Orientation-induced enhancement in electromagnetic properties of ZnFe2O4/SiO2/PANI core/shell/shell nanostructured disks

ZnFe2O4/SiO2/PANI (ZSP) core/shell/shell nanostructured disks are prepared and fabricated into paraffin-bonded ZSP composite rings with random, vertical, and horizontal orientations of the easy magnetization planes of the ZSP disks in the paraffin binder in order to study the effect of directional orientation of the easy magnetization planes on their electromagnetic properties. The easy magnetization planes induced by shape anisotropy and oriented by a magnetic field in the vertically oriented ring result in a general enhancement in permeability of 7–60% in the broad UHF–Ku (0.1–18 GHz) bands, while those in the horizontally oriented ring lead to a significant enhancement of 58–1100% in the low-frequency L and S (1–4 GHz) bands, in comparison with the randomly oriented ring. The observed permeability agrees with the theoretical prediction based on the Landau–Lifshitz–Gilbert equation and the Bruggeman’s effective medium theory. The horizontal and vertical arrangements of dipolar polarizations in the vertically and horizontally oriented rings give rise to 3–11% enhancement and weakening in permittivity, respectively, compared to the randomly oriented ring. The enhancement in permeability also improves and broadens the electromagnetic wave absorption in both vertically and horizontally oriented rings, especially in the L and S bands for the horizontally oriented ring.


I. INTRODUCTION
Electromagnetic (EM) wave absorbers based on magnetic/dielectric core/shell nanocapsules have been a main research focus to alleviate EM interference problems in recent years. [1][2][3][4][5] Core/ shell/shell nanocapsules have been evolved more recently to broaden the absorbing bandwidth and absorber thickness range by the bandwidth-broadening effect in various core/shell/shell material phases. [6][7][8] In fact, the bandwidth-broadening effect is underpinned by the cooperative effect of the multidielectric polarizations in permittivity and the broadened magnetic natural resonance in permeability. 8,9 However, the deficiency in the generally weak absorption caused by the intrinsically small permeability close to unity and the inadequate EM impedance match with the relatively large permittivity has greatly impeded the nanocapsules from commercial uses, especially for the low-frequency UHF (0.3-1 GHz), L (1-2 GHz), and S (2-4 GHz) bands. The applications include commercial radios, mobile communications, satellites, global positioning system (GPS), weather and surface ship radars, etc. [1][2][3][4][5] Today, magnetic cores (e.g., Ni, Fe, FeNi, Fe 3 O 4 , ZnFe 2 O 4 , etc.) with low-dimensional nanostructures (e.g., rod, disk, flake, etc.) have shown the ability to improve the permeability and exceed the Snoek's limit in the gigahertz frequency range because of the contribution of shape anisotropy-induced easy magnetization planes. 9-13 Moreover, Fe 3 O 4 nanoflakes with their easy magnetization flake planes oriented in a preferred direction by a magnetic field have exhibited an improved permeability and an extended Snoek's limit compared to the ones without a preferred orientation. 12 Therefore, complex ferrites, which are capable of showing a higher magnetocrystalline anisotropy when doped with Ni or Zn as well as a stronger shape anisotropy when prepared as a low-dimensional nanostructure, have great potential to enhance permeability and EM wave absorption performance via a directional orientation of their easy magnetization planes. 14 In this paper, we aim to investigate the effect of directional orientation of easy magnetization planes of magnetic nanostructured cores on the EM properties of core/shell/shell nanostructures. Accordingly, ZnFe 2 O 4 /SiO 2 /PANI (denoted as ZSP) core/shell/shell nanostructured disks having a disk-shaped anisotropic ZnFe 2 O 4 magnetic core coated by a 1 st amorphous SiO 2 insulating dielectric shell and a 2 nd amorphous PANI conducting dielectric shell are prepared. The ZSP disks are fabricated into three characteristic types of paraffin-bonded ZSP composite rings in the absence and presence of a dc magnetic field of controlled amplitude to randomly, vertically, and horizontally orient the easy magnetization planes of the ZSP disks during the cure of the paraffin binder. The complex relative permeability and permittivity of the ZSP composite rings are measured in the 0.1-18 GHz range, covering the UHF-Ku bands. The theoretical calculation on permeability is established by the Landau-Lifshitz-Gilbert (LLG) equation and the Bruggeman's effective medium theory (EMT) and is applied to explain the measured permeability with good agreements. The reflection loss is also determined from the measured complex relative permeability and permittivity to investigate the EM wave absorption performance.

II. EXPERIMENTAL DETAILS
The proposed ZSP core/shell/shell nanostructured disks were prepared using a three-step process described elsewhere. 9 In brief, the disk-shaped ZnFe 2 O 4 core was synthesized using a surfactant-assisted hydrothermal method involving the co-precipitation of ZnAc of 2 mmol and FeCl 3 of 4 mmol in a NaOH water solution of 3.3 mol/l as well as the heating of the mixture in a Teflon-lined stainless steel autoclave at 200 • C for 4 h. The 1 st SiO 2 shell was coated on the as-prepared ZnFe 2 O 4 products using a modified stöber method in a solution containing ethanol of 10 ml, water of 3 ml, NH 4 OH of 0.2 ml, and TEOS of 0.1 ml. The 2 nd PANI shell was coated on the as-prepared SiO 2 -coated ZnFe 2 O 4 products using a polymerization method in a mixture of water of 50 ml, SDS of 80 mg, aniline of 8 µl, and (NH 4 ) 2 S 2 O 8 of 10 mg.
Three characteristic types of paraffin-bonded ZSP composite rings, all having 30 wt.% ZSP products dispersed in an EM-transparent paraffin binder, were fabricated in a nonmagnetic brass mold with an inner diameter of 3.04 mm, an outer diameter of 7 mm, and a thickness of 2 mm. These included the ones with random, vertical, and horizontal orientations of the easy magnetization planes (i.e., the two major surfaces) of the ZSP products with respect to the two major torus surfaces of the ring-shaped brass mold during the cure of the paraffin binder (upper inset of Fig. 2). For ease of description, these ZSP composite rings are denoted as the randomly, vertically, and horizontally oriented rings, respectively. The vertically and horizontally oriented rings were formed by applying a dc magnetic field of 1 T amplitude to the vertical (or perpendicular) and horizontal (or parallel) directions of the two major torus surfaces of the ring-shaped brass mold, respectively, in a temperature-controlled chamber at 60 • C for 5 h. No orientation field was required for the randomly oriented ring.
The morphology of the ZSP products was examined by a JEOL JSM-6490 scanning electron microscope (SEM). The core/shell/shell interfaces of the ZSP products were investigated using a JEM-2100F transmission electron microscope (TEM) with an operating voltage of 200 kV. The complex relative permeability (µ r = µ ′ r − j µ ′′ r ) and permittivity (ε r = ε ′ r − jε ′′ r ) of the ZSP composite rings were measured by a transmission/reflection coaxial cable method in the 0.1-18 GHz range using an Agilent 5244A network analyzer. The EM wave incident direction was set along the thickness direction of the ZSP composite rings. The frequency ( f ) dependence of reflection loss is the input impedance of ZSP composite ring, Z 0 ∼377 Ω is the characteristic impedance of air, c = 3 × 10 8 m/s is the velocity of light, and d is the thickness of ZSP composite ring. Figure 1(a) shows the SEM image of a typical ZSP product. The product has a disk-shaped morphology with a diameter of ∼6 µm and a diameter-to-thickness ratio of ∼3:1 (not shown). The two major surfaces of the ZSP disks are the easy magnetization planes because of shape anisotropy.  Fig. 1(b). The periodic stripes of ∼0.254 nm lattice plane spacing, corresponding to the (311) planes of ZnFe 2 O 4 , confirm the crystalline state of the disk-shaped ZnFe 2 O 4 core. The 1 st SiO 2 shell and the 2 nd PANI shell are amorphous with thicknesses of ∼5 and ∼15 nm, respectively.

III. RESULTS AND DISCUSSION
The symbols in Fig. 2 show the measured f dependence of µ ′ r and µ ′′ r for the randomly, vertically, and horizontally oriented rings. The randomly oriented ring exhibits relatively smooth µ ′ r and µ ′′ r spectra, except for a small magnetic natural resonance at ∼1.7 GHz and a negative µ ′′ r in the 13.4-18 GHz range. In particular, the occurrence of the negative µ ′′ r suggests the transformation of electric energy into magnetic energy in the 2 nd conducting dielectric PANI shell of the ZSP disks via the generation of magnetic fields by the electric currents of EM waves. 9 The vertically oriented ring, besides the two small magnetic natural resonances at ∼4.2 and ∼11.7 GHz, has an enhancement of ∼7 and ∼60% in µ ′ r and µ ′′ r , respectively, throughout the whole measurement range of 0.1-18 GHz and covering the broad UHF-Ku bands, in comparison with the randomly oriented one. The horizontally oriented ring has a strong magnetic natural resonance at ∼1.4 GHz, leading to a maximal enhancement of ∼58 and ∼1100% in µ ′ r and µ ′′ r , respectively, in the low-frequency L (1-2 GHz) and S (2-4 GHz) bands. Moreover, µ ′ r and µ ′′ r are generally increased above 4 GHz due to the three higher frequency magnetic natural resonances at 3.1, 7.5, and 10.8 GHz. Comparing with the previous report on measuring the permeability tensor with an in-situ magnetic orientation field, 15 our vertically and horizontally oriented rings, owing to the pre-orientation of the easy magnetization planes of the ZSP disks by a magnetic field during the cure of the paraffin binder, do not require the in-situ magnetic orientation field in measurement and demonstrate an obvious enhancement in permeability.
In order to obtain an improved insight into the measured µ ′ r and µ ′′ r spectra in Fig. 2, a theoretical calculation on µ r was established by the LLG equation and the Bruggeman's EMT. As the double-shell is nonmagnetic and as thin as ∼20 nm, it is ignored from the calculation and the ZSP core/shell/shell nanostructured disk is treated as a ZnFe 2 O 4 nanostructured disk. The LLG equation can be described as 16,17 where M is the magnetization, H is the effective magnetic field including applied static and dynamic fields, anisotropy field, demagnetization field, etc., γ (=2.8 MHz/Oe) is the gyromagnetic ratio, α is the damping coefficient, and M s is the saturation magnetization. Consider a magnetic nanostructured disk having its easy magnetization planes randomly oriented with an incident EM wave (k) in the o-xyz coordinate system as shown in the lower inset of Fig. 2. Since the overall magnetization is zero, the applied static field is zero and the demagnetization field is negligible. H in Eq. (2) can be expressed by the applied dynamic field (h) perpendicular tok as well as the magnetocrystalline anisotropy field (H a ) along the easy magnetization planes of the magnetic nanostructured disk as follows: where H a represents the only static field counted in our case, M 0 is equal to the saturation magnetization M s , and ω is the angular frequency. Combining the Maxwell's equations with Eqs. (2) and (3), the permeability tensor can be obtained as 10-13 1 − sin 2 θ cos 2 θ −sin 2 θ sin ϕ cos ϕ − sin θ cos θ cos ϕ −sin 2 θ sin ϕ cos ϕ 1 − sin 2 θ cos 2 ϕ − sin θ cos θ sin ϕ − sin θ cos θ cos ϕ − sin θ cos θ sin ϕ 1 − cos 2 θ where ω 0 = γH a , ω m = γ4πM s , and ω ′ 0 = ω 0 + jωα. For the randomly oriented ring, 10,000 sets of θ and ϕ are randomly generated to calculate an equivalent average permeability tensor using Eq. (4). For the vertically and horizontally oriented rings, θ = 0 with ϕ = π/2 and θ = ϕ = π/2 are adopted, respectively, to determine the permeability tensor because the easy magnetization planes are along the magnetic field direction as shown in the upper inset of Fig. 2. It is noted that the permeability tensor determined for the vertically oriented ring is similar to the Polder tensor reported elsewhere. 10,15,18 The eigenvalues of the permeability tensors are thus the intrinsic permeability (µ i ). Assuming the paraffin and ZnFe 2 O 4 are both spherical (the double-shell has been neglected in the previous steps due to its nonmagnetic and thinness nature), and since the volume fraction of ZnFe 2 O 4 (∼0.07) is well below the theoretical percolation threshold of 0.33, the effective complex permeability (µ eff ) can be approximately calculated by Bruggeman's EMT as 17,19 p where p is the volume fraction of ZnFe 2 O 4 and µ m (=1) is the permeability of paraffin. It should be noted that although the paraffin-bonded ZSP disks are approximated by paraffin-bonded ZnFe 2 O 4 spheres and the relatively complicated effects/interactions such as EM energy transformation, interfacial effects of core/shell/shell nanostructures, particle shape, etc. are not taken into account, the standard effective medium approximation underlying the Bruggeman's EMT is still applicable to describing the trend and natural resonances in permeability spectra. 17,[20][21][22] In our previous report, M s of ZSP nanostructured disks was measured to be 24.13 emu/g. 9 According to 30 wt.% ZSP disks in our case, and using H a = 800 Oe and α = 0.3 in the calculation, the f dependence of µ ′ eff and µ ′′ eff for the randomly, vertically, and horizontally oriented cases are calculated and plotted as lines in Fig. 2. It is seen that µ ′ eff and µ ′′ eff of the randomly oriented case agree well with the measured µ ′ r and µ ′′ r . The good agreement is also applied to the vertically oriented case, except for the higher magnetic natural resonance at 11.7 GHz. The strong magnetic natural resonance as measured at ∼1.4 GHz in the horizontally oriented ring can still be predicted by the model even though the µ ′ eff and µ ′′ eff values are ∼60% reduced from the measured µ ′ r and µ ′′ r values. The discrepancy may be caused by the relatively complicated effects/interactions mentioned in the previous paragraph, including EM energy transformation, interfacial effects of core/shell/shell nanostructures, particle shape, etc. 23 Nevertheless, the model can be used to predict the shape anisotropy and directional orientation dependent transport anisotropy. 15 Figure 3 shows the measured f dependence of ε ′ r and ε ′′ r for the randomly, vertically, and horizontally oriented rings. All types of rings demonstrate similar quantitative trends in the ε ′ r and ε ′′ r spectra. The vertically and horizontally oriented rings exhibit ∼6% increment and decrement in ε ′ r , respectively, compared to the randomly oriented ring. In the vertically oriented ring, most of