1. Introduction
Hexaferrite materials have attracted significant research interest in the past several decades owing to their interesting physical properties, such as their hard magnetic, magnetoelectric, electromagnetic absorption and magneto-dielectric properties. M-type Sr hexaferrites SrFe
12O
19 (SrM) are well-known hard magnetic materials used in permanent magnets because of their favorable hard magnetic properties, excellent phase stability, and low material cost [
1,
2]. The magnetic properties of SrM can be altered to become either harder or softer through cation substitutions. It has been reported that cation co-substitution of La–Co or La–Ca–Co into SrM increase the magnetocrystalline anisotropy [
3,
4], resulting in an enhancement of the permanent magnet performance, while, in contrast, those of Co
2+–Ti
4+ [
5,
6,
7], Ti
2+–Mn
4+ [
8,
9,
10], Mn
2+–Zr
4+ [
11], and Mn
4+–Zn
2+ [
12] result in a decrease in magnetocrystalline anisotropy. Cation-substituted SrM is also a promising candidate for high-frequency soft magnetic devices such EM wave absorbers [
6,
10,
11,
12,
13,
14,
15].
When EM waves are irradiated into a material, the interactions of absorption, reflection, and transmission are classified based on the complex permittivity ε = ε′ −
jε″ and permeability, μ = μ′ −
jμ″ of the material. The imaginary parts of the permittivity (ε″) and permeability (μ″) are closely related to EM absorbing performances through the dielectric or magnetic loss mechanism, respectively. In addition, good impendence matching characteristics that are functions of these ε′, ε″, μ′, and μ″ material parameters are also important for the high EM absorbing performances without high EM reflection [
16]. Recently, improved EM absorbing or shielding properties at GHz range have been reported by designing the nanocomposites where EM active materials are employed in template materials [
17,
18,
19]. In the research, high EM absorbing performances with a relatively broad absorption bandwidth could be achieved through controlling the composite structures and its complex permittivity and permeability properties. The EM wave absorption of insulating hexaferrites is mostly dependent on the magnetic loss mechanism, which is closely related to the imaginary part of the permeability (μ″). The μ″ of hexaferrites increases at the ferromagnetic resonance (FMR) frequency (
fFMR), which is related to the magnetic anisotropy field (
Hani) by the equation below [
20], where γ is the gyromagnetic ratio and μ
0 is the permeability of vacuum.
SrM has a high
fFMR of ~50 GHz, which is too high for hexaferrites to function as EM absorbers in the commercial radar frequency range, such as the X-band (8–12 GHz) and Ku-band (12–18 GHz). It has been reported that Co–Ti co-substitution effectively decreases the
fFMR from 50 to a few gigahertz for a substitution
x range of 0 ≤
x ≤ 1.5 for SrFe
12−2xCo
xTi
xO
19 [
5]. In our previous research [
7], the EM absorption properties of Co–Ti-substituted SrM were investigated. The
fFMR of Co–Ti substituted M-type Sr-hexaferrites (1.1 ≤
x ≤ 1.3) changed gradually from 6 to 15 GHz, which included the X-band (8–12 GHz) of interest in terms of radar applications. It was demonstrated that the EM absorption area can vary according to the gradual shift of the
fFMR. As cobalt is an expensive element, it is important to find other substitution elements that are more price competitive. The EM absorption properties of Ti–Mn [
8,
9,
10] and Mn–Zr [
11] substituted M-type hexaferrites have been reported. However, systematic studies with varying substitution amounts and correlations among composition, magnetic properties, and EM absorption properties are rare. In particular, to the best of our knowledge, the EM absorption properties of Zn–Zr substituted M-type hexaferrites have not yet been reported. In this study, Zn–Ti, Mn–Ti, and Zn–Zr co-substituted SrM with the chemical formula SrFe
12−2xM
1xM
2xO
19 (0 ≤
x ≤ 2.0, M
1 = Mn or Zn; M
2 = Ti or Zr) were synthesized, and their crystalline structures, microstructures, high-frequency permeability, permittivity, and EM absorption properties were systematically studied.
3. Results and Discussion
Figure 1a–c shows the XRD patterns of the Zn–Ti, Mn–Ti, and Zn–Zr substituted SrM (0 ≤
x ≤ 2.0) powders after second calcination at 1250 °C. The diffraction peaks of the samples were indexed based on the international center for diffraction data (PDF search number; SrM: 00-033-1340) and the hexagonal magnetoplumbite structure with the space group P6
3/
mmc (ICDD 0801198). As shown in
Figure 1a, Zn–Ti substituted SrM (Zn–Ti:SrM) exhibits a single M-type hexaferrite. It is believed that Zn–Ti is fully soluble in the SrM phase in the substitution range of
x ≤ 2.0. For the case of Mn–Ti:SrM shown in
Figure 1b, a single M-type phase can be identified for
x ≤ 1.5 and a small number of second phase peaks of Fe
2TiO
5 can be observed. Unidentified secondary phase peaks are denoted by an asterisk (*). Unlike Zn–Ti and Mn–Ti:SrM, Zn–Zr:SrM exhibits large second phase peaks of ZnFe
2O
4, SrZrO
3, and ZrO
2 for
x ≥ 1.5 in
Figure 1c. For
x = 2.0, ZrFe
2O
4 exhibits a primary peak. In order to reveal the solubility limit of Zn–Zr (
x) in SrM, additional XRD analysis was carried out on samples with
x between 0.6 and 1.1 with an interval of 0.1. A clear second phase peak of the ZrFe
2O
4 phase starts appearing at
x = 1.0 and its intensity grows larger with increasing
x. In the inset of
Figure 1c, the (220) peaks of the samples around 2θ = 65° are presented. Going from
x = 0 to
x = 0.5, the peak shift to the left is large, and the peak position slightly moves to the left between
x = 0.5 and
x = 1.0, but beyond that the peak position does not change. For all samples shown in
Figure 1a–c, the lattice parameters,
a and
c, are calculated from the values of
dhkl corresponding to the (2011) and (220) peaks according to the following equation:
where
dhkl is the interplanar spacing, and
h,
k, and
l are the Miller indices. The values of
a,
c, and the cell volume of the sample are listed in
Table 1, and their % changes are plotted in
Figure 2a–c.
For Zn–Ti and Mn–Ti substitution (0
≤ x ≤ 2.0), shown in
Figure 2a,b,
a,
c, and the cell volume increase gradually with increasing
x. Meanwhile, for the Zn–Zr substitution shown in
Figure 2c, the increase in lattice parameters with
x is much greater, but at
x = 1.0 and above the cell parameter values are constant. Based on the lattice changes with substitution amount
x, the solubility limit for Zn–Ti and Mn–Ti is estimated to be above
x = 2.0, and for Zn–Zr, it is estimated to be
x = ~1.0.
The high-frequency permeability characteristics of the three groups of samples, SrFe
12−2xZn
xTi
xO
19, SrFe
12−2xMn
xTi
xO
19, and SrFe
12−2xZn
xZr
xO
19, were evaluated. In the case of hexaferrites, utilization as an EM absorber in the GHz range requires a peak increase in μ″ in the corresponding frequency band, which can be caused by FMR phenomena.
Figure 3a–f show the μ′ and μ″ spectra of these samples. As can be seen in the μ′ spectra, the samples have μ′ values between 1.5 and 2.0, and μ′ commonly decreases to close to 1.0 in the range of
f < 1 GHz. This μ′ spectral transition (
f < 1 GHz) is associated with magnetic domain wall motion [
21]. In addition, the transition of μ″ in the frequency range of
f < 1 GHz corresponds to the magnetic loss associated with magnetic domain wall motion. Therefore, it is believed that domain wall motion cannot contribute to the permeability at frequencies higher than 1 GHz, and the peak increase of μ′ > 1 and μ″ > 0 at
f > 1 GHz is mostly caused by electron spin motions, that is, FMR [
6,
7]. It is known that non-substituted M-type Sr-hexaferrite, SrFe
12O
19, has
fFMR ~50 GHz. Thus, no μ″ peak is observed in the measured frequency range of
f ≤ 18 GHz. When Zn–Ti is substituted into SrM,
fFMR decreases with increasing
x. In
Figure 3a,b sharp increases in the μ′, μ″ peaks can be observed at the right edge. We can see that
fFMR is approximately 18 GHz for SrFe
12−2xZn
xTi
xO
19 (
x = 2.0), and that it is above 18 GHz for samples with
x < 2.0. For the case of Mn–Ti substitution (
Figure 3c,d), no clear peaks of μ′, μ″ spectra are absorbed at
f > 1.0 GHz for all samples. Meanwhile, a clear FMR signal is absorbed by the Zn–Zr substituted samples, as shown in
Figure 3e,f. In the vicinity of 10 GHz in the μ″ spectra, a peak from FMR is shown for
x = 1.0, and the height gradually decreases as
x reaches 2.0. For the sample with
x = 0.5, there is no FMR peak at
f >1 GHz because its
fFMR is greater than 18 GHz. Although the FMR peak is supposed to shift to a lower frequency upon increasing
x to 1.5, and 2.0, its position is almost the same. This is because even for
x higher than 1.0, no substitution of Zn–Zr can occur, as mentioned previously in
Figure 2c. In addition, the decrease in μ″ peak height with an increase in
x up to 2.0 is due to an increase in the volume fraction of the non-magnetic secondary phase (
Figure 1c).
Figure 4a–e show microstructures of the SrFe
12−2xZn
xZr
xO
19 (
x = 0, 0.5, 1.0, 1.5, 2.0) samples calcined at 1250 °C. The average grain size (
dg) roughly decreased with increasing
x (
dg = 1.0, 1.0, 0.82, 0.80, and 0.65 µm for
x = 0, 0.5, 1.0, 1.5, and 2.0, respectively). It is notable that samples with
x ≤ 1.0 only have a single M-type phase. Second phases (ZnFe
2O
4, SrZrO
3, and ZrO
2) are formed and increase with increasing
x for
x > 1.0, as shown in
Figure 1c. SEM-BSE (back scattered electron) images of the
x = 1.0, 1.5, and 2.0 samples are shown in
Figure 4f–h. In the
x = 1.0 sample (
Figure 4f), all grains show nearly equal contrast, but brighter grains begin to appear at
x = 1.5 (
Figure 4g), and brighter spots increase at
x = 2.0 (
Figure 4h). Considering the XRD analysis results (
Figure 1c) and average atomic weights of the second phases, the bright spots in
Figure 4g,h correspond with SrZrO
3.
Figure 5 shows the magnetization curves for the SrFe
12−2xZn
xZr
xO
19–epoxy composition (
x = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1) samples. Because the solubility limit of SrFe
12−2xZn
xZr
xO
19 was found to be approximately
x = 1.0, sample compositions with smaller intervals of
x below
x = 1.0 (
x = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1) were also studied. The saturation magnetization (4πM
S) and coercivity (H
C) values of these samples are presented in
Table 2. The 4πM–H curves in the low magnetic field range are shown in the inset. The 4πM
S of the sintered samples are expected to be twice these values because the volume fraction of the nonmagnetic epoxy binder is ~50%. The 4πM
S of the
x = 0.5 sample is 1.875 kG, and it decreases with increasing
x. The reason for this is that non-magnetic ions of Zn
2+-Zr
4+ are substituted for the magnetic Fe
3+ ions. It has also been reported that a small amount of Zn substitution (
x ≤ 0.3) into SrM could increase M
S due to a selective substitution of Fe in the down-spin state [
22,
23]. It is notable that the substitution amount (
x ≥ 0.5) in this study is too high to expect such an enhancement of M
S in the SrM. H
C decreases noticeably for an increase in
x from
x = 0.5 to
x = 0.7 but decreases slightly from
x = 0.7 to
x = 0.9 and remains roughly constant above
x = 0.9. The H
C value depends on both the intrinsic and extrinsic characteristics of the magnetic materials. Grain size is a dominating factor influencing H
C. It is well known that H
C decreases with increasing grain size of hexaferrites [
24,
25,
26]. Considering that the average grain size of the
x = 0.5 sample is larger than that of the sample with
x = 1.0, the smaller H
C for a higher
x is due to a strong intrinsic property change caused by the Zn–Zr substitution, which overcomes the disadvantageous extrinsic factor.
The real and imaginary parts of the complex permittivity (ε′ and ε″) and permeability (μ′ and μ″) spectra of the SrFe
12−2xZn
xZr
xO
19 (
x = 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1) powder–epoxy (10 wt%) composite samples are shown in
Figure 6a–d. In
Table 2, the real (ε′) and imaginary (ε″) parts of the permittivity at 1 GHz, the real part of the permeability (μs′) in the steady region after the first transition (~3 GHz), and the frequencies of the maximum μ″ values (
fFMR) are presented. In the ε′ and ε″ spectra shown in
Figure 6a,b, as the frequency increases, for all samples, ε′ decreases and converges upon ~7, and ε″ approaches zero. The real (μ′) and imaginary (μ″) parts of the permeability spectra are shown in
Figure 6c,d, the first transitions of μ′ and μ″ are associated with magnetic domain wall motion (
f < 2 GHz), and the peaks at higher frequencies (
f > 2 GHz) are caused by FMR. In the μ″ spectra (
Figure 6d), a gradual μ″ peak shift to the left is observed upon increasing
x from 0.7 to 0.9, and a very small peak shift can be found between
x = 0.9 and
x = 1.0. The μ″ peak frequency corresponds to
fFMR and is directly proportional to the magnetic anisotropy field (
Ha), as expressed in Equation (1). The change in
fFMR is related to an intrinsic property change and can be caused by cation substitution. This is consistent with the change in H
C shown in
Figure 5, as mentioned above. The μ″ peak positions and H
C values of the samples with
x = 0.9–1.1 are very similar, because the solubility limit of Zn–Zr in the M-phase is approximately
x = 1.0. The gradual increase in μs′ upon increasing
x up to 0.9 can be explained by Snoek’s limit law [
27], presented below:
Here, γ is a constant known as the gyromagnetic ratio, and Ms is the saturation magnetization value. A decrease in static real permeability (μs′) causes an increase in fFMR. This implies that changes in the high-frequency permeability property are governed by the intrinsic magnetic parameter of the magnetocrystalline anisotropy, which can be controlled by Zn–Zr substitution.
According to transmission line theory [
28], the reflection loss (RL), which implies the EM wave absorption performance, can be calculated using the following equations:
where
is the input impedance of the absorber,
is the characteristic impedance of free space,
c is the speed of light,
f is the frequency of the incident EM wave,
d is the thickness of the absorber, and ε
r and μ
r are the complex permittivity (ε
r = ε′
− jε″) and permeability (μ
r = μ′
− jμ″), respectively. Here, the measured μ′, μ″, ε′, and ε″ spectra can be used to obtain
for any thickness
d with respect to
f. RL calculations were plotted in square
f–
d maps, as shown in
Figure 7a–d. The region in which RL ≤ −10 dB, which implies EM absorptions exceeding 90%, is outlined by solid black lines. Inside this area, the regions in which RL ≤ −20, −30, and −40 dB are also outlined by solid lines.
In the RL map shown in
Figure 7a–i, the strong EM absorbing area at lower
d, marked with a rectangular box, starts to be observed at
x = 0.7, and it moves gradually with an increase in
x up to 1.0 (
Figure 7c–f). The left edge of the absorption area already appeared at the right edge of
Figure 7b for the sample with
x = 0.6. EM absorption in the marked area is caused by a magnetic loss mechanism, that is, FMR, which produces a peak in the μ″ spectra. Thus, the gradual movement of the EM absorbing area with
x = 0.7, 0.8, and 0.9 (
Figure 6c–e) is attributed to the μ″ peak shift shown in
Figure 6d. It is also observed that the absorption intensity in the RL maps for
x from 1.1 to 2.0 (
Figure 6g–i) becomes weaker. A decrease in the μ″ peak height shown in
Figure 3f is the reason for the weakening EM absorption. As previously mentioned, the decrease in μ″ peak height for the
x = 1.5 and 2.0 samples is due to an increase in the non-magnetic second phase.
Figure 8 shows the RL spectra of the sample (
x = 0.7, 0.8, 0.9, 1.0, 1.1) at the optimal thickness, at which the minimum RL (RL
min) point was located. The RL
min values and frequency of RL
min (
fRLmin) are presented in
Table 2. Each sample shows an RL
min < −30 dB, and
fRLmin shifts to a lower frequency with increasing
x.
fRLmin shifts to a lower
f in large steps as
x increases from 0.7 to 0.9, but it moves only slightly at
x ≥ 0.9. The tendency for changes in large steps up to
x = 0.9, and then for changes in very small steps for
x > 0.9, is the same for H
C,
fFMR, and
fRLmin. All these changes are related to the Zn–Zr substitution amount in the M-type phase and its magnetocrystalline anisotropy change. As shown,
fRLmin is similar to
fFMR for each sample, and FMR is the dominant EM absorbing mechanism in hexaferrites. The
x = 0.9 sample demonstrates EM absorption properties optimized for the X-band (8–12 GHz) with the lowest reflection loss (RL) of −45 dB and satisfying RL < −15 dB in the 8–13 GHz range, whereas the sample with
x = 0.8 shows an excellent Ku band (12–18 GHz) absorption performance, satisfying RL < −19 dB in the 11–18 GHz range.