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Complex permeability spectra of polycrystalline Li–Zn ferrite and application to EM-wave absorber
Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
Complex permeability spectra of polycrystalline Li–Zn ferrite and application to EM-wave absorber T. Nakamura*, T. Miyamoto, Y. Yamada Department of Electrical Engineering, Graduate School of Engineering, Himeji Institute of Technology, 2167 Shosha, Himeji, 671-2201 Hyogo, Japan Received 20 June 2002
Abstract Polycrystalline Li–Zn ferrites were prepared by the usual ceramic sintering method, and their complex permeability spectra were measured. The low-frequency permeability increased with the fraction of Zn ferrite. However, the natural resonance frequency shifted lower as the fraction of Zn ferrite was increased. According to our previous model, the complex permeability spectra were also numerically separated into spin rotation and domain wall motion contributions. For the spin rotational component, which played an important role in the high-frequency region, the static spin susceptibility increased and the spin resonance frequency shifted lower with an increase in the Zn-ferrite fraction. The product values of the static spin susceptibility and the spin resonance frequency, corresponding to the Snoek’s product value, took a maximum at a certain fraction of Zn ferrite. This was reflected in the performance of the single-layered electromagnetic wave absorber using the polycrystalline ferrite. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.40.Gb; 81.05.Je; 85.70.Ge Keywords: Ferrite; Complex permeability; Snoek’s product; EM-wave absorber
1. Introduction Ferrites have high potential for several electromagnetic devices in the radio frequency region, since they have frequency-dependent physical properties, such as permittivity and permeability. Especially, polycrystalline ferrite has been extensively used in many electronic devices because of *Corresponding author. Tel.: +81-792-67-4867; fax: +81792-67-4855. E-mail address: [email protected] (T. Nakamura).
its high permeability in the radio frequency region, high electrical resistivity, mechanical toughness and chemical stability. There are many experimental and theoretical investigations on the frequency dispersion of complex permeability in polycrystalline ferrite [1–6]. The complex permeability spectra of polycrystalline ferrite depend not only on the chemical composition of the ferrite but also on the post-sintering density and the microstructure such as grain size and porosity. These are attributed to the fact that the permeability of the polycrystalline ferrite is described as the superposition of two different magnetizing processes:
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 6 9 8 - 4
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
spin rotation and domain wall motion [1,6,7]. In addition, there exists a natural resonance related to the effective anisotropy field, and it causes the magnetic losses. This fact has been known as the Snoek’s limit [8]. It gives some limitations such as a threshold frequency to the application of polycrystalline ferrite in the radio frequency devices. In our previous studies, where three series of polycrystalline spinel ferrite (Ni–Zn ferrite, Mg– Zn ferrite and Ni–Zn–Cu ferrite) and Ni–Zn–Cu ferrite specially fabricated by low-temperature process were investigated, the permeability dispersion of the spinel ferrite was examined [9–11]. It was found that the permeability dispersion consisted of two different magnetizing mechanisms, in which the spin rotational component was relaxation-type and the domain wall motion contribution was resonance-like. And it was numerically separated into two contributions using the dispersion parameters. Domain wall motion resonance was sensitive to both the ferrite grain size and the volume loading of the ferrite (the post-sintering density), while spin rotation relaxation, playing a major role in the frequency region greater than hundreds of MHz, depended only on the volume loading of the ferrite [9,10]. The dispersion parameters of the spin rotational component gave the Snoek’s limiting value, hereafter denoted as the Snoek’s product. Additionally, it was found that the Snoek’s product value was almost proportional to the magnetization [10,11]. In our recent work on the complex permeability dispersion [12], it was clarified that the complex permeability of hexagonal ferrite was far beyond the Snoek’s limitation. Therefore, it is expected that the utilization of the hexagonal ferrite enables us to produce radio frequency devices with small dimensions. However, their crystal structure is rather complicated when compared with the spinel ferrite, and preparation of hexagonal ferrite requires that it is calcined and sintered at higher temperatures than spinel ferrite. These difficulties have prevented the production of hexagonal ferrite from being applied at the industrial scale. From these considerations, we studied the complex permeability dispersion of polycrystalline Li–Zn ferrite, which is thought to have a relatively large magnetization in the spinel ferrite and a
341
potential high enough to attain a large Snoek’s product. Here, we compare the complex permeability spectra of Li–Zn ferrite to those of the other spinel. This requires a more detailed discussion on the complex permeability spectra from the viewpoint of Snoek’s rule. Furthermore, we attempt to design a single-layered electromagnetic wave absorber using the polycrystalline Li–Zn ferrite.
2. Experimental procedures Li–Zn ferrites were prepared by the double sintering method. Starting powders of Li2CO3, ZnO and Fe2O3 were mixed together using dry attrition milling. Their cationic molar ratios were adjusted to the stoichiometric compositions: Li0.5XZn1XFe2+0.5XO4 with X ranging from 0.3 to 0.8. The mixtures were subjected to press compacting (to a platelet shape with a diameter of 30 mm and thickness of approximately 3 mm) and calcined in air at 9001C for 5 h. The plates were hand-ground until the particle size reached less than 1 mm using agate pestle and mortar. Then the powders were reground using wet attrition milling. The obtained ferrite powders were mixed with an appropriate amount of polyvinyl-alcohol as a binder, subjected to press compacting into the same shape and size as the above-mentioned one, then sintered in air at 11501C for 5 h, followed by furnace cooling. The density of the sintered plate was calculated by measuring the dimensions and the weight. A scanning electron microscope (JEOL, JSM-5310) was utilized to investigate the microstructure of the polycrystalline ferrite. The magnetization of the sintered ferrite fragment was determined through the use of a vibrating sample magnetometer (TOEI KOGYO, VSM-5). In order to measure the permeability, the sintered ferrite was cut into rings with outer and inner diameters of 7 and 3 mm, respectively. The complex permeability (m ¼ m0 þ jm00 ) of all samples was measured through two different techniques. In the frequency range from 100kHz to 100 MHz, m was calculated from the inductance and the resistance of the toroidal, which was placed at the short plane of the
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
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coaxial line connected to an impedance analyzer (Hewlett-Packard, HP-4194A). In the frequency range from 50 MHz to 6GHz, both the complex permeability m and the complex permittivity e were obtained from the reflection and transmission measured in the coaxial line connected to an RFnetwork analyzer (Hewlett-Packard, HP-8720ES).
3. Results and discussion For the specimen of polycrystalline Li–Zn ferrite, the crystallographic structure was investigated using X-ray diffraction. The powder X-ray diffraction patterns exhibited that all the samples were identified as a single phase of cubic spinel structure and additional lines corresponding to any other phase were not detected. The lattice constant was determined through the Nelson– Relay extrapolation method. The lattice constant variation with the composition X is shown in Fig. 1. It is seen that the lattice constant decreased almost linearly with an increase in X ; and that it obeyed Vegard’s law. All the obtained ferrite ceramics had a relative density larger than 95%, irrespective of the composition, and they were of dense microstructure. Information regarding the ferrite grain size and porosity was obtained from the microstructural observation of the fractured specimen. Fig. 2 shows SEM photographs of the fracture surface for the typical specimen. It was
found that the average grain size estimated from the geometric analysis was approximately 5 mm and it was almost independent of the composition X : The magnetization variation versus the composition X is shown in Fig. 3. As X was increased, the magnetization value increased, reached a maximum around X ¼ 0:75; and then decreased. It is possible to explain this magnetization variation by considering both the spin structure change from the Neel collinear structure to the Yafet– Kittel canted spin structure and the Neel temperature variation [3,13]. The complex permeability spectra of the polycrystalline ferrite are shown in Fig. 4. The real part of the permeability m0 remained almost constant,
Lattice constant (nm)
0.842 0.840 0.838 0.836 0.834 0.832 0.3
0.4
0.5
0.6
0.7
0.8
Chemical composition X Fig. 1. The lattice constant of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4, versus the chemical composition X :
Fig. 2. The SEM photographs of the fracture surface for the polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4: (a) X ¼ 0:4; and (b) X ¼ 0:7:
Magnetization (emu/g)
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
80
60
40
20 0.3
0.4
0.5
0.6
0.7
0.8
Chemical composition X
Real part of permeability
Fig. 3. The magnetization of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4, versus the chemical composition X :
800
X=0.30
600 X=0.40
400
X=0.50 X=0.60
200
X=0.70 X=0.75 X=0.80
0 104
105
Imaginary part of permeability
107
108
109
1010
Frequency (Hz)
(a) 400
X=0.30
300
X=0.40 X=0.50
200
100
X=0.60 X=0.70 X=0.75 X=0.80
until the frequency was raised to a certain value, and then began to decrease at higher frequency. The imaginary permeability m00 gradually increased with the frequency, and took a broad maximum at a certain frequency, where the real permeability rapidly decreased. This feature is well known as the natural resonance. For the chemical composition variation, it was found that the real permeability in the low-frequency region below 2 MHz decreased with an increase in X : But the reverse trend was seen in the high-frequency region. The real permeability above 300 MHz increased with an increase in X : As X was increased, the natural resonance frequency, where the imaginary permeability had a maximum value, shifted toward high frequency (from 2 to 25 MHz). The imaginary permeability in the low-frequency region below 20 MHz decreased with an increase in X : For the imaginary part of permeability as well as the real permeability, the reverse trend was also seen in the high-frequency region. The imaginary permeability above 2.5 GHz increased with an increase in X : In general, the complex permeability is related to two different magnetizing mechanisms: the spin rotational magnetization and the domain wall motion [7,9–11]. In our previous studies, it was possible to separate the complex permeability spectra of the polycrystalline spinel ferrites into the spin rotational component, wsp ð$ Þ; and the domain wall motion contribution, wdw ð$ Þ; using a numerical fitting [9–11]. The spin rotational component is of relaxation type, in which the damping friction is thought to be large enough, and its dispersion is inversely proportional to the frequency. The domain wall contribution is of resonance type and depends on the square of the frequency. Therefore, the following equations are obtained: mð$ Þ ¼ 1 þ wsp ð$ Þ þ wdw ð$ Þ
ð1Þ
and the individual components can be written as
0 104
(b)
106
343
105
106
107
108
109
1010
Frequency (Hz)
Fig. 4. The complex permeability spectra of polycrystalline Li– Zn ferrite, Li0.5XZn1XFe2+0.5XO4, with the chemical composition X : (a) real; and (b) imaginary parts.
wsp ð$ Þ ¼ Ksp =½1 þ jð$ =$ sp Þ;
ð2Þ
wdw ð$ Þ ¼ Kdw $ 2dw =½$ 2dw $ 2 þ jb$ ;
ð3Þ
where $ is the RF magnetic field frequency, Ksp the static spin susceptibility, $ sp the spin
resonance frequency, Kdw the static susceptibility of the domain wall motion, $ dw the domain wall motion resonance frequency, and b the frictional damping factor of the domain wall motion. On the spin resonance frequency $ sp in our studies, it corresponds to the divided value of the usual spin resonance frequency by the damping constant for the spin rotational motion. It is found that the complex permeability spectra of the polycrystalline spinel ferrite can be well reproduced using these equations and the five parameters. It is also clarified that the domain wall motion contribution starts to decrease at lower frequency and only the spin rotational component remains in the higherfrequency region. Consequently, the complex permeability spectra in the frequency region higher than 100 MHz can be described mainly using the spin rotational component. The above model calculation was applied to the experimentally obtained complex permeability spectra of the polycrystalline Li–Zn ferrite, and the dispersion parameters for each component were determined. In our previous studies [9–11], it is known that the complex permeability spectra of the polycrystalline ferrite are affected by the ferrite volume loading (the post-sintering density) and the microstructure such as the grain size. Namely, the spin rotational component depends only on the ferrite volume loading, while the domain wall motion contribution is much more sensitive to the microstructure and related not only to the ferrite volume loading but also to the ferrite grain size, since the domain wall configuration is closely related to the grain size. In this study, all the polycrystalline Li–Zn ferrite had a relative density larger than 95% and it was seen that the ferrite grain size was almost independent of the chemical composition from the result of the SEM observation. In addition, it is also seen that the complex permeability spectra in the frequency region higher than 100 MHz can be described mainly using the spin rotational component. Therefore, only the numerical parameters for the spin rotational component are considered in this study. The variations of the spin rotational component parameters with the chemical composition X are shown in Fig. 5. From the figure, it was found that the static spin susceptibility Ksp decreased with an
500
400 102 300
200 101 100
0
0.3
0.4
0.5
0.6
0.7
Spin resonance frequency (MHz)
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
Static spin susceptibility
344
0.8
Chemical composition X
Fig. 5. The variations of static spin susceptibility (open circle) and spin resonance frequency (open triangle) with the chemical composition of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4.
increase in X ; and that the spin resonance frequency $ sp shifted toward higher frequency as X was increased. The variation of the static spin susceptibility and the spin resonance frequency was similar to that of low-frequency permeability and natural resonance frequency, respectively. These features are explained as follows. Since the spin resonance frequency is proportional to the effective anisotropy field, the higher spin resonance frequency means a greater effective anisotropy field. As a result, increase in X produces greater anisotropy field. Roughly speaking, it is thought that the static spin susceptibility is given by the ratio of the magnetization flux to the effective anisotropy field. The experimental results exhibited that the magnetization flux increased with X and took a maximum around X ¼ 0:75; but decreased with further increase of X : It was clear that the degree of variation in the magnetization flux was much smaller than that of the effective anisotropy field. Therefore, the reduction of the static spin susceptibility with an increase in X is also attributed to the increase of the effective anisotropy field with an increase in X : As we presented in the previous studies [10,11], the product value of the static spin susceptibility and the spin resonance frequency corresponds to Snoek’s product. It provides a limitation on the permeability spectra of spinel ferrite [8]. We calculated the product values for the
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
Snoek's product (GHz)
polycrystalline Li–Zn ferrite, plotted in Fig. 6 as a function of the chemical composition X : It was shown that the Snoek’s product value increased with X ; took a maximum around X ¼ 0:75 and then decreased. This feature is similar to the relationship between the magnetization flux and the chemical composition, as expected from the above arguments on the static spin susceptibility and the spin resonance frequency. Fig. 7 exhibits
10
5
0
0.3
0.4
0.5
0.6
0.7
0.8
Chemical composition X Fig. 6. The variation of Snoek’s product value versus the chemical composition of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4.
Snoek's product (GHz)
15
10
5
0
100
200
300
400
500
Magnetization (emu/cc) Fig. 7. The variation of Snoek’s product value with the magnetization flux for various polycrystalline ferrites: Li–Zn ferrite (open triangle) and the other ferrite studied in the previous paper (solid circle). The dashed line is an extrapolation of the experimentally obtained values.
345
the variation of the Snoek’s product versus the magnetization flux. This figure contains the product values for three series of polycrystalline spinel ferrite (Ni–Zn ferrite, Mg–Zn ferrite and Ni–Zn–Cu ferrite) and Ni–Zn–Cu ferrite specially fabricated by the low-temperature process studied in our previous reports [10,11]. It was clear that the Snoek’s product value almost linearly increased with the magnetization flux, and this was valid for any kind of spinel ferrite and also for the Li–Zn ferrite. It was found from the figure that some Li– Zn ferrite with a large fraction of Li-ferrite have a relatively large Snoek’s product. Finally, we will study the electromagnetic wave absorption using the polycrystalline Li–Zn ferrite. Ferrite sintered ceramics have been used as very thin and extremely wide band electromagnetic wave absorbers in VHF and UHF bands [14]. The wide band characteristics are achieved by the frequency dispersion of the complex permeability: the imaginary part of the permeability m00 is almost inversely proportional to the frequency in these frequency bands, then the value of m00 d=l (d: absorber thickness, l: wave length in the free space) is kept almost constant in these frequency regions. That is, the spin rotational relaxation component plays an important role to give the absorption band. A large Snoek’s product leads to a large m00 value in the frequency region, and it is likely that this results in thinning of the matching thickness and increasing of the center frequency. Consider the single-layered electromagnetic wave absorber, which consists of a polycrystalline Li–Zn ferrite plate with thickness d located on a metal conducting plate. The input impedance Zð$ Þ is given by h i Zð$ Þ ¼ Z0 ðm=eÞ1=2 tanh jð$ d=cÞðemÞ1=2 : ð4Þ Here, Z0 is the characteristic impedance of free space, $ the angular frequency of the incident wave, c the electromagnetic wave velocity in free space, e and m the complex permittivity and permeability. The absorption G($) is obtained by the following equation: Gð$ Þ ¼ 20 log j½Zð$ Þ Z0 =½Zð$ Þ Z0 j:
ð5Þ
Using the experimentally obtained values of the complex permittivity and permeability, it is
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
346
the matching thickness was minimum around X ¼ 0:75; where the Snoek’s product took the maximum value. It indicated that a large Snoek’s product led to thinning of the matching thickness and increasing of the center frequency as expected.
0
Absorption (dB)
-10 -20 -30
4. Conclusions
-40 X=0.80
-50
X=0.75 X=0.60 X=0.50 X=0.70
X=0.40
-60
108
109
Frequency (Hz) Fig. 8. The electromagnetic wave absorption spectra of the single-layered absorbers using the polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4.
Table 1 The center frequency, the matching thickness and the absorption band for the polycrystalline Li–Zn ferrite single-layered absorbers Composition X
Matching thickness (mm)
Center frequency (MHz)
Bandwidth (MHz)
0.4 0.5 0.6 0.7 0.75 0.8
5.5 4.5 4.0 3.5 3.0 4.0
150 250 340 550 850 530
90–220 170–360 240–480 390–750 650–1000 400–650
possible to estimate the absorption characteristics and to design the optimum absorber thickness. The electromagnetic wave absorption characteristics using the polycrystalline Li–Zn ferrite are shown in Fig. 8 and Table 1. They exhibited the potential of relatively wide band absorption in the frequency region from 100 MHz to 1 GHz. The center frequency shifted higher as X was increased, took its highest value around X ¼ 0:75; and then decreased. The center frequency was tunable in the range from 150 to 850 MHz. The matching thickness decreased from 5.5 to 3.0 mm as X was increased, attained the minimum value, and then increased. Consequently, it was found that the center frequency reached the maximum value and
Polycrystalline Li–Zn ferrites were prepared by the usual ceramic sintering method, they were of dense microstructure and the ferrite grain size was almost independent of the chemical composition. The complex permeability spectra were evaluated using two different impedance measurement techniques. As the Zn-ferrite fraction was increased, the low-frequency permeability increased and the natural resonance frequency shifted lower. Using the model calculation previously proposed, the complex permeability spectra were also numerically separated into spin rotation and domain wall motion contributions. For the spin rotational component, the static spin susceptibility increased and the spin resonance frequency shifted lower with an increase in the Zn-ferrite fraction. They are attributed mainly to the variation of the effective anisotropy field with the chemical composition. The product values of the static spin susceptibility and the spin resonance frequency, corresponding to the Snoek’s product value, are proportional to the magnetization flux. The spin rotation component played an important role in the high-frequency region, and the Snoek’s product was a good index of high-frequency devices such as single-layered electromagnetic wave absorber using the polycrystalline ferrite.
Acknowledgements The authors are grateful to Dr. T. Kikuchi of Himeji Institute of Technology for his help with the sample preparation and measurements.
References [1] G.T. Rado, Rev. Mod. Phys. 25 (1953) 81.
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347 [2] D. Polder, J. Smit, Rev. Mod. Phys. 25 (1953) 81. [3] J. Smit, H.M.J. Wijn, Ferrites, Phillips Technical Library, Eindhoven, The Netherland, 1959. [4] E. Scloemann, J. Appl. Phys. 41 (1970) 204. [5] A. Globus, J. Phys. C 1 (1977) 1. [6] J.P. Bouchaud, P.G. Zerah, J. Appl. Phys. 67 (1990) 5512. [7] Y. Naito, Proceedings of the First International Conference on Ferrites, 1970, p. 558. [8] J.L. Snoek, Physica XIV 4 (1948) 207.
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[9] T. Nakamura, T. Tsutaoka, Proceedings of the Fourth International Conference on Electroceramics and Applications, 1994, p. 1149. [10] T. Nakamura, J. Magn. Magn. Mater. 168 (1996) 285. [11] T. Nakamura, J. Appl. Phys. 88 (2000) 348. [12] T. Nakamura, K. Hatakeyama, IEEE Trans. Magn. 36 (5) (2000) 3415. [13] Y. Yafet, C. Kittel, Phys. Rev. 87 (1952) 290. [14] Y. Naito, K. Suetake, IEEE Trans. Microwave Theory Tech. 19 (1971) 65.
Complex permeability spectra of polycrystalline Li–Zn ferrite and application to EM-wave absorber T. Nakamura*, T. Miyamoto, Y. Yamada Department of Electrical Engineering, Graduate School of Engineering, Himeji Institute of Technology, 2167 Shosha, Himeji, 671-2201 Hyogo, Japan Received 20 June 2002
Abstract Polycrystalline Li–Zn ferrites were prepared by the usual ceramic sintering method, and their complex permeability spectra were measured. The low-frequency permeability increased with the fraction of Zn ferrite. However, the natural resonance frequency shifted lower as the fraction of Zn ferrite was increased. According to our previous model, the complex permeability spectra were also numerically separated into spin rotation and domain wall motion contributions. For the spin rotational component, which played an important role in the high-frequency region, the static spin susceptibility increased and the spin resonance frequency shifted lower with an increase in the Zn-ferrite fraction. The product values of the static spin susceptibility and the spin resonance frequency, corresponding to the Snoek’s product value, took a maximum at a certain fraction of Zn ferrite. This was reflected in the performance of the single-layered electromagnetic wave absorber using the polycrystalline ferrite. r 2002 Elsevier Science B.V. All rights reserved. PACS: 75.40.Gb; 81.05.Je; 85.70.Ge Keywords: Ferrite; Complex permeability; Snoek’s product; EM-wave absorber
1. Introduction Ferrites have high potential for several electromagnetic devices in the radio frequency region, since they have frequency-dependent physical properties, such as permittivity and permeability. Especially, polycrystalline ferrite has been extensively used in many electronic devices because of *Corresponding author. Tel.: +81-792-67-4867; fax: +81792-67-4855. E-mail address: [email protected] (T. Nakamura).
its high permeability in the radio frequency region, high electrical resistivity, mechanical toughness and chemical stability. There are many experimental and theoretical investigations on the frequency dispersion of complex permeability in polycrystalline ferrite [1–6]. The complex permeability spectra of polycrystalline ferrite depend not only on the chemical composition of the ferrite but also on the post-sintering density and the microstructure such as grain size and porosity. These are attributed to the fact that the permeability of the polycrystalline ferrite is described as the superposition of two different magnetizing processes:
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 0 6 9 8 - 4
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
spin rotation and domain wall motion [1,6,7]. In addition, there exists a natural resonance related to the effective anisotropy field, and it causes the magnetic losses. This fact has been known as the Snoek’s limit [8]. It gives some limitations such as a threshold frequency to the application of polycrystalline ferrite in the radio frequency devices. In our previous studies, where three series of polycrystalline spinel ferrite (Ni–Zn ferrite, Mg– Zn ferrite and Ni–Zn–Cu ferrite) and Ni–Zn–Cu ferrite specially fabricated by low-temperature process were investigated, the permeability dispersion of the spinel ferrite was examined [9–11]. It was found that the permeability dispersion consisted of two different magnetizing mechanisms, in which the spin rotational component was relaxation-type and the domain wall motion contribution was resonance-like. And it was numerically separated into two contributions using the dispersion parameters. Domain wall motion resonance was sensitive to both the ferrite grain size and the volume loading of the ferrite (the post-sintering density), while spin rotation relaxation, playing a major role in the frequency region greater than hundreds of MHz, depended only on the volume loading of the ferrite [9,10]. The dispersion parameters of the spin rotational component gave the Snoek’s limiting value, hereafter denoted as the Snoek’s product. Additionally, it was found that the Snoek’s product value was almost proportional to the magnetization [10,11]. In our recent work on the complex permeability dispersion [12], it was clarified that the complex permeability of hexagonal ferrite was far beyond the Snoek’s limitation. Therefore, it is expected that the utilization of the hexagonal ferrite enables us to produce radio frequency devices with small dimensions. However, their crystal structure is rather complicated when compared with the spinel ferrite, and preparation of hexagonal ferrite requires that it is calcined and sintered at higher temperatures than spinel ferrite. These difficulties have prevented the production of hexagonal ferrite from being applied at the industrial scale. From these considerations, we studied the complex permeability dispersion of polycrystalline Li–Zn ferrite, which is thought to have a relatively large magnetization in the spinel ferrite and a
341
potential high enough to attain a large Snoek’s product. Here, we compare the complex permeability spectra of Li–Zn ferrite to those of the other spinel. This requires a more detailed discussion on the complex permeability spectra from the viewpoint of Snoek’s rule. Furthermore, we attempt to design a single-layered electromagnetic wave absorber using the polycrystalline Li–Zn ferrite.
2. Experimental procedures Li–Zn ferrites were prepared by the double sintering method. Starting powders of Li2CO3, ZnO and Fe2O3 were mixed together using dry attrition milling. Their cationic molar ratios were adjusted to the stoichiometric compositions: Li0.5XZn1XFe2+0.5XO4 with X ranging from 0.3 to 0.8. The mixtures were subjected to press compacting (to a platelet shape with a diameter of 30 mm and thickness of approximately 3 mm) and calcined in air at 9001C for 5 h. The plates were hand-ground until the particle size reached less than 1 mm using agate pestle and mortar. Then the powders were reground using wet attrition milling. The obtained ferrite powders were mixed with an appropriate amount of polyvinyl-alcohol as a binder, subjected to press compacting into the same shape and size as the above-mentioned one, then sintered in air at 11501C for 5 h, followed by furnace cooling. The density of the sintered plate was calculated by measuring the dimensions and the weight. A scanning electron microscope (JEOL, JSM-5310) was utilized to investigate the microstructure of the polycrystalline ferrite. The magnetization of the sintered ferrite fragment was determined through the use of a vibrating sample magnetometer (TOEI KOGYO, VSM-5). In order to measure the permeability, the sintered ferrite was cut into rings with outer and inner diameters of 7 and 3 mm, respectively. The complex permeability (m ¼ m0 þ jm00 ) of all samples was measured through two different techniques. In the frequency range from 100kHz to 100 MHz, m was calculated from the inductance and the resistance of the toroidal, which was placed at the short plane of the
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
342
coaxial line connected to an impedance analyzer (Hewlett-Packard, HP-4194A). In the frequency range from 50 MHz to 6GHz, both the complex permeability m and the complex permittivity e were obtained from the reflection and transmission measured in the coaxial line connected to an RFnetwork analyzer (Hewlett-Packard, HP-8720ES).
3. Results and discussion For the specimen of polycrystalline Li–Zn ferrite, the crystallographic structure was investigated using X-ray diffraction. The powder X-ray diffraction patterns exhibited that all the samples were identified as a single phase of cubic spinel structure and additional lines corresponding to any other phase were not detected. The lattice constant was determined through the Nelson– Relay extrapolation method. The lattice constant variation with the composition X is shown in Fig. 1. It is seen that the lattice constant decreased almost linearly with an increase in X ; and that it obeyed Vegard’s law. All the obtained ferrite ceramics had a relative density larger than 95%, irrespective of the composition, and they were of dense microstructure. Information regarding the ferrite grain size and porosity was obtained from the microstructural observation of the fractured specimen. Fig. 2 shows SEM photographs of the fracture surface for the typical specimen. It was
found that the average grain size estimated from the geometric analysis was approximately 5 mm and it was almost independent of the composition X : The magnetization variation versus the composition X is shown in Fig. 3. As X was increased, the magnetization value increased, reached a maximum around X ¼ 0:75; and then decreased. It is possible to explain this magnetization variation by considering both the spin structure change from the Neel collinear structure to the Yafet– Kittel canted spin structure and the Neel temperature variation [3,13]. The complex permeability spectra of the polycrystalline ferrite are shown in Fig. 4. The real part of the permeability m0 remained almost constant,
Lattice constant (nm)
0.842 0.840 0.838 0.836 0.834 0.832 0.3
0.4
0.5
0.6
0.7
0.8
Chemical composition X Fig. 1. The lattice constant of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4, versus the chemical composition X :
Fig. 2. The SEM photographs of the fracture surface for the polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4: (a) X ¼ 0:4; and (b) X ¼ 0:7:
Magnetization (emu/g)
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
80
60
40
20 0.3
0.4
0.5
0.6
0.7
0.8
Chemical composition X
Real part of permeability
Fig. 3. The magnetization of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4, versus the chemical composition X :
800
X=0.30
600 X=0.40
400
X=0.50 X=0.60
200
X=0.70 X=0.75 X=0.80
0 104
105
Imaginary part of permeability
107
108
109
1010
Frequency (Hz)
(a) 400
X=0.30
300
X=0.40 X=0.50
200
100
X=0.60 X=0.70 X=0.75 X=0.80
until the frequency was raised to a certain value, and then began to decrease at higher frequency. The imaginary permeability m00 gradually increased with the frequency, and took a broad maximum at a certain frequency, where the real permeability rapidly decreased. This feature is well known as the natural resonance. For the chemical composition variation, it was found that the real permeability in the low-frequency region below 2 MHz decreased with an increase in X : But the reverse trend was seen in the high-frequency region. The real permeability above 300 MHz increased with an increase in X : As X was increased, the natural resonance frequency, where the imaginary permeability had a maximum value, shifted toward high frequency (from 2 to 25 MHz). The imaginary permeability in the low-frequency region below 20 MHz decreased with an increase in X : For the imaginary part of permeability as well as the real permeability, the reverse trend was also seen in the high-frequency region. The imaginary permeability above 2.5 GHz increased with an increase in X : In general, the complex permeability is related to two different magnetizing mechanisms: the spin rotational magnetization and the domain wall motion [7,9–11]. In our previous studies, it was possible to separate the complex permeability spectra of the polycrystalline spinel ferrites into the spin rotational component, wsp ð$ Þ; and the domain wall motion contribution, wdw ð$ Þ; using a numerical fitting [9–11]. The spin rotational component is of relaxation type, in which the damping friction is thought to be large enough, and its dispersion is inversely proportional to the frequency. The domain wall contribution is of resonance type and depends on the square of the frequency. Therefore, the following equations are obtained: mð$ Þ ¼ 1 þ wsp ð$ Þ þ wdw ð$ Þ
ð1Þ
and the individual components can be written as
0 104
(b)
106
343
105
106
107
108
109
1010
Frequency (Hz)
Fig. 4. The complex permeability spectra of polycrystalline Li– Zn ferrite, Li0.5XZn1XFe2+0.5XO4, with the chemical composition X : (a) real; and (b) imaginary parts.
wsp ð$ Þ ¼ Ksp =½1 þ jð$ =$ sp Þ;
ð2Þ
wdw ð$ Þ ¼ Kdw $ 2dw =½$ 2dw $ 2 þ jb$ ;
ð3Þ
where $ is the RF magnetic field frequency, Ksp the static spin susceptibility, $ sp the spin
resonance frequency, Kdw the static susceptibility of the domain wall motion, $ dw the domain wall motion resonance frequency, and b the frictional damping factor of the domain wall motion. On the spin resonance frequency $ sp in our studies, it corresponds to the divided value of the usual spin resonance frequency by the damping constant for the spin rotational motion. It is found that the complex permeability spectra of the polycrystalline spinel ferrite can be well reproduced using these equations and the five parameters. It is also clarified that the domain wall motion contribution starts to decrease at lower frequency and only the spin rotational component remains in the higherfrequency region. Consequently, the complex permeability spectra in the frequency region higher than 100 MHz can be described mainly using the spin rotational component. The above model calculation was applied to the experimentally obtained complex permeability spectra of the polycrystalline Li–Zn ferrite, and the dispersion parameters for each component were determined. In our previous studies [9–11], it is known that the complex permeability spectra of the polycrystalline ferrite are affected by the ferrite volume loading (the post-sintering density) and the microstructure such as the grain size. Namely, the spin rotational component depends only on the ferrite volume loading, while the domain wall motion contribution is much more sensitive to the microstructure and related not only to the ferrite volume loading but also to the ferrite grain size, since the domain wall configuration is closely related to the grain size. In this study, all the polycrystalline Li–Zn ferrite had a relative density larger than 95% and it was seen that the ferrite grain size was almost independent of the chemical composition from the result of the SEM observation. In addition, it is also seen that the complex permeability spectra in the frequency region higher than 100 MHz can be described mainly using the spin rotational component. Therefore, only the numerical parameters for the spin rotational component are considered in this study. The variations of the spin rotational component parameters with the chemical composition X are shown in Fig. 5. From the figure, it was found that the static spin susceptibility Ksp decreased with an
500
400 102 300
200 101 100
0
0.3
0.4
0.5
0.6
0.7
Spin resonance frequency (MHz)
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
Static spin susceptibility
344
0.8
Chemical composition X
Fig. 5. The variations of static spin susceptibility (open circle) and spin resonance frequency (open triangle) with the chemical composition of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4.
increase in X ; and that the spin resonance frequency $ sp shifted toward higher frequency as X was increased. The variation of the static spin susceptibility and the spin resonance frequency was similar to that of low-frequency permeability and natural resonance frequency, respectively. These features are explained as follows. Since the spin resonance frequency is proportional to the effective anisotropy field, the higher spin resonance frequency means a greater effective anisotropy field. As a result, increase in X produces greater anisotropy field. Roughly speaking, it is thought that the static spin susceptibility is given by the ratio of the magnetization flux to the effective anisotropy field. The experimental results exhibited that the magnetization flux increased with X and took a maximum around X ¼ 0:75; but decreased with further increase of X : It was clear that the degree of variation in the magnetization flux was much smaller than that of the effective anisotropy field. Therefore, the reduction of the static spin susceptibility with an increase in X is also attributed to the increase of the effective anisotropy field with an increase in X : As we presented in the previous studies [10,11], the product value of the static spin susceptibility and the spin resonance frequency corresponds to Snoek’s product. It provides a limitation on the permeability spectra of spinel ferrite [8]. We calculated the product values for the
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
Snoek's product (GHz)
polycrystalline Li–Zn ferrite, plotted in Fig. 6 as a function of the chemical composition X : It was shown that the Snoek’s product value increased with X ; took a maximum around X ¼ 0:75 and then decreased. This feature is similar to the relationship between the magnetization flux and the chemical composition, as expected from the above arguments on the static spin susceptibility and the spin resonance frequency. Fig. 7 exhibits
10
5
0
0.3
0.4
0.5
0.6
0.7
0.8
Chemical composition X Fig. 6. The variation of Snoek’s product value versus the chemical composition of polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4.
Snoek's product (GHz)
15
10
5
0
100
200
300
400
500
Magnetization (emu/cc) Fig. 7. The variation of Snoek’s product value with the magnetization flux for various polycrystalline ferrites: Li–Zn ferrite (open triangle) and the other ferrite studied in the previous paper (solid circle). The dashed line is an extrapolation of the experimentally obtained values.
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the variation of the Snoek’s product versus the magnetization flux. This figure contains the product values for three series of polycrystalline spinel ferrite (Ni–Zn ferrite, Mg–Zn ferrite and Ni–Zn–Cu ferrite) and Ni–Zn–Cu ferrite specially fabricated by the low-temperature process studied in our previous reports [10,11]. It was clear that the Snoek’s product value almost linearly increased with the magnetization flux, and this was valid for any kind of spinel ferrite and also for the Li–Zn ferrite. It was found from the figure that some Li– Zn ferrite with a large fraction of Li-ferrite have a relatively large Snoek’s product. Finally, we will study the electromagnetic wave absorption using the polycrystalline Li–Zn ferrite. Ferrite sintered ceramics have been used as very thin and extremely wide band electromagnetic wave absorbers in VHF and UHF bands [14]. The wide band characteristics are achieved by the frequency dispersion of the complex permeability: the imaginary part of the permeability m00 is almost inversely proportional to the frequency in these frequency bands, then the value of m00 d=l (d: absorber thickness, l: wave length in the free space) is kept almost constant in these frequency regions. That is, the spin rotational relaxation component plays an important role to give the absorption band. A large Snoek’s product leads to a large m00 value in the frequency region, and it is likely that this results in thinning of the matching thickness and increasing of the center frequency. Consider the single-layered electromagnetic wave absorber, which consists of a polycrystalline Li–Zn ferrite plate with thickness d located on a metal conducting plate. The input impedance Zð$ Þ is given by h i Zð$ Þ ¼ Z0 ðm=eÞ1=2 tanh jð$ d=cÞðemÞ1=2 : ð4Þ Here, Z0 is the characteristic impedance of free space, $ the angular frequency of the incident wave, c the electromagnetic wave velocity in free space, e and m the complex permittivity and permeability. The absorption G($) is obtained by the following equation: Gð$ Þ ¼ 20 log j½Zð$ Þ Z0 =½Zð$ Þ Z0 j:
ð5Þ
Using the experimentally obtained values of the complex permittivity and permeability, it is
T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347
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the matching thickness was minimum around X ¼ 0:75; where the Snoek’s product took the maximum value. It indicated that a large Snoek’s product led to thinning of the matching thickness and increasing of the center frequency as expected.
0
Absorption (dB)
-10 -20 -30
4. Conclusions
-40 X=0.80
-50
X=0.75 X=0.60 X=0.50 X=0.70
X=0.40
-60
108
109
Frequency (Hz) Fig. 8. The electromagnetic wave absorption spectra of the single-layered absorbers using the polycrystalline Li–Zn ferrite, Li0.5XZn1XFe2+0.5XO4.
Table 1 The center frequency, the matching thickness and the absorption band for the polycrystalline Li–Zn ferrite single-layered absorbers Composition X
Matching thickness (mm)
Center frequency (MHz)
Bandwidth (MHz)
0.4 0.5 0.6 0.7 0.75 0.8
5.5 4.5 4.0 3.5 3.0 4.0
150 250 340 550 850 530
90–220 170–360 240–480 390–750 650–1000 400–650
possible to estimate the absorption characteristics and to design the optimum absorber thickness. The electromagnetic wave absorption characteristics using the polycrystalline Li–Zn ferrite are shown in Fig. 8 and Table 1. They exhibited the potential of relatively wide band absorption in the frequency region from 100 MHz to 1 GHz. The center frequency shifted higher as X was increased, took its highest value around X ¼ 0:75; and then decreased. The center frequency was tunable in the range from 150 to 850 MHz. The matching thickness decreased from 5.5 to 3.0 mm as X was increased, attained the minimum value, and then increased. Consequently, it was found that the center frequency reached the maximum value and
Polycrystalline Li–Zn ferrites were prepared by the usual ceramic sintering method, they were of dense microstructure and the ferrite grain size was almost independent of the chemical composition. The complex permeability spectra were evaluated using two different impedance measurement techniques. As the Zn-ferrite fraction was increased, the low-frequency permeability increased and the natural resonance frequency shifted lower. Using the model calculation previously proposed, the complex permeability spectra were also numerically separated into spin rotation and domain wall motion contributions. For the spin rotational component, the static spin susceptibility increased and the spin resonance frequency shifted lower with an increase in the Zn-ferrite fraction. They are attributed mainly to the variation of the effective anisotropy field with the chemical composition. The product values of the static spin susceptibility and the spin resonance frequency, corresponding to the Snoek’s product value, are proportional to the magnetization flux. The spin rotation component played an important role in the high-frequency region, and the Snoek’s product was a good index of high-frequency devices such as single-layered electromagnetic wave absorber using the polycrystalline ferrite.
Acknowledgements The authors are grateful to Dr. T. Kikuchi of Himeji Institute of Technology for his help with the sample preparation and measurements.
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T. Nakamura et al. / Journal of Magnetism and Magnetic Materials 256 (2003) 340–347 [2] D. Polder, J. Smit, Rev. Mod. Phys. 25 (1953) 81. [3] J. Smit, H.M.J. Wijn, Ferrites, Phillips Technical Library, Eindhoven, The Netherland, 1959. [4] E. Scloemann, J. Appl. Phys. 41 (1970) 204. [5] A. Globus, J. Phys. C 1 (1977) 1. [6] J.P. Bouchaud, P.G. Zerah, J. Appl. Phys. 67 (1990) 5512. [7] Y. Naito, Proceedings of the First International Conference on Ferrites, 1970, p. 558. [8] J.L. Snoek, Physica XIV 4 (1948) 207.
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[9] T. Nakamura, T. Tsutaoka, Proceedings of the Fourth International Conference on Electroceramics and Applications, 1994, p. 1149. [10] T. Nakamura, J. Magn. Magn. Mater. 168 (1996) 285. [11] T. Nakamura, J. Appl. Phys. 88 (2000) 348. [12] T. Nakamura, K. Hatakeyama, IEEE Trans. Magn. 36 (5) (2000) 3415. [13] Y. Yafet, C. Kittel, Phys. Rev. 87 (1952) 290. [14] Y. Naito, K. Suetake, IEEE Trans. Microwave Theory Tech. 19 (1971) 65.