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Tunable double resonance with negative permittivity and permeability in GdFeO3 material by sintering temperature
Journal Pre-proof Tunable double resonance with negative permittivity and permeability in GdFeO3 material by sintering temperature Qiang Li, Jie Li PII:
S0925-8388(19)34024-1
DOI:
https://doi.org/10.1016/j.jallcom.2019.152778
Reference:
JALCOM 152778
To appear in:
Journal of Alloys and Compounds
Received Date: 6 July 2019 Revised Date:
21 October 2019
Accepted Date: 22 October 2019
Please cite this article as: Q. Li, J. Li, Tunable double resonance with negative permittivity and permeability in GdFeO3 material by sintering temperature, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.152778. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Tunable double resonance with negative permittivity and permeability in GdFeO3 material by sintering temperature Qiang Li1 *, Jie Li2 1 School of Instrument and Electronics, North University of China, Taiyuan, China, 030000 2 State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, China, 610054
Abstract In this paper, double negative performance of GdFeO3 in GHz range was investigated. Double negative performance generally occurs in ceramic/metal composites or artificial metamaterials. Therefore, this behavior of single phase ABO3 perovskites is very interesting. Conventional solid phase method was used for synthesis of GdFeO3 ceramics. Double negative performance of GdFeO3 occurred simultaneously, with negative permeability at 2.6-2.8 GHz and negative permittivity at 0.9-1.4 GHz. The reason for the resonance was also analyzed. Furthermore, resonance frequency could be easily adjusted by varying sintering temperature. Results showed that GdFeO3 can be applied in new field of metamaterials for antennas. By placing a double negative metamaterial lens in front of antenna source, the gain and directivity of the antenna can be increased. Therefore, it is necessary to study the properties of metamaterials based on GdFeO3. Keywords: GdFeO3, negative permittivity, negative permeability, double resonant, metamaterial
Introduction In recent years, metamaterials have attracted a large amount of attention from researchers, as they have extraordinary physical properties that materials in nature do not have. Metamaterials are mainly realized by designing and engineering special structures or materials [1, 2]. The electromagnetic properties of materials can be described by two basic parameters: permeability (µ) and permittivity (ε). The most effective description of electromagnetic metamaterial is also based on its permeability and permittivity. Electromagnetic metamaterials have negative µ or negative ε, or both [3]. An electromagnetic metamaterial having a negative µ or a negative ε is generally referred to as a single negative material. Double negative material is a special electromagnetic metamaterial having both negative µ and ε. In double negative materials (ε<0, µ<0), the electromagnetic wave (EM) propagates through the material in a direction completely opposite to the right-handed screw rule used in conventional materials. The EM wave propagation in double-negative materials is determined by the left-handed screw rule [1, 4], so they are also known as left-handed materials. In a previous study by Smith et al. (2001), open-loop resonator (SRR) and gold metal wires were periodically arranged in a certain pattern to fabricate a two-dimensional left-handed medium, which exhibited negative µ and ε in the microwave band for the first time [5]. GdFeO3 is an orthorhombic system belonging to the Pc21n space group and has a regular
octahedral twisted structure [6]. Each GdFeO3 unit cell contains 8 molecules, and the cation has four kinds of placeholders Gd1, Gd2 (mainly occupied by Ga ions), Fe1 and Fe2 (mainly occupied by Fe ions). Gd1, Fe1, and Fe2 positions are surrounded by a distorted oxygen octahedron, which is considered to be the origin of self-generated polarization along b-axis, while Gd1 position is surrounded by a regular oxygen tetrahedron [7, 8]. Previous research work on GdFeO3 mainly focused on the performance of multi-iron derivatives. Application of GdFeO3 in metamaterials has rarely been studied. In this paper, the resonance phenomenon of GdFeO3 was investigated by testing the magnetic permeability and permittivity. The results of this work can make GdFeO3 application in the field of electromagnetic metamaterials and expand the application range of GdFeO3. Experimental details Solid phase method was adopted to synthesize GdFeO3, which has the advantage of being easy to industrialize. Stoichiometric amounts of analytical grade powders of Fe2O3 and Gd2O3 were weighed, and then ball milled in deionized water for 12 h and dried. The dried powder was pre-sintered at 700 ºC for 2 h, ball milled and dried again. Finally, each sample was sintered at a different temperature for 6 h. Specifically, GFO-1 was sintered at 1200 °C, GFO-2 at 1250 °C, GFO-3 at 1300 °C, and GFO-4 at 1350 °C. The phase of the samples was determined by X-ray diffractometer (D/max 2400, Rigaku, Tokyo, Japan) at room temperature with Cu-Kα radiation in Bragg-Brentano geometry. Microstructures were characterized by scanning electron microscope (SEM) (JSM 6490LV, JEOL, Tokyo, Japan). Magnetization hysteresis loops were measured by vibrating sample magnetometer (VSM) (BHV-525, Riken Denshi, Tokyo, Japan). Dielectric behavior was measured by HP-4291B RF Impedance Analyzer. Result and discussion Fig.1 shows the XRD patterns of GdFeO3 samples. In Fig. 1a, the bottom of the figure shows the GdFeO3 theoretical diffraction peaks of ICCD. All diffraction peaks conformed to the standard peaks and absence of any secondary phase verified the single phase of all the GdFeO3 samples. Magnified view of the XRD diffraction peak at 2θ=33 degrees (Fig. 1b) shows that the diffraction peak intensity of crystal face increased as the sintering temperature increased. Moreover, the diffraction peak shifted toward lower angles. This may be due to the fact that at higher temperature, the grain growth was sufficient and the grain size was larger, in a certain sintering temperature range. The diffraction peak shifted toward lower angles, suggesting a shrinkage of the grain size, which is consistent with the results reported by N. Sharma et al. [9]. According to N. Sharma's report, as the sintering temperature increased, the grain size gradually decreased and crystal axis length became smaller.
Figure 1. (a) XRD patterns of GdFeO3 ceramics at room temperature. (b) Magnified XRD patterns in the vicinity of 2θ=33° Figure 2 shows the SEM micrographs of GdFeO3 samples at magnification of ×3000. As can be seen from Figure 2, the sample sintered at lowest temperature of 1200 °C possessed the smallest grain size. Increase in sintering temperature resulted in larger grain size. Figure 2a shows that the grain size was about 1 µm, and its structure was compact. Figures 2b and 2c show the presence of larger grains (2 µm). In Figure 2d, several grains were bonded together, and it was difficult to distinguish the grain boundaries. It was also observed that the porosity increased first and then decreased as the sintering temperature increased. The growth of the grains was closely related to the sintering temperature. The higher the temperature, the larger the grain size, over a certain temperature range. However, excessively high temperature limited the growth of grains and bonded them together, as shown in Figure 2d. In fact, when the sintering temperature exceeded 1350 °C, it was not possible to successfully prepare GdFeO3 ceramics.
Figure 2. SEM images of GdFeO3 samples. (a) GFO-1:1200 °C; (b) GFO-2:1250 °C; (c) GFO-3:1300 °C; (d) GFO-4:1350 °C
Figure 3 shows the real (µ′) and imaginary (µ′′) parts of relative complex permeability. It can be seen that µ′ of all samples was about 1 in the range of 1 MHz to 2.5 GHz, and µ′′ also maintained a low value. Interestingly, a resonance peak appeared at 2.6-2.8 GHz. The appearance of resonance will result in a negative magnetic permeability, which can bring new application scenarios to the material. As can be seen from the figure, as the sintering temperature increased (1200 to 1350 °C), the resonance frequency shifted to a lower angle, and the intensity also increased. The resonance intensity was -430 @ 2.77GHz for GFO-1, -500 @2.74 GHz for GFO-2, 650 @2.71 GHz for GFO-3, and -700 @2.68 GHz for GFO-4. Generally, the frequency dispersion of permeability can be represented using two types of magnetic resonances that are induced by domain wall motion and gyromagnetic spin rotation, respectively [10]. The permeability dispersion formulas are as follows:
µ′ = 1+ µ ′′ =
ωd2 χ d 0 (ωd2 − ω 2 ) χ d 0ωs2 [(ωs2 − ω 2 ) + ω 2α 2 ] + (ωd2 − ω 2 ) 2 + ω 2 β 2 [ωs2 − ω 2 (1 + α 2 )]2 + 4ω 2ωs2α 2
χ d 0ωβωd2 χ s 0ωsωα [ωs2 + ω 2 (1 + α 2 )] + (ωd2 − ω 2 ) 2 + ω 2 β 2 [ωs2 − ω 2 (1 + α 2 )]2 + 4ω 2ωs2α 2
(1)
(2)
where χ d and χ s are the magnetic susceptibilities of domain wall and gyromagnetic spin motions, ωd and ωs are the resonance frequencies of the domain-wall and spin components, χ d 0 and χ s 0 are the static magnetic susceptibilities of domain wall motion and spin, α and β are the damping factors, and
ω = 2π f is the angular frequency of the electric field [11]. In previous studies, it was shown that spin resonance mainly contributes to the frequency dispersion of permeability in high frequency region [12, 13]. This frequency shift can be attributed to the resonance frequency shift of spin component by adding the demagnetizing field, which is induced in GdFeO3 particles by the alternating magnetic field, to the internal magnetic anisotropy field. The change in sintering temperature affects crystallization of the grains, which further changes the magnetic field anisotropy inside the material, and finally causes the shift in resonance frequency point. Therefore, the resonance frequency point can be tuned by varying the sintering temperature.
Figure 3. Frequency dependence of the real part µ′ (a) and imaginary part µ′′ (b) of complex permeability of GdFeO3 Figure 3 shows the real (ε′) and imaginary (ε′′) parts of relative complex permittivity ε=ε′-jε′′ of GdFeO3 as a function of frequency. It can be seen that all the samples displayed dielectric resonance in
the frequency range of 0.9-1.4 GHz. Furthermore, with increase in sintering time, the resonant frequency of the sintered samples shifted monotonically to lower frequency. The dielectric resonance produced a negative relative dielectric constant, which was -370 @ 1.26 GHz for GFO-1, -620 @ 1.17 GHz for GFO-2, -790 @ 1.08 GHz for GFO-3, and -890 @ 1.0 GHz for GFO-4. The low-frequency impedance data shows that there was no piezoelectric resonance in the frequency range of 1 MHz - 1 GHz, and the initial dielectric constant was about 1. Moreover, ε′′ exhibited a large peak in the resonant frequency band. This is because the material absorbs energy from the external electric field and reaches a maximum value. At this time, dielectric resonance occurs and is continuously lost by damping. Thus, a sharp peak was generated. According to previous work [14, 15], negative permittivity can be realized by the plasma oscillation of delocalized electrons when the conductive phase is beyond percolation threshold. The negative behavior can be described well by the Drude model [10],
ω 2p ω 2 + ωr2 ω 2ω ε r′′(ω ) = 3 p r 2 ω + ωω r
ε r′ (ω ) = 1 −
ωp = Where
neff e2 meff ε o
(3)
(4)
(5)
ω is the angular frequency of the applied electromagnetic field, ωr is the damping
parameter, ε o is the permittivity of vacuum (8.85×10−12 F/m), neff is the effective concentration of conduction electrons, meff is the effective mass of the electron, e is the electron charge (1.6×10−19 C), and ω p is the angular plasma frequency. When the content of free electrons in the material reaches a certain value, dielectric resonance occurs at a specific frequency, resulting in a negative dielectric constant.
Figure 4. Frequency dependence of the real part ε′ (a) and imaginary part ε′′ (b) of complex permittivity of GdFeO3 at 1 MHz-2 GHz. Magnetic hysteresis loops of GdFeO3 samples are shown in Figure 5a. Saturation magnetization (Ms) (@5000) and coercivity (Hc) values extracted from the loops are shown in Figure 5b. It can be seen that the samples showed weak magnetic properties as the sintering temperature decreased. Ms of the sample decreased from 5 to 3, and Hc decreased from 4 to 1, when the temperature was varied from 1200 °C to 1350 °C. It is possible that the grain growth was not perfect due to increase in the sintering
temperature, resulting in destruction of magnetic property. This result was also consistent with SEM image of the sample microstructure.
Fig. 5a. Magnetic hysteresis loops of samples. Fig. 5b. Ms and Hc values of samples Magnetic permeability resonance can produce negative magnetic permeability. During the conversion of positive and negative magnetic permeability, a magnetic permeability approximately equal to zero is produced. Such a material is called near-zero-index metamaterial and has novel properties. Similarly, dielectric resonance also produces the same effect. The resonance of dielectric and magnetic permeability at different frequencies is the basis for investigating double negative performance of the material at same frequency. These novel electromagnetic properties of near-zero-index metamaterials present tremendous promise for microwave devices and antenna design. According to Snell's theorem, when the refractive index of a material is zero, the refraction angle will be zero regardless of the incident angle. After the electromagnetic wave is transmitted through the zero refractive index metamaterial plate, direction of the outgoing electromagnetic wave is perpendicular to the exit surface of the material. Therefore, the zero refractive index metamaterial can converge the electromagnetic waves, as illustrated in Fig. 6. If a zero-index metamaterial lens is placed in front of an antenna emitter, the gain and directivity of the antenna will be greatly enhanced. Therefore, this is a useful way to improve the gain and directivity of the antenna.
Figure 6. Schematic diagram of radiation of a metamaterial with refractive index of approximately zero before the antenna source Conclusion Simultaneous negative permeability and permittivity were successfully obtained in GdFeO3. The frequency of resonance generation was adjusted by changing the state of crystallization through different sintering temperatures. GdFeO3 ceramics displayed negative permeability and permittivity
behavior at frequencies of 0.8-2.8 GHz. The resonance frequencies could be further modified by changing microstructural characteristics (grain size, phase interconnectivity) or boundary conditions of the material by varying the sintering temperature. The material can be placed in front of antenna source as a zero-refractive metamaterial lens.
References [1] I. Gil, R. Seager, R. Fernandez-Garcia, Embroidered Metamaterial Antenna for Optimized Performance on Wearable Applications, Phys Status Solidi A 215 (21) (2018). [2] C.Y. Liu, Y.K. Bai, X.R. Ma, Design of a tunable dual-band terahertz absorber based on graphene metamaterial, Opt Eng 57 (11) (2018). [3] S.I. Maslovski, H.R.L. Ferreira, I.O. Medvedev, N.G.B. Bras, Superabsorbing metamaterial wormhole: Physical modeling and wave interaction effects, Phys Rev B 98 (24) (2018). [4] H. Massango, T. Tsutaoka, T. Kasagi, S. Yamamoto, K. Hatakeyama, Complex permeability and permittivity spectra of percolated Fe50Co50/Cu granular composites, J Magn Magn Mater 442 (2017) 403-408. [5] R. A. Shelby, D. R. Smith, S. Schultz. Experimetental verification of a negative index of Refraction [J]. Science, 2001, 292(5514): 77-79 [6] P. Paul, C.L. Prajapat, A.K. Rajarajan, T.V.C. Rao, Low Temperature Magnetic Properties of GdFeO3, Aip Conf Proc 1942 (2018). [7] A. Panchwanee, V.R. Reddy, A. Gupta, A. Bharathi, D.M. Phase, Study of local distortion and spin reorientation in polycrystalline Mn doped GdFeO3, J Alloy Compd 745 (2018) 810-816. [8] Y.M. Sheu, N. Ogawa, Y. Tokunaga, H.C. Chan, Y. Tokura, Selective probe of coherent polar phonon and quasiferromagnetic resonance modes in multiferroic GdFeO3, Phys Rev B 98 (10) (2018). [9] N. Sharma, A.K. Mall, R. Gupta, A. Garg, S. Kumar, Effect of sintering temperature on structure and properties of GaFeO3, J Alloy Compd 737 (2018) 646-654. [10] Q. Hou, K.L. Yan, R.H. Fan, K. Zhang, Z.D. Zhang, S.B. Pan, M.X. Yu, Negative permittivity in Fe-Si-Ni/epoxy magnetic composite materials at high-frequency, Mater Chem Phys 170 (2016) 113-117. [11] Z Zhang, R Fan, Z Shi, S Pan, K Yan, K Sun, et al. Tunable negative permittivity behavior and conductor–insulator transition in dual composites prepared by selective reduction reaction, J. Mater. Chem. C, 2013, 1, 79-85 [12] T Kasagi, T Tsutaoka, K Hatakeyama, Kenichi Hatakeyama. Electromagnetic properties of Permendur granular composite materials containing flaky particles. Journal of Applied Physics 116, 153901 (2014) [13] T Kasagi, T Tsutaoka, A Tsurunaga, Aiko TsurunagaKenichi Hatakeyama. High-frequency permeability of Fe-Co and Co granular composite materials. Journal of the Korean Physical Society. 2013. 62, 2113-2117 [14] M Chen, M Gao, F Dang, N Wang, B Zhang, S Pan. Tunable negative permittivity and permeability in FeNiMo/Al2O3 composites prepared by hot-pressing sintering. Ceramics International, 2016, 42, 6444-6449 [15] H Wu, Y Qi, Z Wang, W Zhao, X Li, L Qian. Low percolation threshold in flexible graphene/acrylic polyurethane composites with tunable negative permittivity. Composites Science
and Technology, 2017, 151, 79-84
Highlights 1. GdFeO3 exhibits double negative performance in the GHz range. 2. The resonance frequency of GdFeO3 can be adjusted by sintering temperature. 3. GdFeO3 can be applied in new field of metamaterials for antennas.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0925-8388(19)34024-1
DOI:
https://doi.org/10.1016/j.jallcom.2019.152778
Reference:
JALCOM 152778
To appear in:
Journal of Alloys and Compounds
Received Date: 6 July 2019 Revised Date:
21 October 2019
Accepted Date: 22 October 2019
Please cite this article as: Q. Li, J. Li, Tunable double resonance with negative permittivity and permeability in GdFeO3 material by sintering temperature, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/j.jallcom.2019.152778. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
Tunable double resonance with negative permittivity and permeability in GdFeO3 material by sintering temperature Qiang Li1 *, Jie Li2 1 School of Instrument and Electronics, North University of China, Taiyuan, China, 030000 2 State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, China, 610054
Abstract In this paper, double negative performance of GdFeO3 in GHz range was investigated. Double negative performance generally occurs in ceramic/metal composites or artificial metamaterials. Therefore, this behavior of single phase ABO3 perovskites is very interesting. Conventional solid phase method was used for synthesis of GdFeO3 ceramics. Double negative performance of GdFeO3 occurred simultaneously, with negative permeability at 2.6-2.8 GHz and negative permittivity at 0.9-1.4 GHz. The reason for the resonance was also analyzed. Furthermore, resonance frequency could be easily adjusted by varying sintering temperature. Results showed that GdFeO3 can be applied in new field of metamaterials for antennas. By placing a double negative metamaterial lens in front of antenna source, the gain and directivity of the antenna can be increased. Therefore, it is necessary to study the properties of metamaterials based on GdFeO3. Keywords: GdFeO3, negative permittivity, negative permeability, double resonant, metamaterial
Introduction In recent years, metamaterials have attracted a large amount of attention from researchers, as they have extraordinary physical properties that materials in nature do not have. Metamaterials are mainly realized by designing and engineering special structures or materials [1, 2]. The electromagnetic properties of materials can be described by two basic parameters: permeability (µ) and permittivity (ε). The most effective description of electromagnetic metamaterial is also based on its permeability and permittivity. Electromagnetic metamaterials have negative µ or negative ε, or both [3]. An electromagnetic metamaterial having a negative µ or a negative ε is generally referred to as a single negative material. Double negative material is a special electromagnetic metamaterial having both negative µ and ε. In double negative materials (ε<0, µ<0), the electromagnetic wave (EM) propagates through the material in a direction completely opposite to the right-handed screw rule used in conventional materials. The EM wave propagation in double-negative materials is determined by the left-handed screw rule [1, 4], so they are also known as left-handed materials. In a previous study by Smith et al. (2001), open-loop resonator (SRR) and gold metal wires were periodically arranged in a certain pattern to fabricate a two-dimensional left-handed medium, which exhibited negative µ and ε in the microwave band for the first time [5]. GdFeO3 is an orthorhombic system belonging to the Pc21n space group and has a regular
octahedral twisted structure [6]. Each GdFeO3 unit cell contains 8 molecules, and the cation has four kinds of placeholders Gd1, Gd2 (mainly occupied by Ga ions), Fe1 and Fe2 (mainly occupied by Fe ions). Gd1, Fe1, and Fe2 positions are surrounded by a distorted oxygen octahedron, which is considered to be the origin of self-generated polarization along b-axis, while Gd1 position is surrounded by a regular oxygen tetrahedron [7, 8]. Previous research work on GdFeO3 mainly focused on the performance of multi-iron derivatives. Application of GdFeO3 in metamaterials has rarely been studied. In this paper, the resonance phenomenon of GdFeO3 was investigated by testing the magnetic permeability and permittivity. The results of this work can make GdFeO3 application in the field of electromagnetic metamaterials and expand the application range of GdFeO3. Experimental details Solid phase method was adopted to synthesize GdFeO3, which has the advantage of being easy to industrialize. Stoichiometric amounts of analytical grade powders of Fe2O3 and Gd2O3 were weighed, and then ball milled in deionized water for 12 h and dried. The dried powder was pre-sintered at 700 ºC for 2 h, ball milled and dried again. Finally, each sample was sintered at a different temperature for 6 h. Specifically, GFO-1 was sintered at 1200 °C, GFO-2 at 1250 °C, GFO-3 at 1300 °C, and GFO-4 at 1350 °C. The phase of the samples was determined by X-ray diffractometer (D/max 2400, Rigaku, Tokyo, Japan) at room temperature with Cu-Kα radiation in Bragg-Brentano geometry. Microstructures were characterized by scanning electron microscope (SEM) (JSM 6490LV, JEOL, Tokyo, Japan). Magnetization hysteresis loops were measured by vibrating sample magnetometer (VSM) (BHV-525, Riken Denshi, Tokyo, Japan). Dielectric behavior was measured by HP-4291B RF Impedance Analyzer. Result and discussion Fig.1 shows the XRD patterns of GdFeO3 samples. In Fig. 1a, the bottom of the figure shows the GdFeO3 theoretical diffraction peaks of ICCD. All diffraction peaks conformed to the standard peaks and absence of any secondary phase verified the single phase of all the GdFeO3 samples. Magnified view of the XRD diffraction peak at 2θ=33 degrees (Fig. 1b) shows that the diffraction peak intensity of crystal face increased as the sintering temperature increased. Moreover, the diffraction peak shifted toward lower angles. This may be due to the fact that at higher temperature, the grain growth was sufficient and the grain size was larger, in a certain sintering temperature range. The diffraction peak shifted toward lower angles, suggesting a shrinkage of the grain size, which is consistent with the results reported by N. Sharma et al. [9]. According to N. Sharma's report, as the sintering temperature increased, the grain size gradually decreased and crystal axis length became smaller.
Figure 1. (a) XRD patterns of GdFeO3 ceramics at room temperature. (b) Magnified XRD patterns in the vicinity of 2θ=33° Figure 2 shows the SEM micrographs of GdFeO3 samples at magnification of ×3000. As can be seen from Figure 2, the sample sintered at lowest temperature of 1200 °C possessed the smallest grain size. Increase in sintering temperature resulted in larger grain size. Figure 2a shows that the grain size was about 1 µm, and its structure was compact. Figures 2b and 2c show the presence of larger grains (2 µm). In Figure 2d, several grains were bonded together, and it was difficult to distinguish the grain boundaries. It was also observed that the porosity increased first and then decreased as the sintering temperature increased. The growth of the grains was closely related to the sintering temperature. The higher the temperature, the larger the grain size, over a certain temperature range. However, excessively high temperature limited the growth of grains and bonded them together, as shown in Figure 2d. In fact, when the sintering temperature exceeded 1350 °C, it was not possible to successfully prepare GdFeO3 ceramics.
Figure 2. SEM images of GdFeO3 samples. (a) GFO-1:1200 °C; (b) GFO-2:1250 °C; (c) GFO-3:1300 °C; (d) GFO-4:1350 °C
Figure 3 shows the real (µ′) and imaginary (µ′′) parts of relative complex permeability. It can be seen that µ′ of all samples was about 1 in the range of 1 MHz to 2.5 GHz, and µ′′ also maintained a low value. Interestingly, a resonance peak appeared at 2.6-2.8 GHz. The appearance of resonance will result in a negative magnetic permeability, which can bring new application scenarios to the material. As can be seen from the figure, as the sintering temperature increased (1200 to 1350 °C), the resonance frequency shifted to a lower angle, and the intensity also increased. The resonance intensity was -430 @ 2.77GHz for GFO-1, -500 @2.74 GHz for GFO-2, 650 @2.71 GHz for GFO-3, and -700 @2.68 GHz for GFO-4. Generally, the frequency dispersion of permeability can be represented using two types of magnetic resonances that are induced by domain wall motion and gyromagnetic spin rotation, respectively [10]. The permeability dispersion formulas are as follows:
µ′ = 1+ µ ′′ =
ωd2 χ d 0 (ωd2 − ω 2 ) χ d 0ωs2 [(ωs2 − ω 2 ) + ω 2α 2 ] + (ωd2 − ω 2 ) 2 + ω 2 β 2 [ωs2 − ω 2 (1 + α 2 )]2 + 4ω 2ωs2α 2
χ d 0ωβωd2 χ s 0ωsωα [ωs2 + ω 2 (1 + α 2 )] + (ωd2 − ω 2 ) 2 + ω 2 β 2 [ωs2 − ω 2 (1 + α 2 )]2 + 4ω 2ωs2α 2
(1)
(2)
where χ d and χ s are the magnetic susceptibilities of domain wall and gyromagnetic spin motions, ωd and ωs are the resonance frequencies of the domain-wall and spin components, χ d 0 and χ s 0 are the static magnetic susceptibilities of domain wall motion and spin, α and β are the damping factors, and
ω = 2π f is the angular frequency of the electric field [11]. In previous studies, it was shown that spin resonance mainly contributes to the frequency dispersion of permeability in high frequency region [12, 13]. This frequency shift can be attributed to the resonance frequency shift of spin component by adding the demagnetizing field, which is induced in GdFeO3 particles by the alternating magnetic field, to the internal magnetic anisotropy field. The change in sintering temperature affects crystallization of the grains, which further changes the magnetic field anisotropy inside the material, and finally causes the shift in resonance frequency point. Therefore, the resonance frequency point can be tuned by varying the sintering temperature.
Figure 3. Frequency dependence of the real part µ′ (a) and imaginary part µ′′ (b) of complex permeability of GdFeO3 Figure 3 shows the real (ε′) and imaginary (ε′′) parts of relative complex permittivity ε=ε′-jε′′ of GdFeO3 as a function of frequency. It can be seen that all the samples displayed dielectric resonance in
the frequency range of 0.9-1.4 GHz. Furthermore, with increase in sintering time, the resonant frequency of the sintered samples shifted monotonically to lower frequency. The dielectric resonance produced a negative relative dielectric constant, which was -370 @ 1.26 GHz for GFO-1, -620 @ 1.17 GHz for GFO-2, -790 @ 1.08 GHz for GFO-3, and -890 @ 1.0 GHz for GFO-4. The low-frequency impedance data shows that there was no piezoelectric resonance in the frequency range of 1 MHz - 1 GHz, and the initial dielectric constant was about 1. Moreover, ε′′ exhibited a large peak in the resonant frequency band. This is because the material absorbs energy from the external electric field and reaches a maximum value. At this time, dielectric resonance occurs and is continuously lost by damping. Thus, a sharp peak was generated. According to previous work [14, 15], negative permittivity can be realized by the plasma oscillation of delocalized electrons when the conductive phase is beyond percolation threshold. The negative behavior can be described well by the Drude model [10],
ω 2p ω 2 + ωr2 ω 2ω ε r′′(ω ) = 3 p r 2 ω + ωω r
ε r′ (ω ) = 1 −
ωp = Where
neff e2 meff ε o
(3)
(4)
(5)
ω is the angular frequency of the applied electromagnetic field, ωr is the damping
parameter, ε o is the permittivity of vacuum (8.85×10−12 F/m), neff is the effective concentration of conduction electrons, meff is the effective mass of the electron, e is the electron charge (1.6×10−19 C), and ω p is the angular plasma frequency. When the content of free electrons in the material reaches a certain value, dielectric resonance occurs at a specific frequency, resulting in a negative dielectric constant.
Figure 4. Frequency dependence of the real part ε′ (a) and imaginary part ε′′ (b) of complex permittivity of GdFeO3 at 1 MHz-2 GHz. Magnetic hysteresis loops of GdFeO3 samples are shown in Figure 5a. Saturation magnetization (Ms) (@5000) and coercivity (Hc) values extracted from the loops are shown in Figure 5b. It can be seen that the samples showed weak magnetic properties as the sintering temperature decreased. Ms of the sample decreased from 5 to 3, and Hc decreased from 4 to 1, when the temperature was varied from 1200 °C to 1350 °C. It is possible that the grain growth was not perfect due to increase in the sintering
temperature, resulting in destruction of magnetic property. This result was also consistent with SEM image of the sample microstructure.
Fig. 5a. Magnetic hysteresis loops of samples. Fig. 5b. Ms and Hc values of samples Magnetic permeability resonance can produce negative magnetic permeability. During the conversion of positive and negative magnetic permeability, a magnetic permeability approximately equal to zero is produced. Such a material is called near-zero-index metamaterial and has novel properties. Similarly, dielectric resonance also produces the same effect. The resonance of dielectric and magnetic permeability at different frequencies is the basis for investigating double negative performance of the material at same frequency. These novel electromagnetic properties of near-zero-index metamaterials present tremendous promise for microwave devices and antenna design. According to Snell's theorem, when the refractive index of a material is zero, the refraction angle will be zero regardless of the incident angle. After the electromagnetic wave is transmitted through the zero refractive index metamaterial plate, direction of the outgoing electromagnetic wave is perpendicular to the exit surface of the material. Therefore, the zero refractive index metamaterial can converge the electromagnetic waves, as illustrated in Fig. 6. If a zero-index metamaterial lens is placed in front of an antenna emitter, the gain and directivity of the antenna will be greatly enhanced. Therefore, this is a useful way to improve the gain and directivity of the antenna.
Figure 6. Schematic diagram of radiation of a metamaterial with refractive index of approximately zero before the antenna source Conclusion Simultaneous negative permeability and permittivity were successfully obtained in GdFeO3. The frequency of resonance generation was adjusted by changing the state of crystallization through different sintering temperatures. GdFeO3 ceramics displayed negative permeability and permittivity
behavior at frequencies of 0.8-2.8 GHz. The resonance frequencies could be further modified by changing microstructural characteristics (grain size, phase interconnectivity) or boundary conditions of the material by varying the sintering temperature. The material can be placed in front of antenna source as a zero-refractive metamaterial lens.
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Highlights 1. GdFeO3 exhibits double negative performance in the GHz range. 2. The resonance frequency of GdFeO3 can be adjusted by sintering temperature. 3. GdFeO3 can be applied in new field of metamaterials for antennas.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: