xiii
List of Figures
2.1 An electron orbiting around the nucleus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Diamagnetic material (a) without and (b) with applied magnetic field. . . . . . . 21
2.3 Paramagnetic material (a) without and (b) with applied magnetic field. . . . . . 21
2.4 Ferromagnetic material (a) without and (b) with external magnetic field. . . . . 22
2.5 e difference between (a) ferromagnetism and (b) antiferromagnetism. . . . . 24
2.6 e unit cell of a spinel crystal structure at various angles. . . . . . . . . . . . . . . . . 26
2.7 Crystal structure of magnetic garnets on the plane z D 0. . . . . . . . . . . . . . . . . 29
2.8 Integration of YIG films into a GGG substrate. . . . . . . . . . . . . . . . . . . . . . . . 31
2.9 Magnetization precession with no damping. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.10 Magnetization precession with damping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.11 Illustration of an arbitrarily oriented DC biasing magnetic field. . . . . . . . . . . 39
2.12 Graphic representation of typical ferrite complex susceptibilities. . . . . . . . . . . 41
2.13 Gyromagnetic resonance and definition of the resonance linewidth
.H or !
0
/. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.14 Relative contributions of the polarizability mechanisms vs. frequency. . . . . . . 43
2.15 Physical mechanisms producing electric dipoles within a medium for
electronic, ionic, permanent dipoles, and space charge polarizabilities [38]. . . 44
2.16 Schematic representation of the physical mechanisms producing electric
dipoles for: (a) electronic, (b) ionic or atomic, and (c) orientational
polarizabilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.17 e relative contribution of the three polarizability mechanisms to the real
and imaginary part of the dielectric constant ("
r
). . . . . . . . . . . . . . . . . . . . . . . 48
2.18 Polarization curves of a ferroelectric crystal and its hysteresis loop when a
periodic electric field is applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.19 Ferroelectric hysteresis loop under small periodic electric field conditions. . . . 50
2.20 Unit cell of the perovskite crystal structure [40, 52, 53]. . . . . . . . . . . . . . . . . . 51
2.21 Perovskite crystalline structure. (a) A and B are cations and X is anion,
(b) SrTiO
3
, and (c) oxygen octahedron. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
xiv
2.22 e crystallic perovskite structure of BaTiO
3
: (a) Cubic lattice symmetry
of a highly symmetric perovskite structure above the Curie–Weiss
temperature > T
C
. (b) Tetragonal lattice symmetry of a distorted
(asymmetric) perovskite structure below the Curie–Weiss temperature
T < T
C
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.23 Crystal and electric polarization response in the ferroelectric and
paraelectric states: (a) “tetragonal” lattice below T
C
, (b) “cubic” lattice
above T
C
, (c) hysteresis loop in the ferroelectric phase, and
(d) non-hysteretic polarization in the paraelectric phase [46]. . . . . . . . . . . . . . 54
2.24 Temperature dependence of the dielectric constant for bulk or thick-film
and thin-film BSTO [42, 44, 46]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.25 Temperature dependence of the dielectric constant for the incipient
dielectric SrTiO
3
, (STO), vs. the DC bias voltage. . . . . . . . . . . . . . . . . . . . . . 55
2.26 e dielectric constant of BSTO, (Ba
X
Sr
1–X
TiO
3
), vs. temperature for
different barium contents (x). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.27 Dielectric constant of Ba
X
Sr
1–X
TiO
3
(BSTO) for
X D .Ba C Sr/=T i D 0:98; 0:9; 0:85, and 0.73 vs. the applied DC biasing
electric field [49, 52]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.28 An orthorhombic perovskite-like crystal structure of a YBCO
superconductor: (a) oxygen-deficient YBa
2
Cu
3
O
6
and (b) fully oxygenated
YBa
2
Cu
3
O
7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.29 Cross-section of a typical tunable microwave circuit exploiting ferroelectric
material features (LTCC modules) [40, 59, 60]. . . . . . . . . . . . . . . . . . . . . . . . . 59
2.30 e LTCC technology.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.31 Contribution of the different mechanisms to the microwave losses of
incipient ferroelectric: 1. ree-quantum, 2. Four-quantum, and 3.
Quasi-Debye mechanisms. ( D
0
=
O
). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.32 Loss tangent vs. temperature for a single crystal and a thin film sample for
zero bias (E
dc
D 0) at a frequency of 10 GHz. . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.1 (a) Directions of internal
N
H
i
D
N
H
0
and external
N
H
a
magnetic fields for a
thin planar ferrite sample magnetized at saturation.
(b) transversely—normal and (c) longitudinally—tangential. . . . . . . . . . . . . . . 74
3.2 Elements N
x
, N
y
, and N
z
of three different shapes of ferrite samples. . . . . . . 75
3.3 Hexagonal crystal where magnetization is oriented at an angle with
respect to the axis of symmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
xv
3.4 A spin wave with ignored dipolar contributions and
N
k=
N
M
s
[20]. . . . . . . . . . . . 88
3.5 e pole avoidance principle causes demagnetization energy minimization
by aligning the magnetization parallel to the surface and maintaining it as
uniform as possible in the interior: (a) parallelepiped and (b) spherical
specimen [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.6 e formation of domains minimizes exchange and demagnetization
energy [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.7 Single domain or a vortex state in very small specimens [24]. . . . . . . . . . . . . . 91
3.8 Spin-wave manifold [12, 18, 20]. e shaded area denotes the
magnetostatic wave spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.9 A visual presentation of spin waves for maximum dipolar interaction,
where
k
D 90
ı
[20]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.10 Spin-wave manifold for YIG including polycrystalline theories without
exchange interaction and magnetostatic waves [28]. . . . . . . . . . . . . . . . . . . . . . 96
3.11 An infinitely extending thin ferrite slab normally biased to saturation. . . . . . 109
3.12 A graphic solution of the transcendental equation of symmetric MSFVW. . 113
3.13 A graphic solution of the transcendental equation of anti-symmetric
MSFVW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.14 e inverse group velocity of MSFVW [12]. . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.15 Infinitely extending thin ferrite slab longitudinally biased to saturation. . . . . 115
3.16 X and .1 C X / vs. circular frequency [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.17 Dispersion curves for backward magnetostatic volume waves
(MSBVW) [12].. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
3.18 Inverse group velocity .1=Vg/ for MSBVW [12]. . . . . . . . . . . . . . . . . . . . . . 125
3.19 Dispersion relation for MSSW in a longitudinally magnetized film [12]. . . . 128
3.20 Inverse group velocity of MSSW [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.21 e magnetic potential f
i
.x/ distribution for MSSW modes in a direction
transverse to the film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.22 Magnetization and magnetic field distribution of a surface wave mode
(MSSW) for k
z
D 0 [13]: (a) transverse magnetization and (b) transverse
magnetic fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3.23 Graphic representation of the two non-reciprocal MSSW modes for the
limiting case when ˛
i
d >> 1 [41]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
xvi
3.24 Definition of the transverse RF magnetic field
N
h
t
and its angular
dependence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
3.25 Graphic representation of an MSFVW [16]. . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.26 Graphic representation of an MSBVW [16]. . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.27 Graphic representation of an MSSW [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
3.28 An infinitely extending longitudinally magnetized ferrite slab. . . . . . . . . . . . 146
3.29 Infinite longitudinally magnetized two dielectric-ferrite layers. . . . . . . . . . . . 152
3.30 Transversely magnetized dielectric-ferrite double layer (demagnetization
H
i
D H
DC
M
S
). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
3.31 Shielded transversely magnetized dielectric-ferrite double layers. . . . . . . . . . 162
3.32 Shielded longitudinally magnetized dielectric–ferrite double layer. . . . . . . . . 163
4.1 (a) Relationships and overlapping of ferro-properties in complex media.
(b) All possible interactions in multiferroic and magneto-electric media [3]. 174
4.2 ree usual multiferroic composites: (a) spherical particles, (b) laminate
composite, and (c) fiber/rod inclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
4.3 eoretical electric field magnetic tunability for three bilayers: (i) nickel
ferrite (NiFe
2
O
4
)/PZT, (ii) lithium ferrite/PZT, and (iii) yitrium iron
garnet (YIG)/PZT. E
DC
can be obtained by a DC voltage of 30 V for a
thin film composite with thickness of 1 m [1]. . . . . . . . . . . . . . . . . . . . . . . . 177
5.1 ree-dielectric-layers microstrip line with the strip conductor located:
(a) between the two dielectrics and (b) printed on the top dielectric layer.
is is defined as the original z-plane, .z D x C jy/. . . . . . . . . . . . . . . . . . . . 181
5.2 Conformal transformation of the three-layer microstrip line to the g-plane
.g D u Cj/ where the semi-infinite cross-section is mapped to a
rectangular area between two conductor segments: (a) for Figure 5.1a and
(b) for Figure 5.1b. ese are approximated according to [7]. . . . . . . . . . . . . 182
5.3 Multiple-dielectric-layer microstrip line: (a) the geometry and (b) the
conformal transformation [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.4 (a) A multilayer microstrip line and (b) reduction to an equivalent single
layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.5 Geometry of coplanar transmission lines, (a) slotline, (b) coplanar
waveguide, and (c) coplanar strips.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5.6 A multilayer asymmetric coplanar waveguide: (a) original z D x C jy plane
and (b) approximate conformal transform in w D u Cj domain. . . . . . . . . 196
xvii
5.7 Generalized multilayer transmission lines with finite ground planes.
(a) Coplanar waveguide (CPW) with finite ground planes and (b) coplanar
strips (CPS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5.8 Microstrip line printed on a demagnetized or partially magnetized
isotropic magnetic substrate [34]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
5.9 Transforming a microstrip line to a slotline based on the classical “duality
principle.” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
5.10 Microstrip line printed on a uniaxial anisotropic substrate with the optical
axis transversely aligned along Oy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
5.11 Microstrip on a uniaxial anisotropic substrate with possible optical axis
misalignment by an angle [43]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
5.12 Microstrip line over a composite dielectric-weakly magnetized ferrite. . . . . . 216
5.13 Definition of the effective permeability of a ferrite-dielectric composite, as
in [53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
5.14 Definition of effective electric permittivity and effective magnetic
permeability for a ferrite-dielectric composite [53]. . . . . . . . . . . . . . . . . . . . . 217
5.15 Discretization of the charge density over the strip conductor [53]. . . . . . . . . 219
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