Introduction: The magnetodielectric materials are attracting attention of microwave researchers as it exhibit both magnetic as well as dielectric

Transcription

1 Introduction: The magnetodielectric materials are attracting attention of microwave researchers as it exhibit both magnetic as well as dielectric properties at the same time. Several classes of natural materials such as metals, iron oxides, garnets etc. exhibit magnetic properties. The most common magnetic materials are ferromagnetic materials such as transition metals- iron, cobalt, nickel and some rare earth metals. These materials are highly conductive and therefore useless as dielectrics. Ferrimagnetic materials exhibit permanent magnetization as well as good dielectric properties. Many ferrites exhibit useful magnetodielectric properties at low frequencies. Hexagonal ferrites are the class of materials with electromagnetic conductivity, permittivity and permeability suitable for electromagnetic interference suppression and radar absorbing material coatings from centimeter to sub millimeter wavelengths of the electromagnetic spectrum, also M type hexaferrites are of interest for the use as absorber in the GHz range as it exhibit FMR in this frequency range. It has been a great challenge to achieve magnetic materials with high µ and ε at microwave frequencies suitable for antenna applications such as magnetodielectric substrates. Hexaferrites are being one of those materials which have a great scope as magnetodielectric material. Various parameters affect the attenuation of electromagnetic waves in the radar absorbing material. The interaction of microwaves with the material is decided by the intrinsic properties of the material such as conductivity, permittivity and permeability therefore there is need to study these properties of the hexaferrite. The technological application of these ferrites at high frequencies needs pure material in planar form. Thick film technology is of interest because it has proved to be cost effective and highly conducive to planarization. Most of the studies on planar ferrites at high frequencies are of the ferrites in thin film form. Although the concept of thick-film structures is quite attractive, they are not very widely used till now. 1

2 In the present work, the synthesis of M type barium hexaferrite and strontium hexaferrite was done by chemical coprecipitation method. The sintered powder was used for the thick film fabrication. These bulk and thick film barium hexaferrite and strontium hexaferrite was characterized for their structural and morphological properties using X ray diffraction, FTIR, FTRaman and Scanning Electron microscopy. The dc and ac electrical properties, dc magnetic properties of bulk and thick film M-type barium and strontium hexaferrite were investigated. The microwave (8-18 GHz) properties such as transmittance, absorbance, reflectance, complex permittivity and complex permeability of these bulk and thick film hexaferrites were studied by different measurement techniques. The measurement of complex permeability of M-type barium and strontium hexaferrite thick films by overlay technique has been reported for the first time. A new technique; a combination of waveguide reflectometer and Voltage standing Wave reflectometer techniques has been introduced for the measurement of complex permittivity of M type barium and strontium hexaferrite. These properties were studied to understand the response of M- type barium and strontium hexaferrite in bulk and planar form (thick films) in view of their application for magnetodielectric materials in the microwave region of the electromagnetic spectrum. 1.1 Need of Magnetodielectric materials: The pure dielectric materials have been widely studied for microwave applications mostly for transmittance or absorbance aspects. Pure magnetic materials such as metals have been studied for microwave reflection and absorption applications. But pure dielectric or magnetic materials exhibit either permittivity µ or permittivity ε. According to Fresnel s equation, the characteristic impedance z of the material is dependent on permittivity as well as permeability. µ z = z (1.1) ε 2

3 Where, z 0 is the system impedance. For microwave applications especially miniaturized components, the impedance matching is a crucial parameter which makes the components useful. More the difference between ε and µ, more is the mismatch between material and system impedance which results in losses due to higher reflection. The composite materials either in the form of multilayers or mechanically mixed materials combining individual magnetic and dielectric phases, possess internal impedance mismatch between layers or grains of magnetic and dielectric materials resulting in reflection of incident electromagnetic waves. Therefore there is a need of materials which exhibit both magnetic as well as dielectric properties. Hexaferrites are the potential candidates for magnetodielectric applications. 1.2 Application of Magnetodielectric materials especially in microwaves: Though magnetodielectric materials have numerous applications [1-3], the applications related to microwaves are only explained in this article. The magnetodielectric materials are potentially applicable as a highly absorbing material or transmitting material depending on the losses of the material. If the losses are larger, the material is more absorbing and viceversa. Another interesting application of magneto-dielectrics is in the area of antenna miniaturization. Using magneto-dielectric substrates, the efficiency and quality factor of miniaturized antenna can be improved [1]. The low loss impedance matched magnetodielectric material is an excellent candidate for embedded antenna miniaturization [2, 3]. Microwave absorbers are also in high demand for defense use. By reducing the energy reflected back to the radar, radar absorbing materials can prevent objects from being detected. With the increasing demand for higher gigahertz electronics and miniaturized components, suppression of electromagnetic interference (EMI) is a matter of high concern. The reduction of electromagnetic backscattering using the microwave absorbing materials has important implications in the field of electromagnetic compatibility. Emerson [4] has given a historical 3

4 summary on the development of microwave absorbers comprising of tiny iron balls, carbon black and aluminum flakes having fixed electromagnetic absorption. The absorption can be achieved through dielectric or magnetic loss mechanisms that convert electromagnetic energy in to heat. The engineers in the field of memory devices, power transformers are usually more interested in obtaining small losses whereas, researchers working in RAM are more interested in high losses. On the contrary, ferrites can be used to tailor their electromagnetic properties and make them absorption tunable. 1.3 Ferrite as the Magnetodielectric material Ferrites have become an integral part of everyday life, industries such as automobile, telecommunication, robotics, medical field, data processing, electronics and communications. For example, starter motors, anti-lock braking system (ABS), motor drives for wipers, loudspeaker, eddy current brakes, microphones, telephone ringers, switches and relays, many microwave passive components such as circulators, gyrators, filters, memory devices, cordless appliances etc. [5-12]. The progress in magnetism in general has been mind boggling exemplified by the digital and other recording media. The classes of magnetic materials viz ferromagnetic, paramagnetic, ferrimagnetic, diamagnetic and antiferromagnetic materials are illustrated in Table 1 [13]. Hard magnets (Ba, Sr hexaferrites) were developed during World War II. Low cost, easy manufacturing and interesting electric and magnetic properties lead these polycrystalline ferrite to be one of the most important magnetodielectric materials in the field of higher gigahertz electronics. Since the dynamic response of these materials are not only dependent on the composition, but also on the domain structure, as well as on the shape of the magnetic elements, the elaboration of microwave materials with new topologies has been a thrilling field of investigation. Among several hexaferrites, M-type hexaferrites can provide large tunable anisotropy (Ha=2k/Ms) causing magnetic resonance in

5 GHz which make them microwave absorbers in higher gigahertz range [14-19]. The barium and strontium hexaferrite have wide range of applications due to their good magnetic properties such as large coercivity and specific magnetic saturation associated with its high chemical and magnetic stability [20]. 1.4 Various aspects of hexaferrites- Preparation techniques, Crystal structure, Properties at DC, AC and microwaves: In this work investigations on M type barium and strontium hexaferrites has been done, therefore only the references related to these two hexaferrites are given in this article Synthesis Techniques: The traditional preparation method of barium ferrite (ceramic) involves the solid state reaction of barium carbonate and iron oxide at high temperatures (~1200 C) for a long period of time (~12h) [21]. J. Temujin et al. have obtained fine particles through ceramic method [22]. Due to topochemical sintering the grains grew in rice shapes [23]. Y. Chen et al. reported the polymer assisted C-axis oriented barium hexferrite by ceramic method [24]. Modified ceramic method for the solvent free synthesis of barium hexaferrite using nitrate and carbonates as starting materials was reported by Y. Du et al. [25]. M.M. Hessein et al. have reported the enhanced magnetic properties of barium hexaferrite [26]. In order to avoid the limitations of physical mixing method, chemical methods have been developed. In the chemical synthesis methods, the mixing of cations in an atomic scale takes place thereby their diffusion distance during the formation of product decreases and thus the temperature of product formation lowers. The methods for formation of ferrite given below have been considered for production of homogeneous, reproducible ferrites. Synthesis of barium hexaferrite by coprecipitation was reported by various authors. Preparation of ultra fine particles and effect of the ph on their size have been reported [27-29]. Barium hexaferrite nanoparticles were obtained 5

6 by microemulsion mediated co-precipitation process [30-32]. K. K. Mallick group have synthesized barium hexaferrite by ceramic as well as coprecipitation method and compared the magnetic properties of those samples [33]. The sol-gel auto combustion method is another chemical method which does not require higher temperature for formation of barium hexaferrite. A. Ataie et al. have reported the nanocrystalline barium hexaferrite powders synthesized by sol gel method and they have also studied the effect of Fe/Ba ratio on their magnetic properties [34]. Influence of citric acid content on the magnetic properties was also studied by M. Zhong et al. [35]. Effect of both ph and citric acid content was studied by L. Junliang et al. for quasi-single domain barium hexaferrite [36]. Synthesis of barium hexaferrite nanoparticles was also reported using combustion technique [37, 38]. Barium hexaferrite soft magnetic nanoparticles obtained by hydrothermal synthesis was reported by S. Che et al. [39, 40]. Various dopants such as Co, Sr, Sc, Gd, Ti, Li were used to tailor the magnetic properties of BaFe 12 O 19 [24, 41-46]. Various reports are available on thin film barium hexaferrite deposited by sol-gel, liquid phase epitaxy, MOCVD, evaporation, pulsed laser deposition and sputtering methods [47-57]. Such films are amorphous and need post deposition thermal annealing [60, 61]. The annealing conditions govern the crystallization and the magnetic properties obtained are strongly linked to the annealing parameters. As a substrate a wide range of materials such as sapphire (Al 2 O 3 ) [59, 62, 63], (111) magnesium oxide (MgO), [64, 65] SiO 2, ZnO, and GaN [66] are used. The effect of underlayers on magnetic properties has been reported by D.H. Kim et al. [67] and Z. Zhuang et al. [68]. But very few reports are available on thick film barium hexaferrite deposited by liquid phase epitaxy, pulsed laser, screen printing, [65, 66, 69-74] Like barium hexaferrite, the reports on synthesis of strontium hexaferrite powder by conventional ceramic method, self propagating hydrothermal 6

7 synthesis, sol-gel autocombustion, self flash combustion, coprecipitation and citrate method are available. Compared to barium hexaferrite, the investigations on strontium hexaferrite are lesser [75-87]. Coprecipitation technique involves two steps- nucleation and crystal growth [88-91]. When the amount of solute in solution increases beyond saturation, then the formation of nucleus takes place. The ionic species from solution adsorbs on the nucleus forming crystals. The process continues till the concentration of solute in the solution reduces below critical concentration i.e. minimum concentration for nucleation. The detailed theory of coprecipitation method will be discussed in chapter II Crystal Structure of Ba/Sr hexaferrite: The general formula unit of M type hexaferrite is AO 6Fe 2 O 3 or AFe 12 O 19, where A is a divalent ion such as Ba 2+, Sr 2+, Pb 2+, etc., which exhibits hexagonal crystal structure with space group P63/mmc and is constructed from 4 building blocks, namely S, S*, R, and R* [92,93] as shown in Fig.1.1. The oxygen atoms are close packed with the A and Fe ions in the interstitial sites. There are ten layers of oxygen atoms along the c axis and the iron atoms are positioned at five crystallographically different sites. An important consideration in the preparation of garnets, spinel ferrites and hexagonal ferrites is the size of the constituent cations. The spinel accepts into its tetrahedral and octahedral interstices a great variety of small cations, mostly ions of the first transition series. The garnets, because of their larger dodecahedral interstices, accept cations which are too large to be incorporated into spinels; there is however, an upper limit to the size of acceptable cations. The hexagonal crystals accept still larger cations. The chemical formula of S and R building blocks of M type hexaferrite is Fe 6 O 8 and BaFe 6 O 11 respectively. 7

8 Fig. 1.1: Schematic structure of barium hexaferrite (BaFe 12 O 19 ). The arrows on Fe ions represent the direction of spin polarization. 2a, 12k, and 4f 2 are octahedral, 4f 1 are tetrahedral, and 2b are hexahedral (trigonal bipyramidal) sites. The unit cell contains a total of 38 O 2- ions, 2 Ba 2+ ions, and 24 Fe 3+ ions. Fe 3+ ions in 12k, 2a, and 2b sites (16 total per unit cell) have their spins up, while the Fe 3+ ions in 4f 1 and 4f 2 sites (8 total per unit cell) have their spins down, which results in a net total of 8 spins up, and therefore, a total moment of 8 5µ B = 40 µ B per unit cell that contains two Ba 2+ ions. The R and S sub-units shown have chemical formulae R = ( Ba Fe O ) and S + = ( Fe 3 O 2 2 ) The asterix (*) indicates that the corresponding subunit is rotated 180 around the hexagonal axis. The S block is the smallest and contains no barium. The oxygen anions and interstitial metal cations are so distributed that they form precisely the spinel arrangement. When the cubic spinel is oriented with the (111) axis vertical, the hexagonal symmetry becomes apparent. The oxygen ions occur in evenly spaced layers, each containing four anions. Between 8

9 each pair of oxygen layers, there are three cations alternately two tetrahedral with their spins antiparallel with those in octahedral sites and one octahedral, and three octahedral with their spins parallel with each other. Since, the octahedral ions always lie halfway between oxygen layers, the cations are confined to the midway plane after every second oxygen layer. A successive pair of such midway planes marks the boundaries of the spinel i.e. S block. The R block BaFe 6 O 11, includes three oxygen layers. The two barium- containing blocks are bounded by the same type of plane that demarks the boundaries of the S block; the plane lies halfway between two oxygen layers in a region free of tetrahedral ions and contains three octahedral ions. Each R block contains six Fe 3+ ions, of which five are in octahedral sites, three having spin up and two having spin down polarization. In addition, one of the Fe 3+ ions is coordinated with five O 2- anions and has spin up polarization. The oxygen ions surround the site in the form of a trigonal bipyramid. The Fe atoms at the 2a site are octahedrally coordinated with equal Fe O distances, while the octahedrally coordinated Fe ions at 4f 2 and 12k sites have different Fe O interatomic distances, from about 1.85Aº to 2.37 A. Of the twelve Fe 3+ ions of the formula unit, the Fe atoms at 4f 1 sites are tetrahedrally coordinated by oxygen, while the Fe atoms at 2b sites are coordinated by five oxygen ions. There are also short Fe Fe distances in the structure, and at 4f 2 sites this Fe Fe distance is about 2.7 A. The Fe ions at 12k sites form a network with every Fe connected to four other Fe ions in the same layer. In terms of spin, in R block one ion in the 2b layer is spin up state and two octahedral ions are spin down state, and in S block seven octahedral ions in spin up state and two tetrahedral ions in spin down state. Because each Fe 3+ ion contributes 5µ B to the magnetic moment at absolute zero, the total magnetization at zero temperature can be calculated knowing that eight Fe 3+ ions are in the spin up state, and four are 9

10 in spin down state resulting in four net spin up Fe 3+ ions. Therefore, the net magnetization per molecular unit is ( ) 5µ B = 20µ B (One Ba ion per molecular unit) DC Magnetic Properties: Magnetism in materials: All materials exhibit magnetism. The magnetic nature of a material is determined by the magnetic moments of the electrons, atoms and ions in the material. The magnetic responses of electrons and of atoms and ions can exhibit a variety of behaviors in materials due to the wide range of interactions that can occur between the magnetic moments and their environment. The transition metals with incomplete 3d shells and rare earth elements with incomplete 4f shells are an integral part of magnetism in general and ferromagnetic and ferrimagnetic materials in particular. Deviation from stoichiometry is also used to cause spin polarization without the need for transition metal being present. The magnetic moment of an atom has three sources: Electron spin, electron orbital momentum about the nucleus and the change in the orbital momentum induced by an applied magnetic field (H). The magnetization of a material, M, is defined as the magnetic moment per unit volume. The magnetic susceptibility, χ, is defined as χ = M H B is the macroscopic field intensity and can be related to H by B = µh Where, µ is a parameter characteristic of the medium called the magnetic permeability. The magnetic materials can be classified into the following five major groups: diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic materials. The characteristic properties of these materials are illustrated in table 1. 10

11 In a ferrite crystal, each atom contains magnetic moment having magnetic field about it. If the magnetic moment is large enough, an applied dc magnetic field can force a nearest neighbor to align in the same direction provided the interaction energy is larger than the vibrational energy, K B T, of the atoms in the lattice. The interaction between atomic magnetic moments is of two types: the dipolar interaction and the exchange interaction, which represents the difference in the Coulomb energy between two electrons with spins that are parallel and antiparallel. This interaction is usually the dominant of the two types. The Curie temperature, Tc, is the temperature at which the interaction energy is greater than the thermal energy and ferromagnetism is present. Ferrimagnetic materials exhibit paramagnetism above the Curie temperature. The establishment of the orientation of the magnetic ions is more complex in hexagonal ferrites than spinels. In these materials, magnetism evolves as a result of incomplete cancellation of spin magnetic moment. Magnetically, S block contributes four octahedral ions to the majority α sublattice and two tetrahedral ions to the minority β sublattice. The R block contributes three octahedral ions and one trigonal ion to the majority and two octahedral ions to the minority. The properties of ferrimagnets can be described through exchange interaction between the A and B sublattices as A A, B B, and A B interactions and through the magnetization of each sublattice. Magnetization requires the alignment of magnetic moments which results from the exchange interaction between the magnetic ion and the host (metal ion). Theory of magnetism developed by considering this exchange field i.e. mean field is known as mean field theory [13, 94, 95]. 11

12 Table 1 Classification of magnetic materials based on susceptibility, atomic behavior etc. [13] The total magnetic field in the absence of external magnetic field acting on a magnetic dipole in each sublattice is (in cgs units) H a λ E, aam a + λe, ab = M H b λ E, abm a + λe, bb b = M b Where, λ E is the temperature independent constant. The magnetization of each sublattice can be described by the Curie relations where they have their own Curie constants Ca and Cb, which are not identical since each sublattice contains different kinds of ions on different crystallographic sites, as C = ( H 0 H a ) T a M a + C = ( H 0 H b ) T b M b + 12

13 Solving Eqs. 1.4, 1.5, 1.6 and 1.7; the inverse susceptibility (cgs units) of a ferrimagnet in the paramagnetic regime can be expressed as follows: where, λ E,bb. 1 H 0 = χ M + M 1 χ 0 a b = T C 1 K + χ T Θ' , K, C, and Θ ' are constants depending on C a, C b, λ E,aa, λ E,ab and At high temperatures, the last term of equation 1.8 becomes negligible, and the equation reduces to Curie-Weiss law: C χ = T + C χ This is the equation of straight line. Equation 1.8 is in good agreement with the experimental results in the various reports except near the Curie point. Below, Tc i.e. in the ferrimagnetic region, each sublattice is spontaneously magnetized by the molecular field acting on it, but the two sublattice magnetization are opposed to each other hence, the net magnetization can be obtained from the difference of equation 1.6 and 1.7. The anisotropy energy for hexaferrites with easy c- axis, depends only on the angle between the Ms vector and the c-axis. Therefore anisotropy energy can be written as, ' ' 2 ' 4 E = K + K cos θ + K cos θ Magnetization process: The process of magnetization is concerned with the processes of the domain wall motion and domain rotation. Magnetic domains are nothing but a region having parallel spins which results in spontaneous magnetization. Domain walls are the interfaces between the two regions having spontaneous magnetization in different directions. At or within the wall, magnetization must change the direction. The spins within the wall are oriented towards non-easy direction. The domain wall has a certain finite width and certain structure.

14 A full cycle of magnetization is called a hysteresis loop. A sample hysteresis loop is shown in figure 1.2. Saturation magnetization Ms, remanent field Mr and coercivity Hc are all strongly dependent on the ferromagnetic material and the conditions by which they are synthesized. The process of alignment of magnetic domains to the external applied field is illustrated in figure 1.3. Fig. 1.2 Plot of the magnetization M versus an applied magnetic field H for a hard ferrite [96] When the hexaferrites composed of randomly oriented magnetic domains are placed in an external dc magnetic field, the domains orient in the direction of applied magnetic field as shown in fig In lower magnetic fields, the induced magnetization increases more rapidly than the field strength due to reversible domain spin which increase its irreversible boundary displacement. The material is then said to be magnetically saturated. Further when the magnetic field is reduced towards zero, the remanance magnetization rises during the alignment of domains and becomes zero at the value of magnetic field known as coercive field. 14

15 Fig. 1.3 Domain arrangements for various states of magnetization [96] Brief literature survey on the magnetic properties of hexaferrites: Barium hexaferrite Various reports are available on the studies of dc magnetic properties of bulk and thin film barium hexaferrite. M. Zhong et al. studied the magnetic properties of barium hexaferrite powder prepared by sol-gel method [35]. Pure single BaFe 12 O 19 of the specific maximum magnetization M (1Tesla) Am 2 /kg, the specific remanent magnetization M r Am 2 /kg and the coercive force H c 467 ka/m was produced when the molar ratios of citric acid to the metal nitrate was 1.5. V.V. Pankov [97] reported that the coercivity of fine barium hexaferrite powders synthesized by modified coprecipitation followed by spray pyrolysis method was lower than that of bulk due to the presence of a magnetically inactive layer of noncollinear spins in the basal plane of the hexagonal particles. The barium hexaferrite particles less than 10nm in size were shown to be in a superparamagnetic state. The high saturation magnetization (4πMs) of 4000 Gauss and coercivity of 1935 Oe was reported by Y. Chen et al. [72]. The 15

16 magnetic properties of barium hexaferrite were tailored by doping of Co, Ti, Sr for Fe as well as Ba [46, 50, 97]. Pereira et al. [46] have reported the structural, dielectric and magnetic properties of the Ba x Sr 1 x Fe 12 O 19 in view of applications as a material for permanent magnets, high density magnetic recording and microwave devices. J. Bursik et al. [50] reported coercivity of KOe and Ms of emu/gm for BaCo x Ti x Fe 12-2x O 19 thin films prepared by dip coating method. J. Slama et al. [98] reported the magnetic properties of BaFe 12-2x (Me 1 Me 2 ) x O 19 prepared by both mechanical alloying and precursor method, where Me 1 =Co, Ni, Zn, Sn and Me 2 =Ru, Ti, Zr, Sn. The permanent magnetization loop with the saturation magnetization (4πMs) of 4.6±0.2 kg and uniaxial anisotropy field of 16.5±0.2 koe has been obtained for BaFe 12 O 19 thin films [99]. The magnetic properties of Indium doped barium hexaferrite thick films was reported by C.N. Chinnasamy et al. [100]. These films had low coercivity of 1210 Oe but also a high hysteresis loop squareness ratio of 0.93, with self-bias properties which make them useful as microwave phase shifters. T. Sakai et al. [101] from the same group have reported Sc doped barium hexaferrite thick films. These in-plane oriented, screen printed thick films show a squareness ratio of about 0.88 and coercivity of 2545 Oe Strontium hexaferrite There are various reports on the magnetic properties of bulk and thin film strontium hexaferrite. A. Yourdkhani et al. [102] have reported saturation magnetization of 60.9 (J/T Kg) and remanent magnetization of 33.5 J/T Kg for carbon monoxide heat treated and re-calcined strontium hexaferrite powder synthesized by conventional method. The synthesis condition dependant magnetic hysteresis parameters of strontium hexaferrite synthesized by coprecipitation technique showing Ms value of ~55 emu/gm has been reported [103]. Similarly, the SrFe 12 O 19 powder synthesized by solgel method was studied by Y.Wang et al. [104] for their magnetic properties. The coercivity, saturation magnetization and remanent magnetization was 16

17 reported as Oe, 70.1 and 42.4emu/g respectively by the authors. The high saturation magnetization (4πMs) of 4320 G and coercive field 6635 Oe was reported by A. Ataie et al.[105] and J.F. Wang et al. [106] respectively. The SrFe 12 x Al x O 19 powder prepared showed the saturation magnetization Ms= 60.2 A.m 2 /kg and the coercive force Hc = 550 ka/m [107]. The influence of Nd Co substitution on the magnetic properties of strontium hexaferrite nanoparticles has also been studied by P.G. Bercoff et al. [108]. The increase in saturation magnetization of strontium hexaferrite was observed. Zinc and niobium doped strontium hexaferrite nanoparticles, Sr(Zn 0.7 Nb 0.3 ) x Fe 12-2x O 19 fabricated using a sol-gel method show coercive force of about 2.3 koe and saturation magnetization of 74 emu/gm [80] Electrical properties of barium and strontium hexaferrite: DC resistivity of hexaferrite: The DC conductivity of barium and strontium hexaferrite has been widely studied by the number of workers [109, 110]. The resistivity of ferrite varying with temperature can be given the well known Arrhenius relation [111] as, ( E kt ) ρ = exp (1.11) ρ 0 Where, ρ 0 is the resistivity of the material at room temperature, E is the activation energy for electron conduction k is the Boltzmann constant and T is the absolute temperature The resistivity of these ferrites at room temperature is very high. The maximum resistivity of ~10 10 Ωcm was reported by these authors as a nanosize effect. As temperature increases, dc resistivity decreases due to hopping mechanism. In case of ferrites, conversion of Fe +2 to Fe +3 or vice-versa leads to the formation of extra electron or hole. Under the influence of external electric energy or thermal energy, these extra electrons (or holes) jump from one valence state of iron to the other and constitute the conduction current. This 17

18 is nothing but hopping of electrons or holes. The rate of process of hopping is proportional to the activation energy and inversely proportional to the temperature. Thus the activation energy can be interpreted as the energy required for jumping (hoping) of the electron from one valence state to the other valence state of iron ion. The activation energy of hexaferrites are quite high lies from 0.72 to 1.06 [82] Dielectric behavior of hexaferrite: The dielectric constant is a measure of the extent to which a substance concentrates the electrostatic lines of flux. It is the ratio of the amount of electrical energy stored in an insulator, when a static electric field is imposed across it, relative to vacuum ε 0 (which has a dielectric constant of 1). Apart from a vacuum, the response of normal dielectrics to external fields generally depends on the frequency of the field. This frequency dependence is because a material's polarization does not respond instantaneously to an applied field. The response must always be causal (arising after the applied field). For this reason permittivity is often treated as a complex function of the frequency of the applied field ω. The definition of permittivity therefore becomes, D e iωt ( ω) E e = iωt ˆ 0 ε 0 (1.12) where D 0 and E 0 are the amplitudes of the displacement and electrical fields, respectively. Since the response of materials to alternating fields is characterized by a complex permittivity, it is natural to separate its real and imaginary parts, which is done by convention in the following way: D0 ε ( ω) = ε '( ω) iε"( ω) = ( cosδ i sin δ ) (1.13) E 0 In the equation above, ε is the imaginary part of the permittivity, which is related to the rate at which energy is absorbed by the medium (converted into thermal energy, etc.). The real part of the permittivity ε, is related to 18

19 the refractive index of the medium. The dielectric constant as well as dielectric loss decreases with increase in frequency. The different mechanisms responsible for the dielectric behavior of the material at different frequencies are illustrated in fig Fig. 1.4: Frequency response of dielectric mechanisms Putting a dielectric material between the plates in a parallel plate capacitor as shown in fig. 1.5 below, causes an increase in the capacitance in proportion to k, the relative permittivity of the material: kε A C = (1.14) d Fig. 1.5 Polarization in parallel plate capacitor 19

20 This happens because an electric field polarizes the bound charges of the dielectric, producing concentrations of charge on its surfaces which creates an electric field antiparallel to that of the capacitor. Thus, a given amount of charge produces a weaker electric field between the plates than it would without the dielectric, which reduces the electric potential. Considered in reverse, this argument means that, with a dielectric, a given electric potential causes the capacitor to accumulate a larger charge polarization. The capacitance of the dielectric varies under the influence of varying AC field. This principle is used for the measurement of dielectric constant of the ferrites at AC frequencies from 20 Hz to 1 MHz. The loss tangent can be calculated as, ε" tanδ = (1.15) ε ' There are various reports on the dielectric permittivity of pure and doped barium and strontium hexaferrite [46, ]. F. Pereira et al. [46] studied the dielectric properties of Ba x Sr 1-x Fe 12 O 19 upto 1 MHz. They observed the decrease in dielectric constant (ε ) from ~750 to ~150 for barium hexaferrite whereas for strontium hexaferrite it was from 230 to 60 with increase in frequency from 100 Hz to 1 MHz. The dielectric loss was observed to be decreased from ~3.1 to ~0.7 for barium hexaferrite and from ~3.9 to ~0.5 for strontium hexaferrite. S. Hussain et al. [112] and M.H. Makled et al. [113] reported a much higher dielectric constant of 959 for strontium hexaferrite at 1 MHz. M.J. Iqbal et al. [114] plotted the dielectric constant of strontium hexaferrite in 600 KHz to 1 MHz showing decrease in values from 221 to 183 and that dielectric loss from to From the review of the literature, it is seen that the work on thick film barium and strontium hexaferrite is very sparse. 1.5 Microwave properties of barium and strontium hexaferrite: The need of magnetodielectric materials in microwave have been discussed in previous articles 1.1 and 1.2. The charge carriers that are responsible for propagating current through the material have different 20

21 behavior for different applied frequencies particularly for high frequency applications, the behavior can be very different from that in dc and ac. The high frequency transport mechanism can be explained if the permittivity and permeability of the material is known. Both these parameters are complex over microwaves and hence can absorb propagating signal. The different elements in the ferrite can induce dipoles that can cause the absorption. The high frequency radiation can be propagated through the oxide ferrimagnetic materials like ferrites with very little attenuation. Such losses that arise in these materials could be either dielectric or magnetic. Ferrites are significant because of the rapidly varying characteristics with composition and are useful for systems that do not obey the reciprocity principle. They are useful at microwave frequencies for some important nonlinear applications such as parametric generation and amplification. It is important to characterize precisely the ferrite materials for microwave applications as the design of the device and its performance depends critically on the material parameters. The ferromagnetic resonance effect and the Faraday rotation effect in magnetized ferrites are used for realizing certain non-reciprocal devices at microwave frequencies. Hexaferrites are the potential candidates for magnetodielectric applications in microwaves since, it exhibit significant permittivity (ε*) and permeability (µ*) at these frequencies and the M-type hexaferrites exhibits ferrimagnetic resonance in GHz range. Most of the ferrite microwave devices are based on the phenomenon of ferrimagnetic resonance (FMR) [7, 96] Ferrimagnetic resonance (FMR): Magnetic resonance in the magnetic material occurs due to both magnetic moment µ and angular momentum S. The rate of change of angular ds r momentum of a system is nothing but the torque. The torque on dt magnetic moment in a magnetic field is µ H r so, 21

22 r ds r r h = µ H dt (1.16) But, µ = γhs r (1.17) Where, γ is the gyromagnetic ratio and is given by, ge γ = (1.18) 2mc Where g is the Lande s splitting factor. For free spin g=2. From above equations, r dµ r r = γ µ H dt ( ) (1.19) The magnetization, M r is defined as sum of all the magnetic moments over a unit volume. Therefore, above equation can be solved as r dm r r = γ ( M H ) (1.20) dt For a system with losses, the equation of motion includes a damping term. Hence, equation becomes, r dm r r λ r r r = γ ( M H ) + ( M ( M H ) (1.21) 2 dt M If a magnetic medium is subjected to a steady magnetic field H 0 in the Z-direction and rf magnetic field h exp (iωt) in the X-direction as shown in fig. 1.6 so that, r r H = H k 0 + hexp( iωt)i (1.22) From equation (dm/dt), the rf magnetization is related to the rf field through a tensor susceptibility and hence, tensor permeability (which will be explained in next subsection). It is obvious that the material has a natural frequencyω = γh 0. The term resonance implies that ω=ω 0. The ferromagnetic resonance can be tuned by applying external dc magnetic field. The combination of a steady magnetic field, and an rf circularly polarized magnetic field H r at frequency f f o is applied perpendicular to 22

23 steady magnetic field H r 0, the angle of precession φ of total magnetic moment M r and also the amplitude of induced precession will tend to increase at f f o when the direction of rotation of H r and M r coincides. Due to magnetic frictional loss, the amplitude and the angle of M r attain a steady state, describing a conical surface around H r 0. The energy continuously supplied by the rf field is dissipated as heat in the ferrite. When the interaction between the microwave field and the electrons is reduced, the ferrites show lower losses. When H r rotates opposite to M r, the ferrite dissipates no time average power and exhibit low loss. Therefore, microwave propagation in ferrites shows a gyromagnetic resonance with a peak of loss for clockwise polarization of H r which coincides with that of M r and a flat low loss for opposite polarization as shown in the Fig.1.7, where the horizontal scale represents H r 0 or frequency f o, since both are linearly related. This ferromagnetic resonance effect is the basis of various applications of a ferrite to device realization. Fig. 1.6: Precession of spinning electron in a steady magnetic field. 23

24 Loss μ' - μ'' H o 2.8 H o Re (μ) μ' - μ' + 1 H o 2.8 H o Fig. 1.7: Gyromagnetic resonance in ferrites. The clockwise and anticlockwise polarizations of propagating waves produce total ac fields B t + = µ o M + + B + = µ + H (1.23) and B t - = µ o M - + B - = µ - H (1.24) Thus the two complex permeabilities for clockwise and anticlockwise polarizations denoted by plus and minus subscripts, are given as µ + = µ + - jµ (1.25) and µ - = µ - - jµ (1.26) From the Fig. 1.7 it is clear that the real and imaginary parts of the relative permeability µ - are independent of the externally applied steady magnetic field. But µ + shows a resonant behaviour at a value of H r 0 for a given frequency. 24

25 Since a linearly polarized plane wave can be considered to be composed of two circularly polarized waves, above analysis explains the non-reciprocal behavior of ferrite materials to microwave propagation Tensor permeability of ferrites: The permeability of the magnetized ferrite at microwave frequencies becomes an asymmetric tensor. Assuming the bias magnetic field to be in the z-direction, the permeability tensor can be represented by µ jk 0 t µ = µ 0 jk µ (1.27) 0 0 µ z where µ 0 is the permittivity of vacuum and µ, k, and µ z are complex quantities. The permeability tensor changes for different bias directions. The permeability tensor of the material depends on the texture i.e. single crystalline or polycrystalline forms and on the magnetic properties such as saturation magnetization, anisotropy field, damping factor etc. also on the external parameters such as the shape of the sample and applied dc magnetic field. The diagonal and off-diagonal component spectra of the permeability tensor exhibit resonant behavior. The relative permeabilities of ferrites are of the order of several thousand. Thus ferrites are good dielectrics, but exhibit magnetic anisotropy. It has non-reciprocal electrical properties i.e., (i) the transmission coefficient for microwave propagation through ferrite is not the same for different directions, (ii) non-reciprocal rotation of the plane of polarization. Another important phenomenon possessed by the ferrites is the Faraday rotation under the influence of microwaves. This phenomenon makes them applicable for many microwave devices such as rotator, gyrator, phase shifter etc. 25

26 1.5.3 Faraday rotation in ferrites: The phenomenon in which the plane of polarization of an electromagnetic wave is rotated while travelling through the medium of propagation is known as Faraday rotation. Magnetized ferrites exhibit nonreciprocal Faraday rotation at microwave frequencies. The splitting of a linearly polarized wave into two oppositely rotating circularly polarized waves which are the normal modes of propagation is the indication of Faraday rotation. When the components were separately excited, they will travel with different phase velocities. If the components are excited together then as the waves travel away from the excitation point there is a progressive shift in their phase. This phase shift denotes a rotation of the plane of polarization in the combined result. Faraday rotation in magnetized ferrites at microwave frequencies is a very interesting effect with device applications Brief literature survey on microwave properties of hexaferrites: The magnetic materials have been associated to information technologies. These technologies are required to work ever faster, which demands a good understanding of the dynamic properties of magnetic materials, as well as the ability to design fast-response systems. There are various reports on the absorption (reflection loss) and some reports on the complex permittivity and permeability of these hexaferrite at GHz frequencies. Most of the reports are available on the absorbing properties of these materials [ ] Some reports on the complex permittivity and complex permeability of barium and strontium hexaferrite are available [43, 46, 81, 116, ]. Most of the reports are on bulk hexaferrites. There are very few reports available on thick film hexaferrites [49, 64, 70, 74, 100, 101]. Characterizing the bulk and thick film barium and strontium hexaferrites using overlay technique has been reported for the first time in this work. 26

27 S.M. Abbas et al. [115] have reported 8-12 GHz absorption properties of BaCo x Si x +y Fe 12-2x-y O 19 dispersed in epoxy resin. They observed the change in absorption and shift in absorption frequency due to change in thickness. P. Singh et al. [116] have studied the permittivity, permeability and absorption properties of hot pressed Co, Ti doped barium hexaferrite pellets at 2-15 GHz. They observed shift in absorption frequencies for normal and hot pressed samples. The permittivity ε of barium hexaferrite decreased from 4.3 to 1.6, ε varied between 01 and 1, permeability µ was around 1.1 and loss µ was around 0.4 was reported by them. The microwave absorption up to 45 db of BaFe 12-2x A x Co x O 19 due to magnetic resonance was reported by H.S. Cho [117]. S. Sugimoto et al. [118] reported a barium hexaferrite wide band absorber (25 db) in Ku band due to the matching of material impedance with that of system. The FMR properties of barium hexaferrite thick film deposited on (111) MgO substrate by LPE method has been studied [64] P. Shepherd et al. [43] reported permittivity spectra of barium hexaferrite from 0.1 GHz to 1 GHz. Real part permittivity ε is almost 15 for the whole frequency range whereas permittivity loss is negligible. The complex permittivity and permeability values of barium hexaferrite are generally reported using vector network analyzer. The microwave dielectric properties of low loss strontium hexaferrite tape at 95 GHz, measure by cavity perturbation technique was reported by F. Quanyuan [119]. Thus most of the reports on the measurement of complex permittivity and permeability of barium and strontium hexaferrite bulk and thin films using vector network analyzer and cavity perturbation technique are available. Reports are also available on the measurement of complex permittivity using overlay technique [ ]. When the overlay is placed over an open microstrip circuit it forms a multilayered structure. There are two types of overlay techniques: 1. in touch overlay and 2. Distant overlay. R.K. Hoffman [123] reported that the overlay effects are mainly governed by the 27

28 dielectric properties of the overlaid material i.e. with the increase in dielectric constant of the overlay, the fringing fields get concentrated resulting in increase in effective width of the microstripline and hence reduction in resonant frequency whereas metallic overlay results in increase in resonant frequency [124]. R. N. Karekar et al and R.C. Aiyer et al. group have done work on the overlay effects of dielectric materials on thin film microstrip components such as microstrip ring resonator and λ/2 rejection filter. [ ]. To the authors knowledge there are no reports on the overlay studies of both bulk and thick film barium hexaferrite as well as strontium hexaferrite on thick film microstrip components. Previous reports from our colleagues in this lab., have shown successful measurement of complex permittivity using overlay technique [ ]. We reported measurement of complex permeability of various ferrites in both bulk and thick films using overlay technique and a simple waveguide technique for the first time [ ]. Overlay technique is a very simple and cost effective method for the perturbation of resonance of microstrip circuits. It has the flexibility to change the strength of perturbation by changing permittivity, permeability, width and thicknesses of the overlay material. Microstrip Integrated Circuits are the planar miniaturized form of microwave circuits. The microwave component size and performance are the primary needs for the design of electronic systems for satellite communications, phased array radar systems, electronic warfare and other military applications. The portable and cost effective components drive the consumer market. The microwave circuits can be integrated by hybrid as well as monolithic technique. 1.6 Methods for measurement of material properties at microwaves: The microwave methods for material properties characterization generally fall into nonresonant methods and resonant methods. Another recent type of measurement method is overlay method. Nonresonant 28

29 methods are often used to get a general knowledge of electromagnetic properties over a frequency range, while resonant methods are used to get accurate knowledge of dielectric properties at single frequency or several discrete frequencies. The overlay technique can be used to study the properties by just keeping the material over microstrip circuits. The restrictions of size and shape of the samples can be overcome by this technique Non-resonant Methods: In non-resonant methods, [137, 138], the properties of materials are fundamentally deduced from their impedance and the wave velocities in the materials. Nonresonant methods mainly include reflection methods and transmission/reflection methods. When an electromagnetic wave propagates from one material to another (from free space to sample), both the characteristic wave impedance and the wave velocity change, resulting in a partial reflection of the electromagnetic wave from the interface between the two materials. Measurements of the reflection from such an interface and the transmission through the interface can provide information for the deduction of permittivity and permeability relationships between the two materials. All types of transmission lines can be used to carry the wave for non-resonant methods, such as coaxial line, hollow metallic waveguide, dielectric waveguide, planar transmission line, and free space. In a reflection method, the material properties are calculated on the basis of the reflection from the sample, and in a transmission/reflection method, the material properties are calculated on the basis of the reflection from the sample and the transmission through the sample. In reflection methods, electromagnetic waves are directed to a sample under study, and the properties of the material sample are deduced from the reflection coefficient at a defined reference plane. Usually, a reflection method can only measure one parameter, either permittivity or permeability. 29

30 Figure 1.8 Coaxial short-circuit reflection [138] This method is widely used in the measurement of the permittivity and permeability of low conductivity materials, and it can also be used in the measurement of the surface impedance of high-conductivity materials. Free space transmission/reflection method also can be used for characterization of materials. Here the material is placed in the path of microwaves in between two antennas in free space. Figure 1.9 Coaxial transmission/reflection method [138] Resonant Methods: Resonant methods usually have higher accuracies and sensitivities than non-resonant methods. Resonant methods generally include the resonator method and the resonant-perturbation method. The resonator method is based on the fact that the resonant frequency and quality factor of a dielectric resonator with given dimensions are determined by its permittivity and permeability. This method is usually used to measure low 30

31 loss dielectrics whose permeability is µ 0. The resonant-perturbation method is based on resonant perturbation theory. For a resonator with given electromagnetic boundaries, when part of the electromagnetic boundary condition is changed by introducing a sample, its resonant frequency and quality factor will also be changed. From the changes of the resonant frequency and quality factor, the properties of the sample can be derived [139]. Resonator or dielectric resonator method can be used to measure the permittivity of dielectric materials and the surface resistance of conducting material In the cavity perturbation method, the sample under study is introduced into an antinode of the electric field or magnetic field, depending on whether permittivity (antinode of the electric field) or permeability (antinode of the magnetic field) is being measured. In a resonator method for dielectric property measurement, the dielectric sample under measurement serves as a resonator in the measurement circuit, and dielectric constant and loss tangent of the sample are determined from its resonant frequency and quality factor. Figure 1.10 shows the configuration often used in the dielectric resonator method. Figure 1.10 A dielectric cylinder sandwiched between two conducting plates 31

32 In general there are three types of resonant perturbations: cavity shape perturbation, wall-loss perturbation, and material perturbation. Cavity shape perturbation is often used to perturb or shift the resonant frequency of a cavity. In the wall-loss perturbation method, part of the cavity wall is replaced by the sample under study, and the resonant frequency and quality factor of the cavity are changed subsequently. The wall-loss perturbation method is usually used to measure the surface resistance of conductor samples. In the material perturbation method, the introduction of the material into a cavity causes changes in the resonant frequency and quality factor of the cavity. The material perturbation method is also called the cavity-perturbation method, and is suitable for measuring complex permittivity and permeability of materials having low-loss. In the cavity perturbation method, the sample under study is introduced into an antinode of the electric field or magnetic field, depending on whether permittivity or permeability is being measured as shown in fig below. Figure 1.11 TM cavity perturbation technique. The a and d are the radius and height of the cavity, respectively [140]. 32

33 These methods however need sample preparation and geometry and size of the sample must be known hence, these methods are destructive Overlay Methods: To find complex permittivity and permeability of the material, planar circuits can be used. By keeping the material whose characteristic dielectric and magnetic properties to be known, over microstrip (planar) microwave circuits, the perturbation in the fringing fields of the microstrip components takes place which leads to the change in transmission, reflection, quality factor, bandwidth and resonant frequency of the microstrip components. From this shift, the complex permittivity and permeability of the overlaid material can be calculated Microstrip Components Ag thick film Microstripline: Various types of microstrip components are available as shown in fig Out of these microstriplines are simplest transmission structures. In this work since this has been used, it is elaborated here. A microstripline used in the present investigation consists of a single ground plane and a thin strip conductor of width W and thickness t deposited on a low loss dielectric substrate, in our case alumina substrate. Although the geometry of microstripline is simple, the electromagnetic fields involved in it are very complex. Due to the absence of a top ground plate and the dielectric substrate above the strip, the electric field lines remain partially in the air above and partially in the lower dielectric substrate. This makes the mode of electromagnetic propagation not purely, transverse electric or transverse magnetic or transverse electromagnetic i.e. TEM but a quasi- TEM mode i.e. superposition of LSE and LSM mode [142, 143]. The microstripline radiates electromagnetic energy. The radiation loss is proportional to the square of the frequency. The use of high dielectric 33

34 material enhances the miniaturization factor but at the same time, reflection also enhances due to impedance mismatch. The propagation delay time for a quasi-tem mode is related to an effective dielectric constant ε eff is given by, ε eff = (ε r + 1)/2 + (ε r - 1)/2(1 + 12h/W) -1/2 ; W/h>> (1.28) Where ε r is the relative dielectric constant of the substrate material. The characteristic impedance of microstrip lines can be expressed by Z o = (376.7/ ε eff ) h/w ohm; for W/h>> (1.29) It has been reported [119, 120] that, characteristic impedance of microstrip lines is also a function of frequency. Fig Various types of microstriplines [141] 34

35 Field Fig. 1.13: Cross sectional view of the microstripline. The guide wavelength for the propagation of quasi-tem mode is given by λ g = λ o / ε eff (1.30) For the non-magnetic substrate material, two types of losses exist in microstrip lines which provide attenuation of signal. (1) Dielectric loss in the substrate and (2) Ohmic loss in strip conductor and the ground plane due to finite conductivity. The radiation losses of microstrip lines are eliminated by enclosing the microstrip within a metallic box having first resonance frequency much above the signal frequency. Microstrip lines are suitable for the design of passive circuits and series mounting of active components across a gap in the strip. Fig shows the non resonant microstrip structures. Apart from these, resonant structures can be fabricated using these components. Among the resonant structures straight resonator, patch antenna and annular ring antenna has been used in this work. Only these components are explained Microstrip patch antenna: The concept of patch antenna was first suggested by Munson [144]. It is a rectangular element can be thought of as a half wavelength. The patch has resonant properties giving rise to the electric field distribution. A directly fed microstrip patch antenna (MPA) consists of a patch of a 35

36 conducting material of any planar geometry on one side of dielectric substrates backed by a ground plane on the other side whereas the electromagnetically coupled (EMC) patch antenna is a layered structure of conducting patch over a bare dielectric substrate must be fed by a feedline on dielectric slab backed by a ground plane as shown in fig The conventional shapes of microstrip patch antennas are rectangular, square and circular because they are easy to analyze and their performance can be predicted. Rectangular element is most commonly used one. It is halfwavelength open circuit patch fed by either a microstrip line in the same plane or by a coaxial probe or by a feedline in other plane fed using electromagnetic coupling. The direct feeding and probe feeding technique are destructive whereas EMC feeding technique is more easy, nondestructive and advantageous. Fig Schematic of electromagnetically coupled Rectangular microstrip patch antenna The electromagnetic coupling is more generally referred to as proximity coupling. It has two degrees of freedom. One is the length of the feedings stub and the other is the patch width to line width ratio. Here due to the case of relative movement of the two substrates of patch and feed line, the feed point can be adjusted for impedance matching. The variation of feed location may affect a small shift in resonant frequency, due to change in coupling 36

37 between the feed line and the antenna, but the radiation pattern remains unaltered a Radiation mechanism of microstrip patch antenna: Radiation from microstrip antennas occurs from the fringing fields between the edge of the microstrip antenna conductor and the ground plane. The radiation from the electromagnetically coupled rectangular microstrip patch antenna is shown in figure 1.15 (a). The electromagnetic wave is launched at the feed line which is on lower substrate. (a) C)Top view Fig.1.15: Radiation mechanism of Microstrip Patch Antenna. Then the electromagnetic coupling takes place between patch and feed line through the substrate. Radiation may be ascribed mostly to the 37