎠ ⎝ 2Ji ⎠ ⎝ 2Ji ⎜

⎟

⎜

⎟

(6)

In view of the assumption (J=S), the Brillouin function are changed to be

BSi (yi ) = with 3

2Si + 1 2S + 1 ⎞ 1 1 coth ⎛ i yi − coth ⎛ yi ⎞, 2Si 2 S 2 S 2 i i ⎠ ⎝ Si ⎠ ⎝ ⎜

⎟

⎜

⎟

(7)

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ya =

gSa μB (ωaa Ma (T ) + ωad Md (T )), kB T

(8a)

yd =

gSd μB (ωda Ma (T ) + ωdd Md (T )), kB T

(8b)

Table 2 The fitting Tc(fit.), calculated Tc(cal.), experimental Tc(test.), and molecular-field coefficients values of the Y3-xCaxFe5-xSnxO12 ferrites with different Ca-Sn cosubstitution content x. x

In Eq. (8), ωaa, ωdd, and ωad = ωda are the molecular-field coefficients, Sa and Sd are the equivalent spin quantum numbers of two sublattices, g is the Lander factor, μB is the Bohr magneton, kB is Boltzmann constant. For the sake of finding the connection between experimental results and Brillouin function, according to the cations distribution, the molecular formula 2+ 3+ 4+ 3+ was supposed to be {Y3+ 3-x Cax }[Fe2-x Snx ](Fe3 )O12. At 0 K, the magnetic moments per mole for each sublattice are given by:

Ma (0) = 2gSa μB NA (1 − ka),

(9a)

Md (0) = 3gSd μB NA,

(9b)

0.0 0.1 0.2 0.3 0.4

ωaa

−68 −66 −66 −65 −65

ωad

96 95 94 93 91

ωdd

−29 −29 −29 −29 −29

R (%)

0.18 0.56 0.78 0.61 1.90

Tc (K) Fit.

Cal.

Test

546 528 505 488 460

546 528 507 488 461

547 531 511 491 470

pure Y3Fe5O12 sample without any ions substitution. When the molecular-field coefficients ωaa = −68, ωad = 96, ωdd = −29 (shown in Table 2), the calculated results are coinciding well with the experimental data Ms(T)test. The cyan line denotes the experimental molecular magnetic moment Ms(T)test versus temperature. The blue line denotes the calculated molecular magnetic moment Ms(T)fit. versus temperature. The black line denotes the calculated tetrahedral d sites molecular magnetic moment Md(T)fit. versus temperature and the red line denotes contrary number of the calculated octahedral a sites molecular magnetic moment Ma(T)fit. versus temperature. Simultaneously, while the value of Ms(T)fit. is less than the negative second power of ten, the approximate temperature is regarded as the fitting Curie temperature Tc(fit). In this study, when the value of Ms(T)cal. is 0.0007μB, the homologous temperature 546 K is supposed to be Tc(fit). The ωaa, ωad, ωdd are shown in Table 2 for different Ca-Sn co-substituted content. As Ca-Sn co-substituted content increases, ωdd is invariable, ωaa has a tiny increase, while ωad = ωda appears the decreasing trend. Moreover, in the same level of Ca-Sn co-substituted content, compared with the values of molecular-field coefficients, ωad = ωda is always bigger than the others, which obviously illustrates the superexchange interaction mainly relies on ωad = ωda. Besides, in order to explain the precision of the fitting results, the error R (shown in Table 2) is expressed as:

where ka represents the fractions of nonmagnetic ions replaces Fe3+ ion in the octahedral a sites and NA is Avogadro's constant. The factors 2 and 3 appearing in Eq. (9) means there are 2 and 3 mol Fe3+ ions per mole sublattice, respectively. For Ca-Sn co-substitution, the relations between ωij and the respective ka variables were determined independently. Through solving undetermined Eq. (9), the specific values of ωaa, ωdd, and ωad were fitted by the experimental data Ms(T)test in a temperature range of 1.8–400 K, as well as matching the Tc for each composition. Fig. 5 shows the variety curves between magnetic moment and temperature for different Ca-Sn co-substituted content. The octahedral a sites magnetic moment Ma(T)fit, the tetrahedral d sites magnetic moment Md(T)fit, and molecular moment Ms(T)fit were calculated in a temperature range of absolute zero to the corresponding Tc, respectively. In addition, the molecular magnetic moment Ms(T)fit matched well with the experimental data Ms(T)test for various Ca-Sn co-substituted content. As the temperature increases, the strengthening thermal commotion energy induces the disorder of magnetic moments, consequently magnetic moments decrease. Fig. 5(a) shows the magnetic moment versus temperature curves for

Fig. 5. Experimental and calculated magnetic moment versus temperature curves of the Y3-xCaxFe5-xSnxO12 ferrites with various Ca-Sn co-substituted content: (a) x = 0.0, (b) x = 0.1, (c) x = 0.2, (d) x = 0.3, (e) x = 0.4. 4

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R=

∑i Ms (Ti )test − Ms (Ti )cal

× 100%,

∑i Ms (Ti )test

(10)

with the increasing Ca-Sn co-substitution content, the errors are all less than 2.00%. According to the structure model of garnet ferrites, for nonmagnetic Ca-Sn co-substitution, the dodecahedral c sites have been occupied by Y3+ and Ca2+ ions. Therefore, the Tc mainly depends on the Fe3+ superexchange interaction between octahedral a sites and tetrahedral d sites, letting the determinant of the coefficients of Eq. (5) equal to zero, the Tc formula has been described as follow:

Tc =

Nad gμB Md (0)(β + φc )(Sd + 1) 3kB

(11) (S + 1) M (0) 2

(S + 1) M (0)

φc =

,

⎡α − β (Sd + 1) Md (0) ⎤ + a a ⎣ ⎦

(S + 1) M (0)

⎡α − β (Sd + 1) Md (0) ⎤ + 4 (Sd + 1) Md (0) a a a a ⎣ ⎦ (S + 1) M (0)

2 (Sd + 1) Md (0) a

,

Fig. 6. ΔHa and ΔHp of the Y3-xCaxFe5-xSnxO12 with different Ca-Sn co-substituted content.

(12)

a

here, Sa = Sd = SFe3+ = 2.5, so that the Eq. (10) can be briefly described as:

φc =

⎡α − ⎣

M (0) β Md (0) ⎤ a ⎦

+

⎡α − ⎣

M (0) 2 β Md (0) ⎤ a ⎦

+

M (0) 2 Md (0) a

M (0) 4 Md (0) a

where P is porosity, θu is the polar angle of the magnon having the same energy as the uniform precession. Referring to a spherical sample, cosθu is approximately 1/3. In short, the separated ΔHa and ΔHp could been obtained through combined Eqs. (16) and (17) as shown in Fig. 6. The variation of ΔHa and ΔHp shows the function of Ca-Sn co-substituted content. As the amount of Ca-Sn co-substitution increases, ΔHa decreases continuously to the minimum value of 4 Oe at x = 0.4, the continuous reduction of K1 and Ha account for this consequence. Simultaneously, ΔHp declines firstly, minimizes at x = 0.3, and then goes up slightly. This variation trend matches well with the porosity. Moreover, the ΔH appears the same trend with ΔHp, which manifests the ΔHp is the majority of contributions to ΔH, thus, densification is the significant approach to reduce the ΔH.

, (13)

where α = ωaa / ωad , β = ωdd / ωad , according to Eqs. (11) and (13), the calculated Tc(cal.) is shown in Table 2. As been shown, the values of the calculated Tc(cal.) are very approximate to the values of the Tc(fit.), which demonstrates the calculation model is reliable. 3.3. Ferromagnetic resonance linewidth To recognize the broadening mechanism of FMR linewidth ΔH, an appropriate calculation for the contribution of ΔH has been adopted using spin wave approach. As well known, the ΔH of polycrystalline ferrites is consisted of three contributions [23]:

ΔH = ΔHi + ΔHa + ΔHp,

4. Conclusions

(14)

The phase, static magnetic property, thermomagnetization characteristics and FMR linewidth of polycrystalline Y3-xCaxFe5-xSnxO12 ferrites have been investigated. The Ms increases gradually with the increasing Ca-Sn co-substituted content, while Hc declines firstly, minimizes at x = 0.3, and then goes up slightly. Besides, the specific values of molecular-field coefficients ωaa, ωdd, and ωad = ωda have been calculated precisely by nonlinear fitting method. With the particular Ca-Sn co-substituted content, the values of ωad = ωda is always the biggest. Meanwhile, with the increasing Ca-Sn co-substituted content, ωaa has a tiny increase and ωdd is invariable, while ωad = ωda appears the decreasing trend leads to the reduction of Tc. More importantly, we propose an accurate formula of Curie temperature Tc for garnet ferrites. Apart from this, the separated ΔHa and ΔHp show the function of Ca-Sn co-substitution content. With the increasing amount of Ca-Sn co-substitution, ΔHa decreases continuously, while ΔHp decreases to minimum value at x = 0.3.

where, ΔHi, ΔHa and ΔHp refer to intrinsic, anisotropy and porosity linewidth, respectively. Usually the ΔHi is negligible because the puny contribution to ΔH, thus, ΔH is mainly influenced by ΔHa and ΔHp. Schlömann established crystalline anisotropy linewidth for two situations [33]: Ha > > 4πMs (independent grain approach) and Ha < < 4πMs (spin wave approach). Then anisotropy field Ha could be acquired (shown in Table 1) by Eq. (15), K1 and Ha continuously reduce with the increase of Ca-Sn cosubstitution content. For nonmagnetic ions substitution, the reduction of magnetic ions weakens the exchange interaction and leads to the decline of K1 and Ha. Furthermore, Ha is much smaller than 4πMs, thus, the spin wave approach would be adopted herein.

Ha =

2 K1 , Ms

ΔHa =

Ha2 8π 3 G (ω, ωi ), 4πMs 21

(15)

Acknowledgements

(16)

Furthermore, through obtained Ha, the anisotropy linewidth ΔHa would be calculated via Eq. (16). In Eq. (16), Ha is the anisotropy field, G(ω, ωi) is a shape factor which depends on the frequency (G(ω, ωi) is nearly equal to 1 at high frequency), ωi is the static internal resonance field normalized to the Ms, ω is the resonance frequency normalized to γ4πMs, where γ is the gyromagnetic ratio of 2.8 MHz/Oe. Besides, ΔHp was approximately calculated by the Eq. (17) raised by Byun [34] as follow:

ΔHp =

8π 1 4πMs P (1 − P ), 45 cos θu

The authors are grateful for the financial support from the National Natural Science Foundation of China under Grants 51472045 and 51772046. References [1] W.F. Faiz Wan Ali, N.S. Abdullah, M. Kamarudin, M.F. Ain, Z.A. Ahmad, Sintering and grain growth control of high dense YIG, Ceram. Int. 42 (2016) 13996–14005. [2] Y.P. Wang, G.Q. Zhang, D.K. Deng, X.Q. Luo, W. Xiong, S.P. Wang, T.F. Li, C.M. Hu, J.Q. You, Magnon Kerr effect in a strongly coupled cavity-magnon system, Phys. Rev. B 94 (2016) 224410.

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Y. Yang et al.

[17] U. Hoeppe, H. Benner, Influence of microstructure on relaxation processes and high power properties in polycrystalline YIG, Phys. Status Solidi A 195 (2003) 447–452. [18] R.F. Pearson, K. Tweedale, Field dependence of anisotropy in ytterbium-doped yttrium iron garnet, J. Appl. Phys. 35 (1964) 1061–1062. [19] C.Y. Tsay, C.Y. Liu, K.S. Liu, I.N. Lin, L.J. Hu, T.S. Yeh, Low temperature sintering of microwave magnetic garnet materials, Mater. Chem. Phys. 79 (2003) 138–142. [20] F.R. Lamastra, A. Bianco, F. Leonardi, G. Montesperelli, F. Nanni, G. Gusmano, High density Gd-substituted yttrium iron garnets by coprecipitation, Mater. Chem. Phys. 107 (2008) 274–280. [21] F. Euler, H. Jerrold Van Hook, Magnetic anisotropy of vanadium-indium-substituted YIG, J. Appl. Phys. 41 (1970) 3325–3331. [22] G. Winkler, P. Hansen, Calcium-vanadium-indium substituted yttrium-iron-garnets with very low linewidths of ferrimagnetic resonance, Mater. Res. Bull. 4 (1969) 825–837. [23] R.D. Guo, Z. Yu, Y. Yang, X.N. Jiang, K. Sun, C.J. Wu, Z.Y. Xu, Z.W. Lan, Effects of Bi2O3 on FMR linewidth and microwave dielectric properties of LiZnMn ferrite, J. Alloy. Compd. 589 (2013) 1–4. [24] G.F. Dionne, Molecular-field coefficients of Ti4+-and Zn2+-substituted lithium ferrites, J. Appl. Phys. 45 (1974) 3621. [25] R.D. Guo, Z. Yu, Y. Yang, L.L. Chen, K. Sun, X.N. Jiang, C.J. Wu, Z.W. Lan, Relationship between Curie temperature and Brillouin function characteristics of NiCuZn ferrites, J. Appl. Phys. 117 (2015) 073905. [26] E.E. Anderson, Molecular field model and the magnetization of YIG, Phys. Rev. 134 (1964) A1581. [27] P. Röschmann, P. Hansen, Molecular field coefficients and cation distribution of substituted yttrium iron garnets, J. Appl. Phys. 52 (1981) 6257–6269. [28] W.M. Yang, L.X. Wang, Y.J. Ding, Q. Zhang, Narrowing of ferromagnetic resonance linewidth in calcium substituted YIG powders by Zr4+/Sn4+ substitution, J. Mater. Sci: Mater. Electron. 25 (2014) 4517–4523. [29] Q.M. Xu, W.B. Liu, L.J. Hao, C.J. Gao, X.G. Lu, Y.A. Wang, J.S. Zhou, Effects of insubstitution on the microstructure and magnetic properties of Bi-CVG ferrite with low temperature sintering, J. Magn. Magn. Mater. 322 (2010) 2276–2280. [30] F. Dorazio, F. Giammaria, F. Lucari, Anomalies in the temperature dependence of Faraday rotation on yttrium iron garnets doped with Sn, Zr, or Sb, J. Appl. Phys. 70 (1991) 6295–6297. [31] Z.Z. Zhang, F. Chen, J.N. Li, Y. Nie, Effect of Sn doping on the room temperature magnetodielectric properties of yttrium iron garnet, J. Appl. Phys. 118 (2015) 154102. [32] D.F. Wan, X.L. Ma, Magnetic Physics (In Chinese), first ed., House of Electronics Industry, Beijing, 1999. [33] E. Schlömann, Spin-wave analysis of ferromagnetic resonance in polycrystalline ferrites, J. Phys. Chem. Solids 6 (1958) 242–256. [34] T.Y. Byun, S.C. Byeon, K.S. Hong, C.K. Kim, Origin of line broadening in Co-substituted NiZnCu ferrites, J. Appl. Phys. 87 (2000) 6220–6222.

[3] A. Speghini, F. Piccinelli, M. Bettinelli, Synthesis, characterization and luminescence spectroscopy of oxide nanopowders activated with trivalent lanthanide ions: the garnet family, Opt. Mater. 33 (2011) 247–257. [4] B.Z. Rameshti, Yunshan Cao, Gerrit E.W. Bauer, Magnetic spheres in microwave cavities, Phys. Rev. B 91 (2015) 214430. [5] H. Serier-Brault, L. Thibault, M. Legrain, X. Rocquefelte, P. Leone, Thermochromism in yttrium iron garnet compounds, Inorg. Chem. 53 (2014) 12378–12383. [6] M.N. Akhtar, A.B. Sulong, M.A. Khan, M. Ahmad, G. Murtaza, M.R. Raza, M. Kashif, Structural and magnetic properties of yttrium iron garnet (YIG) and yttrium aluminum iron garnet (YAIG) nanoferrites prepared by microemulsion method, J. Magn. Magn. Mater. 401 (2016) 425–431. [7] S. Khanra, A. Bhaumik, Y.D. Kolekar, P. Kahol, K. Ghosh, Structural and magnetic studies of Y3Fe5-5xMo5xO12, J. Magn. Magn. Mater. 369 (2014) 14–22. [8] M.A. Musa, R.S. Azis, M. Hashim, N.H. Osman, S.I. Adnan, N. Daud, N.M.M. Shahrani, S. Sulaiman, N.N.C. Muda, A.H. Azizan, Composition and magnetic properties of aluminium substituted yttrium iron garnet waste mill scales derived via mechanical alloying technique, J. Solid State Sci. Technol. Lett. 16 (2015) 62–66. [9] M.N. Akhtar, A.B. Sulong, M. Ahmad, M.A. Khan, A. Ali, M.U. Islam, Impacts of Gd–Ce on the structural, morphological and magnetic properties of garnet nanocrystalline ferrites synthesized via sol-gel route, J. Alloy. Compd. 660 (2016) 486–495. [10] C. Tang, M. Aldosary, Z.L. Jiang, H. Chang, B. Madon, K. Chan, J. Shi, Exquisite growth control and magnetic properties of yttrium iron garnet thin films, Appl. Phys. Lett. 108 (2016) 102403. [11] H.R. Wu, F.Z. Huang, T.T. Xu, R. Ti, X. Lu, Y. Kan, J. Zhu, Magnetic and magnetodielectric properties of Y3-xLaxFe5O12 ceramics, J. Appl. Phys. 117 (2015) 144101. [12] H.T. Xu, H. Yang, W. Xu, S. Feng, Magnetic properties of Ce, Gd-substituted yttrium iron garnet ferrite powders fabricated using a sol-gel method, J. Mater. Process. Technol. 197 (2008) 296–300. [13] C.Y. Tsay, C.K. Lin, H.C. Cheng, K.S. Liu, I.N. Lin, Low temperature sintering and magnetic properties of garnet microwave magnetic materials, Mater. Chem. Phys. 105 (2007) 408–413. [14] R. Nazlan, M. Hashim, I.R. Ibrahim, F.M. Idris, I. Ismail, W.N.W. Ab Rahman, M.S. Mustaffa, Indium-substitution and indium-less case effects on structural and magnetic properties of yttrium-iron garnet, J. Phys. Chem. Solids 85 (2015) 1–12. [15] F.W. Aldbea, N.B. Ibrahim, M. Yahya, Effect of adding aluminum ion on the structural, optical, electrical and magnetic properties of terbium doped yttrium iron garnet nanoparticles films prepared by sol-gel method, Appl. Surf. Sci. 321 (2014) 150–157. [16] N. Jia, H.W. Zhang, J. Li, Y. Liao, L. Jin, C. Liu, V.G. Harris, Polycrystalline Bi substituted YIG ferrite processed via low temperature sintering, J. Alloy. Compd. 695 (2017) 931–936.

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