Tunable ferromagnetic resonance in La-Co substituted barium hexaferrites at millimeter wave frequencies

Microwave ferrites are integral parts of countless electronic components found in both defense and commercial systems.^1,2 As a typical microwave ferrite with permanent magnetic characteristics, barium hexaferrites [M-type BaFe₁₂O₁₉(BaM)] are of great interest for the microwave and millimeter wave (MMW) applications due to their fairly large magnetocrystalline anisotropy, high Curie temperature, relatively large magnetization and corrosion resistivity.^3,4 To improve intrinsic magnetic properties of hexaferrites, many attempts have been made by various techniques, including doping on the Fe or Ba (Sr) sublattices, particularly as represented by La or La-Co substitution.^5,6 However, there are few reports on the dynamic magnetic permeability μ* and dielectric permittivity ε*, which allow to describe the response of ferrites to the static magnetic and electromagnetic fields.

High-Q resonant measurements were utilized for determination of the dielectric and magnetic data in microwave ranges.^7,8 Nevertheless, the accuracy of this method would deteriorate in millimeter-wave ranges due to the decreasing ferrite dimensions aggrandizing uncertainty of filling factor of resonator. The magneto-optical approach had been previously employed for the separation of the dielectric and magnetic effects of ferrites.^9,10 This technique enables the holonomic and precise characterization of ferrites in the entire millimeter-wave ranges. Therefore, this paper examines the complex permittivity and permeability of La-Co substituted barium hexaferrites in a broadband MMW frequency ranging from 30 to 120 GHz.

The composition of Ba_1-xLa_xFe_12-xCo_xO₁₉ (x=0.0, 0.2, and 0.4) were prepared by a conventional ceramic method. The raw materials, BaCO₃, La₂O₃, Co₂O₃ and Fe₂O₃ were weighed according to the above stoichiometric proportion and mixed homogeneously in zirconia ball mills for 12h. The composite mixtures were calcined at 1100∼1200 °C in air for 2 h and then second-milled with 3.0 wt% Bi₂O₃ as a sintering aid for 24 h. After being dried at 90°C, the powders were granulated, pressed and then sintered at 900∼1000°C for 2h.

A couple of horn antennas and a set of polyethylene lenses had been utilized to form a Gaussian beam, as well as to focus the beam into the sample. Broadband millimeter wave measurements were performed using a free space quasi-optical spectrometer, equipped with a series of backwards wave oscillators (BWO’s) as high-power, tunable sources of coherent radiation within the frequency range of 30∼120 GHz. The bulk densities d were measured by Archimedes method. Magnetic properties at room temperature were determined by vibrating sample magnetometer (VSM, Micro-Sense Model EV8) with an applied field 20 kOe.

Free space MMW quasi-optical spectroscopy techniques, including technical details and measurement uncertainties analysis, have been employed and presented by several scientific research groups.^9–12 Note that these measurements were performed on the pure barium hexaferrite powders. Present study presents the characterization of the frequency dependent La-Co substitutions studied by a free space transmittance millimeter wave spectrometer (see Fig. 1). It is observed that strong absorption zones in these transmission spectra reside in the vicinity of the respective center frequencies of 49.0, 56.2, and 64.3 GHz for LaCo substitutions x=0.0, 0.2, and 0.4. This deep absorption is the natural ferromagnetic resonance that shifts to millimeter wave range due to the strong magnetic anisotropy of barium and strontium ferrites.

Considering the saturation of absorption line results in the broadening experimental width, which is also observed in optics, the actual width of resonance could not be obtained directly from the width of these absorption zones.^9,13,14 Concomitantly, a significant shift to higher frequency of the ferromagnetic resonance frequency (FMR) was detected with the increase of LaCo substitutions. It could be concluded that La-Co substituted barium hexaferrites are promising candidates for tunable millimeter wave absorbers, filters and modulators at MMW frequencies, especially at V band.

Additionally, the progressive decline of transmissivity and period of oscillation in the vicinity of resonance were observed in this series of samples. Such variations in the microwave or millimeter range of electromagnetic wave spectrum are associated completely with magnetic permeability. The mathematical relationships between transmittance and reflectance spectra, and refractive and absorption indexes are presented that^11,15

where c is the speed of light, n is the refractive index of the sample material, k is the absorption index, μ is the complex permeability, ε is the complex dielectric permittivity, T is the transmittance, R is the reflectance, φ is the phase of the transmitted wave, and ψ is the phase of reflected wave. It is noteworthy that in order to get better transmittance interferogram spectra, the errors can be significantly reduced by imposing the following restrictions on the sample dimensions D^1/2 ≥ 8 and d ≤ 3, where D and d are the cross section and thickness of a plane-parallel specimen, respectively. The fitting of transmittance spectrum could be performed at the far from magnetic resonance due to high level of absorption of millimeter waves (see Ref. 10 and 12 for more details). The corresponding parameters of magnetic permeability and dielectric permittivity were summarized in Fig. 2, Fig. 3 and Table I. For pure barium hexaferrite, it exhibits the complex dielectric permittivity with the real part ε'=19.4, and imaginary part ε"=0.22. A further comparison indicated that both real and imaginary permeability of this series of samples increase with the increase of LaCo substitutions.

Complex magnetic permeability in nonmagnetized barium hexaferrites is determined by strong magnetocrystalline anisotropy H_a and saturation magnetization 4πM_s. According to Schlömann’s equation for partially magnetized ferrites, we could get¹⁶ 

with ω being the frequency, and γ being gyromagnetic ratio. Demagnetizing factors are determined by the theory of Schlömann’s model for nonellipsoidal bodies.¹⁷ That is, the inhomogeneous demagnetizing field existing in uniformly magnetized nonellipsoidal samples could be described by a generalized demagnetizing factor. Best fitting of the experimentally observed spectrum was carried out: Magnetocrystalline anisotropy H_a can be easy determined by the frequency of the deep absorption zone f_Res, and saturation magnetization 4πM_s strongly depends on absorption level at ferromagnetic resonance. The corresponding values of magnetic properties were also summarized in Table I. For x=0.0, it exhibits 4πM_s=3.78 kGs, and H_a=17.6 kOe, which is similar to previously reported from bulk barium and strontium hexaferrite materials.^18,19 Furthermore, a higher LaCo concentrations leads to increasing magnetocrystalline anisotropy H_a and otherwise lower saturation magnetization 4πM_s. Such enhancements in H_a could result in the shifting of observing FMR to higher frequencies.

The higher La-Co concentrations leads to the increase of magnetocrystalline anisotropy H_a and otherwise lower saturation magnetization 4πM_s. Such enhancements in H_a could result in the shifting of observing FMR to higher frequencies. The resonance phenomena of the ferrites can be described by domain wall motion and spin resonance.^20,21 Domain wall motion resonance is sensitive to both the microstructure of the polycrystalline ferrite (ferrite grain size) and the volume loading of the ferrite (the post-sintering density). The spin rotational relaxation, becoming pronounced in the high frequency range depends only on the volume loading of the ferrite and the dispersion parameters.

In order to confirm the fitting results, magnetic hysteresis loops of La-Co substituted barium hexaferrites were illustrated in Fig. 4. Consistency of saturation magnetization determined independently by both millimeter wave absorption and DC magnetization have been found for all La-Co substituted barium hexaferrite materials.

This paper presents millimeter-wave characterization of La-Co substituted barium hexaferrites. The measurements have been performed using a free-space quasi-optical millimeter-wave spectrometer. Complex dielectric permittivity and magnetic permeability of La-Co substituted barium hexaferrites have been calculated from the transmission spectrum. Magnetic properties of La-Co substituted barium hexaferrites, including saturation magnetization and anisotropy field have been determined based on Schlömann’s theory for partially magnetized ferrites. Consistency of saturation magnetization determined independently by both millimeter wave absorption and DC magnetization measurements have been found for all La-Co substituted barium hexaferrites.

Linear shift of the ferromagnetic resonance to higher frequencies and the broadening bandwidth of the strong absorption in this series of La-Co substituted barium hexaferrites have been revealed in the transmission spectrum. The center frequencies of the ferromagnetic resonance frequency are found to be 49.0, 56.2, and 64.3GHz for La-Co substitutions of x=0.0, 0.2, and 0.4, respectively. Along with the increase of La-Co substitutions, it exhibits lower saturation magnetization, and higher complex dielectric permittivity, magnetocrystalline anisotropy, and especially FMR frequency. It could significantly extend the applicability of barium hexaferrites and allow much stronger tuning of their millimeter wave absorber characteristics.

This work was supported in part by the National Natural Science Foundation of China under Grant No. 51772046. One of the author (KK) is greatly thankful to Dr. S. Chen for many fruitful discussions.