Ferromagnetic resonance induced large microwave magnetodielectric effect in cerium doped Y3Fe5O12 ferrites

In recent years, multifunctional materials contained simultaneous ferroelectric and ferromagnetic ordering have been realized. Here, a real time room temperature adaptive materials system, which demonstrates an RF magnetodielectric (MD) response, i.e., CexY3−xFe5O12 (x = 0, 0.05, 0.1, 0.15, 0.2), is reported. The magnetic and dielectric properties of Ce-doped YIG microwave ferrites processed by a traditional ceramic route have been measured over a frequency range of 4–8 GHz (C-band). The substitution of Ce not only enhances the microwave electromagnetic properties of the YIG, but also modulates the magnetodielectric response. The maximum magnetodielectric response in Ce-doped YIG sample ranges in magnitude from approximately +5% to −5% under an applied field of 1.78 kOe. This effect was attributed to electron fluctuations on the Fe cation sites. Furthermore, the magnitude of the MD response was shown to be enhanced by the cerium content. It is believed that research of the magnetodielectric effect in YIG ferrites is of great importance to the development of next generation multifunctional adaptive microwave materials, devices and integrated circuits.

Scientific RepoRts | 6:28206 | DOI: 10.1038/srep28206 Yttrium iron garnet Y 3 Fe 5 O 12 (YIG) and its variants are the most popular candidates due to their low microwave loss, high resistivity, and structural & chemical stability. Moreover, ME/MD coupling has been observed in YIG ferrites 2,6,22 and its various dopant systems, such as La x Y 3−x Fe 5 O 12 , Yb x Y 3−x Fe 5 O 12 and Y 3 Fe 5−x Ti x O 12 etc. [23][24][25] . The existence of the ME/MD effect in the YIG-based ferrites may prove to be a suitable materials platform for the investigation of the intrinsic mechanism of ME/MD effect.
In this work, we present C-band dynamic MD behavior induced by FMR in a well-known magneto-optical material: Ce x Y 3−x Fe 5 O 12 (Ce-doped YIG) ferrite. The effect of Ce ions upon the MD response in this system has also been discussed in order to investigate the origin and underlying mechanisms responsible for the MD effect.

Results
X-ray diffraction (XRD) patterns of Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0. 15, 0.2) ferrites are shown in Fig. 1. All diffraction peaks of the Ce-doped YIG samples have been indexed to the standard powder diffraction pattern of pure YIG (JCPDS Nos 43-0507). It has been confirmed that all ferrites samples exhibit a pure garnet phase. Based upon the XRD patterns, the calculated lattice constants increase from 12.38 Å to 12.42 Å with the substitution of cerium ions. In comparison to the radius of Y 3+ (0.9 Å), the lattice expansion is attributed to the larger radius of Ce 3+ (1.02 Å).
It is inferred that the Ce-doped YIG ferrites likely contain Fe 2+ ions due to the low oxygen condition during high temperature sintering. This assumption has been verified by the XPS spectra of Ce x Y 3−x Fe 5 O 12 (x = 0.2) ferrite as shown in Fig. 2. The 2p 3/2 and 2p 1/2 peaks of the Fe ion can be observed at 710.6 eV and 724.3 eV in Fig. 2(a) respectively. These features are located between the corresponding values obtained for pure Fe 2 O 3 and Fe 2 SiO 4 which are considered to contain only Fe 3+ and Fe 2+ ions, respectively 26 . Similar phenomena in the binding energy shift for 2p 3/2 and 2p 1/2 peaks can also be found in pure Fe 3 O 4 and other oxides that contain both Fe 2+ and Fe 3+ ions 23,27 . In addition, the 2p 3/2 peak of Fe ions in Ce-doped YIG ferrite can be divided into two peaks located at 710.8 eV for + Fe 2p3/2 3 and 709.5 eV for + Fe 2p3/2 2 as determined by fitting of the spectra using Lorentzian-Gaussian method. Figure 2(b) shows a typical 3d spectrum of Ce 3+ and Ce 4+ ionic mixture 28    temperature sintering 29 . It can be inferred that the amount of Fe 2+ ions and oxygen vacancies will increase with the substitution of Ce ions.
In this report, the magnetodielectric response of Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) ferrites are detected by using an Agilent Technologies E5071C vector network analyzer (VNA) under the application of magnetic fields. The schematic of measurement setup is shown in Fig. 3. It is necessary to emphasize that the two magnetic poles of the magnet are aligned along the sides of the coaxial airline fixture so that the generated dc magnetic field can be made normal to the propagation direction of the microwave signal. By the transmission/reflection method, the accurate microwave electromagnetic properties of the samples can be obtained by an inversion calculation of the S parameters in VNA 30 . Since the dc magnetic field is superimposed upon the microwave signal, it is necessary to clarify whether the applied dc magnetic field will be affected by the microwave field. As a reference, Fig. 4 illustrates the electromagnetic properties of a pure wax coaxial sample with and without the applied dc magnetic field. The overlap of symbols and lines indicates that the permeability and permittivity of wax maintain about 1  and 2.1, which is independent of the magnitude of the applied dc magnetic field. In other words, the measurement of electromagnetic properties will not be influenced by the application of the dc magnetic field. Figure 5 shows the electromagnetic properties of Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) ferrites with and without the applied DC magnetic field. When the magnetic field is absent, the permeability of all the Ce-doped YIG samples (dash lines) remains largely unaltered with the substitution of Ce ions. In addition, the real part of the permeability gradually recovers to about 1 while the imaginary part decreases to near zero, which is a common phenomenon above the cut-off frequency caused by the internal magnetic anisotropy in the ferrites 31 . On the other hand, compared with the YIG/wax sample, all the Ce-doped YIG/wax samples reveal an obvious enhancement in permittivity from 6.1 to about 7.5 at C-band as shown in Fig. 5(f-j). It has been known that the dielectric relaxation polarization of YIG-based ferrites at microwave frequencies is associated with dipoles and interfacial polarization, whereas atomic and electronic polarizations can largely be ignored 32,33 . In Ce-doped YIG ferrites, it is assumed that the extra Fe 2+ ions, arising from the substitution of Ce ions, may result in both hole-electron pairs and Fe 2+ -Fe 3+ dipoles. It is worth noting that the substitution of Ce ions leads to an increase of Fe 2+ ions while the total amount of Fe ions remains constant. As a result, more Fe 2+ -Fe 3+ dipoles will be introduced by substitution of Ce ions. Therefore, the permittivity of Ce-YIG ferrites at C-band increases due to the enhancement of dipole polarization.
The MD behavior in Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) ferrites are presented in this work. Figure 5 also shows the permeability and permittivity spectra of Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) samples under the application of a dc magnetic field (solid lines). It is obvious that the resonance and relaxation phenomena appear to be visible in the permeability and permittivity spectra under the application of a dc magnetic field, respectively. The microwave magnetic field in the coaxial cable can naturally be divided into vertical h ⊥ and horizontal h ∥ components, which is normal and parallel to the applied dc magnetic field, respectively. The ferromagnetic resonance (FMR) peak arises solely from the contribution of the vertical component h ⊥ , since the horizontal component h ∥ is unable to respond to the alternating ac magnetization field 34,35 . On the other hand, an interesting observation is that the relaxation phenomena in permittivity emerge at frequencies corresponding to the FMR. That is, the location of dielectric relaxation peak is coherently related to the FMR over a narrow frequency band. For instance, the FMR frequency f 0 of Ce x Y 3−x Fe 5 O 12 (x = 0.05) sample is about 4.65 GHz that is near to its permittivity relaxation frequency f 1 of 5.44 GHz. It can be inferred that the relaxation of the permittivity is a dynamic MD behavior that is strongly induced by FMR.

Discussion
As illustrated in Fig. 5, both FMR phenomenon and the dynamic magnetodielectric relaxation process happen coherently and simultaneously in the Ce-doped YIG ferrite once a DC magnetic field is applied. It has been reported that MD coupling becomes more pronounced as the measurement is carried out in the vicinity of a resonance 36 . The interrelated dispersion phenomena emerging simultaneously in permeability and permittivity unveil a coupling of the magnetic and dielectric properties 37 . It is therefore inferred that the strong ferromagnetic resonance may give rise to a relaxation in the permittivity spectra, leading to an intrinsic magnetodielectric effect.
As mentioned, the FMR event gives rise to the relaxation in the permittivity spectrum due to the coupling of magnetic and dielectric properties. Additionally, the complex refractive index n of magnetic dielectric material can be described as: It can be found that the poles and zeros of ε(ω) and μ(ω), which may affect the dispersion type and resonance frequency, are reversed 38 . Additionally, it can be further inferred that the complex permittivity can be altered by permeability under certain conditions. As a result, a dielectric relaxation emerges as soon as strong FMR occurs in the permeability spectra due to the intrinsic coupling of magnetic and dielectric properties in the Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) ferrites. In essence, the MD effect originates from the intrinsic coupling between Fe 2+ and Fe 3+ ions, ultimately leading to enhanced polarization 39 . In ferrites, it is evident that dielectric relaxation primarily results from electronic hopping between Fe 2+ and Fe 3+ ions, and Fe 2+ -Fe 3+ electric dipole 40 . As confirmed by the XPS spectra in Fig. 2, the coexistence of Fe 2+ and Fe 3+ ions in Ce-doped YIG ferrites may result in the formation of localized charged regions and dipoles. As soon as the dc magnetic field is applied, the Fe 2+ and Fe 3+ ions rearrange in response to the magnetic field by means of electron hopping between Fe 2+ and Fe 3+ ions 41 . Hence, the applied dc magnetic field leads to the reorientation of Fe 2+ -Fe 3+ dipoles. It is believed that the electron fluctuation on the Fe site is the main contributor to the MD effect 39 . Alternatively, it has been known that the dipoles and interfacial polarization are the main contributors to the dielectric relaxation in ferrites at microwave frequencies, whereas atomic and electronic polarization can be largely ignored 32,33 . As known, the FMR phenomenon is an energy absorption process, whereas a dynamic magneto-dielectric interaction also reflects conversion or consumption of electromagnetic wave energy. Therefore, the dynamic MD behavior induced relaxation dispersion phenomenon occurs in the permittivity spectrum since the rearrangement and reorientation of Fe 2+ -Fe 3+ dipoles in Ce-doped YIG ferrite lags behind the alternating electric field of high frequency electromagnetic wave. In other words, a dynamic MD effect originated from the rearrangement or reorientation of Fe 2+ -Fe 3+ dipoles gives rise to the consumption of electromagnetic wave energy at microwave frequencies, which is observed in terms of a relaxation phenomenon in the permittivity spectrum.
Both the FMR phenomenon and magnetodielectric effect are associated with energy absorption. However, it is inferred that visible energy absorption due to the FMR or MD effect might be measurable at different frequencies, which is determined by the distinct loss mechanisms. In present work, the energy absorption of the Ce-doped YIG ferrite can be calculated by the S parameters measured by the VNA as the following equation: Oe is applied. It can be found that the peak of total energy absorption is located at 4.83 GHz, whereas FMR frequency of Ce-doped YIG (x = 0.05) sample is located at 4.65 GHz. As it has been known, the FMR is a forceful energy absorption phenomenon in the microwave frequency band and the energy will finally be consumed by lattice vibrations through the coupling of phonons. In Ce-doped YIG ferrites, it can be inferred that part of the energy absorbed through FMR is the energy source of the rearrangement and reorientation of Fe 2+ -Fe 3+ dipoles caused by the applied dc magnetic field 42 . Due to the intense energy absorption inherent in the FMR, this resonance can be considered as the most effective way for extra energy to be communicated to the system and enhance the intrinsic magnetic and dielectric losses of the Ce-doped YIG ferrites. It is predictable that the width of the total Scientific RepoRts | 6:28206 | DOI: 10.1038/srep28206 energy absorption peak is tailored by both FMR and MD effects, which is in complete agreement with experimental data. Furthermore, compared with the FMR, the dielectric dispersion caused by the dynamic MD effect is relatively weaker since the MD effect is a weak coupling relationship between permeability and permittivity in single-phase materials. Hence, the peak of energy absorption locates at the frequency that is much closer to the FMR frequency since the dielectric relaxation caused by dynamic MD behavior is a secondary factor of energy absorption.
The MD coefficients of Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2)/wax samples are shown in Fig. 7. The MD responses of all samples display relaxation characteristics as their permittivity spectra do. It is noteworthy that all the MD responses of samples become near zero in the vicinity of f = 5.5 GHz, but exhibit a maximum effect at a frequency slightly lower or higher than 5.5 GHz. Moreover, it can be observed that the relaxation also occurs near 5.5 GHz, which indicates the MD coefficients reveal relative variations in permittivity due to dielectric relaxation induced by FMR. The amplitude of the MD responses at C-band increases with Ce ions, as depicted in the insert table of Fig. 7. It can be inferred that the Fe 2+ ions will increase with the substitution of Ce ions while the total amount of Fe ions remains unchanged. Therefore, we conjecture that the increase of Ce ions may introduce more Fe 2+ -Fe 3+ dipoles in the ferrite, which enhances the electron exchange between Fe 2+ and Fe 3+ ions. An enhanced electron exchange may intensify the polarizability due to more intense electron fluctuations and consequently enhances the MD effect. In the current work, the strongest MD response is measured to be − 5.13%~+ 4.83% for x = 0.2 sample in the relaxation type dispersion region, which is considerably larger than the MD effect previously reported at microwave frequencies.
In conclusion, we have fabricated Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) ferrites by traditional solid-state reaction method. The emergence of Fe 2+ ions due to the substitution of Ce ions affects the electromagnetic properties of the Ce-doped YIG ferrites. We propose that the electron fluctuations on Fe sites are responsible for the ferromagnetic resonance induced large room temperature C-band magnetodielectric effect in the Ce-doped YIG ferrites. In addition, the intensity of the MD response increases with the substitution content of Ce ions. We believed that the investigation of room temperature MD coupling in single-phase microwave materials will prove enabling to the development of next generation multifunctional adaptive materials, devices, and integrated microwave circuits.   = 0, 0.05, 0.1, 0.15, 0.2) were prepared by traditional solid-state reaction method. Powders of Y 2 O 3 (99.9%), Fe 2 O 3 (99.9%), CeO 2 (99.9%) were mixed in appropriate stoichiometric ratios through ball-milling for 4 hours and the dried mixtures were calcined at 1473 K for 4 hours. Some calcined powders were then ground by ball-milling a second time for 4 hours, and then pressed into green pellets with 6 wt. % of polyvinyl alcohol (PVA) binder. The rest of calcined powders and the green pellets were then sintered at 1723 K for 4 hours in air. The sintered powders were finally pressed with 10 wt% wax into coaxial toroidal samples (inner diameter d = 3 mm, outer diameter D = 7 mm and height h = 3 mm) for the measurement of their microwave electromagnetic properties.
The crystalline phases of sintered samples were identified by powder X-ray diffraction (XRD). The elemental spectra of Ce x Y 3−x Fe 5 O 12 (x = 0, 0.05, 0.1, 0.15, 0.2) were measured by X-ray photoelectron spectroscopy (XPS). The microwave electromagnetic properties and magnetodielectric phenomena of Ce-doped YIG ferrites were detected using an Agilent Technologies E5071C vector network analyzer (VNA) with a DC magnetic field applied in the frequency range of 4-8 GHz. The magnetodielectric coefficient can be described by the following formula: where ε '(H) and ε '(0) represent the real part of the complex permittivity with and without applied DC magnetic field, respectively.