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Ultrathin broadband microwave absorbers using ferromagnetic films
Journal of Magnetism and Magnetic Materials 349 (2014) 259–263
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Ultrathin broadband microwave absorbers using ferromagnetic films Ping Chen n, Ren-kai Li, Yan Gu, Yue Shi, Rui-xin Wu School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 24 January 2013 Received in revised form 19 August 2013 Available online 12 September 2013
We have theoretically studied the absorption performances of microwave absorbers made of ferromagnetic films. For films with different frequency dispersive types of permeability, we have found that only the films with relaxation type of permeability can be used to realize broadband microwave absorbers with thin thickness. The condition for optimal absorption has also been derived. As the demonstrations, we have designed the magnetic film absorbers using Ni–Zn–Co ferrite film and iron nanofilm, respectively. Deploying periodic multilayer structure, the absorbers work at the optimal absorption condition. The numerical results show our absorbers have good absorption performances in broadband microwave frequency range. & 2013 Elsevier B.V. All rights reserved.
Keywords: Electromagnetic wave absorption Magnetic film Magnetic multilayer
1. Introduction In the past decades, the problem of electromagnetic (EM) interferences in electronic equipment is getting serious due to the increasing complexity of equipment [1]. To suppress the EM interferences, EM wave absorbers are often used [1–3]. Since the available space inside equipment is usually restricted, the absorber should be as thin as possible [3]. On the other hand, the frequency bands of electromagnetic signals are becoming much wider in many types of modern electronic equipment. For instance, the working frequencies of wireless communication devices and clock frequency of CPU in current computers are from hundreds of MHz to several GHz. The broadband absorbers will be preferable to suppress the EM interferences between such signals with different frequencies. Apparently, the broadband absorber together with thin thickness is in demand. In order to improve the performances of absorber, numerous new designs have been proposed, including the metamaterial absorbers, the resistive frequency selective surface (RFSS) absorbers, the ferromagnetic absorbers and so on [4–11]. The metamaterial absorber made of planar metallic resonators can achieve perfect absorption near the resonance frequency of resonators. The thickness of metamaterial absorber is much thinner than that of traditional absorber. However, the metamaterial absorber is difficult to obtain a broad absorption bandwidth due to its resonance absorption mechanism [4]. The RFSS absorber is similar to the Salisbury screen absorber except that the resistive sheet in Salisbury screen is replaced by the resistive patches with designed shapes [5]. By optimizing the shape of resistive patch, broadband RFSS absorbers can be obtained [5–7]. The main disadvantage of RFSS is that its
n
Corresponding author. Tel./fax: þ 86 2583592595. E-mail address: [email protected] (P. Chen).
0304-8853/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2013.09.010
thickness is not thin enough, typically in millimeter dimension [5–7]. The ferromagnetic materials or their composite structures also can be used to absorb microwave radiation [8–11]. In fact, the ferromagnetic films have large magnetic permeability and characteristic frequencies due to their huge shape anisotropy [12]. This feature suggests that the ferromagnetic films can be used to realize broadband absorbers together with thin thickness [13]. In this work, the EM responses of multilayer structures made of alternant ferromagnetic and dielectric films were studied in the framework of equivalent transmission network theory. It was demonstrated that the structure made of ferromagnetic films with relaxation type of permeability could be a broadband microwave absorber with thin thickness. In order to achieve the optimal absorption, a periodic multilayer structure was proposed. Based on the theoretical model, two microwave absorbers were designed using the ferromagnetic films reported in literatures. The reflectivity was lower than 10 dB (0.5 18 GHz) for the Ni–Zn–Co ferrite film absorber and 4 dB (2 18 GHz) for the iron film absorber, respectively. Meanwhile, the thicknesses of absorbers were only in sub-millimeter dimension. 2. Model and theory The basic magnetic absorber is a sandwich structure as shown in Fig. 1(a). It is composed of a ferromagnetic layer, a spacer layer and a cover layer, respectively. The cover layer is usually a dielectric layer to protect the ferromagnetic film from oxidation. For the convenience of discussion, the spacer layer and cover layer are supposed to be the same. Generally, the absorber is placed against a metallic ground. If the structure is normally illuminated by the EM wave, its EM responses can be modeled by the equivalent transmission network shown in Fig. 1(b) [14], where V1, I1 are the equivalent
260
P. Chen et al. / Journal of Magnetism and Magnetic Materials 349 (2014) 259–263
where ω is the frequency of EM wave, μ0 is the magnetic permeability of free-space, μr is the relative magnetic permeability of ferromagnetic film. The absorption performance of absorber loaded with a metallic background usually can be described by its reflectivity R at the interface between absorber and free-space, which is defined as [14]: Z η R ¼ in 0 Z in þ η0
ð6Þ
where η0 ¼ 120π is the wave impedance of free-space. It is well known that the magnetic permeability of ferromagnetic material is frequency dependent. The dispersion type of permeability will result in quite different absorption performances. The basic dispersion types of magnetic permeability are the resonant type and the relaxation type [16]. For the resonant type, the frequency dependence of permeability is [16]:
μr ¼ 1 þ
χs
ð7Þ
1 þ iβωr ω2r
where ωr ¼ ω=ωr is the normalized frequency versus the resonant frequency ωr , χ s , β are the static susceptibility and damping coefficient of ferromagnetic material, respectively. Substituting Eq. (7) for the μr in Eq. (5), we have the Z in of resonant type of magnetic absorber Z in ¼ Rrc
ðβωr Þ2
þ jRrc ð1ω2r Þ2 þ ðβωr Þ2
"
ð2Dn þ 1Þβωr
χs
þ
βωr ð1ω2r Þ ð1ω2r Þ2 þðβωr Þ2
#
ð8Þ Fig. 1. (a) Sketch of magnetic film absorber and (b) its equivalent transmission network model.
voltage and current at the interface between free-space and absorber, V0, I0 are the equivalent voltage and current at the interface between absorber and metallic ground, β1 and β2 are the propagation constant, and η1, η2 are the wave impedance in dielectric and ferromagnetic layers, respectively. According to the transmission network theory [15], the relationship between V1, I1, V0, I0 can be described by transmission matrix A: ! ! V1 V0 ¼A ð1Þ I1 I0 Here, matrix A is the product of transmission matrix of the ferromagnetic layer and two dielectric layers: A ¼ A1 A2 A1 where 0 1 cos ðβ 1 DÞ jη1 sin ðβ1 DÞ A ð2Þ A1 ¼ @ j sin ηðβ1 DÞ cos ðβ1 DÞ
where Rrc ¼ χ s μ0 Lωr =β is the characteristic resistance for resonant type of ferromagnetic film, Dn ¼D/L is the thickness ratio of dielectric layer to magnetic film. Using Eqs. (6) and (8), the reflectivity of magnetic absorber can be calculated. Fig. 2 plots the numerical results of the absorbers with different characteristic resistances, Rrc . In the calculation, we take values χ s ¼ 100, β ¼ 0:1 and Dn ¼ 0:1. As shown, the reflectivity of absorber with Rrc ¼ η0 is lower than 50 dB at ωr ¼ ω=ωr ¼ 1, which is an excellent absorption performance. However, the results also show that the absorption band is very narrow, indicating that the ferromagnetic films with resonant type of permeability are unsuitable to construct broadband absorbers. On the contrary, the ferromagnetic films with relaxation type of permeability can realize broadband absorbers. The permeability of relaxation type of magnetic material is [16]:
μτ ¼ 1 þ
χs
1 þiωτ
ð9Þ
1
0 A2 ¼ @
cos ðβ 2 LÞ j
sin ðβ2 LÞ
η2
jη2 sin ðβ2 LÞ cos ðβ2 LÞ
1 A
ð3Þ
D, L are the thickness of dielectric layer and ferromagnetic layer, respectively. The input impedance Z in of whole structure can be obtained from Eq. (1): V1 a11 V 0 þ a12 I 0 a11 V 0 =I 0 þa12 Z in ¼ ¼ ¼ I1 a21 V 0 þ a22 I 0 a21 V 0 =I 0 þa22
ð4Þ
where aij (i, j¼ 1, 2) is the element of transmission matrix A. Since magnetic absorber is placed on a metallic background, its load impedance ZL ¼ V0/I0 is zero. If the absorber is made of thin films, so that β1D⪡1 and β2L⪡1, then Z in can be simplified as: a12 jωμ0 ð2D þ μr LÞ Z in ¼ a22
ð5Þ
Fig. 2. Reflectivity spectrums of resonant type of magnetic film absorber with different characteristic resistance Rrc .
P. Chen et al. / Journal of Magnetism and Magnetic Materials 349 (2014) 259–263
where ωτ ¼ ω=ωτ is the normalized frequency versus the relaxation frequency ωτ . Substituting Eq. (9) for the μr in Eq. (5), we have the Z in of relaxation type of magnetic absorber: " # ω2τ ωτ τ ð2Dn þ 1Þωτ þ jR þ Z in ¼ Rτc ð10Þ c χs 1 þ ω2τ 1 þ ω2τ where Rτc ¼ μ0 ωτ χ s L is the characteristic resistance of relaxation type magnetic film. The reflectivity of relaxation type magnetic absorber can be calculated by using Eqs. (10), (6). Fig. 3(a) plots the numerical results with different Rτc . In the calculation, we take values χ s ¼ 100 and Dn ¼ 0:1. As shown in the figure, the reflectivity spectrum of absorber with Rτc ¼ η0 is the lowest one and lower than 15 dB from ωτ ¼ 3 to ωτ ¼ 10. Usually, the ωτ of relaxation type of ferromagnetic materials are from hundreds MHz to several GHz [16]. Therefore, the efficient absorption band of relaxation type of magnetic absorber could be tens GHz, which is a broad absorption band at microwave frequencies. To meet the optimal absorption condition Rτc ¼ η0 , the thickness of magnetic layer L is about hundreds or tens of microns. The reflectivity spectrums of magnetic absorbers with different Dn at Rτc ¼ η0 were plotted in Fig. 3(b), which show that smaller Dn results in better absorption performance. Thus, the total thickness of absorber will be in sub-millimeter dimension, which is much thinner than traditional microwave absorbers. According to the optimal absorption condition Rτc ¼ μ0 ωτ χ s L ¼ η0 , the ferromagnetic materials with larger product of χ s and ωτ can be used to construct thinner absorbers. Usually, the ferromagnetic film with thickness in nanometer or micron dimension has much larger
261
Ferromagnetic Film
Metal Ground
N-th Unit Dielectric Layer
1st Unit
Fig. 4. Sketch of magnetic periodic multilayer absorber.
χ s ωτ than that of ferromagnetic bulk material due to its anisotropy [12]. So, we can use ferromagnetic film to construct thin microwave absorber. The typical value of χ s ωτ for ferromagnetic film is about 1011 1012 Hz [12]. Therefore, the optimal thickness L of ferromagnetic layer should be about hundreds or tens of microns, much larger than the thickness of single film. In order to take advantage of the ferromagnetic films, we used a periodic multilayer structure. As shown in Fig. 4, the absorber is segmented to N units. Each unit has a same symmetric sandwich structure. According to the microwave network theory of cascade [15], the total transmission matrix A of periodic structure can be described as: A ¼ ½A1 A2 A1 N
ð11Þ
Since the thickness of dielectric layer and ferromagnetic film in each unit are in nanometer dimension, we can take for granted that β1D⪡1 and β2L⪡1. So, the high order power of β1D and β2L can be left out in Eq. (11). As a result, the Z in of periodic multilayer structure with a metallic background can be written as Z in jωμ0 ð2ND þ μr NLÞ
ð12Þ
Comparing Eq. (12) with Eq. (5), we can find only the thickness D and L in Eq. (5) are replaced by the total thickness of dielectric layers ND and total thickness of ferromagnetic films NL here. If the Rτc is redefined as Rτc ¼ μ0 ωτ χ s NL, Eq. (10) is still correct for the periodic absorber made of relaxation type of ferromagnetic film. Therefore, just same as the basic absorber, the periodic absorber also can achieve optimal absorption at Rτc ¼ η0 . Apparently, the requirement for optimal thickness L will change to the requirement for the optimal total thickness NL. So, we can meet the new optimal absorption condition by controlling the number of units in a periodic absorber even if it is made of the ferromagnetic film with thickness in nanometer or micron dimension.
3. Results and discussion
Fig. 3. Reflectivity spectrums of relaxation type of magnetic film absorber: (a) with different characteristic resistance Rτc at Dn ¼ 0:1, (b) with different thickness ratio Dn at Rτc ¼ η0 .
We designed the periodic layered magnetic absorbers using practical ferromagnetic films reported in literatures. Because of the reasons mentioned above, only the ferromagnetic films with relaxation type of permeability were considered. It was reported that some spinel ferrites can obtain relaxation type of permeability by changing their compositions or synthesis conditions [17–20]. For example, the Ni–Zn–Co (Ni0.22Zn0.52Co0.03Fe2.23O4) ferrite film synthesized by the spin-spray method has a relaxation type of permeability spectrum [19]. By fitting the reported experimental data, the relaxation frequency and susceptibility of this Ni–Zn–Co ferrite film are obtained, which are 300 MHz and 260, respectively. The thickness of ferrite film should be about 0.62 mm to meet the optimal absorption condition. However, the actual thickness of such ferrite film is only about 1 μm [20]. Therefore, the periodic multilayer structure must be used. The periodic absorber we designed is composed of 620 units with the sandwich structure, in which each cell has L ¼1 μm and D ¼50 nm. The total thickness of ferrite micron film is about 0.62 mm. The reflectivity spectrum of periodic absorber can be calculated by the transmission matrix
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P. Chen et al. / Journal of Magnetism and Magnetic Materials 349 (2014) 259–263
method [21]. Fig. 5 plots the numerical results. It can be found that the reflectivity of this periodic structure is lower than 10 dB from 0.5 GHz to 18 GHz. Considering that its total thickness H is only about 0.68 mm, the periodic multilayer absorber made of Ni–Zn–Co ferrite films is a promising ultrathin broadband microwave absorber. Besides the ferrite films, the metallic ferromagnetic films with relaxation type of permeability also are potential choices for magnetic film absorbers. According to the Snoek's law, the products χ s ωτ of metallic ferromagnetic films will be larger since the saturation magnetizations of ferromagnetic metals usually are larger than those of ferrites [12]. As a result, the thickness of absorbers made of metallic ferromagnetic films could be thinner. Meanwhile, the metallic ferromagnetic film has a higher Curie temperature than that of ferrite film [16], which means the absorber made of metallic ferromagnetic film can work at higher temperature. Usually, the permeability of metallic ferromagnetic film will present the resonant type of dispersion. However, in recent years, a few methods were proposed to tailor the high frequency permeability of metallic ferromagnetic films or their composite structures [22–25]. For example, Iakubov et al. successfully fabricated the iron nanometer film with relaxation type of permeability by controlling the atmosphere during the magnetic sputtering process [25]. The relaxation frequency and susceptibility of iron film fitted from their experimental data in Ref. [25] are 1.1 GHz and 180, respectively. The thickness of iron film for optimal absorption should be hundreds of microns. Apparently, the periodic multilayer structure also must be employed to make use of such iron nanometer film. Fig. 6 plots the calculated
reflectivity spectrums of periodic multilayer absorber composed of iron nanometer films, where L¼ 250 nm and D¼ 20 nm. The periodic absorber is composed of 1050 units. The total thickness of iron films is about 0.26 mm, which meets the condition of optimal absorption. It is known that the conductivity s of metallic film drops rapidly as the thickness of film reduces to nanometers. For instance, the s of CoFeB/SiO2 granular film with thickness of 500 nm was measured about s ¼ 860 S=m [26]. In the calculation, the s of nanometer iron film takes the values of 1000, 500, and 200 S/m, respectively. The numerical results show that the reflectivity of iron film with s¼ 200 S/m can be lower than 4 dB from 2 GHz to 18 GHz. Considering that the total thickness of absorber is only about 0.3 mm, the absorption performance is good enough for many practical applications, e.g. the EM interference suppression in electronic equipment. The results also show that larger s of metallic film can seriously destroy the absorption performance of magnetic absorber. Therefore, controlling conductivity of film is an important issue in the realization of ferromagnetic metallic film absorbers.
4. Conclusion In conclusion, we have studied the absorption performances of magnetic film absorbers in theory. The results indicate that the ferromagnetic films with relaxation type of permeability can be used to construct thin broadband microwave absorbers. A periodic multilayer structure is proposed to meet the optimal absorption condition. Basing on this periodic structure, we have designed magnetic film absorbers using the Ni–Zn–Co ferrite micron film and iron nanometer film, respectively. Such designed absorbers are promising microwave absorbers, which have good absorption performances together with wide band and thin thickness.
Acknowledgments This work is supported by the Natural Science Foundation of China (Nos. 61071007, 61001017 and 61271080), the Specialized Research Fund for the Doctoral Program of Higher Education (Nos. 20100091120045 and 20110091110030), the Natural Science Foundation of Jiangsu province (BK2011338, BK2012722) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. References Fig. 5. Reflectivity spectrums of magnetic periodic multilayer absorber made of Ni–Zn–Co ferrite film.
Fig. 6. Reflectivity spectrums of magnetic periodic multilayer absorber made of iron nanometer film with s ¼1000, 500 and 200 S/m.
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[11] A.V. Osipov, I.T. Iakubov, A.N. Lagarkov, S.A. Maklakov, D.A. Petrov, K. N. Rozanov, et al., Multi-layered Fe films for microwave applications, Proceeding of PIERS 3 (2007) 1303–1306. [12] A.N. Lagarkov, K.N. Rozanov, High-frequency behavior of magnetic composites, Journal of Magnetism and Magnetic Materials 321 (2009) 208292. [13] K.N. Rozanov, S.N. Starostenko, Influence of permeability dispersion on the bandwidth of magnetic radio absorbers, Journal of Communications Technology and Electronics 48 (2003) 652–659. [14] E. Knott, J. Shaeffer, M. Tuley, Radar Cross Section, Artech House, Dedham, MA, 1985. [15] M. Pozar, Microwave Engineering, Wiley, New York, 2005. [16] R. Tebble, D. Craik, Magnetic Materials, Wiley, New York, 1969. [17] G. Herrera, Domain wall dispersions: relaxation and resonance in Ni–Zn ferrite doped with V2O3, Journal of Applied Physics 108 (2010) 103901. [18] K. Tsutaoka, Frequency dispersion of complex permeability of Mn–Zn and Ni–Zn spinel ferrites and their composite materials, Journal of Applied Physics 93 (2003) 2789–2796. [19] N. Matsushita, T. Nakamura, M. Abe, Spin-sprayed Ni–Zn–Co ferrite films with high μ′′ 4 100 in extremely wide frequency range 100 MHz to 1 GHz, Journal of Applied Physics 93 (2003) 7133–7135. [20] A.K. Subramani, N. Matsushita, M. Tada, T. Watanabe, M. Abe, M. Yoshimura, NiZnCo ferrite films by spin spray technique: morphology and magnetic properties, Journal of Materials Science 43 (2008) 2372–2376.
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[21] R.X. Wu, Effective negative refraction index in periodic metal–ferrite–metal film composite, Journal of Applied Physics 97 (2005) 076105. [22] M. Mruczkiewicz, M. Krawczyk, R.V. Mikhaylovskiy, V.V. Kruglyak, Towards high-frequency negative permeability using magnonic crystals in metamaterial design, Physical Review B 86 (2012) 024425. [23] O. Dmytriiev, M. Dvornik, R.V. Mikhaylovskiy, M. Franchin, H. Fangohr, L. Giovannini, et al., Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation, Physical Review B 86 (2012) 104405. [24] R.V. Mikhaylovskiy, E. Hendry, V.V. Kruglyak, Negative permeability due to exchange spin-wave resonances in thin magnetic films with surface pinning, Physical Review B 82 (2010) 195446. [25] I. Iakubov, A.N. Lagarkov, S.A. Maklakov, A.V. Osipov, K.N. Rozanov, I.A. Ryzhikov, et al., Experimental study of microwave permeability of thin Fe films, Journal of Magnetism and Magnetic Materials 358–359 (2003) 195–197. [26] M. Munakata, M. Motoyama, M. Yagi, T. Ito, Y. Shimada, M. Yamaguchi, et al., Very high electrical resistivity and heteroamorphous structure of soft magnetic (Co35.6Fe50B14.4)–(SiO2) thin films, IEEE Transactions on Magnetics 38 (2002) 31479.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Ultrathin broadband microwave absorbers using ferromagnetic films Ping Chen n, Ren-kai Li, Yan Gu, Yue Shi, Rui-xin Wu School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, People's Republic of China
art ic l e i nf o
a b s t r a c t
Article history: Received 24 January 2013 Received in revised form 19 August 2013 Available online 12 September 2013
We have theoretically studied the absorption performances of microwave absorbers made of ferromagnetic films. For films with different frequency dispersive types of permeability, we have found that only the films with relaxation type of permeability can be used to realize broadband microwave absorbers with thin thickness. The condition for optimal absorption has also been derived. As the demonstrations, we have designed the magnetic film absorbers using Ni–Zn–Co ferrite film and iron nanofilm, respectively. Deploying periodic multilayer structure, the absorbers work at the optimal absorption condition. The numerical results show our absorbers have good absorption performances in broadband microwave frequency range. & 2013 Elsevier B.V. All rights reserved.
Keywords: Electromagnetic wave absorption Magnetic film Magnetic multilayer
1. Introduction In the past decades, the problem of electromagnetic (EM) interferences in electronic equipment is getting serious due to the increasing complexity of equipment [1]. To suppress the EM interferences, EM wave absorbers are often used [1–3]. Since the available space inside equipment is usually restricted, the absorber should be as thin as possible [3]. On the other hand, the frequency bands of electromagnetic signals are becoming much wider in many types of modern electronic equipment. For instance, the working frequencies of wireless communication devices and clock frequency of CPU in current computers are from hundreds of MHz to several GHz. The broadband absorbers will be preferable to suppress the EM interferences between such signals with different frequencies. Apparently, the broadband absorber together with thin thickness is in demand. In order to improve the performances of absorber, numerous new designs have been proposed, including the metamaterial absorbers, the resistive frequency selective surface (RFSS) absorbers, the ferromagnetic absorbers and so on [4–11]. The metamaterial absorber made of planar metallic resonators can achieve perfect absorption near the resonance frequency of resonators. The thickness of metamaterial absorber is much thinner than that of traditional absorber. However, the metamaterial absorber is difficult to obtain a broad absorption bandwidth due to its resonance absorption mechanism [4]. The RFSS absorber is similar to the Salisbury screen absorber except that the resistive sheet in Salisbury screen is replaced by the resistive patches with designed shapes [5]. By optimizing the shape of resistive patch, broadband RFSS absorbers can be obtained [5–7]. The main disadvantage of RFSS is that its
n
Corresponding author. Tel./fax: þ 86 2583592595. E-mail address: [email protected] (P. Chen).
0304-8853/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2013.09.010
thickness is not thin enough, typically in millimeter dimension [5–7]. The ferromagnetic materials or their composite structures also can be used to absorb microwave radiation [8–11]. In fact, the ferromagnetic films have large magnetic permeability and characteristic frequencies due to their huge shape anisotropy [12]. This feature suggests that the ferromagnetic films can be used to realize broadband absorbers together with thin thickness [13]. In this work, the EM responses of multilayer structures made of alternant ferromagnetic and dielectric films were studied in the framework of equivalent transmission network theory. It was demonstrated that the structure made of ferromagnetic films with relaxation type of permeability could be a broadband microwave absorber with thin thickness. In order to achieve the optimal absorption, a periodic multilayer structure was proposed. Based on the theoretical model, two microwave absorbers were designed using the ferromagnetic films reported in literatures. The reflectivity was lower than 10 dB (0.5 18 GHz) for the Ni–Zn–Co ferrite film absorber and 4 dB (2 18 GHz) for the iron film absorber, respectively. Meanwhile, the thicknesses of absorbers were only in sub-millimeter dimension. 2. Model and theory The basic magnetic absorber is a sandwich structure as shown in Fig. 1(a). It is composed of a ferromagnetic layer, a spacer layer and a cover layer, respectively. The cover layer is usually a dielectric layer to protect the ferromagnetic film from oxidation. For the convenience of discussion, the spacer layer and cover layer are supposed to be the same. Generally, the absorber is placed against a metallic ground. If the structure is normally illuminated by the EM wave, its EM responses can be modeled by the equivalent transmission network shown in Fig. 1(b) [14], where V1, I1 are the equivalent
260
P. Chen et al. / Journal of Magnetism and Magnetic Materials 349 (2014) 259–263
where ω is the frequency of EM wave, μ0 is the magnetic permeability of free-space, μr is the relative magnetic permeability of ferromagnetic film. The absorption performance of absorber loaded with a metallic background usually can be described by its reflectivity R at the interface between absorber and free-space, which is defined as [14]: Z η R ¼ in 0 Z in þ η0
ð6Þ
where η0 ¼ 120π is the wave impedance of free-space. It is well known that the magnetic permeability of ferromagnetic material is frequency dependent. The dispersion type of permeability will result in quite different absorption performances. The basic dispersion types of magnetic permeability are the resonant type and the relaxation type [16]. For the resonant type, the frequency dependence of permeability is [16]:
μr ¼ 1 þ
χs
ð7Þ
1 þ iβωr ω2r
where ωr ¼ ω=ωr is the normalized frequency versus the resonant frequency ωr , χ s , β are the static susceptibility and damping coefficient of ferromagnetic material, respectively. Substituting Eq. (7) for the μr in Eq. (5), we have the Z in of resonant type of magnetic absorber Z in ¼ Rrc
ðβωr Þ2
þ jRrc ð1ω2r Þ2 þ ðβωr Þ2
"
ð2Dn þ 1Þβωr
χs
þ
βωr ð1ω2r Þ ð1ω2r Þ2 þðβωr Þ2
#
ð8Þ Fig. 1. (a) Sketch of magnetic film absorber and (b) its equivalent transmission network model.
voltage and current at the interface between free-space and absorber, V0, I0 are the equivalent voltage and current at the interface between absorber and metallic ground, β1 and β2 are the propagation constant, and η1, η2 are the wave impedance in dielectric and ferromagnetic layers, respectively. According to the transmission network theory [15], the relationship between V1, I1, V0, I0 can be described by transmission matrix A: ! ! V1 V0 ¼A ð1Þ I1 I0 Here, matrix A is the product of transmission matrix of the ferromagnetic layer and two dielectric layers: A ¼ A1 A2 A1 where 0 1 cos ðβ 1 DÞ jη1 sin ðβ1 DÞ A ð2Þ A1 ¼ @ j sin ηðβ1 DÞ cos ðβ1 DÞ
where Rrc ¼ χ s μ0 Lωr =β is the characteristic resistance for resonant type of ferromagnetic film, Dn ¼D/L is the thickness ratio of dielectric layer to magnetic film. Using Eqs. (6) and (8), the reflectivity of magnetic absorber can be calculated. Fig. 2 plots the numerical results of the absorbers with different characteristic resistances, Rrc . In the calculation, we take values χ s ¼ 100, β ¼ 0:1 and Dn ¼ 0:1. As shown, the reflectivity of absorber with Rrc ¼ η0 is lower than 50 dB at ωr ¼ ω=ωr ¼ 1, which is an excellent absorption performance. However, the results also show that the absorption band is very narrow, indicating that the ferromagnetic films with resonant type of permeability are unsuitable to construct broadband absorbers. On the contrary, the ferromagnetic films with relaxation type of permeability can realize broadband absorbers. The permeability of relaxation type of magnetic material is [16]:
μτ ¼ 1 þ
χs
1 þiωτ
ð9Þ
1
0 A2 ¼ @
cos ðβ 2 LÞ j
sin ðβ2 LÞ
η2
jη2 sin ðβ2 LÞ cos ðβ2 LÞ
1 A
ð3Þ
D, L are the thickness of dielectric layer and ferromagnetic layer, respectively. The input impedance Z in of whole structure can be obtained from Eq. (1): V1 a11 V 0 þ a12 I 0 a11 V 0 =I 0 þa12 Z in ¼ ¼ ¼ I1 a21 V 0 þ a22 I 0 a21 V 0 =I 0 þa22
ð4Þ
where aij (i, j¼ 1, 2) is the element of transmission matrix A. Since magnetic absorber is placed on a metallic background, its load impedance ZL ¼ V0/I0 is zero. If the absorber is made of thin films, so that β1D⪡1 and β2L⪡1, then Z in can be simplified as: a12 jωμ0 ð2D þ μr LÞ Z in ¼ a22
ð5Þ
Fig. 2. Reflectivity spectrums of resonant type of magnetic film absorber with different characteristic resistance Rrc .
P. Chen et al. / Journal of Magnetism and Magnetic Materials 349 (2014) 259–263
where ωτ ¼ ω=ωτ is the normalized frequency versus the relaxation frequency ωτ . Substituting Eq. (9) for the μr in Eq. (5), we have the Z in of relaxation type of magnetic absorber: " # ω2τ ωτ τ ð2Dn þ 1Þωτ þ jR þ Z in ¼ Rτc ð10Þ c χs 1 þ ω2τ 1 þ ω2τ where Rτc ¼ μ0 ωτ χ s L is the characteristic resistance of relaxation type magnetic film. The reflectivity of relaxation type magnetic absorber can be calculated by using Eqs. (10), (6). Fig. 3(a) plots the numerical results with different Rτc . In the calculation, we take values χ s ¼ 100 and Dn ¼ 0:1. As shown in the figure, the reflectivity spectrum of absorber with Rτc ¼ η0 is the lowest one and lower than 15 dB from ωτ ¼ 3 to ωτ ¼ 10. Usually, the ωτ of relaxation type of ferromagnetic materials are from hundreds MHz to several GHz [16]. Therefore, the efficient absorption band of relaxation type of magnetic absorber could be tens GHz, which is a broad absorption band at microwave frequencies. To meet the optimal absorption condition Rτc ¼ η0 , the thickness of magnetic layer L is about hundreds or tens of microns. The reflectivity spectrums of magnetic absorbers with different Dn at Rτc ¼ η0 were plotted in Fig. 3(b), which show that smaller Dn results in better absorption performance. Thus, the total thickness of absorber will be in sub-millimeter dimension, which is much thinner than traditional microwave absorbers. According to the optimal absorption condition Rτc ¼ μ0 ωτ χ s L ¼ η0 , the ferromagnetic materials with larger product of χ s and ωτ can be used to construct thinner absorbers. Usually, the ferromagnetic film with thickness in nanometer or micron dimension has much larger
261
Ferromagnetic Film
Metal Ground
N-th Unit Dielectric Layer
1st Unit
Fig. 4. Sketch of magnetic periodic multilayer absorber.
χ s ωτ than that of ferromagnetic bulk material due to its anisotropy [12]. So, we can use ferromagnetic film to construct thin microwave absorber. The typical value of χ s ωτ for ferromagnetic film is about 1011 1012 Hz [12]. Therefore, the optimal thickness L of ferromagnetic layer should be about hundreds or tens of microns, much larger than the thickness of single film. In order to take advantage of the ferromagnetic films, we used a periodic multilayer structure. As shown in Fig. 4, the absorber is segmented to N units. Each unit has a same symmetric sandwich structure. According to the microwave network theory of cascade [15], the total transmission matrix A of periodic structure can be described as: A ¼ ½A1 A2 A1 N
ð11Þ
Since the thickness of dielectric layer and ferromagnetic film in each unit are in nanometer dimension, we can take for granted that β1D⪡1 and β2L⪡1. So, the high order power of β1D and β2L can be left out in Eq. (11). As a result, the Z in of periodic multilayer structure with a metallic background can be written as Z in jωμ0 ð2ND þ μr NLÞ
ð12Þ
Comparing Eq. (12) with Eq. (5), we can find only the thickness D and L in Eq. (5) are replaced by the total thickness of dielectric layers ND and total thickness of ferromagnetic films NL here. If the Rτc is redefined as Rτc ¼ μ0 ωτ χ s NL, Eq. (10) is still correct for the periodic absorber made of relaxation type of ferromagnetic film. Therefore, just same as the basic absorber, the periodic absorber also can achieve optimal absorption at Rτc ¼ η0 . Apparently, the requirement for optimal thickness L will change to the requirement for the optimal total thickness NL. So, we can meet the new optimal absorption condition by controlling the number of units in a periodic absorber even if it is made of the ferromagnetic film with thickness in nanometer or micron dimension.
3. Results and discussion
Fig. 3. Reflectivity spectrums of relaxation type of magnetic film absorber: (a) with different characteristic resistance Rτc at Dn ¼ 0:1, (b) with different thickness ratio Dn at Rτc ¼ η0 .
We designed the periodic layered magnetic absorbers using practical ferromagnetic films reported in literatures. Because of the reasons mentioned above, only the ferromagnetic films with relaxation type of permeability were considered. It was reported that some spinel ferrites can obtain relaxation type of permeability by changing their compositions or synthesis conditions [17–20]. For example, the Ni–Zn–Co (Ni0.22Zn0.52Co0.03Fe2.23O4) ferrite film synthesized by the spin-spray method has a relaxation type of permeability spectrum [19]. By fitting the reported experimental data, the relaxation frequency and susceptibility of this Ni–Zn–Co ferrite film are obtained, which are 300 MHz and 260, respectively. The thickness of ferrite film should be about 0.62 mm to meet the optimal absorption condition. However, the actual thickness of such ferrite film is only about 1 μm [20]. Therefore, the periodic multilayer structure must be used. The periodic absorber we designed is composed of 620 units with the sandwich structure, in which each cell has L ¼1 μm and D ¼50 nm. The total thickness of ferrite micron film is about 0.62 mm. The reflectivity spectrum of periodic absorber can be calculated by the transmission matrix
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method [21]. Fig. 5 plots the numerical results. It can be found that the reflectivity of this periodic structure is lower than 10 dB from 0.5 GHz to 18 GHz. Considering that its total thickness H is only about 0.68 mm, the periodic multilayer absorber made of Ni–Zn–Co ferrite films is a promising ultrathin broadband microwave absorber. Besides the ferrite films, the metallic ferromagnetic films with relaxation type of permeability also are potential choices for magnetic film absorbers. According to the Snoek's law, the products χ s ωτ of metallic ferromagnetic films will be larger since the saturation magnetizations of ferromagnetic metals usually are larger than those of ferrites [12]. As a result, the thickness of absorbers made of metallic ferromagnetic films could be thinner. Meanwhile, the metallic ferromagnetic film has a higher Curie temperature than that of ferrite film [16], which means the absorber made of metallic ferromagnetic film can work at higher temperature. Usually, the permeability of metallic ferromagnetic film will present the resonant type of dispersion. However, in recent years, a few methods were proposed to tailor the high frequency permeability of metallic ferromagnetic films or their composite structures [22–25]. For example, Iakubov et al. successfully fabricated the iron nanometer film with relaxation type of permeability by controlling the atmosphere during the magnetic sputtering process [25]. The relaxation frequency and susceptibility of iron film fitted from their experimental data in Ref. [25] are 1.1 GHz and 180, respectively. The thickness of iron film for optimal absorption should be hundreds of microns. Apparently, the periodic multilayer structure also must be employed to make use of such iron nanometer film. Fig. 6 plots the calculated
reflectivity spectrums of periodic multilayer absorber composed of iron nanometer films, where L¼ 250 nm and D¼ 20 nm. The periodic absorber is composed of 1050 units. The total thickness of iron films is about 0.26 mm, which meets the condition of optimal absorption. It is known that the conductivity s of metallic film drops rapidly as the thickness of film reduces to nanometers. For instance, the s of CoFeB/SiO2 granular film with thickness of 500 nm was measured about s ¼ 860 S=m [26]. In the calculation, the s of nanometer iron film takes the values of 1000, 500, and 200 S/m, respectively. The numerical results show that the reflectivity of iron film with s¼ 200 S/m can be lower than 4 dB from 2 GHz to 18 GHz. Considering that the total thickness of absorber is only about 0.3 mm, the absorption performance is good enough for many practical applications, e.g. the EM interference suppression in electronic equipment. The results also show that larger s of metallic film can seriously destroy the absorption performance of magnetic absorber. Therefore, controlling conductivity of film is an important issue in the realization of ferromagnetic metallic film absorbers.
4. Conclusion In conclusion, we have studied the absorption performances of magnetic film absorbers in theory. The results indicate that the ferromagnetic films with relaxation type of permeability can be used to construct thin broadband microwave absorbers. A periodic multilayer structure is proposed to meet the optimal absorption condition. Basing on this periodic structure, we have designed magnetic film absorbers using the Ni–Zn–Co ferrite micron film and iron nanometer film, respectively. Such designed absorbers are promising microwave absorbers, which have good absorption performances together with wide band and thin thickness.
Acknowledgments This work is supported by the Natural Science Foundation of China (Nos. 61071007, 61001017 and 61271080), the Specialized Research Fund for the Doctoral Program of Higher Education (Nos. 20100091120045 and 20110091110030), the Natural Science Foundation of Jiangsu province (BK2011338, BK2012722) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. References Fig. 5. Reflectivity spectrums of magnetic periodic multilayer absorber made of Ni–Zn–Co ferrite film.
Fig. 6. Reflectivity spectrums of magnetic periodic multilayer absorber made of iron nanometer film with s ¼1000, 500 and 200 S/m.
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