Chapter Ten - Dielectric Resonance in Ferrites for Sub-THz Signal-Processing Devices

Magnetoelectric composite ceramics were prepared to study their phase compatibility, magnetic and piezoelectric/ferroelectric properties, and coupling between magnetic and ferroelectric properties. The synthesis of various BaFe12O19 and SrFe12O19 hexaferrites was undertaken with different sintering temperatures, and exploring four different methods: solid state reaction, coprecipitation, sol-gel and citrate (Pechini) routes. Ceramic composites of BaM and SrM with BaTiO3 (BT) as a ferroelectric/piezoelectric phase, were prepared with both uniaxial and isostatic pressing, and then sintered. The composites were characterised by XRD, SEM and VSM. Results showed that BaM and BT did not react in the composites, while SrM-BT composites possess SrM, BT and SrTiO3 phases.

The observation of dielectric resonance over the frequency range 40-110 GHz in single crystal yttrium iron garnet (YIG) and its magnetic field tuning characteristics are reported. The dimensions of YIG are appropriately chosen in order to have the dielectric resonance occur at a much higher frequency than the ferromagnetic resonance and avoid any hybrid spin-electromagnetic modes. The dielectric modes are magnetically tunable by 1 GHz with a magnetic field of ∼1.75 kOe. The tuning range and required bias magnetic fields, however, can be controlled with the sample dimensions (or the demagnetization factor Nzz). Theoretical calculations on magnetic field tuning characteristics for the dielectric modes are in reasonable agreement with the data. The theory also predicts a similar magnetic tuning of the dielectric modes in the sub-THz frequency range as well. The dielectric modes that can be tuned with a magnetic field are of importance for the realization of low-loss tunable devices, including resonators, isolators, and phase shifters operating in the sub-THz region.

Magnetoplumbite-type (M-type) strontium ferrites doped with varying molar ratio of cobalt and titanium (SrFe12−2x Co x Ti x O19; x = 0.2, 0.4, 0.6, 0.8 and 1.0) were prepared via sol–gel technique employing ethylene glycol as a gel precursor. The prepared samples were characterized using X-ray diffractometry (XRD), field emission scanning electron microscopy, superconducting quantum interference devices and high-resolution transmission electron microscopy (HRTEM). The XRD patterns confirmed the formation of a highly homogeneous M-type strontium ferrite at molar substitution of 0.2 in the SrFe12−2x Co x Ti x O19 system (SF02) with calculated crystallite size of 48.5 nm. Sample SF02 showed the desired magnetic properties of a reduced coercivity at 4946 (192) Oe while having enhanced remnant and saturation magnetizations of 30.33 (0.81) and 61.45 (2.14) emu/g, respectively. HRTEM imaging of SF02 showed high regularity in the stacking sequence with corresponding lattice spacings matching that commonly found in the M-type ferrite structure.

Magnetic and dielectric resonances in the sub-terahertz (sub-THz) frequency range are observed in pure and Al-substituted hexagonal barium ferrite. A resonator based on magnetic excitations has been fabricated and its performance characteristics have been studied. The possible use of the resonator at sub-THz frequencies has been demonstrated. The resonator exhibited a loaded Q-factor of 150-330 in the frequency range 97-108 GHz. Dielectric resonances in a single-crystal barium hexaferrite are observed in the frequency range 75-110 GHz. The modes excited by circularly polarized electromagnetic waves show nonreciprocal propagation characteristics. The dielectric resonances may occur at a much higher frequency than ferromagnetic resonance. It is shown that degeneracy in the dielectric modes is lifted with an applied magnetic field H and that the modes can be tuned by 10 GHz or more with H. Data on frequencies of the modes versus H shows hysteresis. Theoretical predictions on H-tuning characteristics of the principal dielectric E11δ mode are in agreement with the data. The dielectric modes are of importance for the realization of low-loss devices, including resonators, isolators and phase shifters.

The SrFe12O19/poly (vinyl pyrrolidone) (PVP) composite fiber precursors were prepared by the sol-gel assisted electrospinning with ferric nitrate, strontium nitrate and PVP as starting reagents. Subsequently, the M-type strontium ferrite (SrFe12O19) nanofibers were derived from calcination of these precursors at 750–1,000 °C.The composite precursors and strontium ferrite nanofibers were characterized by Fourier transform infrared spectroscopy, X-ray diffraction, scanning electron microscopy and vibrating sample magnetometer. The structural evolution process of strontium ferrite consists of the thermal decomposition and M-type strontium ferrite formation. After calcined at 750 °C for 2 h the single M-type strontium ferrite phase is formed by reactions of iron oxide and strontium oxide produced during the precursor decomposition process. The nanofiber morphology, diameter, crystallite size and grain morphology are mainly influenced by the calcination temperature and holding time. The SrFe12O19 nanofibers characterized with diameters of around 100 nm and a necklace-like structure obtained at 900 °C for 2 h, which is fabricated by nanosized particles about 60 nm with the plate-like morphology elongated in the preferred direction perpendicular to the c-axis, show the optimized magnetic property with saturation magnetization 59 A m2 kg−1 and coercivity 521 kA m−1. It is found that the single domain critical size for these M-type strontium ferrite nanofibers is around 60 nm.

Two techniques are evaluated for the accurate measurement of the microwave permittivity of polycrystalline yttrium iron garnet (YIG) at frequencies between 5.5 and 12.5 GHz: split post dielectric resonator (SPDR) and ferrite disc resonator (Courtney). Both techniques separate YIG permittivity from that of YIG permeability by applying a magnetic induction bias to the YIG sample under test. The SPDR method needs no special sample preparation in the case of YIG substrates, whereas the Courtney method requires the grinding of rods from bulk YIG. The Courtney measurements of the YIG real permittivity are found to be higher on average than SPDR measurements. Agreement between the two techniques improves with increasing magnetic induction bias.

M-type strontium ferrite has attracted widespread attention in the field of permanent magnet materials due to its unique magnetic properties, dielectric performance, and thermal stability. However, compared with rare-earth permanent magnets such as Nd<sub>2</sub>Fe<sub>14</sub>B, strontium ferrite (SrFe<sub>12</sub>O<sub>19</sub>) permanent magnets possess relatively lower comprehensive magnetic properties, which limits their application range. The effects of Ca-Co (Zn) doping on the electronic structure, mechanical properties, and magnetic properties of M-type strontium ferrite are systematically investigated by first-principles plane-wave pseudopotential method based on density functional theory (DFT), combined with the generalized gradient approximation (GGA + <i>U</i>) in the paper. The calculated results indicate that the Ca-Co (Zn) co-doped M-type strontium ferrite systems exhibit good structural stability and mechanical properties. In the Ca-Zn co-doped structures, the conductivity of the system is enhanced because of the substitution of trivalent Fe ions at the 4<i>f</i><sub>1</sub> site by divalent Zn ions. The Ca-Co (Zn) co-doping increases the total magnetic moment of the system, while the magnetocrystalline anisotropy energy decreases. However, compared with the Co and Zn single doping system, the magnetocrystalline anisotropy energy of the co-doped systems has been improved, indicating that Ca-Co (Zn) co-doping can effectively enhance the magnetic properties of strontium ferrite. The study also analyzed the mechanisms of the effect of Ca-Co and Ca-Zn co-doping on the magnetocrystalline anisotropy energy of strontium ferrite. The results indicated that the decrease in magnetocrystalline anisotropy energy in the Ca-Co co-doped system was mainly due to the influence of <i>d</i><sub>xy</sub> and <i>d</i><sub>x</sub><sup>2</sup><sub>-y</sub><sup>2</sup> orbital electrons of Co<sup>3+</sup> ion and <i>d</i><sub>xy</sub> and <i>d</i><sub>x</sub><sup>2</sup><sub>-y</sub><sup>2</sup> orbital electrons of Fe ions at the 2<i>b</i> site. In the Ca-Zn co-doped system, the reduction was mainly influenced by Fe-3<i>d</i> orbitals at the 4<i>f</i><sub>1</sub> site, while the <i>d</i><sub>xy</sub> and <i>d</i><sub>x</sub><sup>2</sup><sub>-y</sub><sup>2</sup> orbital electrons of the 2<i>b</i> site enhance the magnetocrystalline anisotropy energy of the system. These results provide theoretical guidance for subsequent research on the modification of M-type strontium ferrite.

Resonant photon modes of a 5-mm-diameter yttrium iron garnet (YIG) sphere loaded in a cylindrical cavity in the 10--30-GHz frequency range are characterized as a function of applied dc magnetic field at millikelvin temperatures. The photon modes are confined mainly to the sphere and exhibited large mode filling factors in comparison to previous experiments, allowing ultrastrong coupling with the magnon spin-wave resonances. The largest observed coupling between photons and magnons is $2g/2\ensuremath{\pi}=7.11$ GHz for a 15.5-GHz mode, corresponding to a cooperativity of $C=1.51\ifmmode\pm\else\textpm\fi{}0.47\ifmmode\times\else\texttimes\fi{}{10}^{7}$. Complex modifications, beyond a simple multioscillator model, of the photon mode frequencies were observed between 0 and 0.1 T. Between 0.4 and 1 T, degenerate resonant photon modes were observed to interact with magnon spin-wave resonances with different coupling strengths, indicating time-reversal symmetry breaking due to the gyrotropic permeability of YIG. Bare dielectric resonator mode frequencies were determined by detuning magnon modes to significantly higher frequencies with strong magnetic fields. By comparing measured mode frequencies at 7 T with finite element modeling, a bare dielectric permittivity of $15.96\ifmmode\pm\else\textpm\fi{}0.02$ of the YIG crystal has been determined at about 20 mK.

:In this work, Sm–Co doped strontium ferrite, SrFe12-xSmxCoxO19 (x = 0·1–0·5) composites were prepared by adding Sm3+ and Co2+ cations into M-type strontium ferrite using one-step chemical coprecipitation method. The composites were characterized by FTIR and XRD. The magnetic properties of the samples were measured and analyzed by VSM. The results indicated that the average crystallite sizes located in a range of 29·7–32·9 nm. Lattice constants, a and c were close to 5·88 and 23·05 Å for the M-type strontium ferrite phase. The analyses of magnetic properties demonstrated that when x = 0·2 and 0·4, Sm3+ and Co2+ ions substituted Fe3+ ions at 12 k (↑) or 2a (↑) site. While, as x = 0·1, 0·3, and 0·5, Fe3+ ions at 12 k (↑) or 2a (↑) site were replaced by Sm3+ ions and Fe3+ ions at 4f2 (↓) site were substituted by Co2+ ions. Meanwhile, the proposed substitute mechanism in this work was expected to provide a good concept to modify directionally M-type strontium ferrite in order to extend its application field.

M-type strontium ferrites Sr1-xLnxFe12-xMxO19 (Ln: Sm; M: Mn; x = 0, 0.03, 0.06, 0.09, 0.12) doped with equivalent Sm-Mn ions were synthesized via the sol-gel method. The products were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), scanning electric microscopy (SEM) and vibrating sample magnetometer (VSM). The samples with x from 0.00 to 0.12 were confirmed to the single-phase M-type strontium ferrite, and the impurity phases Fe2O3 and SmFeO3 were detected when the content of dopants x ≥ 0.09. When x = 0.09, the saturation magnetization (Ms) and the remanent magnetization (Mr) of strontium ferrites Sr1-xSmxFe12-xMnxO19 reached to the maximum values of 37.19 emu/g and 22.48 emu/g, respectively. When x = 0.06, the coercive force (Hc) of strontium ferrites Sr1-xSmxFe12-xMnxO19 reached to the maximum values of 6224 Oe. Acid-treatment reduces the magnetic properties of the Sr1-xSmxFe12-xMmxO19 (x = 0.03). Compared to 950 °C preparation, preparation at 1200 °C decreases its magnetic properties and the Hc drop is very significant.

The M-type hexagonal strontium ferrites substituted by Gd-Mn ions were synthesized by the sol-gel self-combustion method. The synthesized samples were researched by X-ray diffraction (XRD), Fourier transform infrared spectroscopy analysis (FT-IR), scanning electric microscopy (SEM), and vibrating sample magnetometer (VSM). The XRD and the FT-IR results show that the pure M-type hexagonal ferrites phase is successfully obtained in the samples with the substitution amount (x) from 0.00 to 0.09 of Gd-Mn. The VSM results show that, as the substitution amount (x) of Gd-Mn increases, the remanent magnetization (Mr) and saturation magnetization (Ms) of the Sr1-xGdxFe12-xMnxO19 gradually increase, and the maximum values of 39.53 emu/g and 23.73 emu/g were obtained when x = 0.09. When x continues to increase, Mr and Ms decrease slightly, but they are still higher compared with those of the unsubstituted one. The coercivity (Hc) of the samples after doping is much higher than the coercivity of the pure sample, but as the substitution amount x increases, the coercivity first increases and then decreases, while the maximum value of Hc is 6738 Oe at x = 0.06.

In millimeter wave frequency range, hexagonal ferrites with high uniaxial anisotropic magnetic fields are used as absorbers. These ferrites include M-type barium ferrite (BaFe12O19) and strontium ferrite (SrFe12O19), which have natural ferromagnetic resonant frequency range from 40 GHz to 60 GHz. However, the higher frequency range lacks suitable materials that support the higher frequency ferromagnetic resonance. A series of gallium-substituted ε-iron oxides (ε-GaxFe2−xO3) are synthesized, which have ferromagnetic resonant frequencies appearing over the frequency range of 30 GHz to 150 GHz. The ε-GaxFe2−xO3 is synthesized by the sol-gel method. The particle sizes are observed to be smaller than 100 nm. In this paper, in-waveguide transmission and reflection method and the free space magneto-optical approach have been employed to study these newly developed ε-GaxFe2−xO3 particles in millimeter waves. These techniques enable to obtain precise transmission spectra to determine the dielectric and magnetic properties of both isotropic and anisotropic ferrites in the microwave and millimeter wave frequency range from single set of direct measurements. The complex dielectric permittivity and magnetic permeability spectra of ε-GaxFe2−xO3 are shown in this paper. Strong ferromagnetic resonances at different frequencies determined by the x parameter are found.

In millimeter wave frequency range, hexagonal ferrites with high uniaxial anisotropic magnetic fields are used as absorbers. These ferrites include M-type barium ferrite (BaFe12O19) and strontium ferrite (SrFe12O19), which have natural ferromagnetic resonant frequency range from 40 GHz to 60 GHz. However, the higher frequency range lacks suitable materials that support the higher frequency ferromagnetic resonance. A new series of gallium-substituted ε-iron oxides (ε-GaxFe2−xO3) are synthesized which have ferromagnetic resonant frequencies appearing over the frequency range 30 GHz–150 GHz. The ε-GaxFe2−xO3 is synthesized by the combination of reverse micelle and sol-gel techniques or the sol-gel method only. The particle sizes are observed to be smaller than 100 nm. In this paper, the free space magneto-optical approach has been employed to study these newly developed ε-GaxFe2−xO3 particles in millimeter waves. This technique enables to obtain precise transmission spectra to determine the dielectric and magnetic properties of both isotropic and anisotropic ferrites in the millimeter wave frequency range from a single set of direct measurements. The transmittance and absorbance spectra of ε-GaxFe2−xO3 are shown in this paper. Strong ferromagnetic resonances at different frequencies determined by the x parameter are found.

In this work, M-type hexagonal barium ferrites co-doped with Co and Zr atoms were prepared by a solid-phase method based on the sintering temperature and doping concentration. First, the influences of the sintering temperature on the crystal structure, microstructure, and magnetic properties of ferrites were studied. The crystallinity of the materials increases with the sintering temperature and obtaining high density and uniform grain size at 1300 °C, which promotes grain-boundary diffusion and suppresses grain-boundary migration. Second, the dependence of the crystal structure, microstructure, magnetic, and dielectric properties of Ba(CoxZrx)Fe12−2xO19 on the doping concentration (x = 0, 0.2, 0.4, 0.6) was investigated at sintering temperature of 1300 °C. The increase of the crystal parameter c with x value reveals that the ions of Co2+ and Zr4+ successfully replace the Fe3+ ions. Additionally, the co-doping ions of Co2+–Zr4+ promote the grain-boundary migration and result in some large size grain (> 20 mm) that appeared and increased with the doping concentration. The magnetic hysteresis loops reveal the saturation magnetization increases from 60.45 to 68.6 emu/g, and the coercivity decreases from 1800 to 190 Oe with the x increased to 0.6. The dielectric properties measurement displays the Co–Zr co-doping can improve the dielectric and reduce the dielectric loss. The highest value of the real part of permittivity (e′) and the lowest value of the imaginary part of permittivity (e″) can be obtained at a doping concentration of x = 0.4.

Co-Zr substituted M-type hexagonal barium ferrites, with chemical formula BaCoxZrxFe12-2xO19 (where x = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0), have been synthesized by double sintering ceramic method. The crystallographic properties, grain morphology and magnetic properties of these ferrites have been investigated by X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Vibrating Sample Magnetometer (VSM). The XRD patterns confirm the single phase with hexagonal structure of prepared ferrites. The magnetic properties have been investigated as a function of Co and Zr ion composition at an applied field in the range of 20 KOe. These studies indicate that the saturation magnetization (Ms) in the samples increases initially up to the Co-Zr composition of x=0.6 and decreases thereafter. On the other hand, the coercivity (Hc) and Remanent magnetization (Mr) are found to decrease continuously with increasing Co-Zr content. This property is most useful in permanent magnetic recording. The observed results are explained on the basis of site occupation of Co and Zr ions in the samples.