Corresponding author: Vladimir G. Kostishin ( drvgkostishyn@mail.ru ) © 2019 Alexey S. Semenov, Aleksey G. Nalogin, Sergey V. Shcherbakov, Alexander V. Myasnikov, Igor M. Isaev, Vladimir G. Kostishin, Natalya E. Adiadulina, Albert A. Alekseev, Evgeny A. Belokon, Marina P. Mezentseva.
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Citation:
Semenov AS, Nalogin AG, Shcherbakov SV, Myasnikov AV, Isaev IM, Kostishin VG, Adiadulina NE, Alekseev AA, Belokon EA, Mezentseva MP (2019) Measurement of effective magnetic anisotropy field and ferromagnetic resonance bandwidth at ferromagnetic resonance frequency in magnetically uniaxial hexagonal ferrites. Modern Electronic Materials 5(1): 3339. https://doi.org/10.3897/j.moem.5.1.51295

In this work we have considered metrological problems and measurement of magnetic parameters and presented methods of measuring effective magnetic anisotropy field H_{Aeff} and ferromagnetic resonance bandwidth ∆H in magnetically uniaxial hexagonal ferrites in the electromagnetic microwave working frequency range. The methods allow measuring H_{Aeff} in the 10–23 and 28–40 kE ranges and ∆H in the 0.5–5.0 range. One method (suitable for wavelength measurements in free space in the 3mm wavelength range) has been implemented for the 78.33–118.1 GHz range. The other method (based on the use of microstrip transmission lines) has been implemented for the 25–67 GHz range.
The methods have been tested for polycrystalline specimens of hexagonal barium and strontium ferrites with nominal composition or complex substituted and having high magnetic texture. The measurement results have been compared with those obtained using conventional measurement methods and spherical specimens. Our methods prove to be highly accurate and reliable.
magnetic crystallographic anisotropy, ferromagnetic resonance, magnetically uniaxial hexagonal ferrites, method of measurement in free space, measurement method based on the use of microstrip transmission lines
Microwave electronics are currently the main development trend of the entire electronics industry [
The most promising microwave electronics materials are hexagonal ferrites in the form of single crystals or textured polycrystals [
The demand for highquality magnetically uniaxial hexagonal ferrites for microwave applications in electronics stimulates the improvement of existing and the development of new hexagonal ferrite technologies and studies of their properties [
The main parameters of ferromagnetic resonance (FMR) in polycrystalline magnetically uniaxial hexagonal ferrites (MUHF) are the effective anisotropy field H_{Aeff} and the ferromagnetic resonance bandwidth ∆Н [
General problems of material properties measurement in microwave electromagnetic range were reported earlier [
Below we consider methods for H_{Aeff} and ∆Н measurement in polycrystalline MUHF in the following ranges:
The method is based on the dependence of the FMR resonance frequency f_{r} in hexagonal ferrites on their effective magnetic anisotropy field H_{Aeff}. The principles of this method were partially described earlier [
H _{Aeff} and ∆Н were measured in polycrystalline MUHF with H_{Aeff} = 28–40 kE using demagnetized planeparallel plates of MUHF materials with the texture axis orthogonal to their planes. Quasiplanar electromagnetic waves were passed through the plates in free space.
The wave impedance of the hexagonal ferrite plates (ε_{f} = 13÷18) was matched with the wave impedance of the free space using planeparallel quartz plates (ε_{q} = 3.8÷3.9) located at both sides of the hexagonal ferrite plates. The thickness of the quartz plates was λ_{q}/4 where λ_{q} is the wavelength in the quartz plate at the measurement frequency. The specimen and the quartz plates were placed between two horn waveguide transitions one of which generated a quasiplanar electromagnetic wave and the other was excited by the quasiplanar electromagnetic wave after passage through the specimen.
The linear horn aperture size of horn waveguide transitions should be at least 3λ_{0} where λ_{0} is the wavelength in the free space at the measurement frequency and be matched with the free space and the electromagnetic source. The voltage standing wave ratio of the horn waveguide transition entrance is max. 1.1).
Since the test specimen was demagnetized it could not excite a secondary wave and therefore the wave attenuated while passing through the specimen only due to the electromagnetic absorption at natural FMR. This effect is used for H_{Aeff} determination from resonance frequency f_{r} of natural FMR which is the minimum transmission coefficient at electromagnetic wave frequency measurement.
The H_{Aeff} determination method semiempirically takes into account that f_{r} is affected by alternating demagnetizing fields caused by fluctuations of alternating magnetization at grain layer boundaries (Fig.
Therefore H_{Aeff} is determined using the following formula:
${H}_{{\mathrm{A}}_{\mathrm{eff}}}=\frac{{f}_{\mathrm{r}}}{\gamma}\frac{2}{3}4\pi {M}_{\mathrm{s}}$, (1)
where γ is the gyromagnetic ratio and 4πΜ_{s} is the saturation magnetization which is measured using other methods.
The ferromagnetic resonance bandwidth ∆H and f_{r} are determined from the frequency dependence of the transmission ratio using the following expressions:
$\Delta H=\frac{{f}_{2}{f}_{1}}{\gamma}$, (2)
${f}_{\mathrm{r}}=\frac{{f}_{1}{f}_{2}}{2}$, (3)
where f_{1} and f_{2} are the magnetic resonance band frequencies corresponding to the half of the absorbed energy.
The method was tested for the 3mm wave range using a panoramic device for voltage standing wave ratio and attenuation measurement Rem2.648.020 developed at Shokin NPP Istok JSC. The measurement results for polycrystalline hexagonal ferrite plates with H_{Aeff} = 28÷35 kE in free space were compared with the H_{Aeff} and ∆H measurement results for magnetized spherical specimens placed in the waveguide transmission line of the voltage standing wave ratio and attenuation meter. The spherical specimens were made from the same hexagonal ferrite material as the test plates. The difference of the H_{Aeff} and ∆H measurement results was within instrumental error (max. ±4 %).
The panoramic device for voltage standing wave ratio and attenuation measurement R2124M for 3mm wave range (working frequency range 78.33–118.1 GHz) was used as a basis for the experimental unit for H_{Aeff} and ∆H measurement in free space.
The measurement unit included the panoramic device for voltage standing wave ratio and attenuation measurement R2124M and the measurement module developed by the Authors which is connected into the measurement circuit.
The general appearance of the panoramic device for voltage standing wave ratio and attenuation measurement R2124M is shown in Fig.
General appearance of R2124M panoramic voltage standing wave ratio and attenuation meter.
The measurement module included a platform and two horn waveguide transitions (the waveguide crosssection is 1.2 × 2.4 mm^{2} and the horn aperture is 10 × 10 or 14 × 14 mm^{2}) with the entrance voltage standing wave ratio being max. 1.1 in the working frequency range of the R2124M meter.
Schematic of the measurement module with the test specimen and the matching quartz plates installed between horn waveguide transitions is shown in Fig.
Schematic of measuring module: (1) platform, (2) measuring horns, (3) mobile plate, (4) adjustment screw, (5) specimen, (6) matching quartz plates and (7) connection hardware.
The experimental unit had the following parameters:
The saturation magnetization is measured using an AMT4 automatic hysteresis recorder of Mianyang Shuangji Electronic Co. Ltd. (relative error of saturation magnetization measurement ±1%).
We studied the possibility of measuring effective anisotropy field and FMR bandwidth based on analysis of interaction between a smallsized hexagonal ferrite specimen with electromagnetic field in a microstrip transmission line (MTL) and the dependence of magnetic resonance bandwidth in hexagonal ferrite specimens on H_{Aeff} using advanced broadband panoramic circuit analyzers.
Broadband measurements were carried out using an Agilent N5227A vector circuit analyzer as an MTL microwave meter with the test hexagonal ferrite specimen. The coaxial entrance crosssection of the circuit analyzer was 1.85/0.8 mm (working frequency range 10 MHz – 67 GHz). The MTL was synthesized on an aluminum substrate (ε ≈ 9.6) with a wave impedance of 50 Ohm (substrate thickness 0.25 mm). The MTL substrate dimensions were chosen so to avoid excitation of higherorder modes in the MTL at frequencies of up to 67 GHz. The MTL was connected to the vector circuit analyzer using an Anritsu 3680V coaxial microstrip measurement module. The measurement module was in the form of a platform with two coaxial microstrip transitions (coaxial crosssection 1.85/0.8 mm). The MTL length (l ≈ 30 mm) was chosen so the points of MTL connection to the coaxial lines be located as far as possible from each other in order to reduce the straight signal (outside the MTL).
The polycrystalline MUHF specimens were in the form of planar regular prisms with square bases and linear dimensions of within 0.5 × 0.5 mm^{2}, a thickness of 0.15–0.25 mm and the texture axis perpendicular to the prism base. The choice of these specimen dimensions allowed us to avoid the effect of dielectric resonance in the test hexagonal ferrite specimens (ε_{f} ≈ 13÷18) on the shape of the FMR band in the 25–67 GHz range and provide for the excitation of the test specimen with a relatively homogeneous external electric field generated by the MTL.
The measurement unit included an Agilent N5227A vector circuit analyzer (working frequency range 10 MHz – 67 GHz), an Anritsu 3680V coaxial microstrip measurement module and an MTL section installed into the measuring module.
The measurement sequence was as follows.
If the specimen is magnetized and the measurements are carried out with an external magnetic field then the ∆H_{Aeff} equation will be as follows:
${H}_{{\mathrm{A}}_{\mathrm{eff}}}=\frac{{f}_{\mathrm{r}}}{\gamma}+\frac{1}{2}(3N1)4\mathrm{\pi}{M}_{0}{H}_{0}$, (4)
where γ is the gyromagnetic ratio, 4πM_{0} is the current saturation magnetization of the test specimen, H_{0} is the external magnetic field magnitude and N is the demagnetization factor along the axis perpendicular to the prism base (for an oblate inellipsoid of revolution
$N=\frac{1}{1{\vartheta}^{2}}\left(1\frac{\sqrt{\vartheta}}{\sqrt{1{\vartheta}^{2}}}\mathrm{arccos}\vartheta \right)$
where ϑ is the ellipsoid height to diameter ratio).
If the specimen is magnetized the measurements are carried out without an external magnetic field:
${H}_{{\mathrm{A}}_{\mathrm{eff}}}=\frac{f}{\gamma}+\frac{1}{2}(3N1)4\pi {M}_{0}$, (5)
where 4πΜ_{s} is the saturation magnetization of the test specimen and 4πM_{r} is the remanence of the test specimen.
If the specimen is demagnetized then:
${H}_{{\mathrm{A}}_{\mathrm{eff}}}=\frac{{f}_{\mathrm{s}}}{\gamma}+\zeta 4\pi {M}_{\mathrm{s}}$, (6)
where ζ is the coefficient determined by the domain structure of the demagnetized test specimen.
When calculating H_{Aeff} using Eqs (4) and (5) one can approximate M_{0} = M_{r.} As can be seen from Eqs (4), (5) and (6), more accurate H_{Aeff} calculation requires, depending on measurement mode, 4πM_{0}, 4πM_{r}, H_{0}, N and ζ be known, these parameters being determined from additional calculations. Otherwise the H_{Aeff} calculation error increases by an order of ±4πM_{s}.
When calculating H_{Aeff} using Eq. (6) for a demagnetized specimen we took ζ = 2/3 based on the results of our studies.
The experimental unit had the following parameters:
– working frequency range 20–67 GHz;
– measured parameter ranges: effective anisotropy field 10–23 kE, magnetic resonance bandwidth 0.1–5 kE;
The saturation magnetization was measured using an AMT4 automatic hysteresis recorder of Mianyang Shuangji Electronic Co. Ltd. (relative error of saturation magnetization measurement ±1%).
Figure
Interface with typical FMR spectrum in a plate of polycrystalline magnetically uniaxial hexagonal BaFe_{12}O_{19} ferrite (measured in free space, specimen HB13) [in Russian].
The diameter of the test planeparallel demagnetized plates of barium MUHF was 30 mm, the thickness being 0.37 mm. The results of frequency measurements (f_{1} and f_{2}) and H_{Aeff} and ∆H calculation using Eqs (1), (2) and (3) are summarized in Table
Results of FMR parameter measurements for demagnetized MUHF plates in free space in millimeter wave range.
Parameter  Specimen  
HB13  HB14  
f _{1}, GHz  88.8  102.8 
f _{2}, GHz  97.2  107.5 
f _{r}, GHz  92.9  105.15 
4πM_{s}, Gs  1800  1400 
H _{Aeff}, kE  32.0  36.5 
ΔH, kE  3.0  1.68 
H
_{Aeff} and ∆H measurements using MTL were carried out for magnetized to saturation specimens from polycrystalline barium and strontium MUHF sized 0.5 × 0.5 × 0.25 (N = 0.53) using the above described method. Figure
Typical FMR spectra in a plate of polycrystalline magnetically uniaxial hexagonal ferrite measured with the MTL method: (a) BaFe_{12}O_{19} (specimen HB25) and (b) Sr(Fe,Al,Si,Ca)_{12}O_{19} (specimen HS81).
The results of frequency measurements (f_{1} and f_{2}) and H_{Aeff} and ∆H calculation using Eqs (4), (6) and (8) are summarized in Table
Results of HAeff and ∆H measurement for MUHF in the 25–67 GHz range using a microstrip transmission line.
Parameter  Specimen (h = 0.25)  

HB25  HS81  
f _{1}, GHz  41.18  45.88 
f _{2}, GHz  53.32  56.04 
Δf, GHz  12.14  10.16 
f _{r}, GHz  47.25  51.00 
H _{Aeff}, kE  17.8  19.22 
ΔH, kE  4.34  3.63 
4πM_{r}, Gs  3200  3500 
Our methods of measuring effective magnetic anisotropy field H_{Aeff} in the 10–23 and 28–40 kE ranges and ferromagnetic resonance bandwidth ∆H in the 0.5–5 kE range in magnetically uniaxial hexagonal ferrites were presented.
Testing of the methods for measuring H_{Aeff} and ∆H in polycrystalline magnetically uniaxial hexagonal barium and strontium ferrites of M type (nominal composition and complex substituted) showed their high accuracy and reliability. As compared with conventional H_{Aeff} and ∆H measuring methods for spherical specimens, our methods increase the measurement accuracy by 10–12 %.
We showed that our methods are effective in the measurement of electromagnetic parameters of magnetically uniaxial hexagonal ferrites used in microwave electronics and they will speed up the implementation of millimeter wave range devices on substrates made from these materials.
This work was performed within the Hexagonal Ferrite R&D Project funded by Shokin NPP Istok JSC with financial support from the Ministry of Education and Science of the Russian Federation under Subvention Agreement No. 14.575.21.0030 as of June 27, 2014 (RFMEFI57514X0030).