Recent progress in some composite materials and structures for specific electromagnetic applications

Resonance mechanisms

Permeability spectra of natural resonance

Permeability spectra are determined by three parameters, namely static real permeability μ ₀, intrinsic resonance frequency f _r and damping coefficient λ. μ ₀ (or ) is closely associated with the static magnetic parameters, saturation magnetisation M _s and anisotropy fields H _a or H_θ and H_φ . Here, two parameters, f _r and λ, will be discussed in detail.

Two types of dispersions

Dispersion types of permeability spectra (or shapes of the spectra) are related to λ. In practice, there two types of spectra, namely resonance-like and relaxation-like dispersions, according to the magnitudes of λ. Small λ leads to resonance-like dispersion. On the other hand, for large λ, the permeability spectra demonstrate a relaxation-like dispersion. Composites with relaxation-like dispersion are often of broad band absorption.

Substitution effect

Hexagonal ferrites, except Y-type one, have c-axis anisotropy. Based on the above discussion, in order to obtain large and , one of the basic requirements is that the hexagonal ferrites should have c-plane anisotropy. To achieve this, the most effective method is ion substitution. It has been shown that Co²⁺ ion often contributes negative first order magnetocrystalline anisotropy constant K ₁ and the second magnetocrystalline anisotropy constant K ₂ is nearly zero in all hexagonal ferrites not containing Co ions.33 Therefore, Co substitution can increase c-plane anisotropy. In fact, it is possible to modify the anisotropy of a hexagonal ferrite from c-axis to c-plane by Co doping. Figure 2 shows the dependence of anisotropy type and anisotropy fields as a function Co substitution level x, for composites made with Z-type barium ferrite, Ba₃Co_xZn_2−xFe₂₄O₄₁. Anisotropy of the ferrite is c-axis without any Co substitution and changes to c-plane anisotropy at Co concentration of x≈0·6. With further substitutions from x = 0·8 to 2·0, the anisotropy fields H_θ is increased from 3·5 to 12 kOe, while f _R of the composites is shifted from 1·6 to 3·0 GHz.34

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Figure 2.

Dependence of anisotropy types, anisotropy fields H_θ and resonance frequencies f _R on Co substitutions in Ba₃Co_xZn_2−xFe₂₄O₄₁ ferrites or their composites

Besides Co ion, non-magnetic ion substitutions can also modify the magnetocrystalline anisotropy of hexagonal ferrites. The magnitude of anisotropy depends on the distribution of the ions at inequivalent sites.35 ^– 37 Al³⁺ and Ga³⁺ ions preferentially occupy the 12k sites.38,39 Substitution of Al³⁺ and Ga³⁺ ions for Fe³⁺ ions enhances the c-axis anisotropy of hexagonal ferrites, thus increasing their resonance frequency f _R.38 ^– 40 On the other hand, complex ions, such as Ti⁴⁺Mn²⁺, Zr⁴⁺Zn²⁺ and Sn⁴⁺Zn²⁺, tend to weaken the c-axis anisotropy and, consequently f _R is shifted to relatively low frequencies.41 ^– 44

It is found that, to a good approximation, f _R of hexagonal ferrites or their composites is approximately proportional to H _a for c-axis anisotropy15 and to the out-of-plane anisotropy field H_θ for c-plane anisotropy45 respectively, as shown in Fig. 3. Therefore, f _R can be controlled by the anisotropy field, which is closely associated with ion substitutions.

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Figure 3.

Relationship between resonance frequency f _R and anisotropy fields a H _a and b H_θ respectively, for composites of hexagonal ferrites with c-axis and c-plane anisotropies

The distributions of non-magnetic ions on various sites are related not only to the magnetocrystalline anisotropy, but also to saturation magnetisation M _s. Among various non-magnetic ions, Zn ion has been confirmed to preferentially occupy the spin-down sites of M-,43,46,47 W-,48,49 Y-,50,51 and Z-types hexagonal ferrites.52 In addition, substitutions of Zn for Fe³⁺ ion also weaken the anisotropy field, H _a or H_φ . The enhancement in M _s and the reduction in H _a or H_φ are benefit to an increase in , based on equation (3) or (4). Therefore, Zn²⁺ substitution has often been used to raise .

Doping effect

In general, a small amount of doping oxides (usually <1·0 wt-%) is not able to significantly modify the intrinsic properties of hexagonal ferrites, such as saturation magnetisation and magnetocrystalline anisotropy. However, microstructure and magnetic domain of the ferrites can be modified by the doping of oxides with a low concentration. The microstructure and magnetic domain characteristics are also decisive factors to achieve special properties, for example, low coercivity H _c and high electric resistivity. Various oxides have been used as dopants to optimise the static magnetic properties and microstructures of spinel ferrites53 ^– 56 and hexagonal ferrites.45,57

It has been shown that doping of oxides can increase and of the composites made with W- and Z-type hexagonal ferrites.45,57 Figure 4 shows measured and curve fitted permeability spectra of the composites derived from BaCoZnFe₁₆O₂₇ without and with the doping of 0·5 wt-%CaO. As stated above, ferrites or ferrite composites have two resonances, namely natural resonance at higher frequencies and wall resonance at lower frequencies. The value of contributed by natural resonance retains almost unchanged (∼2·0), while produced by wall resonance increases from 2·2 to 2·8, before and after the doping of 0·5 wt-%CaO. As a result, the total increases from 3·2 to 4·0. The increase in , therefore, is mainly attributed to the significantly enhanced domain wall resonance due to the oxide doping.58

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Figure 4.

a measured (symbols) and curve fitted (solid lines) permeability spectra and b curve fitted μ′(f) of natural and wall components for composites of BaCoZnFe₁₆O₂₇ undoped and doped with 0·5 wt-%CaO

Based on the rotation model, static permeability is related to M _s and in-plane anisotropy field H_φ , i.e. ( −1)∝ M _s/H_φ for particles with c-plane anisotropy (see equation (4)). The values of H _φ are estimated to be 100–1000 Oe for W- and Z-type hexagonal ferrites. However, when domain walls are present, an enhanced permeability caused by the reversible wall movement can be obtained, due to the decreased coercivity, H _c ( H_φ ), by ( –1)∝ M _s/H _c.63 The linear dependence of ( −1) on M _s/H _c, has been confirmed, as shown in Fig. 5. In general, with a small amount of oxide doping M _s remains almost constant, while H _c significantly decreases. Therefore, the increase in is mainly attributed to the decrease in H _c.34

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Figure 5.

Relationship between ( –1) and ratio M _s/H _c for W- and Z-type hexagonal ferrites doped with various oxides

Volume concentration effect

High frequency magnetic properties of composites are also closely related to volume concentration of the ferrite particles p. Composites have two important characteristics, which are significantly different from those of their bulk materials. First, of composites is much smaller than that of their corresponding bulk materials and f _R is shifted to higher frequencies comparatively. This difference is more pronounced when the bulk materials have relatively large permeability. Second, and f _R are not in linear correlation to p. An example is shown in Fig. 6, where the symbols are experimental data, showing the dependence of and f _R on p for Co₂ Z ferrite composites.

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Figure 6.

Dependence of a , b f _R and c product of ( –1) and on volume concentration p of two representative ferrite composites, where symbols are experimental data and dashed lines are fitted results based on equations (10)–(12)

Several models, such as Bruggeman and Maxwell Garnett mixing rules, magnetic circuit model,64 ^– 66 simulation EM energy,67 magnetic percolation model68 and two-particle model,69 have been proposed to predict the dependences of and f _R on p for magnetic composites. In the two-particle model, an effective demagnetising factor N _eff, was introduced and two energies, the magnetocrystalline anisotropy energy and the demagnetising energy between the two particles, were considered. and f _R can be deduced from N _eff and the correlation between f _R and free energy of the system respectively69 (9) (10) where and f _R,b are the static permeability and resonance frequency respectively, of the corresponding bulk material, N _eff = F(p)N _d, N _d is the general demagnetising factor determined by shape of the particles and F(p) is a correct function associated with p. For spherical particles, F(p)  = (1–p) and equation (9) is just the same as the Maxwell–Garrett mixing law (11) By multiplying equation (9) with the square of equation (10), a simple relationship is obtained (12) for composites, C is a constant that is related to μ _b and f _R,b of the corresponding bulk material. Equation(12) is similar to Snoek’s law,70 where the product of with f _R, instead of square of f _R, is a constant, i.e.  = C.

Figure 6 also shows the predicted dependence of , f _R and the product of ( –1) and on p. The dependence, as shown in the dashed lines in the figure, is obtained by curve or linear fitting based on equations (10) and (12). The predicted results are well consistent with the experimental data.

Shape effect

Based on Maxwell–Garrett mixing law (equation (11)), of a composite is also related to demagnetising factor N _d, which is determined by shapes of the particles. values of composites with particles of different shapes have been calculated, as shown in Fig. 7.71 For particles of sphere, plate with the normal parallel and perpendicular surface plane, and bar or needle, the values of N _d are 1/3, ∼0, 1/2 and 0 respectively. Consequently, (bar)> (plate)> (sphere)> (plate). On the other hand, resonance frequency f _R is ranked as: f _R (bar)>f _R (spherical)>f _R (plate) (see Table 2).

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Figure 7.

Relationship between and , where and are static permeability respectively, for bulk materials and corresponding composite with different shape particles (1: long rod; 2: plate which is along the magnetic field; 3: sphere; 4: plate which is normal to the magnetic field)

It has been shown that doping of V₂O₅ can significantly modify high frequency magnetic properties of the composites made with BaCoZnFe₁₆O₂₇, through the modification in shape of the ferrite particles.31 As shown in Fig. 8, of the composite derived from the doped ferrite particles increases from 3·1 to 4·6 and increases from 1·2 to 1·7, while f _R shifts from 5·9 to 4·0 GHz, as compared to the undoped sample. Scanning electron microscope (SEM) revealed that the shape of the ferrite particles was modified from cuboid-like to hexagonal-plate-like due to the doping. The averaged N _d along the direction of ac magnetic field is estimated to be ∼0·1 for the hexagonal plate particles. N _d of the undoped particles is approximately considered to be 1/3. Based on equation (11) with a bulk permeability μ _b = 11, the calculated is 2·9 and 4·3 for the composites made with the ferrite particles undoped and doped with V₂O₅ respectively. f _R can be estimated from equation (6). If M _s of 4·9 kGs, H_θ and H_φ of 8·5 and 0·6 kOe respectively, are used, the calculated natural resonance frequencies, f _R of the composites with undoped and doped ferrite particles are approximately 6·3 and 4·0 GHz respectively. The calculated and f _R are in a good agreement with the experimental results. Therefore, the increase in and the decrease in f _R are attributed to the modification of particle shape caused by the doping of V₂O₅.31

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Figure 8.

Permeability spectra for composites of BaCoZnFe₁₆O₂₇ without and with the doping of V₂O₅, (inset) particle shape after doping

Size effect

For metallic fillers, size of the particles, in general, must be smaller than a certain value, due to the presence of eddy effect. In this regard, because of their very high electric resistivity (10⁴–10¹⁰ Ω cm), ferrite fillers have no problem of eddy effect. However, ferrite particle sizes still play an important role in determining permeability values of their composites. For example, experimental results showed that of the composite with BaCoZnFe₁₆O₂₇ particles of 80–320 nm is ∼2, which is greatly increased to 4·0, as the particle size is increased to 300 μm,72 as shown in Fig. 9. Similar effect is also observed in Co₂ Z hexagonal ferrite composites.73

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Figure 9.

Static real permeability of composites with ferrite particles of various sizes, and (inset) permeability spectra of composites

As mentioned earlier, is determined by the reversible domain wall movement and magnetic moment rotation. The critical size of single domain particles is ∼1 μm for hexagonal ferrites. Therefore, the nanoparticles are of single domain structure, whereas the particles of 300 μm possess multidomain structure. As a result, the composite with nanoparticles of ferrite has no contribution by domain walls and thus smaller value of (∼2), while that made with microsized particles has both contributions from domain wall and the natural resonance. For meddle size particles, with an averaged size of 3 μm, a part of them with sizes of <1 μm are single domain and the others with size of >1 μm are multidomain. Hence, composite with these particles has a of ∼3.

In addition, M _s and H _c are also closely associated with the size d of the particles. M _s almost linearly decreases from 55·3 emu g⁻¹ for d = 10 μm to 49·4 emu g⁻¹ for d = 20 nm. H _c increases from 45 to 450 Oe correspondingly. The decrease in M _s and the great increase in H _c with decreasing particle size are also responsible for the decrease in static permeability.73

Damping effect

and f _R depend not only on and intrinsic resonance frequency f _r, but also on the damping coefficient λ. Figure 10 shows dependences of and f _R on λ, calculated using equations (7) and (8). For given and f _r, the ratio of f _R/f _r gradually increases with decreasing λ. The ratios of to ( –1) is about 0·5–0·7, as λ is varied from ∞ to 1. However, the ratios can increase rapidly to ∞, as λ is varied from 1 to 0. Therefore, a small λ can lead to both large and high resonance f _R.

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Figure 10.

Dependence of /( –1) and f _R/f _r on damping coefficient λ

An example is shown in Fig. 11.74 The curve fitting results indicate that λ is significantly different between the two composites (I and II), where I is CoTi substituted Co₂ Z and II is Co₂ Z ferrite particles respectively. λ of composite I is only 0·74, while that of composite II is 1·36. Although the two composites have almost same value of , of composite I (1·8) is significantly larger than that of composite II (1·2). Because their values are almost the same, the increase in for composite I is attributed to its considerably small λ. Therefore, a decrease in λ is an effective way to raise both and f _R.

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Figure 11.

Permeability spectra and their fitted curves for composites I and II

Dispersion effect

According to the magnitude of damping coefficient λ, permeability spectra of composites can exhibit either relaxation-like dispersion (relatively large λ) or resonance-like dispersion (relatively small λ).

The permeability spectra of hexagonal ferrite composites with c-plane anisotropy exhibit usually relaxation-like dispersion. Due to relatively large and , the composites are good candidates as EM absorbing materials with broad bandwidth. On the other hand, the permeability spectra of ferrite composites with c-axis anisotropy show resonance-like dispersion. The spectra have several special and interesting properties. First, near the range of resonance frequency, μ rapidly increases to the maximum of much larger than , and μ″(f) exhibits a relatively narrow absorption peak. Second, owing to the small λ, the ratio of /( –1) can be much larger than 0·5, which is the typical value for permeability spectra with relaxation type dispersion. Finally, high f _R can be obtained, owing to the large c-axis anisotropy of the ferrites.

As an example, typical permeability spectra with resonance-like dispersion are shown in Fig. 12. The composite was made with MnTi substituted M-type barium ferrite with c-axis anisotropy at p = 0·35. Although ( –1) is very small (∼0·11), ( −1) is as large as 0·8. Furthermore,  = 0·75 and /( −1) = 6·8 are achieved, which is much higher than 0·5 for permeability spectra with relaxation-like dispersion. The experimental values of and f _R are consistent with the theoretic values of  = 1·18 and f _R = 36·4 GHz, derived from equation (3), with M _s = 3·5 kGs and H _a = 13 kOe.75 For permeability spectra with relaxation-like dispersion, to obtain of 0·75, should be at least 2·5. However, it is very difficult to acquire of 2·5 at such an high frequency (32 GHz). Therefore, at high microwave or millimetre wave frequencies, relatively large can only be obtained by using the composites with permeability spectra of resonance-like dispersion.

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Figure 12.

Permeability spectra with resonance-like dispersion for M-type ferrite composite with c-axis anisotropy

M-type barium ferrite composites

In general, M-type hexagonal ferrite, BaFe₁₂O₁₉, are hard magnetic materials with c-axis anisotropy. Its saturation magnetisation, M _s is 4·8 kGs, magnetocrystalline constant K ₁ is 3·2×10⁶ erg cm⁻³ and anisotropy field, H _a is 16·8 kOe.13,76 Owing to its high c-axis anisotropy, its static real permeability is only 1·3 and resonance frequency f _R is as high as 45 GHz, as confirmed experimentally77,78 and predicted theoretically (equation (3)). Therefore, to bring down the resonance frequency to the range 1–18 GHz, it is necessary to decrease the anisotropy field, H _a or modify the anisotropy from c-axis to c-plane.

Co²⁺, Ru²⁺ and Ir⁴⁺ ions, which are able to provide very large c-plane anisotropy, are often used to substitute for Fe³⁺ ions to modify the anisotropy of BaFe₁₂O₁₉ from c-axis to c-plane,79 ^– 82 so as to achieve relatively large permeability and .46,83 ^– 85 The concentration of substitution was found to be a critical factor. For instance, the substituting concentrations should be x≧1·2 and x≧0·4 for CoTi and CoRu substituted BaFe_12−2xCo_xMe_xO₁₉ (Me = Ti and Ru). With CoRu substitution, as x is increased from 0·2 to 0·4, saturation magnetisation M _s is almost unchanged, while coercivity H _c is reduced from 500 to 250 Oe,85 which confirms the modification of anisotropy. Consequently, increases significantly from 3 to 7, and f _R decreases rapidly from 14 to ∼1 GHz. With further substitutions, decreases from 7 to 4 at x = 0·8, while f _R rises from 1 to 7 GHz.84

Ferromagnetic resonance has shown that f _R decreases from 46 to 18 and 10 GHz respectively, for the M-type hexagonal ferrites substituted by CoTi and Sc with x = 1·6.86 High frequency magnetic properties and EM absorbing performances, of MnTi,87 ^– 89 ZnZr and ZnSn90 substituted M-type hexagonal ferrites and their composites, have been studied. For example, the composites derived form BaFe_12−2xMn_xTi_xO₁₉ with x = 1·5 and 2·0 had broad bandwidths of 14·1 to ∼20 GHz and 7·4–12 GHz, at thickness of 1·6 and 2·7 mm respectively, for RL≤−20 dB.87,88

Figure 13 shows permeability spectra of the composites made with MnTi substituted BaFe_12−2xMn_xTi_xO₁₉ (x = 1·4, 1·6 and 1·8) ferrites. The spectra exhibit resonance-like dispersions with damping coefficient λ, of only ∼0·1, which is much smaller than λ of about 1–1·5, generally observed in composites with permeability spectra of relaxation-like dispersion. Away from resonance range, is very small (only ∼1·2), while near the resonance range, μ′≈2·0 and ≧1·0 are achieved. With decreasing x from 0·18 to 0·14, f _R is shifted from 8·5 to 14·5 GHz.89

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Figure 13.

a permeability spectra and b attenuation characteristics of BaFe_12−2xMn_xTi_xO₁₉ ferrite composites (p = 0·5) with substitutions x = 1·4, 1·6 and 1·8 (Ref. 89)

Figure 13b shows that the composites with resonance-like dispersion can exhibit low reflection loss RL with considerably broad bandwidth. The frequency bands of RL≤−15 dB cover from 8·5 to 13 GHz and 11 to 16·5 GHz, at thickness of 0·22 and 0·18 cm respectively, for x = 1·8 and 1·6. These composites are good candidates for EM attenuation at K _u bands.89

W-type barium ferrite composites

The hexagonal ferrites, Me₂ W, i.e. BaMe₂Fe₁₆O₂₇ (Me = bivalent metallic ions), have the highest Curie temperatures T _c and the highest saturation magnetisation M _s at room temperature, which are related to their highest ratio (0·62∶0·38) of magnetic ions to oxygen ions. Their intrinsic magnetic properties are listed in Table 3.12 Fe₂ W, Ni₂ W and Zn₂ W are of c-axis anisotropy, with large c-axis anisotropy fields. The resonance frequency, f _R of Ni₂ W ferrite can reach as high as 36 GHz,91 which is well consistent the value derived from the anisotropy field of 12·5 kOe. Co substitution was used to modify the anisotropy from c-axis to c-plane. From ferromagnetic resonance92 and magnetic measurement of aligned samples,93 Co₂ W is c-plane anisotropy with an out-of-plane anisotropy, H_θ of 21·2 kOe. Since Zn substitutions are also able to increase , CoZn substitutions are often used to improve high frequency magnetic properties of W-type barium ferrite.

High frequency magnetic properties of BaCo_xZn_2−xFe₁₆O₂₇ have been comprehensively studied by Paoluzi et al. 94 and Li et al. 93 Representative experimental results are listed in Table 4.93,95 X-ray diffraction (XRD) patterns of the aligned samples showed that the transition of magnetic anisotropy occurred at x≈0·7, which was also confirmed by the dependence of coercivity H _c on x.93 With Co substitutions from x = 1 to 2, and decrease from 14·5 to 4·0 and from 6·5 to 1·5 respectively, while f _R is shifted from 0·7 to 2·5 GHz, for W-type ferrite ceramics.96 For the corresponding composites with volume concentration p = 0·35, as Co is varied from 0·7 to 1·5, and decrease from 2·4 to 1·8 and 0·8 to 0·6 respectively, while f _R is shifted from 2·5 to 12 GHz.93 For those with p = 0·5, values are 3·6, 2·8, 2·0 and 1·5 and values 1·3, 1·1, 0·8 and ∼0·3, while f _R values are 2·5, 6·0, 12·0 and >16·5 GHz respectively, for x = 0·7, 1·0, 1·5 and 2·0.95

As mentioned in the section on ‘Doping effect’, doping of hexagonal ferrites with oxides can increase and of their composites. The doping effect of various oxides on high frequency magnetic and dielectric properties of ferrite composites has been comprehensively studied by Li et al. 58,97,98 Representative results are listed in Table 5 for CoZn substituted BaCoZnFe₁₆O₂₇ composites.

For the composites made with the undoped ferrite, , and f _R are 3·2, 1·2 and 5·9 GHz respectively. The doping of almost all oxides can raise and together with a decrease in f _R. The doping of CaO, CuO and MnO₂ increases to 4·0–4·6, reduces f _R to low frequencies (2–3 GHz). The composites with the ferrites doped with IrO₂ and RuO₂ have highest f _R (4·6 and 4·2 GHz), which is attributed to the larger anisotropy of these ions. Unfortunately, most additives lead to a significant increase in ϵ′ of the composites. For example, 0·5 wt-%CaO increases from 3·2 to 4·0; however, it also increases ϵ′ from 7·5 to 22. The increase in ϵ′ has been attributed to the formation of Fe²⁺ ions in the ferrites. The stronger polarisation of Fe²⁺ ions than that of Fe³⁺ ions and the electron hopping between the Fe²⁺ and Fe³⁺ ions on equivalent sites are responsible for the increase in ϵ′ and ϵ″.99,100 Because resistivity of grain boundaries is much higher than that of grains, more hoping electrons are piled up at the grain boundaries at lower frequencies. Consequently, ϵ′ exhibits a strong dependence on frequency; ϵ′ increases with decreasing frequency.101

From Table 5, the doping of V₂O₅ (perhaps Nb₂O₅ also) is very interesting.31 and increase by 40–50%, while ϵ′ and ϵ″ remain almost the same, before and after the doping. The ferrite doped with V₂O₅ had almost the same resistivity as the undoped one (8·06×10⁶ Ω cm). This could imply that the presence of V₂O₅ prevented the formation of Fe²⁺ ions or inhibited electron hopping between Fe²⁺ and Fe³⁺ ions. Because of the unchanged ϵ′ and the significantly enhanced and , attenuation performances of the composite made with the V₂O₅ doped ferrite are greatly improved. Permeability spectra of the composites of the ferrites without and with the doping of V₂O₅ are shown in Fig. 8. TheirRL–f curves at optimum thickness t are shown in Fig. 14. The frequency bands for RL≤−10 dB cover over 3·5–13·8 GHz at t = 0·3 cm, with a relative bandwidth W _R of 1∶3·9, as compared to 1∶3·0, for the undoped case.

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Figure 14.

Attenuation characteristics of BaCoZnFe₁₆O₂₇ composites, where 0 and 1 denote composites of ferrites undoped and doped with 1 wt-%V₂O₅ respectively

The effect of CoZn substitution, combined with the doping of 1 wt-%V₂O₅, on high frequency magnetic properties and attenuation characteristics of the composites of BaCo_xZn_2−xFe₁₆O₂₇ with x = 0 to 2·0, has been studied by Li et al. and Wu et al. 102 ^– 104 According to permeability spectra, the composites can be divided two groups. The ferrites with x = 1·0, 1·3 and 1·5 have c-plane anisotropy and permeability spectra of their composites exhibit relaxation-like dispersion, as shown in Fig. 15. decreases from 4·2, 3·6 to 3·1, while f _R is shifted to higher frequency, from 4·0, 6·5 to 8·0 GHz. Figure 16a shows attenuation characteristics of the composites. The frequency bands of both lowerlimit f _low and upper limit f _up for RL≤−10 dB are shifted to higher frequencies. f _low increases from 3·8, 5·0 to 6·3 GHz, while f _up increases from 13·5, 16·2 to >16·5 GHz, with corresponding W _R of 1∶3·6 at t = 0·30 cm, 1:3·2 at 2·6 cm and >1∶2·6 at 0·22 cm respectively.102,103

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Figure 15.

a real and b imaginary permeability spectra of composites with BaCo_xZn_2−xFe₁₆O₂₇+1 wt-%V₂O₅ at p = 0·5

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Figure 16.

Attenuation characteristics of BaCo_xZn_2−xFe₁₆O₂₇+1 wt-%V₂O₅ composites with p = 0·5

On the other hand, the ferrites with x = 0·5, 0·6 and 0·65 are of c-axis anisotropy, and permeability spectra of their composites have resonance-like dispersion,104 as shown in Fig. 15. is rather small, about 1·3–1·6. However, because the damping coefficient λ is very small (about 0·2–0·3), relatively large ≈1 and a high ratio of /( −1) = 2·7–1·6 are achieved. Owing to the relatively large c-axis anisotropy, high f _R values of 13, 9·8 and 6·4 GHz are observed for x = 0·5, 0·6, and 0·65 respectively. Figure 16b shows RL–f curves of the composites at optimum thicknesses. The composites can achieve quite broad bandwidth at very low reflectivity and small thickness. Bandwidths of the composites with x = 0·5, 0·6 and 0·65 for RL≤−20 dB cover over 12·5–16·5 GHz, 8·3–12·5 GHz and 6·5–9·0 GHz at t = 0·16, 0·22 and 0·28 cm respectively. These composites are potential candidates as EM attenuation composites with low reflectivity (RL≤−20 dB) at X and K _u bands.

Y-type barium ferrite composites

Most Me₂ Y (except Cu₂ Y) hexagonal ferrites, Ba₂Me₂Fe₁₂O₂₂, have c-plane anisotropy, which is attributed to their special crystal structure: 3×(ST) blocks without any R block. It is known that the 2b or 2d sites in the R block contribute to much larger c-axis magnetocrystalline anisotropy than other sites, due to their large asymmetry. Without any R block, Y-type ferrites, in general, are of c-plane anisotropy even without the presence of Co ions.12

Static magnetic parameters of Me₂ Y are listed in Table 6. As compared to other types of hexagonal ferrites, Me₂ Y ferrites have relatively small M _s and low Curie temperature T _c. For example, T _c of Zn₂ Y is only 130°C. The highest T _c of 390°C is found in Ni₂ Y.12 However, owing to its very small H_φ of ∼1 Oe, Zn₂ Y is still able to show large permeability.12,16

High frequency and attenuation properties of Zn₂ Y ferrites and their composites have been reported by various researchers.105 ^– 110 Permeability spectra of single crystal Zn₂ Y ferrite were measured over 0·1–10 GHz by Obel et al.,105 with of ∼13 and of 12 at f _R = 1·3 GHz. For Ba₂Zn_1·2−xCo_xCu_0·8Fe₁₂O₂₂ ferrites, with Co substitutions from x = 0 to 0·2, decreases from 27 to 18, while f _R is shifted to higher frequency.106 For Ba₂Co_2−xZn_xFe₁₂O₂₂ ferrites, with Zn substitutions from x = 0 to 1·6, and increase from 4 to 15 and from 2 to 8 respectively, while f _R is shifted from 1·5 to 0·5 GHz.96 For the composites with p = 0·43, high frequency magnetic and attenuation properties in the frequency range of 0·2–14 GHz were reported. and are 3–4 and 0·8–1·2 respectively.107 The attenuation materials comprising Mg₂ Y or (CoZn)₂ Y ferrites with multilayer structures showed broad band attenuation characteristics with RL<−20 dB; the percentage bandwidth W _P is 43% at a total thickness of 2·85 mm for (CoNi)₂ Y ferrites and 91% at 8·3 mm for Mg₂ Y ferrites.108 For ZnCuCo substituted Y-type ferrite composites with p≈0·25,  = 4 and f _R ∼1 GHz are achieved at Zn concentration of 1·2.109

Tables 7–9 list static and high frequency magnetic properties of (CoZn)₂ Y, (NiZn)₂ Y and (CoNi)₂ Y hexagonal ferrites and their composites.111 The permeability spectra of all composites comprise two or three components from natural and wall resonances. With Co substitutions, the anisotropy field, H_θ increases, and, therefore, (about 2–4) decreases and resonance frequency f _R (both natural and wall resonance) is shifted to higher frequency, for both the (Co_xZn_2−x)₂ Y and (Co_xNi_2−x)₂ Y composites. Owing to the relaxation-like dispersion, is between 1·6 and 0·6, about half of −1.

In terms of EM attenuation performances, Cu substituted Y-type ferrite composites are the most interesting, as reported in Ref. 74. Permeability spectrum of the Ba₂CuZnFe₁₂O₂₂ composites consists of natural and wall resonance components with roughly equal weight. The spectrum is of a typical relaxation-like dispersion, with of 6·6, of 2·7 at 1·6 GHz, from natural resonance and 2·5 at 0·5 GHz, from wall resonance, as shown in Fig. 17a . The inset of Fig. 17 shows the calculated reflection loss RL versus frequency. Two characteristics, significantly different from those of the W-type ferrite composites, are observed. First, a broader bandwidth is obtained due to the large and . The frequency band covers from 2·6 to 11·0 GHz for RL≤−10 dB and the relative bandwidth W _R is 1∶4·2 at a thickness of t = 0·35 cm. Second, the lower limit of frequency band is shifted to lower frequency of 2·6 GHz due to the lower f _R. Therefore, this composite is a potential EM attenuation material with broad bandwidth at S, C and X bands.

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Figure 17.

Permeability spectra and attenuation characteristics (inset) of Ba₂CuZnFe₁₂O₂₂ composites with p = 0·5 (Ref. 74)

For Ba₂CuZnFe₁₂O₂₂ ferrite composite, permeability spectrum, with  = 1·8 and  = 1·0 at f _R = 9 GHz, has resonance-like dispersion for natural resonance, as shown in Fig. 18. The frequency band for RL≤−15 dB is from 8·0 to 16·2 GHz at a small thickness of t = 0·22 cm. This composite is promising EM attenuation materials at X and K _u bands.

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Figure 18.

a permeability spectra and b attenuation properties of Ba₂CuZnFe₁₂O₂₂ composites with p = 0·5 (Ref. 74)

Z-type barium ferrite composites

Among the soft magnetic hexagonal ferrites, Z-type ferrites are the most attractive. Static magnetic properties of representative Z-type ferrites are listed in Table 10.12 Co₂Z ferrite, Ba₃Co₂Fe₂₄O₄₁, is one of most important microwave ferrite materials, with relatively large permeability. Its saturation magnetisation is 51 emu g⁻¹ at room temperature and Curie temperature is 690 K. At room temperature, Co₂Z ferrite has c-plane anisotropy with a large out-of-plane anisotropy field, H_θ of 12 kOe and a small in-plane anisotropy field, H_φ of ∼0·12 kOe.16,112 Its static real permeability is 8–12 and resonance frequency f _R is ∼1·5 GHz.96,113,114

Great efforts have been made to improve the high frequency properties of Co₂Z ferrites, especially in order to increase its , and f _R. One of the effective methods is to substitute for Co²⁺ with other divalent ions. For example, of Co₂Z can be increased to 16, by substituting Co²⁺ with Zn²⁺ at Zn concentration x = 1·35.12 A significantly increased permeability  = 21 was obtained in Fe²⁺ substituted Fe₂Z ferrite, after the ferrite was sintered in oxygen partial pressure of 101·3 kPa.116 By Cu²⁺ substitution, Z-type hexagonal ferrites can be synthesised at low sintering temperature of 1180°C.117,118 Doping of small amount of SiO₂ can increase of Co₂ Z.119 Significant increase in was found in aligned Co₂Z ferrite ceramics obtained by applying a rotating magnetic field during preparation of the samples, with and being increased to 28 and ∼23 at frequency of 1·5 GHz respectively.12,83

Zn²⁺Ti⁴⁺ (without Co ion) substitutions resulted in Z-type ferrites with c-axis anisotropy. Although is decreased, the temperature dependence of anisotropy field is improved.120,121 The anisotropy of Ba₃Ni_xCo_2−xFe₂₄O₄₁ was modified from c-plane to c-axis at x≧1. As x is varied from 0·5 to 1·0, rapidly decreases from 14 to 3·5.122 For Ba₃Co_2−xZn_xFe₂₄O₄₁, with Zn substitutions from x = 0 to 1·2, and increase from 15 to 21 and from 10 to 12 respectively, while f _R is shifted from 0·8 to 0·3 GHz.96 For Ba₃Co_0·8Zn_1·2Fe₂₄O₄₁ ferrites, after doping with 0·1 wt-%Y₂O₃, decreases from 10 to 6, owing to the formation of garnet phase.123 La substitution for Ba in Co₂Z leads to a decrease in both and , but to large ϵ′, owing to the increase in conductivity of the ferrite.124

Besides the typical ceramic technique, various other processes have been used to prepare Co₂Z hexagonal ferrites. For instance, the addition of Bi–Zn–B glass can shift the resonance of Co₂Z to higher frequencies.125 Co₂Z prepared by using hot pressing technique has a resonance frequency of 2·5 GHz.126 Almost phase pure Co₂Z with of 19·3 was synthesised from preliminarily milled M- and Y-type particles.59 Co₂Z ferrite particles have also been prepared by sol–gel methods.60 ^– 62,127 The Co₂Z ferrites made by this method can have of 14·5 at 10 MHz.61 The addition of SiO₂ can lead to a decrease in and due to the suppression of grain growth, and an increase in f _R.62 Bi₂O₃ and CuO were used to lower the sintering temperature of Co₂Z ferrites, but the obtained is only 5·9.127 By substituting for Co with Cu, Co₂Z phase can be formed at relatively low temperature of 1180°C and  = 13 was obtained at Cu substitution x = 0·6.128

As compared to bulk Co₂Z ferrites, and of the corresponding ferrite composites are significantly decreased, while f _R is shifted to higher frequency. For example, the composite with p = 0·5 exhibited  = 3,  = 1·2 and f _R = 3 GHz,34 while that with p = 0·35 showed  = 2·5 and  = 0·8.73

Static magnetic properties of CoZn substituted Z-type hexagonal ferrites, Ba₃Co_xZn_2−xFe₂₄O₄₁, are listed in Table 11. By CoZn substitution, and of the ferrite composites can be considerably raised, as shown in Fig. 19. With Zn ion substitution from x = 0 to 1·2, and increase from 2·6 to 4·0 and from 1·1 to 1·6 respectively. However, at x<0·8, both and rapidly decrease due to the modification of anisotropy from c-plane to c-axis.34

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Figure 19.

a real and b imaginary permeability spectra of Ba₃Co_xZn_2−xFe₂₄O₄₁ composites with p = 0·5

Relatively low f _R is a main drawback of the CoZn substituted Z-type ferrite composites. The highest f _R is only ∼3·0 GHz in the sample with the maximum Co concentration of x = 2. To further elevate f _R, substituting for Fe³⁺ with Co²⁺Ti⁴⁺ to form Ba₃Co_2+xTi_xFe_24−2xO₄₁ was proposed. Representative permeability spectra and attenuation characteristics are shown in Fig. 20.32 As CoTi substitutions are increased from 0 to 0·5 and 1·0, retains almost unchanged, while increases from 1·2 to 1·6 and 1·8, and f _R is elevated from 3·0 to 3·5 and 4·5 GHz. The increase in both and f _R is attributed to the decreased damping coefficients λ, from 1·44 to 1·22 and 0·88. In terms of RL–f curves, the lower limit f _low of the frequency bands for RL≤−10 dB is almost the same, while the upper limit f _up is significantly shifted to higher frequencies. As a result, as CoTi substitution x is increased from 0 to 0·5 and 1·0, the relative bandwidth, W _R is expanded from 1∶2·4 to 1∶3·0 and 1∶3·3 respectively, due to the enhanced and the thickness of the composites corresponding to W _R decreases from 0·35 to 0·30 and 0·25 cm, due to the increased f _R.

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Figure 20.

a permeability spectra and b attenuation characteristics of Ba₃Co_2+xTi_xFe_24−2xO₄₁ ferrite composites with p = 0·5

Using Ru⁴⁺ or Ir⁴⁺ instead of Ti⁴⁺ ions can significantly increase f _R, because the two ions contribute a very large magnetocrystalline anisotropy. Experimental results have shown that, f _R of Ba₃Co_2+xTi_xFe_24−2xO₄₁ ferrite composites is increased from 2·5 to 4·2 and 11·5 GHz, as RuCo substitution x is varied from x = 0 to x = 0·2 and 0·8. However, and decrease rapidly from 3·1 to 2·4 and 1·6, and from 1·7 to 1·7 and 0·8 respectively, as shown in Fig. 21.74

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Figure 21.

a real and b imaginary permeability spectra of Ba₃Co_2+xRu_xFe_24−2xO₄₁ ferrite composites with p = 0·5 (Ref. 74)

Molten salt technique has also been used to improve the properties of ferrites through controlling over their particle morphologies. Example of molten salt method was reported by Lin et al.,129 using NaCl as flux. Co₂ Z ferrite powder prepared by this method had particles with hexagonal plate shapes of ∼40 μm. The large and plate shape Co₂ Z particles as fillers lead to composite with increased , and f _R. f _R is increased from 2·3 to 3·3 GHz and is increased by 8%, as compared to the composite with the ferrite particles synthesised by conventional ceramic technique. Correspondingly, bandwidth W _R is expanded from 1∶3·0 to 1∶3·8.129

Similar to W-type ferrite, doping of oxides is also able to increase and of the Co₂ Z ferrite composites. Representative results are listed in Table 12 and 13.57,74 Among the oxides studied, the most interesting dopant is TiO₂, which led to an increase in all , and f _R. The experiment results show that, with increasing doping content δ (wt-%), increases from 12 for δ = 0 to the maximum of ∼19 for δ = 1·0–1·5, and then decreases to 16 for δ = 2·0.130 The increase in is attributed to the increase in density of the ferrites as a result of the doping. For the composites of Co₂ Z doped with 1 wt-%TiO₂, , and f _R are increased to 4·0, 2·4 and 2·6 GHz, as compared to 3·6, 1·9 and 2·3 of the undoped Co₂ Z ferrite composite.

Figure 22 shows permeability spectra and EM attenuation characteristics of the composites made with the 1 wt-%TiO₂ doped Co₂ Z ferrite. The frequency band for RL≤−10 dB is from 3 to 12·5 GHz, corresponding to W _R of 1∶4·2, at a thickness of t = 0·3 cm. For a comparison, the undoped Co₂ Z ferrite composite exhibits W _R of 2·4–3·1. The TiO₂ doped Co₂ Z composite is a good candidate EM attenuation material with broad bandwidth and thin thickness at S, C and X microwave bands.74

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Figure 22.

a permeability spectra and b attenuation characteristics of the composites made of Co₂ Z ferrite (p = 0·5) doped with 1 wt-%TiO₂: inset shows of Co₂ Z ferrites as function of TiO₂ content130

Metallic magnetic nanosized powders

Magnetic nanoparticles, that have been used to fabricate composites for microwave attenuation applications, include metallic element and alloy nanopowders, nanofibre, hybrid nanoparticles of metallic alloys and oxides, and nanosized ferrite powders. Various methods, such as chemical precipitation (reduction),177 ^– 197 chemical vapor deposition,198 dc arc discharge method200 ^– 204 and high energy ball milling,205 ^– 213 have been used to derive the powders mentioned. EM properties of composites made with the synthesised nanosized particles together with the methods used are described as follows.

Chemical methods

Interesting EM properties of nanosized particles of Co, Co_xNi_100−x,177 ^– 181 and Fe_z(Co_xNi_100−x)_1−z,182 ^– 184 have been reported by Viau et al. The nanoparticles were synthesised by precipitation from metallic salts dissolved in polyols which acted as both solvents and reducing agents. In a typical synthesis of Fe_z(Co_xNi_100−x)_1−z, for example, Cu(II) and Ni(II) acetate tetrahydrates and Fe(II) chloride tetrahydrate were dissolved with sodium hydroxide in 1,2-propanediol, with desired concentrations. The particle size was well controlled by using heterogeneous nucleation, which was realised by using a small amount of K₂PtCl₄ or AgNO₃ dissolved in a mixture of 1,2-ethanediol and dihydroxydiethylether (1 vol.-%∶1 vol.-%). Magnetic metallic alloys of various composites could be readily synthesised with average sizes ranging from microns to submicrometre and to nanometre. Figure 28 shows representative TEM and SEM images of the metallic alloy nanoparticles,179,183 where the average sizes of the Co₅₀Ni₅₀,179 and Fe₁₄Co₄₃Ni₄₃ particles are 6 and 120 nm respectively. It is worth mentioning that the powders reported were all quasi-spherical and non-agglomerated particles with very narrow size distribution.

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Figure 28.

Representative TEM and SEM images of nanosized magnetic alloys

To address the percolation problem when compacting the metallic alloy powders, they were coated by oxide layers with thickness of a few nanometres.182 For example, a layer of manganese oxide (MnO₂) was produced to coat the metallic alloy particles by using potassium permanganate (KMnO₄). This allowed to compact the alloy powders into high volume concentration composites without the occurrence of electric percolation. To further improve EM performances of the alloys, they were also thermally treated at high temperatures (120–350°C) in argon by using a rotating furnace.

Microwave EM properties of the metallic alloy particles were demonstrated by their intrinsic permeability characteristics which were derived from measured data of composites with various volume concentrations. Figure 29 shows representative EM properties of the metallic alloy powders with different particle sizes. Two distinctive characteristics in EM responses of the materials were identified: the presence of multiple resonance as the particle size was decreased from microns to nanometres and shift of resonance to high frequencies with decreasing particle size. The multiple resonance behaviours of the nanosized particles had been attributed to the coexistence of non-uniform resonance modes that were resulted from the exchange energy contribution to the magnetisation precession within the particle.182,184 Since there was no permittivity data available, no attempt was made to evaluate microwave attenuation properties of the metallic alloy composites, which could be of great interest to the research community of EM materials. It is reasonably expected that such composites should be promising capability of microwave attenuation due to their broad and multiple resonance peaks.

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Figure 29.

Imaginary parts of intrinsic permeability versus frequency for Co₈₀Ni₂₀ of micrometre and nanometre sizes (left) and nanosized Fe₁₄Co₄₃Ni₄₃ of different diameters (right): reproduced with permission from Ref. 183, copyright 1997, American Institute of Physics

Enhanced microwave attenuation was also observed in composites based on Ni nanofibres.185 Dong et al.185 developed a method to direct synthesise Ni fibres via the reduction of Ni²⁺ ions by using hydrazine hydrate. Composite made with the Ni fibres had higher dielectric loss tangent over the microwave frequency range than that made with Ni particles, while their magnetic loss tangents were almost the same. As expected, the composite with Ni fibres demonstrated better microwave attenuation behaviour.185 The high dielectric loss tangent of the Ni fibre composite was attributed to the space charge polarisations at the adjacent of contacting fibres and electron vibration along the fibre axle directions.

Zhou et al.186 reported a method to synthesise low density ordered mesoporous carbon silica nanocomposites with controllable content of Fe. The method was called solvent evaporation induced self-assembly. Fe nanocrystals were highly dispersed in the composites via in situ carbothermal reduction. One of the basic ideas for this approach was to reduce dielectric permittivity by introducing pores so as to maintaining a desired impedance matching. Porous materials would also have the advantage of low density. Depending on processing conditions, magnetic components in the C–SiO₂–Fe nanocomposite powders were Fe or Fe₃C. Composites with epoxy resin as matrix and 40 wt-%C–SiO₂–Fe powders were fabricated and characterised. Promising EM performances of the composites were observed over 12–18 GHz frequency range.

Submicrometre α-Fe/SmO powders were prepared by a disproportionation reaction method from Sm₂Fe₁₇ in H₂, followed by annealing in air.187 The powder was used to fabrication composite with epoxy resin at a ratio of 80 mass-%, which was 54 vol.-% (34 vol.-% α-Fe). This composite had microwave reflection loss RL less than −20 dB in the frequency range 0·73–1·3 GHz, while the composite derived from the unproportionated power exhibited almost no attenuation capability. The authors also claimed that the performance of the α-Fe/SmO composite was better than carbonyl iron.187

Fe–graphite oxide nanocomposite was reported by Zou et al. 188 The nanocomposites were prepared by inserting Fe³⁺ ions into the layers of graphite oxide, followed by reducing the Fe³⁺/graphite oxide compound at elevated temperatures in H₂. Starting materials were equivalent amounts of Fe(NO₃)₃.9H₂O and graphite oxide. The mixture was pyrolysed at 300°C and then reduced at high temperatures. The optimum reducing temperature was 600°C. Low temperature (300°C) was not sufficient to reduce Fe³⁺ into Fe, while high temperature led to the formation of Fe₃C. Typical particle sizes of Fe were 10–100 nm. Electromagnetic properties were presented in the report, but no information was available on what types of materials were used for the measurement. In addition, microwave attenuation performance was not very promising, which could be attributed to the poor impedance matching of the materials if the Fe–graphite oxide nanopowders were directly used to make the samples for microwave characterisation.

Wei et al.189 synthesised Fe–SiO₂ composite particle by H₂ reducing a Fe₂O₃–SiO₂ precursor prepared via a sol–gel process. The Fe₂O₃–SiO₂ precursor was prepared to have a Fe/Si ratio of 13∶1, which corresponded to Fe content of 78·2 vol.-% in the final composite powders. Composites with 15 vol.-%Fe–SiO₂ and paraffin were prepared and characterised. It was found that the powder treated at 800°C possessed optimum EM properties.

There are also reports on fabrication of FeCo–hexaferrite nanocomposite particles by reducing ferrite in H₂.190,191 It was found that the FeCo metal nanoparticles precipitated coherently as thin flakes along the a–b planes of the lattice of the hexaferrites. BaCo₂Fe₁₆O₂₇ and Ba₂Co₂Fe₁₂O₂₂ were used to fabricate nanocomposite particles. Although permeability of the nanocomposites was increased as compared to that of their original ferrites, their permittivity was promoted even more.190 In this respect, they are not ideal candidates for microwave attenuation applications due to their poor impedance matching.

Recently, Liu et al.198 synthesised Fe nanowires by using a CVD method. The Fe nanowires had a diameter of 70–200 nm and a length of 20–50 μm, synthesised through the decomposition of Fe(CO)₅ at 523 K in Ar flow. Resin epoxy composites with 29 vol.-%Fe nanowires displayed much better dielectric and magnetic properties as compared to their flake-like and microwires counterparts. On the one hand, the nanowire composite had almost constant permittivity (ϵ′≈10 and ϵ″≈0·5) over the frequency range measured, while the composites with microwires and flake-like particles possessed much higher real and imaginary permittivity values. On the other hand, the nanowire composite showed high real and imaginary permeability values than the other two composites. This means that impedance value of the nanowire composite is closer to that of free space than the composites made of microwires and flake-like particles. As discussed earlier, reflection loss of a composite is determined by both impedance matching of the material with free space and the energy absorption capability of the material. Therefore, the nanowire composite had lower EM wave reflection loss than the microwire and flake-like particle ones.198

More recently, Sun et al. 199 synthesised a new type of nanosized Fe with hierarchical dendrite-like structures, which was made into composites with paraffin at 70 wt-% and a thickness of 2 mm that showed −10 dB reflectivity over 3–18 GHz. The nanostructured Fe powder was derived by reducing α-Fe₂O₃ that was synthesised by using a hydrothermal technique. The hierarchical nanostructure of the α-Fe₂O₃ was kept after the reducing reaction. Furthermore, by controlling the reduction temperature and flow rate of reducing agent (H₂/Ar), Fe₃O₄ powder with the same hierarchical nanostructure was obtainable. The Fe₃O₄ could be transfered into nanosized γ-Fe₂O₃.

Other chemical methods, such as hydrogen thermal reduction,193 ^– 195 self-propagating combustion196 and thermal annealing, have also been reported.197 For example, Zhen et al. 193 used NiFe₂O₄ particles as starting materials to synthesise FeNi alloy nanoparticles by hydrogen thermal reducing at 400°C for 1 h. The obtained FeNi alloy particles had a diameter of ∼150 nm. Composite made with the FeNi nanoparticles of 15 vol% in wax had promising EM performances within the frequency range of 11–18 GHz. It is expected that EM properties of the composites can be further improved by increasing their volume concentrations. The method was also used to produce CoFe alloy nanoflakes from CoFe₂O₄ and CoFe/Al₂O₃ composite nanoparticles from CoFe_xAl_2−xO₄ particles for microwave composites.194,195 Specifically, the CoFe/Al₂O₃ composite nanoparticles were very good candidates for composite with impedance matching layer to achieve wide band microwave absorbers. A multilayer structured composite with impedance matching layer exhibited an ultra wideband at 10 dB reflection loss from ∼2·5 to 18 GHz.195

Non-metallic magnetic nanosized powders

Compared to their metallic magnetic counterparts, non-metallic magnetic (ferrites) nanosized powders are much less reported. Representative examples of nanosized ferrites and ferrite based nanocomposites are discussed as follows.173,199,217 ^– 223

Nanosized ferrite powders, Mn_0·7Zn_0·3Fe₂O₄ and Ni_0·7Zn_0·3Fe₂O₄, were synthesised via a chemical coprecipitation method. The powders had average particles of 10–52 nm, depending on calcination temperature. Composite made of 60% Ni_0·7Zn_0·3Fe₂O₄ displayed microwave attenuation at −10 dB reflection loss over 9–12 GHz.218 Xiao et al. 219 synthesised a core–shell structured MnFe₂O₄– TiO₂ nanocomposites. Nanosized MnFe₂O₄ powder was prepared by using a polymer pyrolysis method, which was then coated with TiO₂ via a sol–gel process. Composites with 60 vol.-% of the nanocomposite powders were prepared and characterised. It was found that dielectric permittivity increased with increasing content of TiO₂. This is readily understandable, because TiO₂ has higher permittivity than MnFe₂O₄. However, a maximum permeability was observed in the sample derived from the nanocomposite with 20%TiO₂, which was not explained in the report. In fact, it is not suggested to use TiO₂ to make composite with ferrites, because it has a relatively high dielectric permittivity (∼80). The presence of TiO₂ will make it more difficult to reduce the permittivity of a composite for impedance matching.

More recently, Stojak et al.221 prepared polymer nanocomposites with 10 nm CoFe₂O₄ and Rogers polymer. The nanosized CoFe₂O₄ particles are synthesised via a chemical processing method. Composites with the CoFe₂O₄ nanoparticles up to 80 wt-% dispersed in Rogers polymer in hexane. Different from those composites prepared by mechanically mixing powders and epoxy resin, the nanocomposites reported by Stojak et al. 221 had very uniform distribution of the CoFe₂O₄ nanoparticles. A two-port microstrip linear resonator was used to characterise microwave responses of the nanocomposites. It was found that microwave response properties of the nanocomposites could be tuned by applying external dc field.

There are increasing number of reports on EM properties of composites based on nanosized magnetite (Fe₃O₄) powders.199,222,223 For example, as stated earlier, Sun et al. 199 prepared hierarchical nanosized dendrite-like Fe₃O₄ powders from α-Fe ₂ O ₃ of same structures. Wang et al. 223 synthesised monodispersed hollow Fe₃O₄ spheres with diameter of ∼500 nm and shell thickness of ∼150 nm by using a solvothermal process. Both types of Fe₃O₄ powders were of promising EM properties in the form of composites.199,223

Shift of resonance frequency of composites embedded with long conductive fibres

It has been shown that the shift in resonance of conductive fibres embedded in a sheet sample depends on the sample thickness.278 For thin samples, the resonance frequency drops rapidly with increasing thickness, but remains relatively unchanged beyond a certain thickness. For samples with thickness larger than this critical thickness, the resonance frequency is approximately the same as that of an infinite bulk material and depends only on material properties of the composites.

Resonance frequencies of the samples between thin and thick were reported in Ref. 255. The experimental results shown in Fig. 37 corresponded to host matrix with 15% mass concentration of aluminium powder. Thin sample presents the measured permittivity for a 0·2 mm thick sample, while the data of thick sample correspond to a 1 mm thick sample. As the thickness increases from zero to 0·2 mm, the resonance frequency shifts from 13·6 GHz to 6·7 GHz. When the thickness is further increased to 1 mm, the resonance frequency shifts to 4·3 GHz. Therefore, the samples should be as thick as possible. On the other hand, the samples under study should not be too thick, otherwise the measurement accuracy would degraded. In view of this, samples that are several times the critical thickness could be regarded as optimal. Unfortunately, no analytical expression for the critical thickness is available in the literature. For this reason, the thickness dependence of the resonance frequency was investigated by numerical simulation, using HFSS. The model consists of a 10×10×30 mm box filled with air. A composite layer with dimensions of t×10×30 mm is placed at centre of the box. The thickness t is varied from 0·1 to 1·5 mm. A copper fibre with length of 10 mm and thickness of 0·1 mm is located at centre of the layer. A plane wave illuminates the layer at normal incidence, with electric field parallel to the fibre. A radiation boundary condition is defined on surface of the air box. Resonance frequency of the fibre is derived from the calculated frequency response of RCS of the layer.

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Figure 37.

Calculated resonance frequency from RCS of thin fibre with length of 10 mm embedded in composite layers of various thickness: reproduced with permission from Ref. 255, copyright 2003, American Institute of Physics

Based on the numerical results, for all permittivity values used in that study, the samples with 1·5 mm thick sheets can be regarded as bulk materials in relation to the dipole resonance of a 10 mm long fibre.

Composites filled with carbonyl iron powder were also studied. These composites are isotropic. The size of the particles (5 μm) was small as compared to the thickness of the fibres (100 μm). Therefore, the composite with these iron particles was homogeneous as compared to that with the fibres. However, these composites possessed magnetic properties that must be taken into account in the analysis. This is because permeability affects the resonance frequency in the same way as permittivity. The resonance frequency is inversely proportional to the refractive index defined by n = (ϵ′μ′)^1/2.

Another filler was aluminium powder. The maximum size of the particles was 15 μm. Therefore, these particles also formed a homogeneous host matrix. The data on the location of the resonance frequency for this case are shown in Fig. 38. The results obviously deviate from the 1/2 law that is expected of a non-magnetic, infinite, homogeneous, isotropic medium. Instead, the measured data vary gradually as a function of ϵ, and can be fitted by an exponential law with an index of ∼0·3. In Fig. 38, the exponential law is represented by a solid line that is normalised so that f ₀ = 13·6 GHz for ϵ = 1.

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Figure 38.

Measured resonance frequency plotted against refractive index for copper fibres embedded in composites filled with carbonyl iron of different concentrations: reproduced with permission from Ref. 255, copyright 2003, American Institute of Physics

Therefore, for a fibre embedded in a matrix containing aluminium power, the measured resonance frequency shift did not obey the ϵ ^1/2 law. The aluminium samples were highly anisotropic, in contrast to the iron powder samples. Hence, it is necessary to consider the effect of the anisotropy in permittivity of the host matrix on resonance behaviours of the embedded copper fibres. In other words, the anisotropy of the composites filled with aluminium powder could be responsible for the anomaly observed in location of the fibre resonance frequency. The same is true concerning the composites filled with carbon fibres.

Effect of distribution of fibres on resonance and effective permittivity

It has been shown that Q-factors of composites with periodically distributed fibres are significantly higher than those of the composites with randomly distributed fibres. Comparatively, Q-factors of the former were also more sensitive to changes in resonance frequency. First, the inter-element spacing D _x, perpendicular to the fibre axis, had an effect on resonance frequency. Numerical (empty circles) and experimental (filled circles) results are shown in Fig. 39, where the inter-element spacing parallel to the fibre axis D _y is 20 mm. The resonance frequency f ₀ can be related to the equivalent lumped circuit parameters as follows (22) where L and C are the equivalent lumped inductance and capacitance of the fibres. Although these equivalent parameters are difficult to obtain quantitatively, they can be used to explain qualitatively the effects of the interactions among fibres. The interaction between the two ends of an individual fibre is quite weak, owing to the small cross-section and larger separation (length) of the fibre. Therefore, the shift in resonance frequency could be due to the partial cancellation of magnetic fields in the region between closely spaced adjacent parallel fibres, resulting in reduced effective inductance of the fibres that raised the resonance frequency. As the spacing between adjacent parallel fibres is increased, this cancellation effect is weakened. Thus, the resonance frequency approaches to that of a single fibre (∼13 GHz) as D _x is increased.

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Figure 39.

Dependence of resonance frequency on periodic of composite with periodically distributed fibres: reproduced with permission from Ref. 255, copyright 2003, American Institute of Physics

Figure 39 also shows the results for the case of varying D _y, with D _x being sufficiently large for negligible interactions between adjacent parallel fibres. In this case, the resonance shifts to lower frequency when D _y is decreased. The downward shift in resonance frequency can also be explained by equation (22). The effective lumped capacitance is due mainly to the two ends of two collinear fibres (one above the other) that are closest to each other, as well as the entire lengths of both fibres from one end to the other. Since these two ends have opposite charges, a capacitance is built up and varies inversely with the end-to-end separation. As D _y is decreased, the end-to-end separation is correspondingly reduced, leading to a higher capacitance which lowers the resonance frequency. However, the shift is only ∼0·35 GHz as the separation decreases from 20 to 0·2 mm.

Cluster effect inside fibre composites with high concentrations

Figure 40 shows transmission coefficients of the composites with 0·5% randomly distributed fibres with and without overlapping.257 Solid lines are measured results of the fibre composite without overlapping of fibres. A single resonance peak can be observed. For the sample with clusters of overlapping fibres, the resonance amplitudes are smaller and the resonance peaks spread over a wider frequency range as compared to the case without overlapping. Differences in the frequency spread of resonances and resonance amplitude between samples with and without cluster at other concentrations and fibre lengths were also observed. It is found that cluster effect can reduce the amplitude and broaden the bandwidth of the resonance peak.

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Figure 40.

Transmission coefficients of composites with randomly distributed fibres with and without overlapping of fibres: reproduced with permission from Ref. 257, copyright 2007, Institute of Physics

The bandwidth of EM response is extremely important for various applications, such as frequency selective surface. However, it is difficult to determine the contribution of each fibre cluster, because it is always a collection of different clusters with different orientations in a sample. To fully understand the response of clusters to incident EM wave with different polarisations, it is necessary to consider an array with a fibre cluster within each unit cell. The simplest case is to have two overlapping fibres in each cell. This simplified approach is sufficient to demonstrate the basic response of a single cluster for the case where the interaction between clusters is much smaller than that between fibres within the cluster. The assumption is valid because similar response can be found in array with the same cluster but different periodicity.

Figure 41 shows measured (line) and calculated (symbols) transmission coefficients of a cluster with two fibres. The difference between the measured and the calculated resonance peaks (frequency and amplitude) is attributed to insufficient accuracy of the geometrical parameters in the implemented sample or the simplification of the numerical modeling. For E field along 0° (horizontal polarisation), only one resonance (at ∼13 GHz) is observed. The resonance frequency is close to that of a single fibre. For E field along 90° (vertical polarisation), one more resonance (at 9·5 GHz) is observed. The resonance frequency is corresponding to the effective length of the fibre cluster (∼15·6 mm). For E field along the 45° direction (parallel to the axial direction of one fibre), both resonances (at 9·5 and 13 GHz) of similar amplitude are noted. Owing to the limited frequency range (2–20 GHz) of the free space system, transmission coefficient at higher frequency is not available. Most probably, one more resonance peak would appear at higher frequency (>30 GHz) owing to the symmetry of the fibre cluster. However, the peak is quite far away from the first resonance peak and therefore is of no significant interest for real applications.

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Figure 41.

Transmission coefficients of two fibre cluster array at different polarisation angles: reproduced with permission from Ref. 257, copyright 2007, Institute of Physics

When the two overlapping fibres were isolated by a dielectric adhesive tape, similar resonance behaviour was also observed in the measurement, only with a slight upward shift in resonance frequency of the clusters. This means that cluster effect is due to the interaction between the two overlapping fibres and is not due only to physical or electrical contact. When the fibre cluster is replaced by a bended fibre of identical shape and length (15·6 mm), multiple resonances were not observed, regardless of the polarisation of the incident electric field. Therefore, when modeling randomly distributed fibres, long fibres cannot be simply used as substitutes for overlapping short fibres, as the interactions involved in the two configurations are different. Single fibre may have resonance even if it is close to or is in physical contact with other fibres. This explains why the observed resonance is close to the single fibre resonance frequency in a composite with randomly distributed fibres.

Cluster formed by overlapping fibres has multiple resonance frequencies, which is related to the lengths of the cluster or that of single fibre. Interactions between fibres within a cluster are not eliminated by electrical isolation. Cluster effect well explains the observations that the broadening of the resonance peak in composites with randomly distributed fibres and that the resonance frequency remains close to that of a single fibre. The Lorentzian formula with curve fitting parameters provides adequate description on the EM properties of the composites with fibres at various length and concentrations.257

Metamaterial absorbers without conducting ground planes

In 2006, Bilotti et al. 296 proposed an electrically thin (λ/20) SRR based absorber without conducting ground planes. The absorber was comprised of a certain number of parallel columns of SRRs and a conventional resistive sheet, whose resistance was equal to the free space characteristic impedance. When the SRRs were excited by the magnetic fields of the incident waves, at the resonant frequency, the magnetic fields were very high in the centre of the SRRs, while the electric fields had maximum around the stems of the SRRs. The resistive sheet located near the resonating SRRs absorbed the EM energy of the incoming waves. Experimental verification of the design concept can be found in Ref. 295. As mentioned in Refs. 295 and 297, metamaterial absorbers without conducting ground planes are useful to reduce reflectivity from non-metallic objects at desired frequencies, without increasing the response at other frequencies.

In 2008, Landy et al. 298 and Tao et al. 299 reported a design of polarisation dependent one-dimensional absorbing metamaterial with near unity absorbance at a single frequency. Electric coupling was supplied by an electric resonator. Magnetic coupling was created by combining the centre wire of the electric resonator with a cut wire in a parallel plane separated by a substrate. Both the electric and the magnetic couplings could be tuned rather independently. Therefore, ϵand μ were decoupled. Each resonance could be tuned individually. By manipulating the lossy ϵ and μ of the metamaterial to match each other at certain frequency, zero reflection of incident EM waves was realised, since the wave impedance of the metamaterial was equal to the free space value at that frequency. Perfect absorption was then achievable by the lossy metamaterial with enough thickness. Based on similar principle, Wang et al. designed a polarisation dependent wide angle three-dimensional metamaterial absorber.300 The polarisation dependent design can be further modified to be polarisation independent, as reported in Refs. 301 and 302.

Besides planar configurations, metamaterial absorbers with other physical shapes have also been widely reported. In Ref. 303, Ng et al. theoretically demonstrated a metamaterial frequency selective superabsorber which consisted of an absorbing core material coated with a shell of isotropic double negative metamaterials. Theoretically, for a fixed volume, the absorption cross-section of an absorber can be made arbitrarily large at one frequency. In Ref. 304, loss manipulation in EM cloaks for perfect EM wave absorption was discussed. Based on the theoretical work in Ref. 305, Cheng et al. 306 experimentally demonstrated an omnidirectional metamaterial absorber at microwave frequencies in 2010, which could trap and absorb EM waves coming from all directions spirally inwards without any reflections due to the local control of EM fields.

Metamaterial absorbers with conducting ground planes

Metamaterial absorbers with conducting ground planes can be effectively used to reduce reflectivity from metallic planes just as effectively as the conventional absorbers based on composites with various magnetic or non-magnetic inclusions, as discussed above. These metamaterial absorbers are generally constructed by placing a resistive or highly conductive flat surface with either periodic or non-periodic patterns on top of a grounded dielectric or magnetic substrate (see e.g. Refs. 307–319). In this respect, the strong coupling between the pattern and the conducting ground plane differentiates this kind of metamaterial absorbers from the conventional absorbers with similar configuration but thicker substrates. For a thin substrate, the patterns and their images with respect to the conducting ground plane effectively construct resonant units functioning like SSPs. The top patterned surface, together with the whole structure sometimes, are also called metamaterial surface, frequency selective surface, high impedance surface or artificial magnetic conducting surface, etc., by different researchers. The top surface can be multilayered structures, which are not covered here.

According to the transmission line theory, surface impedance at top surface of the metamaterial absorbers can be expressed as307,320 ^– 323 (23) where Z _shunt is shunt impedance of the resistive or conductive flat surface, and Z _tml is surface impedance of the dielectric or magnetic substrate backed by a metallic wall. Since Z _tml is usually inductive for thin absorbers, Z _shunt has to be capacitive at the absorption band.324

For lossless substrate and highly conductive flat surface, Z _s is very high at around the resonant frequency. A resistive sheet with proper impedance can then be placed on top of the conductive flat surface to reduce reflectivity.307,325,326 This idea resembles that of Salisbury screens.327 ^– 329 However, the resistive sheet has to be placed at a λ/4 distance away from the conducting ground plane of Salisbury screens. The capacitive Z _shunt can be tailored in a large range by changing not only permittivity of the substrate but the periodic pattern. Therefore, very low resonant frequency can be achieved even for electrically ultra thin substrates by using metamaterial absorbers.

The resistive sheet and the highly conductive flat surface can be replaced by a resistive flat surface with proper periodic patterns.308,330 ^– 333 Furthermore, the patterned resistive sheet can be replaced by alternatively soldering lumped resistors between highly conductive periodic patterns.334 ^– 340 This configuration is similar to that of the circuit analogue (CA) absorbers.329,341 Therefore, some researchers also called it circuit analogue absorber. However, for normal CA absorbers, the distance between the conducting ground plane and the CA sheet is approximately λ/4, while the equivalent RLC series circuit of the CA sheet resonates at the centre frequency f ₀.329 In other words, normal CA absorbers are similar to the Salisbury screens, whereas the metamaterial CA absorbers have reactive components, due to the periodic patterns of the resistive sheet. Below (above) f ₀, reactive components of the CA sheet are capacitive (inductive), cancelling the inductive (capacitive) components of Z _tml. The cancelling effect leads to an increase in the absorption bandwidth. Owing to the large distance between the CA sheet and the conducting ground plane, the equivalent RLC series circuit of the CA sheet can even be obtained without considering the influence of the conducting ground plane. For metamaterial absorbers, thickness of the substrates is usually much less than λ/4. Strong coupling exists between the periodic patterns and the conducting ground plane. Furthermore, the performances of metamaterial absorbers can be additionally optimised by considering properties of the substrates.309 ^– 311,314,316

The pattern on the top surface of the metamaterial absorbers is not necessarily periodic. For example, Zhu et al. 342 ^– 344 showed that disorder metallic dendritic cells342 placed on top of grounded dielectric substrates can also be used as metamaterial absorbers. In Ref. 345, Liu et al. developed a chemical double template technique, a low cost way to fabricate disorder dendritic cells of large areas, which provided metamaterials operating at infrared and even visible frequencies. As reported in Ref. 343, disorder metamaterial absorbers had sufficiently high absorptivity.

Ultra thin metamaterial absorbers

Ultra thin EM absorbers based on metamaterials have been systematically studied in the authors lab. As shown in Fig. 42, the matamaterial absorbers are comprised of periodic highly conductive arrays on top of a grounded ultra thin substrate. The thickness of the substrates is much less than λ/4. For the polarisation direction of the incident fields shown in Fig. 42, the performance of square arrays is similar to that of strip arrays, since the electric fields on the plane of the square arrays nearly vanishes in the space between the edges parallel with the incident electric fields, thus reducing the square arrays to strip arrays.346 Reducing the doubly periodic square arrays into singly periodic strip arrays results in great reduction in analysis complexity.

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Figure 42.

Schematic diagram of metamaterial absorbers under consideration: reproduced with permission from Ref. 323, copyright 2009, American Institute of Physics

With the periodic and symmetric characteristics and taking into account of the metamaterial absorbers comprising of strip arrays, the computational model was deduced as a parallel plate waveguide as shown in Fig. 43.347 Mode matching method was then used to efficiently solve the EM response of the metamaterial absorbers. With a proper fitness function defined related to the absorption bandwidth, genetic algorithm can be effectively used to optimise the performances of the metamaterial absorbers.347

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Figure 43.

Computational model of metamaterial absorbers in Fig. 42b (w = D−g): reproduced with permission from Ref. 347, copyright 2009, The EMs Academy.

Owing to the image effect caused by the conducting ground plane in the metamaterial absorbers, as shown in Fig. 44, the strips and their images effectively formed strip pairs which worked similarly as SSPs.294,347 ^– 350 The scattering parameters of the structure in Fig. 44 can be solved by using the mode matching method. As shown in Fig. 45, the effective μ of the strip pairs retrieved by using the approach in Ref. 351 show a strong magnetic resonance in the metamaterial absorbers.

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Figure 44.

Equivalent computational model of the metamaterial absorbers as in Fig. 46: reproduced with permission from Ref. 347, copyright 2009, The EMs Academy

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Figure 45.

Retrieved effective relative permeability ( ) of two metamaterial absorbers comprising strip arrays (D = 6·2 mm, g = 0·4 mm) (no markers: dielectric substrate with ϵ = 6·15×(1−0·103j)ϵ ₀; circle markers: magnetic substrate with μ = 1·5×(1−0·1j)μ and ϵ = 6·15×(1−0·103j)ϵ ₀; solid lines: effective ; dot lines: effective ): reproduced with permission from Ref. 347, copyright 2009, The EMs Academy

An accurate analytical formula for reflection coefficients was derived in Ref. 323, based on strip type of the metamaterial absorbers with normal incidence (see Fig. 42b ), which can be written as follows (24) where Z ₀ is the wave impedance in free space and Z _s is the surface impedance of the metamaterial absorber and can be expressed as (25) (26) (27) In equations (26) and (27), kand k ₀ are wave numbers in the substrate and free space respectively.

As mentioned above and shown in equation (26), Z _tml is inductive for ultra thin metamaterial absorbers. The inductance L is determined by permeability and thickness of the substrate. The shunt impedance Z _shunt can be characterised by the capacitance C shown in equation (27). The ctanh function containing the substrate thickness t clearly indicates an interaction between the conducting ground plane and the periodic patterns. From equation (25), it can be seen that equivalent circuit of the metamaterial screens is composed of an inductor L (L′−jL″) and a capacitor C (C′−jC″) in parallel. With certain manipulation, the equivalent circuit can be transformed into an RLC circuit shown in Fig. 46. The parameters of the equivalent circuit shown in Fig. 49 can be written as follows (28) (29) where tan δ_μ is magnetic loss tangent of the substrate.

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Figure 46.

Equivalent circuit of metamaterial screens: reproduced with permission from Ref. 323, copyright 2009, American Institute of Physics

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Figure 49.

Illustrations of periodic units of metamaterial absorbers with non-uniform patterns

In Ref. 322, a simple analytical model was proposed for similar structures to that shown in Fig. 42. Based on the analytical models for thin strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface, analytical expressions were derived for the grid impedance of capacitive strips and square patches, i.e. Z _shunt. The surface impedance and the reflection coefficients can then be obtained according to equations (23) and (24) respectively. Since Z _shunt was derived without considering the conducting ground plane, the model neglected the coupling between the metallic patches and the ground plane. As can be found in Refs. 323 and 352, when thickness of the substrate is small, the transmission line model will produce great errors if the coupling is neglected.

Bandwidth limits of ultra thin metamaterial absorbers, with frequency non-dispersive and frequency dispersive substrates, were investigated in Ref. 323. Since ultra thin metamaterial absorbers are narrow banded, in many cases μ and ϵ of the substrates can be regarded as frequency non-dispersive in the absorption band. In this case, the maximum bandwidth of ultra thin metamaterial absorbers was found to be323 (30) where ρ ₀ is the required reflectivity magnitude, is the real part of complex relative permeability of the substrate and λ ₀ is the wavelength in free space corresponding to ω ₀, the resonant frequency of the LC circuit in Fig. 46. ω ₀ can be taken approximately as the centre frequency in the concerned waveband Δω. The optimum condition to reach the maximum bandwidth can be expressed as follows323 (31) It can be found from equation (30) that the maximum bandwidth of ultra thin metamaterial absorbers is linearly determined by both the real part of permeability of the substrates and the relative thickness with respect to the free space wavelength at the centre frequency in the concerned waveband. From equation (31), it can be seen that, for a thicker substrate with higher permeability, the optimum loss tangents should be larger. Equations (30) and (31) provide us with the basic design rules to construct ultra thin metamaterial absorbers with frequency non-dispersive substrates.

Equation (30) indicates that the maximum bandwidth is not related to the real part of permittivity ϵ′. Actually, substrates with different values of real permittivity ϵ′ can be used to design ultra thin metamaterial absorbers with the same physical thickness to achieve the same maximum fractional bandwidth as long as the loss tangents are appropriate to meet the requirements given by equation (31).323 It is noted that for Dallenbach absorbers the thickness is approximately λ/4. Thus for smaller ϵ′, the physical thickness of the substrate has to be increased. However, for metamaterial absorbers, since the maximum bandwidth is not related to ϵ′, the substrate of a given physical thickness can be fabricated with a wide variety of materials. Furthermore, according to the maximum bandwidth expressed in equation (1) derived by Rozanov10 for normal frequency non-dispersive dielectric Dallenbach absorbers, it can be found that the maximum bandwidth of metamaterial absorbers is ∼1·2 times that of the Dallenbach absorbers.

If the equivalent circuit components in Fig. 46 are strongly frequency dispersive in the absorption band, equations (30) and (31) are no longer valid. If μ and/or ϵ are decreasing with increasing frequency so that the equivalent LC circuit in Fig. 46 resonates over a broad band, large absorption bandwidth can be possibly achieved when the resistive component R in Fig. 46, which is mainly determined by loss tangent of the substrates, is close to the wave impedance in free space. Examples are given as follows for metamaterial absorbers with dielectric substrates. The relative permittivity of physically realisable dielectrics can be expressed as summation of n resonant terms as follows10 (32) Figure 47 shows the permittivity with one resonant term ( ; A = 0·189; f _res = 9 GHz; f _rel = 50 GHz) and the permittivity with two resonant terms ( ; A ⁽¹⁾ = 0·078; ; ; A ⁽²⁾ = 0·088; ; ) and the frequency non-dispersive one (ϵ _r = 6·15×(1−0·1j)) respectively.323 The parameters determining the permittivity values have been optimised by using genetic algorithm to maximise the −10 dB absorption bandwidth of an ultra thin metamaterial absorber (D = 6·2 mm, g = 0·4 mm, t = 0·5 mm). The reflectivity of the absorber for different permittivity values of the substrate is shown in Fig. 48.323 It is found from Fig. 48 that the absorption bandwidth can be increased greatly when the substrate has a proper frequency dispersive permittivity.

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Figure 47.

Permittivity with different frequency dispersion (solid lines: ϵ_rwith one resonant term; dash lines: ϵ_r with two resonant terms; dash dot lines: constant ϵ_r; dot line in a: ideal for broadband resonance; dot lines in b: range of for −10 dB reflectivity when takes the values as the dot line in a): reproduced with permission from Ref. 323, copyright 2009, American Institute of Physics

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Figure 48.

Reflectivity of metamaterial absorbers made of dielectric substrates with different frequency dispersion (solid line: one resonant term; dash line: two resonant terms; dash dot line: frequency non-dispersive): reproduced with permission from Ref. 323, copyright 2009, American Institute of Physics

As pointed by Rozanov, the absorption performance of normal grounded slab absorbers is determined by the following expression10 (33) Actually, equation (33) is also applicable to metamaterial absorbers.323,347 It can be seen from equation (33) that if the x axis in Fig. 48 is changed to the wavelength in free space, the area enclosed by the x axis (reflectivity = 0 dB) and the reflectivity curve is limited by a constant determined by the relative static permeability μ _s and the physical thickness t of the substrate. Generally, an increase in the absorption band is at the expense of a decrease in absorption strength if the right hand side term in equation (33) is kept constant, which can also be found in Fig. 48.

From equation (33), we can get323 (34) where ρ ₀ is the acceptable maximum reflectivity over the absorption band.

By comparing equations (30) and (34), it can be found that the limit of the bandwidth is increased greatly by replacing the frequency non-dispersive substrates with appropriate frequency dispersive ones.

In Ref. 347, metamaterial absorbers were proposed by using non-uniform conducting strip arrays or rectangular patches arrays, whose periodic units are illustrated in Fig. 49. The non-uniform conducting arrays provided multiple resonances. As shown in Fig. 50, two absorption peaks are observed. Therefore, the metamaterial absorbers with non-uniform arrays have broader absorption bandwidths than those with uniform arrays. However, the periodicity of the non-uniform arrays is much larger than that of the uniform arrays. As a result, grating lobes341 shift to much lower frequencies.

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Figure 50.

Simulated reflectivity of metamaterial absorbers with non-uniform conducting arrays on top of 0·8 mm dielectric substrate (ϵ = 5·44×(1−0·1j)ϵ₀, L ₁ = 3·1 mm, L ₂ = 0·4 mm, L ₃ = 5·5 mm, L ₄ = 1·0 mm, L ₅ = 2·8 mm)

The bandwidth could be increased by incorporating magnetic materials with high permeability,312,323 but at the expense of increased weight. As demonstrated in Figs. 49 and 50, and in Refs. 337, 338 and 353–358, multiple resonance can be created in metamaterial absorbers by combining units with different resonant frequencies, so as to achieve broadband absorption. The absorption bandwidth can also be expanded by matching the effective lossy permeability and permittivity in a broadband, as demonstrated by Gu et al. in Ref. 359. As shown in Ref. 323, it is also possible to expand the absorption bandwidth by using frequency dispersive materials as the substrate of the resonant units.

It is well known that the absorption bandwidths of currently available metamaterial absorbers with conducting ground planes are still much below the theoretical limit. A practical approach to expand the bandwidth of metamaterial absorbers is to push it as close as possible to the theoretical limit.

Tuning mechanisms

Besides their inferior bandwidth as stated earlier, EM responses of most metamaterials are not tunable or controllable. Namely, once fabricated, their properties (such as working frequency and amplitude, etc) cannot be modified or altered. This could be a problem in cases where active or tunable responses are required. It is therefore appealing to develop smart or adaptive metamaterials which can be adjusted to have tunable or active responses to variable incident signals.

Tuning of metamaterials with non-linear insertions, such as diodes, varactors, relay or MEMS, has been proposed conceptually and realised experimentally.360 ^– 365 It has been proved theoretically that a non-linear metamaterials slab can be switched between transmitting and absorbing states by tuning the effective resistance of the resonant conductive elements. Self-tuning mechanism of non-linear split ring resonators with varactor diodes has been investigated theoretically362 and measured with waveguide system.363 Figure 51 shows photograph of a patch arrary metamaterials tunable with varactors.380 It has also been proved that structural tuning (relative shift of staggered lattice) can be used to adjust the resonance over a wide bandwidth.364 The tuning was realised by the staggered lattice shifting with a lateral displacement of every other layer. Similar tuning mechanism has also been used for reconfigurable metamaterials operating at Terahertz frequencies.365 Tunability of the SRR arrays at THz was realised through different bending at heating temperatures from 350 to 500°C.

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Figure 51.

Electromagnetic smart screen with patch array loaded with varactors: reproduced with permission from Ref. 380, copyright 2010, Elsevier

There has been report on metafilm as a two-dimensional metamaterials, constructed by a single layer surface distributed with electrically small scatters characterised by electric or magnetic polarisability densities. A metafilm composed of resonant magnetodielectric spherical particles could be used to achieve controllable surface characteristics through external bias magnetic fields.366 Electrically tuned active frequency selective surface (FSS) loaded with pin diodes has been used to constructed low microwave reflection layer with reflectivity varying as a function of diode bias current.367 ^– 369 Electrically tunable high impedance surface with periodic surface texture loaded with varactors is able to steer the reflected beam over ±40° in two dimensions which has potential for transmission or reflection applications.370 A reconfigurable beam steering reflector made of similar tunable high impedance surface can be tuned as adjusting the relative position between two layers of the circuit boards.371 The limitation of the mechanically tuned surfaces is that the respond of tuning is not prompt enough to meet the requirement of fast operating.

Electromagnetic smart screens (ESS) containing conductive strip arrays loaded with pin diodes have been studied both numerically and experimentally. Transmission coefficient of such screens can be simulated using the FEM, which has already been validated by free space measurement.372 Tunable EM properties were observed between 3 and 8 GHz, which could find applications in antenna designs. However, only two states, namely on and off, have been investigated.372 Recently, it was found that the effective properties of such metamaterials can be continuously adjusted over certain frequency ranges.373 These metamaterials could be used for both civil and denfence applications, such as hybrid radome, band stop filters, subreflectors and CA absorbers.

To increase tunability of the metamaterials or metafilms, other approaches than loading with electronic components or mechanical movements, have also been employed to tune their microwave responses. Among them, smart materials with electrically or magnetically adjustable properties are commonly combined with periodic metamaterials to achieve certain tunability. Ferroelectric374 or ferromagnetic thin films375 are normally employed as the control units of the smart structures or systems. Comparatively, it is not popular to drive actuators with magnetic field in practical applications, because producing a large and uniform magnetic field is more difficult.

Tunable microwave reflection coefficients of TiO₂ coated kaolinite and Y-doped BaTiO₃ electrorheological (ER) fluid have been reported.376 It was found that the magnitude of reflection coefficient of the BaTiO₃ ER fluid was reduced gradually when the particle concentration was low (25%). It decreased to a minimum value and then increased when the particle concentration was >25%. Recently, CNTs or graphene based components or structures have been paid more attention with potential application for sensor or actuator at microwave, millimetre wave or THz frequencies. For example, large tunability at radiowave frequency was realised in CNT–polymer composites with CNT loading close to the percolation ratio.377

Advantages and limitations of different tuning methods are summarised in Table 14. Although any materials with certain responsive stimulus can be used as the controlling elements of smart metamaterials, tunings with bias electrical field, magnetic field and mechanical force or movement are among the easiest ways currently. The carbon or ER fluid based metamaterials have better power handling capability as compared with those of diodes or varactors which usep–n junctions with certain power limit. However, responding times of the tunable materials could be many times longer than that of diodes due to their difference in the tuning mechanism. Also, the tunability of tunable materials is normally inferior than diodes. So, no single approach could be able to fulfill all of the request from real applications.

Tunability of smart metamaterials loaded with diodes

Traditionally, the properties of active FSS or phase switchable screen were calculated based on transmission line model.378 However, the one-dimensional transmission line model does not account the contribution of each scatter and control unit quantitatively. The MOM is a common algorithm to model the induced current of the wire elements in FSS.329 The FEM can be used to model geometries with extreme aspect ratio and anisotropic media, which has been proved by experimental results. It is also found that the FEM has better accuracy than the MOM for thick wire structures and anisotropic materials.372 Typical unit cell of the FSS sheet comprises two strips of conductors, power lines and a diode, as shown in Fig. 52. The diode is modeled using the lumped RLC boundary conditions with the circuit lumped parameters RLC. A plane wave with electric field E parallel to the conductors and wave vector k perpendicular to the layer surface illuminates the model at normal incidence. Boundary conditions of the PML are imposed on the surfaces that are perpendicular to the wave vector. Periodic or linked boundary conditions are applied to the surfaces parallel to the wave vector. The coherent transmission of the composite sheet is obtained from the ratio of the average transmitted electric field intensity to the incident field intensity.

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Figure 52.

Model of FEM and equivalent circuit of pin diode: reproduced with permission from Ref. 372, copyright 2008, John Wiley & Sons

Since most periodic metamaterials are designed based on resonating elements, shifting resonance frequency and damping the resonance peak could be the most effective ways to adjust the behaviours of metamaterials. These can be realised by tuning the circuit parameters RLC though bias voltages. Qualitatively, the resonance frequency f _res and amplitude A _res are described as a function of the RLC parameters (35) To understand the effect of circuit parameters on resonance frequency of the ESS, numerical model was solved with diodes of different capacitances, inductances and resistances.372 Figure 53 shows the dependence of resonance frequency on the capacitance value of the control unit. It is found that when the capacitance increases from 0·001 to 8 pF, the resonance frequency decreases from 9·6 to 4·8 GHz, which stands for 50% frequency shift. From 0·01 to 1 pF, the resonance decreases almost linearly with the capacitance with log–log scale. It also implies that equation (35) is applicable only for circuit parameters of certain ranges. When the inductance increases from 0·05 to 5000 nH, the resonance frequency decreases from 11·35 to 9·7 GHz only. It means that the pattern is not so sensitive to the change in inductance as compared to capacitance. In practice, it is unrealistic to adjust capacitance or inductance values of a component by a few thousand times. Circuit parameters of normal pin diodes or varactors are only variable by ∼10 times at microwave frequencies. Nevertheless, the simulation results predict the limitation in tunability of such structures and reveal the routes to maximise the resonance frequency of smart metamaterials.

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Figure 53.

Resonance frequency versus capacitance of component: reproduced with permission from Ref. 372, copyright 2008, John Wiley & Sons

Various EM smart absorbers have been proposed, which use a tunable single layer periodic resonating structure loaded with tunable components, such as varactor and pin diode.379,380 For example, the absorption peak of a patch ESS with thickness of 0·6 mm could be shifted from 4 to 5 GHz with the absorption reduced from 15 to 7 dB when the pin diodes were switched on.379 Patch structure was used because of its strong resonance. Figure 54 shows a unit cell of the smart absorber and equivalent circuit of the pin diode.380 In this study, the reflection coefficient was measured with a free space setup. The measurement setup included a vector network analyser, a power source, vertically mounted broadband transmitting and receiving lens horn antennas, pyramidal absorber and a styrofoam board to hold the sample. They were mounted on a three-deck wooden frame to minimise the unnecessary reflection from the environment. The measurement frequency range was from 2 to 18 GHz. To eliminate multiple scattering between the sample and the horns, time domain gating was applied. Diffraction effects at the edges of the sample were minimised by the absorber attached to the styrofoam board.

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Figure 54.

Unit cell of smart absorber and equivalent circuit of pin diode: reproduced with permission from Ref. 380, copyright 2010, Elsevier.

The dependence of absorption on EM parameters (such as permittivity and permeability) of the substrate was investigated numerically in Ref. 380. The resonance frequency is a function of ϵ and μ, according to . Therefore, tunable smart absorbers can be achieved by varying dielectric or magnetic properties of the substrate.

Therefore, tunable responses of smart metamaterials can be realised by shifting the resonance frequencies and reducing the resonance peaks. Shift of resonance peak can be achieved by tuning capacitance or inductance of the control components or changing permittivity or permeability of the substrate. Tunabilities of representative smart metamaterial are summarised in Table 15. Different criteria are used to evaluate tunabable performances of different types of smart metamaterials. Here, Δf _res/ f _res and ΔA _res/A _res are used, with meaning shown in equation (35) to evaluate the tunability of smart metamaterials, which was also adopted in Ref. 362.

Metamaterials with inductive components

Effective permeability produced by resonances in microwave frequency range has been observed in a variety of metamaterials comprising non-magnetic materials such as inductive patterns. For example, effective magnetic responses can be generated by using non-magnetic split ring resonator,283 short wire pairs or short strip pairs,381,385 as shown in Fig. 55a and b . Negative real permeability can be obtained at certain frequency bands. High dielectric constant materials, as well as a combination of conductors and dielectric materials, can also be used as artificial magnetic metamaterials with real effective permeability μ>1.386 ^– 388

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Figure 55.

Sketch of inductive patterns for magnetic metamaterials

However, the effective permeability and resonance effect of above mentioned metamaterials without using magnetic components is rather small. To amplify the inductive behaviour of meatmaterials, it is necessary to use magnetic components. Inductive patterns, consisting of Cu coils wound on a magnetic core, have been widely used to produce LC resonances with considerably large imaginary effective permeability.383,384,389 ^– 394 Recent progress of such metamaterials has been comprehensively reviewed by Acher.382

A tunable metamaterial based on conducting coils loaded with an electric circuit containing a varactor diode was reported by Reynet and Acher.390 As a biased voltage was increased from 1 to 24 V, the varactor could be tuned to be from 15 to 2 pF. The maximum real and imaginary effective permeability of this metamaterial was 2–3, and its resonance frequency f _R could be shifted from 0·2 to ∼0·5 GHz. The degree of the shift was dependent on the the number of coil turns. Recently, a metafilm was fabricated by using a magnetic thin film, wrapped into a hairpin-like metallic structure. An insulator was used to prevent electrical contacts between the metal and the magnetic film,394 as shown in Fig. 55c . The metafilm exhibited two resonances, one below the gyromagnetic resonance frequency of the magnetic core and the other at much higher frequency. Large imaginary effective permeability of ∼100 and large negative real effective permeability of −55 at 0·4 GHz were observed. In addition, a torus with inner diameter of 20·9 mm and outer diameter of 22·2 mm, as a magnetic core, was fabricated by gluing bundles of CoFeSiB amorphous microwires. Metamaterial consisting of the core and Cu coils with various turns392,393 was similar to that shown in Fig. 55e . As the number of coil turns was increased from N = 0 to 16, the real and imaginary effective permeability increased and resonance frequency was shifted from 1·3 to 0·2 GHz.

Construction and properties of core–coil metamaterials

With the background discussed above, a metamaterial, consisting of a ferrite core and a set of coil with various turns, has been developed in the authors lab.383 A representative sample is shown in Fig. 55d . Typically, the cores had outer and inner diameters of 13·2 and 7·5 mm respectively, with thicknesses of 0·56–1·80 mm. The cores were wound by a Cu wire coil with 8–32 turns.

Figure 56 shows representatively permeability spectra of the metamaterials with different numbers of coil turns over 100 MHz–1 GHz measured using Agilent E4991A RF impedance/materials analyser with open-short-load calibration. It was found that effective permeability of the metamaterial strongly depends on permeability and permittivity of the core materials, size of the core and number of coil turns.384 Figures 57 and 58 show the dependences of maximum imaginary effective permeability , positive and negative real effective permeability and , and resonance frequency f _R on coil turns N, of two metalmaterials with t = 0·56 and 0·85 mm. Their magnetic responses have three important characteristics: greatly enhanced , large negative and f _R dependent on the turn number of coil.

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Figure 56.

Effective permeability of metamaterial with ferrite core and Cu coil (inset shows permeability and permittivity of ferrite core): core is Z-type hexagonal ferrite, with dimension of outer and inner diameters of 13·2 and 7·5 mm respectively, and thickness is 0·85 cm

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Figure 57.

Linear dependence of , and on coil turns N of metamaterials with t = 0·56 and 0·85 mm, where symbols are experimental data and dashed lines are predicted based on equations (41) and (42)

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Figure 58.

Dependence of f _R on N for metamaterial with t = 0·56 and 0·85 mm respectively, where dashed lines show reversely proportional correlation between f _R and N (inset: f _R is reversely proportional to product of t ^1/2 and N for two metamaterials)

Based on the equivalent lumped parameter model, an equivalent capacitance N ² C _eq is introduced to lump the total effects of the stray capacitance. C _eq acts as a capacitive load of the equivalent transformer. The input impedance can be written as (36) where L _eq is the equivalent inductance, given by (37) where t, R₂ , R₁ , and μ _c are the height, the outer radius, the inner radius and the complex permeability of the toroidal core respectively. On the other hand, the stray capacitance C _eq among the N conductors can be calculated based on a network method.395 Thus, effective permeability μ _eff of the metamaterial is simply expressed as (38) Figure 59 shows some typical permeability spectra measured (solid lines) and calculated (dot lines) based on equation (38) for two metamaterials with t = 0·56 and 0·85 mm. For the metamaterial with t = 0·85 mm, the calculated spectra are in a good agreement with the measured spectra. For the material with t = 0·56 mm, the calculated spectra has a small displacement from the measured spectra. However, the magnitudes of , and are comparable for the calculated and measured spectra. Therefore, the equivalent lumped parameter model can be used to well describe permeability characteristics of the metamaterial.

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Figure 59.

Comparison between measured (solid lines) and calculated (dashed lines) permeability spectra: black lines are for metamaterial with t = 0·56 mm and N = 16, blue and red lines are for those with t = 0·85 mm and N = 28 and 20 respectively; reproduced with permission from Ref. 384, copyright 2009, American Institute of Physics

Permeability theory

In equation (36), both L _eq and C _eq are complex functions. and are expanded to a polynomial expression of frequency, i.e. and . As the amplitude of resonance is sensitive to loss in the LC resonance, only the first term, α ₀, is taken in , and the first two terms, β ₀ andβ ₁, are taken in . The permeability spectrum shape of the metamaterial with a ferrite core and a coil can be obtained from equations (36) and (38) (39) where μ _c0 is the static real permeability. From equation (39), f _R , and respectively, are deduced to be384 (40) (41) (42) Figure 58 shows that the resonance frequency f _R is reversely proportional to N for the metamaterials with thickness t, of both 0·56 and 0·85 mm, which is well predicted by equation (40). Furthermore, consider that the inductance L _eq is proportional to thickness of the ferrite core t (equation (37)), f _R should be reversely proportional to the product of N and t ^1/2. Experimental data demonstrate that almost all of the f _R fall on the straight line of f _R versus 1/t ^1/2 N for the two metamaterials with t = 0·56 mm and t = 0·85 mm, as shown in Fig. 58. However, the data for the samples with less turns of coil deviate from the straight line slightly. The deviation could be attributed to the fact that the equivalent capacitance C _eq cannot be simply considered as a constant in the samples with less turns coil.

Equations (41) and (42) show that and are proportional to N, which is confirmed by the dashed lines in Fig. 57a and b . In addition, based on equations (41) and (42), it is concluded that, to obtain large and , high frequency magnetic and dielectric properties of the ferrite core play an important role; high real permeability, sufficiently low magnetic and dielectric losses are necessary.

Potential applications

Frequency tunable device

The metamaterial can also be used as frequency switchable device by using two sets of coils connected by a switch. Figure 60 shows measured permeability spectra of such metamaterial with two coils of eight turns. In OFF state, it has a resonance peak at 0·82 GHz, while in ON state, the coils are connected into one coil with 16 turns and the resonance is shifted to 0·46 GHz.

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Figure 60.

Measured permeability spectra of metamaterial, where solid and dashed lines are corresponding to ON and OFF states respectively: thickness of ferrite core is 1·8 mm

Meta fillers of composites

A meta filler is fabricated by using a thin plate ferrite piece and a coil wound on it. Figure 61 shows photographs of some meta fillers. Composites are fabricated by mixing the meatfillers with polymers (e.g. epoxy or silicone).

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Figure 61.

Metafillers consisting of ferrite pieces and Cu wire coils

Figure 62a shows effective permeability and permittivity of a composite made with silicone and the metafillers with a volume concentration of p = 0·3. The composite has an outer diameter of 14 mm, inner diameter of 6 mm and thickness of ∼2 mm. It has a of 13 at 1·25 GHz and a of 8. Based on the values of μ and ϵ, reflection loss RL–f, of the composite can be evaluated. As shown in Fig. 62b , A minimum RL≤−15 dB is achieved at 1·25 GHz and the per cent bandwidth W _p for RL≧−10 dB is 5·3%, at such a thickness. The ratio of thickness to wavelength is <0·009, which can be considered as a thin EM attenuation material at low microwave frequency, L band. However, narrow band is a main drawback of the composite with the metafillers, which remains as a challenge to be widened.

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Figure 62.

a measured permeability spectra and b predicted reflectivity properties of composite made with silicone and metafillers with volume fraction of p = 0·3

Metamaterials with periodic inductive patterns

A ring type of metamaterial was fabricated by gluing the ferrite coil pieces. An example is shown in Fig. 55e . The ring has outer and inner diameters of 12·5 and 7·5 mm respectively. Length, width and thickness of the ferrite pieces are about 5, 2·5 and 1 mm respectively. Cu wire coil has N = 12.

The complex permeability and permittivity, of the ring metamaterial, measured using PNA with 14 mm coaxial airline, are shown in Fig. 63a . is as large as 80, is ∼40, ϵ′is ∼9 and ϵ″ is close to zero. RL–f curve predicted based on μ and ϵ, is shown in Fig. 63b . It has a RL<−16 dB at the frequency of 0·44 GHz. The ratio of the thickness (1 mm) to the wavelength is only 0·0015. However, the bandwidth W _p is only 2%, which is too narrow. The reflectivity of the metamaterial was also simulated using the commercial software HFSS, based on periodical inductive patterns, as shown in Fig. 55f . The simulated and experimental RL–f curves are fairly consistent with each other. The metamaterial will be a candidate as ultra thin EM attenuation materials at UHF band, if the bandwidth can be expanded.

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Figure 63.

a measured permeability and permittivity spectra and b RL–f curves measured and simulated from permeability and permittivity of composite

Mg ferrite based ceramics

Magnesium ferrite (MgFe₂O₄) has a cubic spinel type structure, with a lattice constant of a = 0·83998 nm and space group . It is a well known soft magnetic n-type semiconductive material, with high resistivity and low magnetic and dielectric losses. Magnesium ferrite and its derivatives have been widely used in microwave technologies.411 ^– 413

Pure MgFe_1·98O₄ ceramics was found to have close permeability and permittivity of 6 and very low magnetic and dielectric loss tangents, over 2–30 MHz (high frequency band). The MgFe_1·98O₄ ceramics was sintered at 1125°C with a density of 3·1 g cm⁻³, which is ∼68·5% of its theoretical density (4·523 g cm⁻³). This can be attributed to the fact that MgFe_1·98O₄ ceramics has a poor sinterability. For real applications, materials with poor densification may suffer from mechanical problems. Almost fully dense MgFe_1·98O₄ ceramics should be sintered at temperatures of >1200°C. However, high temperature sintering would lead to high dielectric loss tangent of ferrite ceramics, due mainly to the formation of Fe²⁺, which increased the conductive loss and hence the total dielectric loss tangent. Therefore, to develop ferrite ceramics with low dielectric loss tangent, it is necessary to improve their sinterability.

Using sintering aids is one of the most popular techniques to improve the sintering behaviours of various materials. Various sintering aids have been used for ferrite ceramics in open literature.414 ^– 427 CuO and Bi₂O₃ are two representative sintering aids for ferrite ceramics. CuO can be incorporated into the chemical formula of spinel or barium ferrites. CuO was reported to decompose into Cu₂O, which has a low melting point. In the presence of Cu₂O, a eutectic Cu rich liquid phase may be formed at even lower temperatures than the melting point of Cu₂O. This cu rich liquid phase provided an environment to facilitate liquid phase sintering. Specifically, Bi₂O₃ is not able to enter lattice of spinel ferrites. However, similarly, with a low melting point (∼820°C), Bi₂O₃ forms liquid phase layer during sintering at high temperatures and thus also providing liquid phase sintering.

Sintering behaviour, grain growth, magnetic and dielectric properties of Mg_1−xCu_xFe_1·98O₄ ceramics have been systematically studied.402,403 It was found that, with increasing content of Cu from x = 0·1 to x = 0·30, shrinkage onset temperature of the samples gradually decreased, with peak shrinkage rate decreasing from 1214 to 1055°C. Comparatively, the shrinkage onset temperature of MgFe_1·98O₄ was >1250°C. It was very easy to attain 95% of their theoretical densities for Mg_1−xCu_xFe_1·98O₄ ceramics, while the relative density of MgFe_1·98O₄ was only 94% after sintering at 1250°C for 2 h. Typically, the sintering temperatures of Mg_1−xCu_xFe_1·98O₄ were nearly 200°C lower than that of MgFe_1·98O₄.

The Mg_1−xCu_xFe_1·98O₄ ceramics also processed different microstructures from MgFe_1·98O₄. The poor densification behaviour of MgFe_1·98O₄ is probably attributed to the presence of rigid skeleton structure with many point contacts, which requires a high temperature to collapse. The introduction of Cu not only altered the densification behaviour of MgFe_1·98O₄, but also promoted its grain growth. For example, the grain sizes of MgFe_1·98O₄ ceramics were <3 μm after sintering at 1250°C for 2 h, which were almost an order of magnitude smaller than those of Mg_1−xCu_xFe_1·98O₄.

The average grain size of the Mg_1−xCu_xFe_1·98O₄ ceramics did not show a monotonic increase with Cu concentration. At a given sintering temperature, the average grain size was maximised at x = 0·20. The variation in grain size for Mg_1−xCu_xFe_1·98O₄ ceramics was explained in terms of the mechanism for the grain growth. During liquid phase sintering, grain growth occurs via a dissolving/solution precipitation process. Energetically, small grains are less stable than large ones due to their higher specific surface area. As a consequence, small grains would be dissolved in the liquid phase layers. Once the concentration of the dissolved phase reached a critical level, precipitation took place. This means that larger grains grow at the expense of smaller grains. It also means that small grains have to ‘swim’ through a barrier (liquid phase layer) to combine with a large grain. At low concentration (x<0·2), it is understood that an increase in the amount of Cu resulted in an increase in the coverage of the grains by the liquid phase layers, and this was beneficial to grain growth. As a result, the average grain size increased with increasing concentration of Cu. Once a critical point was reached at which all grains were covered by the liquid phase, further increase in the Cu concentration would lead to an increase in the thickness of the liquid layers. An increased thickness of the liquid layers means a widened diffusion path, i.e. it would take longer time for smaller grains to reach the larger ones. Hence, the grain growth rate of the samples above the critical concentration of Cu would be lower than that of the samples below the critical concentration of Cu. In other words, the amount of the liquid phase became saturated when its concentration reached the critical point (x = 0·20).

Electrical properties of ferrite ceramics are closely related to their microstructures. Direct current resistivity is one of the most important parameters of ferrite ceramics. In general, high resistivity is required for most applications. The dc resistivities of ferrite ceramics are determined by several mutually related factors, including composition, density (porosity), grain size, crystal structure perfection, microstructural homogeneity and impurity levels. The presence of porosity usually increases the dc resistivity of ferrite ceramics, since air/vacuum is a good insulator if the pores are closely trapped and uniformly distributed. Otherwise, porosity can reduce resistivity of ferrite ceramics. Another factor that greatly reduces the dc resistivities of ferrite ceramics is the formation of Fe²⁺ ions, due to electron hopping between Fe²⁺ and Fe³⁺. As the transfer of electrons from Fe²⁺ ion to Fe³⁺ ion occurs within the octahedral sites, it does not cause a change in the energy state of the crystal as a result of the transition. The abrupt drop in dc resistivity after sintering at 1250°C was due mainly to the formation of Fe²⁺ ions.402

The difference in microstructure between MgFe_1·98O₄ and Mg_1−xCu_xFe_1·98O₄ can be used to explain their difference in DC resistivities. MgFe_1·98O₄ and Mg_1−xCu_xFe_1·98O₄ had different porous characteristics. MgFe_1·98O₄ sample had a rigid skeleton structure, while Mg_1−xCu_xFe_1·98O₄ sample comprised rounded grains that were loosely compacted together. The pores in MgFe_1·98O₄ were isolated while the pores in Mg_1−xCu_xFe_1·98O₄ were interconnected. Consequently, the porosity of MgFe_1·98O₄ acted as an insulator, whereas the porosity of Mg_1−xCu_xFe_1·98O₄ could form easy conduction paths when conductive impurities (such as H₂O) were trapped.

High frequency permittivity of ferrite crystals is mainly due to the atomic and electronic polarisation in the ceramic grains. The permittivity of polycrystalline ferrite ceramics is further affected by their microstructure, grain size, density and the presence of impurities. The dependence of permittivity on grain size is explained by the Maxwell–Wagner effect,428 where ferrite ceramics are considered to comprise conductive grains separated by layers (grain boundaries) of lower conductivity. The increase in grain size reduces the volume fraction of the grain boundaries, resulting in an increased permittivity. Porosity (density) also has a double sided effect on the permittivity. Close pores (interior grains or at grain boundaries) will reduce the permittivity because the dielectric constant of air (pores) is 1. Open (interconnected) pores, with absorbed impurities (e.g. water) may increase the permittivity, due to the high dielectric constant of water. Structural defects/imperfections would also increase the polarisation.

The presence of Fe²⁺ in ferrites always leads to high permittivity because Fe²⁺ has a larger polarisation than Fe³⁺. Fe³⁺ ion has a stable d-shell configuration with spherical symmetry of the charge cloud, due to its five d-electrons distributed according to Hund’s rule, whereas Fe²⁺ ion has an extra electron as compared to Fe³⁺, which disturbs the symmetry of the electron cloud. As a result, the presence of Fe²⁺ increases the polarisation in ferrites. Hence, ferrites with a larger number of Fe²⁺ ions are likely to exhibit higher permittivity.

Dielectric loss tangent of polycrystalline ferrite ceramics is determined by several factors, for example, microstructures and the presence of impurities and imperfection in the ferrite structure. However, the most significant contribution to dielectric loss tangent comes from the conduction loss due to electron hopping between Fe²⁺ and Fe³⁺ ions, especially at low frequencies. In this respect, the increase in permittivity due to the presence of Fe²⁺ ions is generally undesirable because it is always accompanied by an extremely high dielectric loss tangent.

Owing to their improved densification and grain growth, Mg_1−xCu_xFe_1·98O₄ always had higher permittivity than MgFe_1·98O₄. A jump in permittivity and dielectric loss tangent (especially at low frequencies) is observed in the MgFe_1·98O₄ and Mg_1−xCu_xFe_1·98O₄ samples as the sintering temperature is increased from 1200 to 1250°C and 1100 to 1150°C, respectively. This was attributed to the formation of Fe²⁺ ions. The relative permittivity of Mg_1−xCu_xFe_1·98O₄ increased almost monotonically with increasing Cu concentration and sintering temperature. The increasing trend in relative permittivity was attributed to the increased grain size and improved densification due to the presence of Cu. The critical concentration of Cu was not observed in the permittivity of Mg_1−xCu_xFe_1·98O₄, probably due to the less pronounced porosity effect.

It was found that the concentration of Cu had no significant impact on magnetic properties (complex permeability) of the Mg_1−xCu_xFe_1·98O₄ ceramics. The effect of sintering temperature on complex permeability of the ferrites was well explained by a magnetic circuit model.64,403 The Mg_1−xCu_xFe_1·98O₄ ceramics had no very promising magneto-dielectric properties, due to their relatively high dielectric loss tangent. In this respect, CuO is not good enough as a sintering aid for ferrite ceramics in case that low dielectric loss tangent is a critical dielectric parameter.

Further improvement in dielectric and magnetic properties of Mg_1−xCu_xFe_1·98O₄ ceramics was achieved by introducing Co to form Mg_{0·90−x−y}Co_xCu_yFe_1·98O₄. A representative example was Mg_{0·90−x−y}Co_xCu_yFe_1·98O₄ (y = 0·10). As a result of the addition of Co, DC resistivity was increased by nearly an order of magnitude for the samples sintered at lower temperatures (1050 and 1100°C).403 This was attributed to the fact that the presence of Co altered the conduction mechanism of the ferrite ceramics. With the substitution of Co in ferrites, p-type conduction takes place via the hole transfer between Co²⁺ and Co³⁺,429,430 which compensates for the n-type conduction of the host ferrites. At a given sintering temperature, the permittivity of Mg_0·90−xCo_xCu_0·10Fe_1·98O₄ decreases almost constantly with increasing concentration of Co.

The magnetocrystalline anisotropy of most spinel ferrites is a relatively smaller negative value. Co ions contribute larger positive magnetocrysalline anisotropy. Introduction of Co is able to compensate or change the magnetocrystalline anisotropy of the host ferrites. Specifically, the Mg_0·85Co_0·05Cu_0·10Fe_1·98O₄ ceramics sintered at 1100°C for 2 h, had almost permeability and permittivity of ∼10, with both magnetic and dielectric loss tangents of <0·01, over 2–30 MHz. Therefore, the refraction of Mg_0·85Co_0·05Cu_0·10Fe_1·98O₄ (n = 10) is fairly higher than that of MgFe_1·98O₄ (n = 6).

Li ferrite based ceramics

Li_0·50Fe_2·50O₄ has a high Curie temperature (670°C), high resistivity and low magnetic and dielectric losses.406 ^– 408 However, pure Li_0·50Fe_2·50O₄ cannot be fully sintered at temperature of <1100°C, due to its poor densification characteristics. The effect of Bi₂O₃ on densification, microstructural development, dielectric and magnetic properties of Li_0·50Fe_2·50O₄ ceramics has been systematically investigated.406 ^– 408

As shown in Fig. 65, 1 wt-%Bi₂O₃ brought down the linear shrinkage peak temperature of Li_0·50Fe_2·50O₄ from ∼1100 to 900°C and increased significantly the maximum shrinkage rate and the final linear shrinkage of Li_0·50Fe_2·50O₄ 406 The enhancement in densification was also clearly demonstrated by the measured densities of the ferrite ceramics, as shown in Fig. 66, and representative SEM images shown in Fig. 67.406 Combined with the grain growth behaviors of the materials, this improvement was readily attributed to the presence of liquid phase sintering mechanism with the addition of Bi₂O₃, which is similar to that observed in the Mg_1−xCu_xFe_1·98O₄ ceramics discussed above.

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Figure 65.

Sintering behaviours of Li_0·50Fe_2·50O₄ ceramics with different concentrations of Bi₂O₃: reproduced with permission from Ref. 406, copyright 2008, Elsevier

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Figure 66.

Densities of Li_0·50Fe_2·50O₄ ceramics with different amount of Bi₂O₃ as function of sintering temperature: reproduced with permission from Ref. 406, copyright 2008, Elsevier

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Figure 67.

Representative SEM images of Li_0·50Fe_2·50O₄ ceramics sintered at 1000°C for 2 h a without Bi₂O₃ and b with 1%Bi₂O₃: reproduced with permission from Ref. 406, copyright 2008, Elsevier

Direct current resistivities of the Li_0·50Fe_2·50O₄ ceramics as a function of the contents of Bi₂O₃ were found to be quite interesting. As shown in Fig. 68, there was a minimum in resistivity was observed in the samples with 0·2%Bi₂O₃, almost irrespective with the sintering temperature.407 As the concentration of Bi₂O₃ was increased from 0·2 to 5%, the resistivity was increased by nearly three orders of magnitude. The relatively low resistivities of pure Li_0·50Fe_2·50O₄ and those with lower concentrations of Bi₂O₃, sintered at low temperatures, were due mainly to their poorly densified microstructures. Their loose compact microstructure of indicated the presence of open pores, which could absorb water vapors or other contaminants and thus decreased their dc resistivities.

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Figure 68.

Direct current resistivities of Li_0·50Fe_2·50O₄ ceramics sintered at various temperatures as function of concentration of Bi₂O₃ (solid line is guided for eyes): reproduced with permission from Ref. 407, copyright 2008, Elsevier

The dispersion of resistivity and dielectric constant of ferrite ceramics can be simply described by using the Koops model.99 In this model, polycrystalline ferrite ceramics are considered to consist of well conducting grains (with diameters of d ₂ and resistivity of ρ ₂ separated by layers of lower conductivity (with thickness of d₁ and resistivity of ρ ₁).431 As and , resistivity can be expressed by99 (43) Using this formula, the trend in dc resistivity of the Li_0·50Fe_2·50O₄ ceramics as a result of the addition of Bi₂O₃ was qualitatively understood. The grain resistivity ρ ₂ kept unchanged with the concentration of Bi₂O₃, because there was no reaction between Bi₂O₃ and Li_0·50Fe_2·50O₄. As a result, the dc resistivities of the samples were determined by x and ρ ₁. Because the grain size of the samples had only a slight decrease with increasing concentration of Bi₂O₃ (from 0·5 to 5%),406 both x and ρ ₁ were expected, which thus led to an increase in resistivity.

But this model was not able to explain the minimum resistivities of the samples with 0·2%. To understand this exception, it is necessary to closely examine the microstructure evolution of the Bi₂O₃ doped Li_0·50Fe_2·50O₄ ceramics. It was a multistep process. First, a liquid phase was formed during heating of the materials above the melting point of Bi₂O₃. The liquid layer surrounded and wetted grains by filling at grain boundaries. Second, densification and grain growth occurred in the presence of the liquid phase during heating and dwelling. Finally, during cooling process, the Bi₂O₃ rich liquid phase retracted from the two grain boundaries to triple and multiple grain junctions. The degree of retraction was dependent on the amount of the liquid phase.

It was expected that there should be a critical concentration below which all the liquid phase would be brought to grain junctions so that there would be no more liquid phase left at the two grain boundaries. In this case, the two grain boundaries became clean, as was reported in Mn–Zn ferrite.418 Samples with clean grain boundaries were expected to have low resistivities, because both x and ρ ₁ in the above mentioned formula become smaller. This could be the possible reason why the dc resistivities of the 0·2% samples are lower than those of the pure ones.

This assumption was supported by dielectric properties of the 0·2%Bi₂O₃ doped Li_0·50Fe_2·50O₄ ceramics. As shown in Fig. 69, the sample sintered at 1100°C for 2 h had an extremely high real and imaginary permittivity, especially at low frequencies. With a similar model mentioned above, the static value ϵ _s of the apparent relative permittivity ϵ _r of polycrystalline ferrite ceramics can be given by432 (44) where ϵ _s can be represented by the real permittivity at 1 MHz, ϵ _i is the relative permittivity at infinite frequency (at 100 MHz), d ₁and d ₂ have similar definition as in equation (43). The extremely high permittivity of the 0·2% samples was closely related to their very small effective thickness of d ₁ due to the relatively clean two grain boundaries. It was found that to achieve sufficiently low dielectric loss tangent the content of Bi₂O₃ should be 3% and lowest dielectric loss tangent was obtained in the sample sintered at 900°C for 2 h.407

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Figure 69.

Complex permittivity of 0·2%Bi₂O₃ doped Li_0·50Fe_2·50O₄ ceramics sintered at 1100°C for 2 h: reproduced with permission from Ref. 407, copyright 2008, Elsevier

Real permeability of the Li_0·50Fe_2·50O₄ ceramics with promising dielectric properties was much higher than their permittivity. To bring down permeability of the ferrite, Co was used to substitute Li in the form of Li_{0·50−0·50x}Co_xFe_{2·50−0·50x}O₄ (x = 0–0·07). The static permeability values, of the Li_{0·50−0·50x}Co_xFe_{2·50−0·50x}O₄ samples, sintered at different temperature, as a function of concentration of Co, are depicted in Fig. 70.408 The increase in permeability with increasing sintering temperature at a given composition was attributed to the increase in grain size of the materials. The variation trend in static permeability was explainable by both the single-ion model and the domain wall stabilisation effect of Co ions.

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Figure 70.

Real permeability (at 1 MHz) of Li_{0·50−0·50x}Co_xFe_{2·50−0·50x}O₄ ceramics sintered at different temperature as function of concentration of Co (inset shows curves of real permeability versus concentration of Co over x = 0·03–0·07): reproduced with permission from Ref. 408, copyright 2008, Elsevier

In Li_0·50Fe_2·50O₄, Li and Fe ions contributed to negative magnetocrystalline anisotropy, while Co ion provided a very large positive anisotropy. Therefore, when a small amount of Co was added into Li_0·50Fe_2·50O₄, its total magnetocrystalline anisotropy would be varied from a negative value to a positive value. In this case, the absolute anisotropy would experience a minimum at a certain concentration of Co. Permeability of a polycrystalline ferrite is contributed by domain wall motion and spin rotation.433 The permeability due to spin rotation can be expressed as: (where M _s is the saturation magnetisation and k is the magnetocrystalline anisotropy constant). According to the single ion model,434 the magnetic ions in ionic crystals like ferrite are isolated by other surrounding anions so that the total magnetic anisotropy is determined by the sum of individual magnetic ions. Since Li_{0·50−0·50x}Co_xFe_{2·50−0·50x}O₄ is a solid solution of Li_0·50Fe_2·50O₄ (−8·5×10⁴ erg cm⁻³) and CoFe₂O₄ (180×10⁴ erg cm⁻³), its magnetocrystalline anisotropy constant could be calculated at different concentrations of Co. A minimum absolute value was obtained at x = 0·05, which implied that this composition was expected to have maximum permeability, but the experimental peak was at x = 0·01.408 It means that the experiment result could be explained solely by using this model.

The effect of Co ions on domain wall stabilisation should also be taken into account. The ordering of Co²⁺ ions at B sites of spinel structure induced local uniaxial anisotropy (Ku), especially in the presence of cation vacancies. Co substitution usually produces p-type conduction in ferrite, due to the electron transfer between Co²⁺ and Co³⁺. As a Co²⁺ is oxidised to a Co³⁺, a cation vacancy is formed. Therefore, Co ions have a function to immobilise domain walls. The locally induced anisotropy caused by the cation vacancies also increases with Co concentration. This additional effect made the maximum permeability happen at lower concentrations of Co. Moreover, Co³⁺ ions acted as a pinning centre to immobilise domain wall movement, which also made permeability to start decreasing at lower concentration of Co. Collectively, the maximum permeability appeared at x = 0·01 instead of 0·05.

Representative magnetodielectric properties of the Li_{0·50−0·50x}Co_xFe_{2·50−0·50x}O₄ (x = 0·032) ceramics sintered at 900°C for 2 h are shown in Fig. 71.408 It was found that the samples with Co concentration between x = 0·030 and x = 0·035 possessed promising magnetodielectric properties. The real permeability and permittivity ϵ′≈μ′≈13−15) of the Li–Co ferrite ceramics obtained in the present study were higher than those of ferrite composites (ϵ′≈μ′≈6−7)400,401 and Mg ferrite based ceramics (ϵ′≈μ′≈6−12)402 ^– 405 discussed above.

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Figure 71.

Magnetodielectric properties (over 3–30 MHz) of Li_{0·50−0·50x}Co_xFe_{2·50−0·50x}O₄ (x = 0·032) ceramics sintered at 900°C for 2 h: reproduced with permission from Ref. 408, copyright 2008, Elsevier

Ni ferrite based ceramics

The effect of Bi₂O₃ on the properties of nickel ferrite (NiFe_1·98O₄) ceramics is similar. Pure NiFe_1·98O₄ cannot be fully sintered at temperatures of below 1200°C. The addition of 3%Bi₂O₃ led to full densification of NiFe_1·98O₄ ceramics at 1050°C.409 To obtain a dielectric loss tangent of <10⁻², the concentration of Bi₂O₃ should be higher than 5%, which was higher than that required by Li_0·50Fe_2·50O₄. The sample doped with 5%Bi₂O₃, sintered at 1050°C for 2 h, had promising magnetodielectric properties, together with sufficiently low magnetic and dielectric loss tangent. Its real permeability and permittivity were ∼12 over 3–30 MHz. Modification of NiFe_1·98O₄ with small amount of Co further improved its magnetic and magnetodielectric properties. For example, magnetic dielectric tangent of the Ni_0·99Co_0·01Fe_1·98O₄ ceramics sintered at 1050°C for 2 h was reduced by two time as compared to that of NiFe_1·98O₄. The matching frequency of Ni_0·98Co_0·02Fe_1·98O₄ ceramics was extended up to 90 MHz (VHF band), which was not achievable in Mg ferrite and Li ferrite based ceramics.

Nanosized ferrite ceramics

The above mentioned achievements indicate that it is difficult to develop magnetodielectric materials with matching real permeability and permittivity up to 100 MHz by using spinel ferrite ceramics processed via the conventional ceramic processing technique. Recent studies demonstrated that the matching frequencies of ferrites could be significantly pushed up by using nanosized ceramics. For example, a nanosized ferrite ceramic with a composition of Ni_0·35Zn_0·35Co_0·2Mn_0·05Fe_1·98O₄ possessed almost equal permeability and permittivity of ∼6, with magnetic loss tangent of 0·03 and dielectric loss of 0·008, over a frequency range of up to 200 MHz.435 The nanosized ferrite ceramics was derived from a fine powder prepared by a coprecipitation method, with a calcination temperature of 800°C and a sintering temperature of 900°C. A further extension in matching frequency up to 700 MHz was realised by using nanosized ferrite ceramics of Ni_0·5Zn_0·3Co_0·2Fe₂O₄.436,437 Their real permeability and permittivity were ∼5. In a latest report,438 the same authors developed a Ni–Zn nanosized ferrite ceramics, by using a small amount of Cu, i.e. Ni_0·4Zn_0·4Co_0·2Cu_0·02Fe_1·98O₄, which required a sintering temperature of as low as 900°C. The nanosized ferrite ceramics had unchanged permeability of 10·8 and permittivity of 6·5, with a magnetic loss tangent of 0·04 and dielectric loss tangent of 0·006, up to 200 MHz. Since the impedance is 1·3, which is higher than 1, it is still possible to further extend the upset frequency by introducing more content of Co.

Comparatively, barium ferrite ceramics have not been widely reported to show promising magnetodielectric properties. It was mentioned that matching real permeability and permittivity of 26 can be obtained in Z-type barium ferrite, with low loss tangent up to 500 MHz,396 but only magnetic properties were presented, no dielectric properties were available. Generally, barium ferrites have higher dielectric constant than most spinel ferrites due to the high dielectric polarisation of Ba²⁺ ions and higher resonant frequencies due to their large magnetocrystalline anisotropy. Therefore, barium ferrites would provide higher refraction index and thus would be more efficient for antenna miniaturisation and can push the applications to higher frequencies, which could not be achievable by using spinel ferrites. However, the phase formation and sintering temperatures of barium ferrites are higher than those of spinel ferrites. High temperature processing would inevitably promote the formation of Fe²⁺ ions, leading to high conductivity and high dielectric loss tangent. In this respect, to achieve low dielectric loss barium ferrite ceramics, they should be either sintered in O₂ environment or annealed at low temperatures in O₂ after normal sintering.

Potential applications in antenna miniaturisation by using this class of materials have been reported in the open literature,440,441 which is not within the scope of this paper.