close

Вход

Забыли?

вход по аккаунту

?

Microwave Devices Utilizing Magnetoelectric Hexaferrite Materials for Emerging Communication Systems

код для вставкиСкачать
Microwave Devices Utilizing Magnetoelectric Hexaferrite
Materials for Emerging Communication Systems
A Dissertation Presented
by
Khabat Ebnabbasi
to
The Department of Electrical and Computer Engineering
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in
Electrical Engineering
Northeastern University
Boston, Massachusetts
November, 2012
UMI Number: 3548281
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3548281
Published by ProQuest LLC (2012). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
All rights reserved. This work is protected against
unauthorized copying under Title 17, United States Code
ProQuest LLC.
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346
NORTHEASTERN UNIVERSITY
Graduate School of Engineering
Thesis Title: Microwave Devices Utilizing Magnetoelectric Hexaferrite Materials for
Emerging Communication Systems
Author: Khabat Ebnabbasi
Department: Electrical and Computer Engineering
Approved for Dissertation Requirement for the Doctor of Philosophy Degree
______________________________________________
Dissertation Advisor: Carmine Vittoria
____________________
Date
______________________________________________
Thesis Reader: Fabrizio Lombardi
____________________
Date
______________________________________________
Thesis Reader: Matteo Rinaldi
____________________
Date
______________________________________________
Department Chair: Ali Abur
____________________
Date
Graduate School Notified of Acceptance:
______________________________________________
Director of the Graduate School: Sara Wadia Fascetti
____________________
Date
ABSTRACT
Ferrite materials are widely used in passive and tunable electromagnetic signal
processing devices such as phase shifters, circulators, isolators, and filters. These materials
can also be used as tunable antenna substrates and EMI suppression cores. Due to their
excellent dielectric properties, ferrites possess the advantages of low loss and high power
handling relative to semiconductors. Typically, parameters of magnetic materials are
controlled by an external magnetic field thus allowing for tuning of device performance.
Magnetic fields are usually generated using permanent magnets or current driven coils,
leading to relatively large component size, weight, and cost, as well as slow response time
in comparison to semiconductor-based technologies. Magneto-electric materials can be a
practical solution to control the magnetic parameters of ferrites by electric field and/or
voltage and would eliminate permanent magnets and tuning coils to overcome most of the
disadvantages in the use of ferrites for microwave devices. A situation where ferrites are
compatible with active components based on semiconductors would become a reality.
Furthermore, key advantages of ferrites, including low insertion loss and high power
handling capability could be exploited without the penalty of added size, weight, and cost,
as well as increased response time.
Recently, magnetically induced ferroelectric materials have been discovered giving rise
to the hope that it may be feasible to tune ferrites by applying voltage. From a practical
point of view, however, their magneto-electric effects are useless because they operate
i
only far below room temperature (for example, 28 K in TbMnO3 and 230K in CuO).
Furthermore, many such materials require a strong magnetic field, on the order of Tesla, in
order to magnetically induce ferroelectric response, rendering them impractical.
Multi-ferroic composite materials have been proposed to generate internal magnetic
fields via voltage. Multi-ferroic composites usually consisted of magnetostrictive and
ferroelectric or piezoelectric slabs in physical contact whereby magnetic field sensors have
been implied and fabricated so far. Also, small shifts in ferromagnetic resonance (FMR)
have been observed using magnetoelectric composites in the presence of an electric field.
Tuning of ferrite microwave devices by an electric field or voltage is still not practical with
present composite structures.
In this work we propose an alternative approach to this problem. A single layer of
magneto-electric Z-type, Sr3Co2Fe24O41, which has strong ME effects at room
temperature, is proposed to induce magnetic parameter changes with application of
voltage. The advantage of a single layer is that it is simpler to utilize to tune ferrite
devices. Sr3Co2Fe24O41 is identified as a Z-type hexaferrite consisting of S, R, and T
“spinel” blocks which in the T block the Fe-O-Fe bond angles were slightly deformed to
affect the super exchange interaction between the Fe ions and induce the spiral spin
configuration in Sr3Co2Fe24O41. Changes in the spin spiral configuration in the presence
ሬሬԦ. This physical mechanism
of an electric field ‫ܧ‬ሬԦ induce changes in the magnetization ‫ܯ‬
for the ME effect is very different from the mechanisms applicable to multiferroic
materials in the past. This new mechanism opens up new properties or opportunities in
ii
the physics and applications of ME materials in engineering. The previously most used
technique to explore ME effects was ferromagnetic resonance (FMR). In the past FMR
frequency shifts were measured with an applied ‫ܧ‬ሬԦ in the presence of a permanent
magnet. There has never been a report on permeability measurement in ME material with
application of an electric field, although there are many reports on FMR shifts. The
measurement of FMR frequency shifts is ineffectual in our case, because (a) the shifts are
extremely small, (b) they are strongly damped in the new mechanism, and (c) and a
permanent magnet still is needed. Hence, we have devised a new measurement method
whereby the permeability of our material is measured directly via a modified coaxial line
technique. We refer to these measurements as “converse” ME measurements and a
physical model for the effect is provided. The application of ‫ܧ‬ሬԦ strains the material
thereby changes the physical structure of the spiral spin configuration. It is this physical
ሬሬԦ. We refer
motion of the spiral response to ‫ܧ‬ሬԦ that induces a change in magnetization ‫ܯ‬
to this model as the “slinky helix” model. Our model should be contrasted with the model
for the ME effect in multiferroics as well as ferromagnetic metal films wherein the band
energies of the up and down spin are modified by the electric fields at the interface
between phase separated ferromagnetic and ferroelectric films. The change in band
splitting leads to a change in surface magnetization.
iii
Table of Contents
Chapter 1. Magnetoelectric Overview............................................................................1
1. Introduction...........................................................................................................1
1.1 Ferroic Materials.............................................................................................1
1.2 Multiferroics ...................................................................................................2
2. Magnetoelectric Coupling.....................................................................................3
3. Parity and time reversal symmetry in Ferroics......................................................7
4. Nonlinear coupling................................................................................................8
5. Indirect coupling...................................................................................................9
6. Coupling constants calculation...........................................................................10
7. Single-phase studies............................................................................................11
8. Multiferroics.......................................................................................................12
9. Devices...............................................................................................................13
References..............................................................................................................15
Chapter 2. Magnetoelectric Effects on Single Phase of Z-type and M-type
Hexaferrites at Room Temperature...........................................................20
1. Introduction........................................................................................................20
2. Sr Z-type Experimental Material Growth Procedure..........................................22
2.1 Sr Z-type Indirect Converse Magnetoelectric Experimental Analysis.........27
2.2 Orientation of Polycrystalline Sr Z-type.......................................................31
3. M-type Experimental Material Growth Procedure..............................................38
4. Z- and M-type Hexaferrites ME Effect Comparison...........................................39
4.1 Resistivity Measurements..............................................................................39
4.2 ME Effect Measurements..............................................................................40
5. Conclusions..........................................................................................................43
References...............................................................................................................45
Chpater 3. Coaxial Line Technique to Measure Constitutive Parameters in Magneto
Electric Ferrite Materials............................................................................47
1. Introduction..........................................................................................................47
2. Theory of the Design...........................................................................................49
2.1 Two port design..............................................................................................49
2.2 One port design..............................................................................................52
3. Experimental Measurements................................................................................56
4. Conclusions..........................................................................................................62
References................................................................................................................63
iv
Chapter 4. Converse Magnetoelectric Experiments on a Room-Temperature
Spirally Ordered Hexaferrite......................................................................64
1. Introduction..........................................................................................................64
2. Experimental Results...........................................................................................68
2.1 Experimental Material Growth......................................................................68
2.2 Magnetoelectric Measurement Technique.....................................................68
2.3 Experimental Magnetoelectric Measurements..............................................74
3. Conclusions..........................................................................................................80
4. Appendix..............................................................................................................80
References................................................................................................................85
Chapter 5. Strong Magnetoelectric Coupling in Hexaferrites at Room
Temperature..................................................................................................87
1. Introduction..........................................................................................................87
2. Experimental Measurements................................................................................88
3. Conclusions..........................................................................................................94
References................................................................................................................95
Chapter 6. Microwave Magnetoelectric Devices...........................................................96
1. Introduction..........................................................................................................96
2. Multi-Phase Magnetoelectric Microwave Phase Shifter......................................99
3. Single-Phase Magnetoelectric Microwave Phase Shifter..................................102
3.1 Meander Line Micro-strip............................................................................103
3.2 LC Phase Shifter Theory and Design...........................................................104
References..............................................................................................................111
Chapter 7. Discussion and Conclusion.........................................................................113
v
Table of Figures
Figure 1-1 Circular loop model of magnetic material lattice structure............................................................1
Figure 1-2 Coupling order of Ferroics and their relations and distinctions.....................................................2
Figure 1-3 Time-reversal and parity symmetry in Ferroelectric, Ferromagnetic and Multiferroic materials..3
Figure 2-1 Orientation of magnetic moment of Sr-Z, Ba-Z and BaSr-Z hexaferrites.....................................4
Figure 2-2 Planetary mono mill Pulverisette 6 to grind particles....................................................................5
Figure 2-3 X-ray diffraction pattern of the polycrystalline Sr3Co2Fe24O41 at room temperature. The black
line represents the reference peak positions for the Ba Z-type hexaferrite (Ref. ICDD # 19-0097. Space
group: P63/mmc(194)).....................................................................................................................................6
Figure 2-4 Ferromagnetic resonance measuring instrumentation...................................................................7
Figure 2-5 FMR spectrum of polycrystalline Sr3Co2Fe24O41 at room temperature for magnetic field (H)
applied parallel to slab plane............................................................................................................................8
Figure 2-6 I-E and ρ-E curves of the polycrystalline Sr3Co2Fe24O41 at room temperature after sintering in
O2......................................................................................................................................................................9
Figure 2-7 Vibrating sample magnetometer (VSM) instrumentation. The sample is placed between the
pickup coils and voltage is applied to the sample through the conductor plates............................................10
Figure 2-8 Polycrystalline Sr3Co2Fe24O41 magnetization as a function of external applied H parallel to slab
plane and perpendicular to applied E field at room temperature....................................................................11
Figure 2-9 The zoomed in change in remanence magnetization measurements shown in Figure 2-7 over
low magnetic field..........................................................................................................................................12
Figure 2-10 Polycrystalline Sr3Co2Fe24O41 remanent magnetization change vs electric feild for a typical
sample with 0.5mm thickness at room temperature.......................................................................................13
Figure 2-11 Change in temperature in the Sr Z-type sample versus electric field........................................14
Figure 2-12 Change in dielectric constant over frequency versus applied external magnetic field..............15
Figure 2-13 Polycrystalline Sr3Co2Fe24O41 powder orientation set up..........................................................16
Figure 2-14 SEM photographs of the ground particles for different milling durations.................................17
Figure 2-15 Photograph of 0.5T rotating permanent magnet........................................................................18
Figure 2-16 Schematic of orientation procedure...........................................................................................19
Figure 2-17 VSM data of Sr-Z. Red and black dashed lines represent after orientation before orientation,
respectively.....................................................................................................................................................20
Figure 2-18 X-ray diffraction pattern of polycrystalline SrCo2Ti2Fe8O19 at room temperature. The black
line represents the reference peak positions for the Ba M-type hexaferrite (PDF # 27-1433. Space group:
vi
P63/mmc(194))...............................................................................................................................................21
Figure 2-19 Current versus electric field for Sr-Z and SCTFO.....................................................................22
Figure 2-20 Change in remanence magnetization (Mr) of M-type (sintered in air) for (a) Edc perpendicular
to H and (b) Edc parallel to H..........................................................................................................................23
Figure 2-21 The change in remanence magnetization (Mr) of Z-type sintered in O2, M-type sintered in air
and O2 versus DC electric field.......................................................................................................................24
Figure 3-1 Non-reciprocal ferrite network equivalent of transmission line..................................................50
Figure 3-2 Two port coaxial line schematic for ferrite magneto-electric (ME) effect measurement............51
Figure 3-3 Circuit model of the medium in connection with the dangling wires..........................................52
Figure 3-4 One port coaxial line schematic for ferrite magneto-electric (ME) effect measurement.............53
Figure 3-5 Coaxial line parts and assembled device......................................................................................58
Figure 3-6 Measured I-V characteristic of polycrystalline Sr Z-type hexaferrite.........................................59
Figure 3-7 Measured real and imaginary parts of the ME ferrite permeability versus frequency for E=0
kV/cm.............................................................................................................................................................59
Figure 3-8 The theoretical calculation and experimental measurement of magnetic permeability change
versus frequency for E=5 kV/cm....................................................................................................................60
Figure 3-9 The magnetic permeability change versus electric field and frequency when Mr is parallel and
anti-parallel to E.............................................................................................................................................60
Figure 3-10 The magnetic permeability change versus electric field and frequency when Mr is
perpendicular to E..........................................................................................................................................61
Figure 3-11 Phase change versus electric field and frequency when Mr is parallel to E...............................61
Figure 3-12 Phase change versus electric field and frequency when Mr is anti-parallel to E......................62
Figure 4-1 (a) Crystal structure of a part of the hexagonal unit cell. (b) Spiral spin order............................65
Figure 4-2 Real and imaginary parts of the polycrystalline Sr Z-type permeability versus frequency.........69
Figure 4-3 Coaxial line schematic.................................................................................................................71
Figure 4-4 Static electric and magnetic fields bias conditions of the hexaferrite slab in (a) E parallel or
anti-parallel to Mr and in (b) E perpendicular to Mr......................................................................................73
Figure 4-5 Magnetic permeability change versus electric field over a microwave frequency range when M
is parallel and antiparallel to E. (a) Theoretical calculation and (b)experimental measurement for E = 5
KV/cm.............................................................................................................................................................75
Figure 4-6 Magnetic permeability change versus electric field over a microwave frequency range when M
is perpendicular to E.......................................................................................................................................76
Figure 4-7 (a) Applied electric field over the slab to measure strain, (b) Electrostriction strain of
polycrystalline Sr Z-type versus electric field................................................................................................77
Figure 4-8 Spin spiral configuration for different directions of E. (a) E = 0, (b) E parallel to M, and (c) E
antiparallel to M..............................................................................................................................................80
Figure 5-1 SEM micrograph of single crystal of Z-type hexaferrites, Sr3Co2O24O41....................................89
Figure 5-2 Room-temperature X-ray diffraction pattern...............................................................................89
Figure 5-3 Ferromagnetic resonance at room-temperature (derivative absorption versus Hext)....................90
Figure 5-4 Hysteresis loops change versus electric field with the magnetic field applied parallel (//) and
vii
perpendicular (┴) to the slab plane.................................................................................................................91
Figure 5-5 Remanence magnetization change versus electric field with the magnetic field applied parallel
(//) to the slab plane........................................................................................................................................92
Figure 5-6 Change in remanence magnetization versus electric field...........................................................92
Figure 5-7 change in capacitance versus magnetic field...............................................................................93
Figure 6-1 Potential and current applications of ferrite materials and devices in communication systems
and their operating frequency range...............................................................................................................97
Figure 6-2 Schematics of fabricated magnetoelectric nonreciprocal microwave phase shifter in [10]......101
Figure 6-3 Schematics of meander line microstrip......................................................................................104
Figure 6-4 Microwave network consisting of elements connected in series...............................................105
Figure 6-5 Phase shift by applying electric field or voltage........................................................................107
Figure 6-6 Simulated phase shifter structure (a) without and (b) with the ME material introduced with
Lorentz model...............................................................................................................................................108
Figure 6-7 Insertion loss and phase simulation results................................................................................109
Figure 6-8 The fabricated phase shifter........................................................................................................110
Figure 6-9 Measured phase shift by applying voltage for the fabricated phase shifter with no capacitor..110
viii
Chapter 1. Magnetoelectric Overview
1. Introduction
In this chapter, the physical concepts of single phase ferroically ordered materials and
multi-ferroic composite structures are presented. A ferroic material may be magnetically
or electrically ordered without the application of external magnetic, H, or electric, E,
fields. Combining various ferroics potentially can be used in different applications such
as sensors and communication devices and circuits. Understanding of magnetic and
electrical properties of ferroic materials helps us to take advantage of special coupling
phenomena in ferroics to push current technology toward smaller, cheaper, more compact
and more efficient devices [1].
1.1 Ferroic Materials
Here are some basic definitions of ordered ferroic materials that we plan to utilize for
various applications:
•
Antiferromagnetic: magnetic moments cancel each other completely within each
magnetic unit cell for temperatures below the Neel temperature. An example is
the
heavy-fermion
superconductor
URu2Si2.
Better
known
examples
include chromium, alloys such as iron manganese (FeMn), and oxides such as
nickel oxide (NiO).
•
Ferrimagnetic: magnetic moments cancel each other incompletely and there is a
net magnetization that can be rotated by an external magnetic field. The ordering
1
temperature is the Neel temperature which for most ferrites is well above room
temperature.
•
Ferromagnetic: possesses spontaneous magnetization. Ferrites are usually
insulators for temperatures below the Currie temperature. Most ferromagnets tend
to be metallic.
•
Antiferroelectric: electric dipole moments cancel each other completely within
each crystallographic unit cell. This is the analogue of antiferromagnetism.
•
Ferroelectric: possesses a spontaneous electric polarization for temperatures
below the Currie temperature. It is the analogue of ferromagnetism.
•
Ferroelastic: possesses a stable spontaneous deformation with hysteretically
versus an external stress.
Figure 1-1 Circular loop model of magnetic material lattice structure.
1.2 Multiferroics
Multiferroics are materials that exhibit two or more ordered ferroic phases. In most
cases of interests the multiferroics interact with each other.
•
Magnetoelectric coupling: represents a change in magnetization or polarization
of a multiferroic material upon application of a magnetic or electric field.
2
•
Piezoelectricity: describes the influence of an applied linear electric field on
strain, or a change in polarization as a linear function of applied stress.
•
Piezomagnetism: represents a change in strain as a linear function of applied
magnetic field, or a change in magnetization as a linear function of applied stress.
•
Electrostriction: describes a change in strain as a quadratic function of applied
electric field.
•
Magnetostriction: describes a change in strain as a quadratic function of applied
magnetic field.
•
Single Phase Multiferroic: a material possessing at least two of ferroic properties:
ferroelectricity, ferromagnetism and ferroelasticity [2].
2. Magnetoelectric Coupling
A ferroelectric crystal exhibits a stable and switchable electrical polarization in the
form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and
switchable magnetization that arises through the quantum mechanical phenomenon of
spin exchange. The relationship between multiferroic and magnetoelectric materials is
shown in Figure 1-2. A multiferroic material is not necessarily magnetoelectric. There are
few multiferroic materials that exhibit both ferroelectric and ferromagnetic properties
without coupling between the two.
Magnetoelectric coupling can exist wherever magnetic and electrical orderings occur
in the same temperature range. Also magnetoelectricity may occur in paramagnetic
3
ferroelectrics [3]. Usually, the mediator for the coupling is strain as related to crystal
phases.
Figure 1-2 Coupling order of ferroics and their relations and distinctions.
As shown in Figure 1-2, ME materials have been classified in four categories. Type I,
is the ME materials which are multiferroic, type II, refers to ME materials being just
Ferroelectric, type III, is the analogue of type II and it represents the ME materials which
are just Ferromagnetic, and type IV, is neither Ferroelectric or Ferromagnetic.
The magnetoelectric effect in single-phase crystals is traditionally described [4-8] in
Landau theory ,see equation (1), by writing the free energy F of the system in terms of an
applied magnetic field H whose ith component is denoted as Hi, and an applied electric
field E whose ith component is denoted Ei. This convention is unambiguous in free space,
but Ei within a material includes the resultant field that a local site would experience. In a
non-ferroic material, where both the temperature dependent electrical polarization Pi(T)
(µCcm-2) and the magnetization Mi(T) (µB per formula unit, where µB is the Bohr
4
magneton) are zero in the absence of applied fields. F may be represented in an infinite,
homogeneous and stress-free medium under the Einstein summation convention as:
, (1)
where the SI and CGS units of the parameters and their relations are:
. . 4
!"
/
!
=
, #$ $%&''%( )*+
,! "
;
!"
'0%01230
;
,!
10
/
!
)*+
,! "
'0%01230
4
,!
×1054
( 16 7898:;<8 )
. !
, #$ $%&''%( ,
#$ $%&''%( >?
;
=
!
4A×1054 >?
( 1B 78989CD?E? )
*It is noted that Equation (1) is in standard (SI) unit system.
The first term on the right hand side of eq.(1) describes the contribution resulting from
the electrical response to an electric field, ε0 is the permittivity of free space, and the
relative permittivity εij(T) is a second-rank tensor that is typically independent of Ei in
non-ferroic materials. The second term is the magnetic equivalent of the first term, where
µij(T) is the relative permeability and µ0 denotes the permeability of free space. The third
term describes linear magnetoelectric coupling via αij(T); the third-rank tensors βijk(T)
and γijk(T) represent higher-order (quadratic) magnetoelectric coefficients.
All magnetoelectric coefficients incorporate the field independent material response
functions εij(T) and µij(T). The magnetoelectric effects can then easily be established in
5
the form Pi(Hj) or Mi(Ej). Pi(Hj) is obtained by differentiating F with respect to Ei, and
then setting Ei = 0 and a complementary operation involving Hi establishes the Mi(Ej) as:
FG HIJK
(2)
and
L MNOP
(3)
In multiferroic materials, the above analysis is less rigorous because εij(T) and µij(T)
display field hysteresis. This is because it is then possible to account for the potentially
significant depolarizing/demagnetizing factors in finite media, and also because the
coupling constants would then be functions of temperature alone, as in the standard
Landau theory. In practice, resultant electric and magnetic fields may sometimes be
approximated by the polarization and magnetization respectively [9]. A multiferroic that
is ferromagnetic and ferroelectric is liable to display large linear magnetoelectric effects.
This follows because ferroelectric and ferromagnetic materials often (but not always)
possess a large permittivity and permeability respectively, and αij is bounded by the
geometric mean of the diagonalized tensors εii and µjj such that [10]:
Q (4)
This is obtained from Einstein summation convention free energy equation by forcing
the sum of the first three terms to be greater than zero that is ignoring higher-order
6
coupling terms. It represents a stability condition on εij and µij, but if the coupling
becomes so strong that it drives a phase transition to a more stable state, then αij, εij and µij
take on new values in the new phase. Note that a large εij is not a prerequisite for a
material to be ferroelectric (or vice versa); and similarly ferromagnets do not necessarily
possess large µij. For example, the ferroelectric KNO3 possesses a small ε = 25 near its
Curie temperature of 120 0C whereas paraelectric SrTiO3 exhibits ε > 50,000 at low
temperatures [11]. Therefore large magnetoelectric couplings need not arise in, or be
restricted to, multiferroic materials.
3. Parity and Time Reversal Symmetry in Ferroics
In Ferroelectric material the electric dipole moment p is represented by a positive
point charge that lies asymmetrically within a crystallographic unit cell that has no net
charge, R SE, where R is polarization, q is electric charge and E is the charges
distance. There is no net time dependence, but spatial inversion E T E reverses p,
shown in Figure 1-2. In Ferromagnets the magnetic moment m is represented classically
by a charge tracing dynamically an orbit, C AE US⁄U8 , where U7 AE , see
Figure 1-2, and 8 is time. A spatial inversion produces no change, since E T E
,
but time reversal switches the orbit and thus m. In summary, p obeys time symmetry but
not parity. However, m obeys parity but not time symmetry.
Multiferroics that are both
ferromagnetic and ferroelectric break time reversal and parity symmetries.
7
Figure 1-3 Time-reversal and parity symmetry in Ferroelectric, Ferromagnetic and Multiferroic materials.
4. Nonlinear Coupling
Most materials have small values of either εij or µij or both, so the linear
magnetoelectric effect will also be small, given that permittivity and permeability appear
as a product in equation (4). However, no such restriction applies to higher-order
couplings, such as those described by βijk and γijk. For example, in some materials terms
such as βijkHjHk can dominate the linear term αijHj in equation (2), as first shown
8
experimentally at low temperatures in the piezoelectric paramagnet NiSO4.6H2O [12]. In
order to achieve large magnetoelectric effects at room temperature through higher-order
terms, investigating magnetic materials with reduced dimensionality can be a good choice.
Indeed, two dimensional spin order associated with β(T) can persist to a temperature T2D
that exceeds the temperature T3D at which three-dimensional spin order associated with
α(T) is destroyed. This scenario arises at low temperature in BaMnF4 [13].
5. Indirect Coupling
In linear and higher-order magnetoelectric coupling the strain effects have not been
included. Such effects could be significant or even dominant. For example, the inclusion
of piezomagnetism (magnetostriction) would generate cross terms in equation (1) that are
proportional to strain and vary linearly (quadratically) with Hi. Analogous expressions
would arise from piezoelectricity or electrostriction. Furthermore, mixed terms involving
products of strain, Hi and Ej have been predicted [14]. In two-phase materials, magnetic
and electrical properties are strain-coupled by design in the quest for large
magnetoelectric effects. The strength of this indirect coupling is not restricted by equation
(4), and enhancements over single-phase systems of several orders of magnitude have
been achieved [15].
9
6. Coupling Constants Calculation
The magnetoelectric behavior of a material can only be fully understood if its
magnetic point group symmetry is known. This is because the magnetoelectric
coefficients αij, βijk and γijk possess the symmetry of the material. For example, αij is
non-zero for materials that do not have a centre of symmetry and are time-asymmetric.
Conversely, information regarding the magnetoelectric coefficients based on electrical or
optical experiments can aid the determination of magnetic point group symmetries. The
major challenge is to make samples sufficiently insulating to prevent leakage currents
contributing to the measured signal, a widespread problem undermining the measurement
of ferroelectric polarization loops [8, 16]. Another complication arises if ferroic domains
are present, and care should be taken to prepare single-domain polarization states [17].
Magnetoelectric coupling can be measured indirectly by simply recording changes in
either the magnetization near, say, a ferroelectric transition temperature or the dielectric
constant near a magnetic transition temperature. The resulting effects are described using
various terms such as magnetocapacitance or magnetodielectric response. Catalan has
recently shown that the frequently reported effects could be misleading due to
magnetoresistance effects alone, and that the signature of true magnetocapacitance effects
is persistent to high frequencies and low loss [18]. However, even magnetocapacitance
measurements may not provide insight nor yield coupling constants. Direct
measurements are more challenging. They record either a magnetic response to an
applied electric field or an electrical response to an applied magnetic field. The first way
10
typically requires placing the sample in a magnetometer apparatus. In the other method,
the electrical response can be measured in terms of either current or magnetic field. The
time-integrated current per unit area directly represents the magnetically induced change
of polarization in equation (2), that is, WF⁄W , ignoring higher-order terms.
Measurements of voltage, however, yield empirical coupling coefficients commonly also
denoted α, assuming linearity take the form W ⁄W.
7. Single-Phase Studies
In 1957, the linear magnetoelectric coupling coefficient α was predicted to occur in
Cr2O3 [19]. Then, in the 1960s, α was experimentally observed to be non-zero below the
anti-ferromagnetic Neel temperature of 307K, peaking to a value of WF⁄W X
4.1D7C5 [20-21]. Potential fapplications of multiferroic materials include the possibility
of reversing the magnetization by applying an electric field or vice versa. In the boracite
Ni3B7O13I,
magnetic
and
electrical
ordering
occurred
below
60K,
and
a
magnetic-field-induced reversal of the magnetization was found to flip the polarization
(0.076 µCcm-2) [17]. Alternatively, in the paramagnetic ferroelectric Tb2(MoO4)3, a
magnetically induced persistent polarization can arise in large part to applied magnetic
fields [3]. Recently, magnetoelectric switching has been observed in orthorhombic
manganites, REMnO3 or REMn2O5, where RE is a rare earth element. These are
anti-ferromagnets that display weak ferroelectricity. A small polarization appears at the
Neel temperature (~30 K) because the magnetic transition gives rise to crystalline
11
distortions. The polarization of 0.04 µCcm-2 in TbMn2O5 has been magnetically reversed
[22], and the polarization of 0.08 mCcm-2 in TbMnO3 has been magnetically rotated by
90o [23]. Similarly, in the hexaferrite Ba0.5Sr1.5Zn2Fe12O22, a polarization of 0.015µCcm-2
may be magnetically induced and subsequently rotated 360o about the C-axis. These
changes in polarization are not persistent, and arise at low temperatures only [24].
8. Multi-Phase Studies
An alternative strategy for engineering enhanced magnetoelectric effects is to
introduce indirect coupling between two materials such as a ferromagnet and a
ferroelectric [25]. Each phase may then be independently optimized for room temperature
performance, and the coupling limit of equation (4) is lifted. Strain coupling requires
intimate contact between a piezomagnetic (or magnetostrictive) material and a
piezoelectric (or electrostrictive) material. This can be achieved in the form of composites
[25-26], laminates [15], [27-28] or epitaxial multilayers. The coupling constant depends
on the frequency of the a.c. applied magnetic field [29], and such multiferroic structures
could thus find applications in microwave frequency transducers. Epitaxial thin-film
heterostructures could
permit
precise
magnetoelectric
because crystallographic
orientation, layer thickness and interfacial roughness may be controlled accurately, but
direct measurements of an epitaxial systems have not been forthcoming. However,
ferroelectric layers can generate strains of the order of 1% in magnetic epilayers owing to
structural phase transitions. For example, the tetragonal to monoclinic structural phase
12
transition in a BaTiO3 substrate at 278K produces [30] a 70% change in the
magnetization of an epitaxial film of the ferromagnetic manganite La0.67Sr0.33MnO3.
Alternatively, one may attempt to alter the magnetic structure of a film by applying a
voltage to the underlying piezoelectric material [31-33]. Promising results [34] were
found for a thin film heterostructure of CoPd and Pb(Zr,Ti)O3 (PZT), where the
application of an electric field to the PZT layer rotated the magnetization of the CoPd
film by 90o. The ferromagnetic and ferroelectric phases may be distributed laterally in a
film while preserving an epitaxial relationship with one another and the substrate. This
has been achieved for nanopillars of CoFe2O4 in a BaTiO3 matrix, grown on a SrRuO3
electrode with a SrTiO3 substrate. However, the observed change in magnetization of the
CoFe2O4 pillars at the ferroelectric Curie temperature was just 5%, possibly due to either
clamping from the underlying epitaxial structure which is not piezoelectric, or electric
field effects associated with the ferroelectric. Nevertheless, when the matrix was changed
to BiFeO3, an electrically induced magnetization reversal in the CoFe2O4 nanopillars was
reported [35].
9. Devices
Ferroelectrics may be used to address magnetic materials in devices for two reasons
that in practice are not easy to separate [36-37]. First, their superlative piezoelectric
properties permit them to strain intimately connected layers. Second, the large
polarization can be used in field effect transistor geometry to influence the charge density
13
in a magnetic channel. Various other two-phase magnetoelectric devices that have been
explored include a heterostructure comprising PZT and a magnetic garnet between
crossed polarizers, where it is possible to electrically influence the Faraday rotation in the
garnet and thus control the optical transmission of the device [38]. Exchange bias in
Cr2O3/(Co/Pt)3 may be electrically reversed but requires thermal cycling, whereas
exchange bias in YMnO3/permalloy heterostructures can be electrically tuned directly
[39-40].
Also,
tunable
microwave
devices
with
superconductor/
ferroelectric/ferromagnetic multilayers have been proposed [41]. In other devices,
strain-coupled magnetostrictive and piezoelectric layers can lead to voltage gain, and the
detection of magnetic fields [42-43]. The sensor devices seem particularly promising
compared to existing superconducting quantum interference device (SQUID) technology
because not only would they be cheaper and simpler, but also they can operate at room
temperature.
14
References
[1]
W. Eerenstein, N. D. Mathur & J. F. Scott, Multiferroic and magnetoelectric
materials, Nature, Vol 442, August 2006.
[2]
Schmid, H. Multi-ferroic magnetoelectrics. Ferroelectrics 162, 665-685 (1994).
[3]
Ponomarev, B. K. et al. Magnetoelectric properties of some rare earth molybdates.
Ferroelectrics 161, 43-48 (1994).
[4]
Ponomarev, B. K. et al. Magnetoelectric properties of some rare earth molybdates.
Ferroelectrics 161, 43-48 (1994).
[5]
Schmid, H. Introduction to the proceedings of the 2nd international conference on
magnetoelectric interaction phenomena in crystals, MEIPIC-2. Ferroelectrics 161,
1-28 (1994).
[6]
Fiebig, M. Revival of the magnetoelectric effect. J. Phys. D 38, R123-R152
(2005).
[7]
Rivera, J.-P. On definition, units, measurements, tensor forms of the linear
magnetoelectric effect and on a new dynamic method applied to Cr-Cl boracite.
Ferroelectrics 161, 165-180 (1994).
[8]
Lines, M. E. & Glass, A. M. Principles and Applications of Ferroelectrics and
Related
[9]
Materials (Clarendon Press, Oxford, 1977).
Lottermoser, T. et al. Magnetic phase control by an electric field. Nature 430,
541-544 (2004).
15
[10]
Brown, W. F. Jr, Hornreich, R. M. & Shtrikman, S. Upper bound on the
magnetoelectric susceptibility. Phys. Rev. 168, 574-577 (1968).
[11]
Saifi, M. A. and Cross, L. E. Dielectric properties of strontium titanate at low
temperatures. Phys. Rev. B 2, 677-684 (1970).
[12]
Hou, S. L. & Bloembergen, N. Paramagnetoelectric effects in NiSO4z6H2O. Phys.
Rev. 138, A1218-A1226 (1965).
[13]
Scott, J. F. Mechanisms of dielectric anomalies in BaMnF4. Phys. Rev. B 16,
2329-2331 (1977).
[14]
Grimmer, H, The piezomagnetoelectric effect, Acta Crystallogr. A 48, 266-271
(1992).
[15]
Ryu, J., Vasquez Carazo, A., Uchino, K. and Kim, H.-E, Magnetoelectric
properties in piezoelectric and magnetostrictive laminate composites. Jpn. J. Appl.
Phys. 40, 4948-4951 (2001).
[16]
Dawber, M., Rabe, K. and Scott, J. F. Physics of ferroelectric thin film oxides.
Rev. Mod. Phys. 77, 1083-1130 (2005).
[17]
Ascher, E., Rieder, H., Schmid, H. & Sto¨ssel, H. Some properties of
ferromagnetoelectric nickel-iodine boracite, Ni3B7O13I. J. Appl. Phys. 37,
1404-1405 (1966).
[18]
Catalan, G. Magnetocapacitance without magnetoelectric coupling. Appl. Phys.
Lett. 88, 102902 (2006).
16
[19]
Dzyaloshinskii, I. E., On the magneto-electrical effects in antiferromagnets, Zh.
Eksp. Teor. Fiz. 37, 881-882 [Sov. Phys. JETP 10, 628-629] (1959).
[20]
Astrov, D. N. The magnetoelectric effect in antiferromagnetics. Zh. Eksp. Teor.
Fiz. 38, 984-985 [Sov. Phys. JETP 11, 708-709] (1960).
[21]
Folen, V. J., Rado, G. T. and Stalder, E. W. Anisotropy of the magnetoelectric
effect in Cr2O3. Phys. Rev. Lett. 6, 607-608 (1961).
[22]
Hur, N. et al. Electric polarization reversal and memory in a multiferroic material
induced by magnetic fields. Nature 429, 392-395 (2004).
[23]
Kimura, T. et al. Magnetic control of ferroelectric polarization. Nature 426, 55-58
(2003).
[24]
Kimura, T., Lawes, G. & Ramirez, A. P. Electric polarization rotation in a
hexaferrite with long-wavelength magnetic structures. Phys. Rev. Lett. 94, 137201
(2005).
[25]
van Run, A. M. J. G., Terrell, D. R. and Scholing, J. H. An in situ grown eutectic
magnetoelectric composite material. J. Mater. Sci. 9, 1710-1714 (1974).
[26]
Nan, C.-W. et al. A three-phase magnetoelectric composite of piezoelectric
ceramics, rare-earth iron alloys, and polymer. Appl. Phys. Lett. 81, 3831-3833
(2002).
[27]
Cai, N., Nan, C.-W., Zhai, J. & Lin, Y. Large high-frequency magnetoelectric
response in laminated composites of piezoelectric ceramics, rare-earth iron alloys
and polymer. Appl. Phys. Lett. 84, 3516-3519 (2004).
17
[28]
Srinivasan, G. et al. Magnetoelectric bilayer and multilayer structures of
magnetostrictive and piezoelectric oxides. Phys. Rev. B 65, 134402 (2002).
[29]
Bichurin,
M. I. et
al. Resonance magnetoelectric effects in layered
magnetostrictive piezoelectric composites. Phys. Rev. B 68, 132408 (2003).
[30]
Schroder, K. Stress operated random access, high speed magnetic memory. J.
Appl. Phys. 53, 2759-2761 (1982).
[31]
Novosad, V. et al. Novel magnetostrictive memory device. J. Appl. Phys. 87,
6400-6402 (2000).
[32]
Iwasaki, Y. Stress-driven magnetization reversal in magnetostrictive films with
in-plane magnetocrystalline anisotropy. J. Magn. Magn. Mater. 240, 395-397
(2002).
[33]
Kim, S.-K. et al. Voltage control of a magnetization easy axis in piezoelectric/
ferromagnetic hybrid films. J. Magn. Magn. Mater. 267, 127-132 (2003).
[34]
Zheng, H. et al. Multiferroic BaTiO3-CoFe2O4 nanostructures. Science 303,
661-663 (2004).
[35]
Zavaliche, F. et al. Electric field-induced magnetization switching in epitaxial
columnar nanostructures. Nano Lett. 5, 1793-1796 (2005).
[36]
Mathews, S., Ramesh, R., Venkatesan, T. & Benedetto, J. Ferroelectric field effect
transistor based on epitaxial perovskite heterostructures. Science 276, 238-240
(1997).
18
[37]
Wu, T. et al. Electroresistance and electronic phase separation in mixed-valent
manganites. Phys. Rev. Lett. 86, 5998-6001 (2001).
[38]
Inoue, M. Magnetophotonic crystals. Mater. Res. Soc. Symp. Proc. 834,
J1.1.1-J1.1.19 (2005).
[39]
Borisov, P. et al. Magnetoelectric switching of exchange bias. Phys. Rev. Lett. 94,
117203 (2005).
[40]
Laukmin, V. et al. Electric-field control of exchange bias in multiferroic epitaxial
heterostructures. Preprint at khttp://arxiv.org/cond-mat/0607381l (2006).
[41]
Hontsu,
S.
et
superconducting
al.
Preparation
heterostructures
of
all-oxide
for
advanced
ferromagnetic/ferroelectric/
microwave
applications.
Supercond. Sci. Technol. 12, 836-839 (1999).
[42]
Dong, S. et al. A strong magnetoelectric voltage gain effect in magnetostrictivepiezoelectric composite. Appl. Phys. Lett. 85, 3534-3536 (2004).
[43]
Dong, S., Li, J. F. & Viehland, D. Ultrahigh magnetic field sensitivity in laminates
of Terfenol-D and Pb(Mg1/3Nb2/3)O3-PbTiO3 crystals. Appl. Phys. Lett. 83,
2265-2267 (2003).
19
Chapter 2. Magnetoelectric Effects on Single Phase of Z-type
and M-type Hexaferrites at Room Temperature
1. Introduction
Since modern technologies will require miniaturization and efficient performances
from the use of magnetic materials, inexpensive and simpler device structures must be
developed in order to be compatible with the semiconductor technology. This may be
achieved if all devices have the flexibility to be tuned by an electric field and/or voltage
only- including ferrite devices. There have been a lot of efforts in the past decade to do
away with magnetic fields and/or permanent magnets in the fabrication of microwave
ferrite devices so that they may be tuned by an electric field or voltage.
Multi-ferroic
composite materials have been proposed to generate internal magnetic fields via voltage.
Multi-ferroic composites usually consisted of magnetostrictive and ferroelectric or
piezoelectric slabs in physical contact whereby magnetic field sensors have been implied
and fabricated so far. For example, small shifts in ferromagnetic resonance (FMR) fields
have been observed using magnetoelectric composites in the presence of an electric field.
Tuning of ferrite microwave devices by an electric field or voltage is still not practical
with present composite structures, because they still require fields.
We propose an alternative approach to this problem. The change in remanence
magnetization is measured by applying a DC voltage or electric field across a slab of
hexaferrite. A single layer of magnetoelectric hexaferrite is proposed to induce magnetic
20
parameter changes with application of voltage. The advantage of a single layer is that it is
simpler to utilize to tune ferrite devices.
Hexagonal ferrites of the M, Y and Z-types are of interest, since they exhibit high
permeability at wireless frequencies [1-2]. In particular, Co2Z-type ferrite, Sr3Co2Fe24O41,
is a member of the planar hexaferrite family called ferroxplana, in which the easy axis of
magnetization direction lies in the basal plane (c-plane) of the hexagonal structure at
room temperature. In this crystal, a large field is required to rotate the magnetic moments
from the c plane to the c-axis direction, but a small field is enough for the moment in the
c-plane to rotate in the plane. Hence, these materials are magnetically "soft" for H,
external magnetic field, in the c-plane. As such the magnetic moments can follow an
alternating field even in the gigahertz region, giving rise to high permeability even in the
ultra high frequency (300 MHz–3 GHz) region. Therefore, Y and Z-types materials are
regarded as promising candidates for inductor cores and electromagnetic noise absorbers
to be used in this frequency region.
In this chapter, converse magnetoelectric effects of Sr Z-type, Sr3Fe24Co2O41, and
M-type, SrCo2Ti2Fe8O19, hexaferrite materials at room temperature were measured. The
change in remanence magnetization(Mr) for M-SCTFO sintered in oxygen and sintered in
air are similar and approximately equal to ~3% in 13kV/cm electric field and for Z-type
was ~12% in ~10kV/cm E-field. The measured magnetoelectric coupling coefficient, α,
values at room temperature for Z-type and M-type hexaferrites sintered in O2 were
measured to be 7.6×10-10 sm-1 and 2.4×10-10 sm-1, respectively.
21
Sintering the M-type in
air reduced α to 1.7×10-10 sm-1. As it is well known lack of oxygen in local oxygen sites
imply lower resistivity and a modified magnetic structures or state. However, in
magnetoelectric hexaferrites there is an additional effect due to lack of oxygen and that is
the spin spiral configuration is significantly modified to lower the induced magnetization
upon the application of a DC voltage or electric field. In magnetoelectric effects
measurements high resistivity is critical in order to reduce current flow in the hexaferrite.
The resistivity of the hexaferrite was raised to 4.28×109 Ωcm by annealing under oxygen
pressure. The measurements indicate that indeed electric polarization and magnetization
changes were induced by the application of static magnetic and electric fields,
respectively. The implications for microwave applications appear to be very promising at
room temperature.
2. Sr Z-type Experimental Material Growth Procedure
Substitution of Sr2+ for Ba2+ was reported in order to reduce the sintering temperature
from 1250 (0C) to 1210 (0C) and oxygen partial pressure in synthesizing Co2Z-type ferrite
[3]. This substitution also increased the zero field FMR frequency and, therefore,
extended the frequency range of the permeability. These results also indicate that Sr2+
substitution would be favorable for lowering cost in manufacturing and putting this type
of ferrite material into practical uses. The magnetic cation distribution in Sr-Z is
significantly different that of Ba-Z and Ba Sr-Z hexaferrites. Magnetic moments in Ba1.5
Sr1.5 Co2Fe24O41 and Ba3Co2Fe24O41 lie in the c-plane while that in Sr3Co2Fe24O41 are at
22
oblique angle to the plane, shown in Figure 2-1, and with respect to c-axis is 52.3o [4].
Figure 2-1 Orientation of magnetic moment of Sr-Z, Ba-Z and BaSr-Z hexaferrites.
Sr3Co2Fe24O41 samples were prepared by the solid-state reaction method by our group
[5]. The calculated amount of the oxide mixtures were: SrO (99.5%), Co3O4 (99.7%), and
Fe2O3 (99.8%). 25 g of the starting reagents mixture were blended with a liquid
dispersing agent (reagent alcohol). To grind uniformly, the ball milling machine, shown
in Figure 2-2, was used with a set of agate balls with 300 rpm rotation speed for 4 hours.
The slurry was dried at room temperature and five 5(gr) pellets were made. The pellets or
discs were placed in the tube furnace in an oxygen atmosphere over the sample with 5
deg/min temperature rate and set in 1210 (0C) for 16 hours. To prevent formation of other
impurity phases, including W-, M- or/and Y-phases, it was found most favorable to
quench the sample immediately to room temperature. The X-ray diffraction pattern is
shown in Figure 2-3. The ferromagnetic resonance (FMR) measurement instrumentation
and result are shown in Figures 2-4 and 2-5, respectively. The line-width (∆H) is quite
23
high and about 2400 Oe. This is due to the polycrystalline structure of sample. In order to
obtain low line-width one needs to either improve materials homogeneity or reduce the
thickness of the slab or produce single crystals. This will be shown in following chapter
when the single crystalline of the Sr-Z type is presented.
Figure 2-2 Planetary mono mill Pulverisette 6 to grind particles.
24
Figure 2-3 X-ray diffraction pattern of the polycrystalline Sr3Co2Fe24O41 at room temperature. The black
line represents the reference peak positions for the Ba Z-type hexaferrite (Ref. ICDD # 19-0097. Space
group: P63/mmc(194)).
Figure 2-4 Ferromagnetic resonance measuring instrumentation.
25
Figure 2-5 FMR spectrum of polycrystalline Sr3Co2Fe24O41 at room temperature for magnetic field (H)
applied parallel to slab plane.
In order to increase resistivity, samples were annealed at 600 0C in an oxygen
atmosphere for 6 hours [6]. The high resistivity of the sample was required for the
magnetoelectric measurements to minimize current flow through the sample in the
presence of high electric fields. I-E and ρ-E curves of a typical sample are shown in
Figure 2-6. Increasing the oxygen pressure during anneals reduced current flow or
increased resistivity and dependence of current with voltage is almost linear. The
resistivity estimated from the experimental linear I-V characteristic is ρ = 1.43×109 Ωcm
for samples of 1mm in thickness. The preparation in oxygen leads to Fe2+ concentration
reduction which then lowers the hopping of electrons between Fe2+ and Fe3+ ions [6-7].
26
Figure 2-6 I-E and ρ-E curves of the polycrystalline Sr3Co2Fe24O41 at room temperature after sintering
in O2.
2.1 Sr Z-type Indirect Converse Magnetoelectric Experimental Analysis
In general, the linear magnetoelectric (ME) effect implies the following: the
application of a magnetic field, H, induces a change in electric polarization, P, and the
application of an electric field, E, induces a change in magnetization, M. In this work the
latter is called the "indirect converse ME effect". To measure changes in remanence
magnetization versus electric field a Vibrating Sample Magnetometer (VSM) instrument
was used, shown in Figure 2-7. In Figures 2-8 and 2-9, the magnetization, M, is plotted as
a function of H, magnetic field, for a given applied electric field or voltage. We note that
the remanence magnetization (for H=0) was indeed affected by voltage. The change in
remanence magnetization was as much as 16% with the application of an electric field of
5 kV/cm. In Figure 2-10, the percentage change in remanence versus the applied electric
field is shown. Changes in remanence magnetization scale with polarity changes of the
electric field or applied voltage. Thus, heating effects, shown in Figure 2-12, may be
27
eliminated as a source of the remanence magnetization changes, since heating effects
induce changes in remanence in one polarity sense only.
The implication to microwave properties of this material is straightforward. The
permeability expression for the Z or Y-type hexaferrite may be readily found in [8].
Typically, the zero field FMR for these materials ranges near 3 GHz. However, below the
FMR frequency the permeability is approximately for this material to be
µr ≈1+(4πMr / Hφ)
(1)
where Mr is the remanence magnetization and Hφ is the c-plane magnetic anisotropy field.
Typically, Hφ is in the order of 40 (Oe) implying µr ≈3.5, since 4πMr ≈105 G. Clearly, any
changes in remanence magnetization are reflected in the microwave permeability at
wireless communication frequencies. Certainly, application of DC voltages will not affect
the Hφ.
Figure 2-7 Vibrating sample magnetometer (VSM) instrumentation. The sample is placed between the
pickup coils and voltage is applied to the sample through the conductor plates.
28
In the ME experiment where changes in the dielectric constant were measured as a
function of frequency for a given application of magnetic field, H, the measurements are
shown in Figure 2-12. Remarkably, the applied field is small in affecting changes in
dielectric constants in comparison to other reports [7]. For example, at 1 GHz and with an
applied magnetic field equal to 32 mT, the change in relative dielectric constant was
almost 3.5, a change of 16%. The measurements were performed using an
impedance/material analyzer (Agilent). According to Ref. [7], the mechanism for the ME
effect is due to a local distortion of the Co ions giving rise to a spiral spin configuration
which is a pre-required condition for this effect in hexaferrite materials to exist.
Figure 2-8 Polycrystalline Sr3Co2Fe24O41 magnetization as a function of external applied H parallel to
slab plane and perpendicular to applied E field at room temperature.
29
Figure 2-9 The zoomed in change in remanence magnetization measurements shown in Figure 2-8 over
low magnetic field.
Figure 2-10 Polycrystalline Sr3Co2Fe24O41 remanent magnetization change vs electric feild for a typical
sample with 0.5mm thickness at room temperature.
30
Figure 2-11 Change in temperature in the Sr Z-type sample versus electric field.
Figure 2-12 Change in dielectric constant over frequency versus applied external magnetic field.
2.2 Orientation of Polycrystalline Sr Z-type
In order to obtain low FMR linewidth and, therefore, higher permeability as given in
equation (1) it is required to improve materials homogeneity to increase remanence
magnetization. The grown Sr-Z material was polycrystalline and this implies that the easy
plane surfaces are randomly distributed in the crystal. The random distributions of the
c-axis needs to be aligned parallel to each other so that a much softer Z-type hexaferrite
31
can be produced. In order to align all c-axis of each particle in a powder an orientation
technique is used to orient Z-type hexaferrite particles with c-axis normal to the disc
plane. The orientation set up is shown in Figure 2-13 [15].
Figure 2-13 Polycrystalline Sr3Co2Fe24O41 powder orientation set up.
Generally in polycrystalline hexaferrites each particle has its own easy direction, free
poles are expected to appear on the grain boundaries, unless the domains are well aligned
as in single crystals. That means the grain size is the critical issue of the domain structure
in magnetic materials. The critical domain size is the largest domain size that prevents the
existence of domain wall. The only mechanism for demagnetization is rotation of the
magnetization direction, which may be critical for high anisotropy material such as
hexaferrites materials. For Sr-Z the domain size is usually 0.5-2µm. The orientation
32
procedure is as following:
Step 1- The grown polycrystalline Sr-Z disk is ground to powder. The particles are sieved
to uniform the size of 75µm or smaller.
Step 2- Using the ball milling machine with specified agate balls indicate size of the balls,
rotation speed and duration of rotation provide particle size as small as 0.5-2µm.
These parameters are experimental. To find out the duration of rotation providing
uniform particles Scanning Electron Microscope (SEM) is used. This is shown in
Figure 2-14 for different milling durations. It was found most favorable to rotate
3gr for 22 hours.
(a) 2 hours
(b) 4 hours
33
(c) 6 hours
(d) 8 hours
(e) 10 hours
(f) 12 hours
(f) 14 hours
(g) 16 hours
34
(h) 20 hours
(i) 22 hours
Figure 2-14 SEM photographs of the ground particles for different milling durations.
Step 3- The slurry is casted together with pure distilled water inside a stainless cylinder
die in the mechanical press apparatus. This is shown in Figure 2-13.
Step 4- A 0.5T permanent magnet, shown in Figure 2-15, is placed on a rotating platform
such that the direction of the applied field was in a radial direction perpendicular
to the force direction that is normal to the disk plane. The applied pressure on the
die was 500 psi and they were pressed into a disk shape to dehydrate the disc.
The schematic of the procedure has been plotted in Figure 2-16.
Figure 2-15 Photograph of 0.5T rotating permanent magnet.
35
(a) Step 1 and Step 2.
(b) Step 3 and Step 4.
(c) Pressed oriented disk.
Figure 2-16 Schematic of orientation procedure.
36
The oriented Sr-Z disks showed magnetically soft behavior for fields in the plane, as
illustrated by VSM measurements in Figure 2-17 where the horizontal axis is the external
magnetic field (kOe), and vertical axis is normalized magnetization.
Figure 2-17 VSM data of Sr-Z. Red and black dashed lines represent after orientation before orientation,
respectively.
We also note that for the external magnetic, H, applied normal (┴) to the slab plane it
is required higher values to saturate the sample after orienting the particles. This means
that the disc plane is “made” much easier magnetically after orientation. This is further
confirmed for H in the disc plane (║). For H~0, there is sufficient curvature of M versus
H curve to conclude either there is another phase of material, some local stress, or local
particles that are not completely aligned. Complete alignment implies a linear
relationship for H~0.
37
3. M-type Experimental Material Growth Procedure
We have adopted a procedure similar to that in [9] to prepare a single phase
polycrystalline M-type hexaferrite SrCo2Ti2Fe8O19 (SCTFO) and it was prepared through
conventional solid state reaction technique. The high-purity powders of SrCO3, Fe2O3,
Co3O4, and TiO2 were mixed stoichiometrically and sintered at 1200 (oC) for 10 hours
twice in air and oxygen atmosphere. The powder X-ray diffraction measurement of
SCTFO at room temperature was carried out to identify the sample as single phase and it
is shown in Figure 2-18.
Figure 2-18 X-ray diffraction pattern of polycrystalline SrCo2Ti2Fe8O19 at room temperature. The black
line represents the reference peak positions for the Ba M-type hexaferrite (PDF # 27-1433. Space group:
P63/mmc(194)).
38
4. Z- and M-type Hexaferrites ME Effect Comparison
4.1 Resistivity Measurements
Resistivity is very important in magnetoelectric materials to prevent current flow in the
sample. I-E curves of the prepared M- and Z- type hexaferrite materials are shown in
Figure 2-19. The Resistivity of the Z-type and M-type hexaferrites sintered in oxygen are
1.43×109 Ωcm and 4.36×1010 Ω-cm, respectively [9-12]. This value for M-type sintered
in air is 1.12×107 Ωcm. The resistivity of the Z-type sintered in air is 6×103 Ωcm which is
low for ME measurements, since current flow in the sample is inversely proportional to
resistivity [13].
Figure 2-19 Current versus electric field for Sr-Z and SCTFO.
39
4.2 ME Effect Measurements
The change in magnetization with the application of a DC voltage is proportional to α.
Hence, α is the most important parameter that dictates the application of the hexaferrite in
terms of sensor and/or ferrite device applications, when using magnetoelectric
hexaferrites. One emphasis in this section is our measurements of α as related to previous
section. The magnetoelectric effects on two types of hexaferrites: M- and Z-types are
presented. We measured the change in magnetization with the application of DC voltages.
The changes in permeability, µ, are due to changes in remanence magnetization.
The magnetization, M, is plotted versus H, magnetic field, for a given direction of
applied electric field or voltage for M-type hexaferrite in Figure 2-20. The remanence
magnetization is affected by DC voltage, and we measured changes as much as 3% at
16kV/cm where the electric field was applied parallel to H and perpendicular to the slab
plane. For the Z-type we measured 12% change in Mr, shown in Figure 2-9, with the
application of an electric field of 10kV/cm.
40
Figure 2-20 Change in remanence magnetization (Mr) of M-type (sintered in air) for (a) Edc perpendicular
to H and (b) Edc parallel to H.
The magnetoelectric coupling coefficient, α, for all the samples were deduced using
the formula, ∆L* ⁄∆ , and has been summarized in Table I. In CGS α may be
determined from ∆L* ⁄∆ , where ∆L* is in emu/cm3 and ∆ in esu units. The value
of α for Z-type is higher than the M-type as seen in Figure 2-21 and Table I. α=1.7×10-10
for the M-type sintered in air at room temperature is ~40 times bigger than the α value
measured in Cr2O3 (αX4.1×10-12sm-1) [14]. The implication to microwave applications of
these materials is straightforward. The permeability expression for the Z or Y-type
41
hexaferrite may be readily determined analytically [8].
Table I: Converse magnetoelectric coupling coefficient and resistivity for Z-type and M-type hexaferrites
at room temperature.
Material
ρ[Ω cm]
α [sm-1]
Z-type (Sr3Co2Fe24O41)
1.43×109 (Ref.11)
7.6×10-10
M-type (SrCo2Ti2Fe8O19, sintered in O2)
4.36×1010 (Ref.9)
2.4×10-10
M-type (SrCo2Ti2Fe8O19, sintered in air)
1.12×107 (This chapter)
1.7×10-10
Figure 2-21 The change in remanence magnetization (Mr) of Z-type sintered in O2, M-type sintered in air
and O2 versus DC electric field.
Zero field FMR for Z-type hexaferrite is about 3GHz, but for M-type may range to
frequencies above 20GHz.
Z [ \ ]1.4 ^ 10_ \` ` a 4AL' 42
(2)
a (Uniaxial magnetic anisotropy field), ` (six-fold magnetic anisotropy field or
azimuth magnetic anisotropy), and ] factor were measured and their corresponding
values for Sr-Z were 105 G, 25 kOe, 40 Oe, and ~2.
The difference in zero fields FMR of these two similar materials is due to the fact that
Z-type hexaferrites are planar and M-type is intrinsically uniaxial symmetry materials.
Hence, the types of microwave applications are much different for the two materials. For
the Z-type hexaferrite the permeability as given in equation (1) is approximately 3.8.
Application of DC voltages will not affect ` . Any changes in remanence
magnetization are reflected in the microwave permeability at wireless communication
frequencies. M-type hexaferrites have been used most often in self biased circulators
whereby the Mr is typically above 90% of the saturation magnetization after orienting the
particles. The bandwidth and center frequency of circulator is approximately proportional
to Mr. Here we have a unique situation whereby * is readily changed by varying Mr
with the application of a DC voltage to affect the operation of a circulator. We have
illustrated two potential applications where the special property of magnetoelectricity is
important to the applications. There are many applications that can be conceived that
depend upon the ability to change the magnetization value in a ferrite device.
5. Conclusions
In this chapter changes of remanence magnetization and magnetoelectric coupling
coefficient
in
polycrystalline
slabs
of
43
Z-type,
Sr3Co2Fe24O41,
and
M-type,
SrCo2Ti2Fe8O19 ,sintered in air and oxygen, with the application of voltage or electric
field at room temperature were measured. Sintering in oxygen increased not only
resistivity but also the magnetoelectric coupling. We believe that sintering in air reduced
the magnetoelectric effect as predicted by the "slinky helix" model which will be
demonstrated in chapter 4. We have identified two potential applications whereby the
application of a DC voltage can affect the operation of a microwave ferrite device. We
anticipate that sensor applications that depend on magnetization changes have a high
potential for success.
44
References
[1]
T. Tachibana, T. Nakagawa, Y. Takada, T. Shimada, T. Yamamoto, J. Magn. Magn.
Mater. 284, 369 (2004).
[2]
M. Pardavi-Horvath, J. Magn. Magn. Mater. 171.215 (2000)
[3]
O. Kimura, M. Matsumoto, and M. Sakakura, J. Jpn. Soc. Powder, Powder Metall.
42, 27 (1995).
[4]
Y. Takada, T. Tachibana, T. Nakagawa, T. A. Yamamoto, T. Shimada, and S.
Kawano, J. Jpn. Soc. Powder , Powder Metall. 50, 618 (2003).
[5]
Y. Takada, T. Nakagawa, M. Tokunaga, Y. Fukuta, T. Tanaka, and T. A. Yamamoto,
J. Appl. Phys., 100, 043904 (2006).
[6]
O. Kimura, M. Matsumoto and M. Sakakura,. J. Am. Ceram. Soc. 78, 2857
(1995).
[7]
Y.Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,
Nature Mater. 2826, 797 (2010).
[8]
C. Vittoria, "Magnetics, dielectrics, and wave propagation with MATLAB codes",
(CRC press, New York 2011).
[9]
Wang, D. Wang, Q. Cao, Y. Zheng, H. Xuan, J. Gao, and Y. Du, Sci. Rep., 2, 223
(2012).
[10]
K. Ebnabbasi,Y. Chen, A. Geiler, V. Harris, and C.Vittoria, J. Appl. Phys. 111,
07C719 (2012).
[11]
K. Ebnabbasi, C. Vittoria, and A. Widom, Phys. Rev. B 86, 024430 (2012).
45
[12]
K. Ebnabbasi, Marjan Mohebbi, and C. Vittoria, Appl. Phys. Lett.
101, 062406
(2012).
[13]
Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,
Nature Mater. 9, 797 (2010).
[14]
Schmid, H, in Introduction to Complex Mediums for Optics and Electromagnetics
167-195 (SPIE Press, 2003).
[15]
Mahmut Obol and Carmine Vittoria, "Microwave permeability of Y-type
hexaferrites in zero and low fields", Journal of Magnetism and Magnetic
Materials 2004.
46
Chpater 3. Coaxial Line Technique to Measure Constitutive
Parameters in Magneto-Electric Ferrite Materials
1. Introduction
In this chapter an experimental measurement technique is presented to measure the
constitutive parameters of magneto-electric ferrite materials in the presence of high DC
voltages. The traditional coaxial line design was modified in a manner that it allowed for
the introduction of high DC voltage (~2000V) in the coaxial line and also it minimized
electromagnetic radiation loss via connections to the magnetoelectric sample in the
coaxial line. The modified coaxial line was tested from 50MHz to 10GHz.
Ferrite materials are widely used in passive and tunable electromagnetic signal
processing devices, such as phase shifters, circulators, isolators, filters, antenna substrates,
and EMI suppression cores. Due to their excellent dielectric properties, ferrites possess
the advantages of low loss and high power handling capability relative to semiconductors.
Usually, parameters of magnetic materials are controlled by an external magnetic field
and/or permanent magnets thus allowing for tuning of device performances. Permanent
magnets or current driven coils imply relatively large component size, weight, and cost,
as well as slow response time in comparison to semiconductor-based technologies. In
recent years, self biased hexagonal M-type ferrites have been utilized in circulators to
reduce or eliminate magnetic bias field requirements and permanent magnets. However,
their applicability is limited in terms of frequency range and minimum achievable
47
insertion loss. Ferrite magneto-electric (ME) materials can be a practical solution in
controlling the magnetic parameters of ferrites by tuning the electric field and/or voltage
instead of external magnetic fields and would eliminate permanent magnets and tuning
coils to overcome most of the disadvantages in the use of ferrites for microwave devices.
Circuits where ferrites and semiconductors can be used on the same integrated circuit or
chip may become a reality. Furthermore, key advantages of ferrites, including low
insertion loss and high power handling capability could be exploited without the penalty
of added size, weight, and cost, as well as increased response time.
Recently, there has been considerable interest in the nature of ME materials and, in
particular, hexaferrites which have strong magneto-electric effects at room temperature.
Most often ME materials are operational at low temperatures. In previous chapter we
prepared hexaferrite of the Z-type which are intrinsically magneto-electric at room
temperature exhibiting very high magneto-electric coupling coefficient [1]. The material
preparation is similar to the method used in [2]. Previous papers on ME hexaferrite
materials reported on the DC properties of these materials upon the application of DC
magnetic field for example, the low frequency (~1 kHz) permittivity as a function of DC
magnetic field. Since these materials are ME we conceived that the converse must hold.
That is, the application of DC voltage (electric field) must necessarily affect the
permeability. Indeed, we applied a DC voltage and measure the permeability, µ, as a
function of frequency (50MHz-10GHz) utilizing a coaxial line. This measurement
implied the introduction of a DC voltage in the coaxial line apparatus. Coaxial line
48
techniques to measure µ (permeability) and ε(permittivity) have been around for many
years. These measurements were never performed in high DC voltage, since there was
never a need for that.
High DC voltage could easily damage delicate microwave testing instrumentation.
Conventional measuring technique does not permit the use of high DC voltage in testing
or characterization of microwave parameters, since there is no provision to isolate high
voltage from the instrumentation. ME materials respond to the application of an electric
field or DC voltage and, as such, the tested ME sample was necessarily in electrical
contact with an external DC voltage. It was required to make electric contact to the
sample and simultaneously prevent radiation loss in the connections. We were able to
eliminate wire contacts with the sample and, therefore, eliminate radiation loss through
the wires. Also, radiation loss was minimized by shorting out a small gap on the coaxial
line using a novel use of capacitors in the gap. As a result of these we could measure
permeability and permittivity of ME hexaferrite toroidal sample as a function of
frequency, DC voltages, and magnetic fields.
2. Theory of the Design
2.1
Two Port Design
In conventional coaxial line measurement technique mostly the two port or
transmission through lines are used to measure the constitutive parameters. In this case as
shown in Figure3-1 these parameters can be calculated as follows [3]:
49
1 1 4
1
the + or - sign selection is based on the rule that the reflection coefficient should not
exceed 1.
Figure 3-1 Non-reciprocal ferrite network equivalent of transmission line.
1 2 !" 1 1 $
%
ln
$
%
ln # 1 ln 1 1 1
1 & & & $
% ln $
%
2 !" # 1 where b and a are the outer and inner diameters of the coaxial line, respectively.
50
2
3
Figure 3-2 Two port coaxial line schematic for ferrite magneto-electric (ME) effect measurement.
The advantage of this method is that the S-parameters can be collected by the network
analyzer at one time in comparison with the one port measurement which is done in two
steps. And the phase adjustment can be performed by providing the sample thickness and
its distance from port1. However, with the introduction of high DC voltage it might be
very complicated to apply external DC voltage to do the same measurement. If a very
thin wire is put in the coaxial line, see Figure 3-2, such that the thickness is very small in
comparison with the skin depth it results in antenna radiation and, therefore, uncertainty
in the accuracy of the measurement. The circuit model of the wire in contact with the ME
material is given in Figure 3-3. The wires influence the measurement precision, although
it is possible to cancel out its effect through calibration techniques. However, the
dangling of the wires and their position is not fixed and we cannot consider it as a fixed
51
object to remove its effect precisely from calibration runs. In order to properly
characterize ME ferrite materials the material should just experience the DC voltage
without external radiation effects due to contacts to the sample.
Figure 3-3 Circuit model of the medium in connection with the dangling wires.
2.2 One Port Design
In the case of one port transmission line which is used in this work the analysis makes
use of the matrix representation given in Figure 3-1 [3]. The port1 S-parameter is:
!"( !" !"( !"
!"( !" !"( !"
where the (a) matrix in the case of a material with the thickness of t is [3]:
where
)
)
$ % $ %,
*
*
, cos 1#
!2341#
6.
- sin 1#
cos 1#
!
52
4
The permeability, µ, can be calculated from the reflection coefficient, S11, as [3]:
!#41# !" 8
where Z=< ⁄& and 1 √&.
9
1 9 :
1 5
Figure 3-4 One port coaxial line schematic for ferrite magneto-electric (ME) effect measurement.
9
Here is the reflection coefficient for the shorted port of the coaxial transmission
line, Z is the coaxial line characteristic impedance of the sample, k is the propagation
constant and is equal to 2⁄?, and Z0 is characteristic impedance of the coaxial line
which is 50. The permeability may then be determined from:
9
1
1 @ !" $
%8
9 :
# 1 53
6
where is 2πf and f the frequency. We should notice this is an approximate formula and
it is valid as long as kt << 1. The advantage of this approach is that the permittivity, ε,
does not enter in the analysis in this limit of approximation. This is extremely important
point in that dielectric changes can not influence the changes in µ as measured by this
technique, see (6). In the same way ε can be calculated independent from µ:
&@
B
1 1 1
$
%8
B :
!" # 1 7
B
where is the reflection coefficient for the open port of the coaxial transmission line.
It should be noticed that there is no longer wire connections in this design, see Figure 3-4,
and capacitors are used to short out radiation losses in the gap.
In general µ and ε may be deduced from:
where
&
1
<D D DE
8
1
<DE /D D
D !" 8
9
B
1 B :
1 9
!" 1 D 8
9 :
1 54
, and
DE K
1
1 <D ⁄D ln L .
2#
1 <D ⁄D
Let’s now address the accuracy of the measurement for µ and ε, in (8) and (9). We require
the thickness of the toroidal sample to be much less than the wavelength of the coaxial
line. The thickness of the toroid was 0.1cm and the wavelength exceeded 10cm.
Nevertheless, we compared µ obtained from (8) and (9) to conventional techniques using
(2) and (3). The error was less than 2%. Other concerns are explained below.
1) Skin depth: As shown in Figures 3-2 and 3-4, in order to connect the DC voltage to
the toroidal sample it is required to cover at least one side of the ME ferrite material with
a conductor so that the electric field is perpendicular to the toroidal plane. Clearly, the
conductive plating might reflect the electromagnetic wave and affect the precision of
Eqs.8 and 9. If the thickness of the conductor metallic surface is well below the skin
depth, most of the electromagnetic energy is coupled to the toroid. We used a conductor
with as low conductivity as possible and still make electrical contact at DC voltage. We
used liquid silver paint for this purpose. The paint was convenient to apply on the toroid,
be removed from the surface by acetone, and control the thickness. Furthermore, the
resistivity was increased by diluting the silver paint in acetone with 1:3 ratio.
2) Isolator and shorting capacitor: It is desirable to measure the constitutive
parameters of the ME material while maintaining isolation of the DC voltage from
55
coaxial line and instrumentation. For this purpose, as shown in Figure 3-4, the DC
voltage is applied outside of the coaxial line. Thin Teflon slabs separate the DC voltage
between the two terminations of the DC power supply. The gap (10 mils) introduced by
the Teflon sheets was filled with 0.22µF capacitors. The purpose of the capacitors was to
short out at high frequencies the coaxial line across the gap. In this design wire
connections were eliminated and isolation between the DC voltage and microwave
equipment was achieved. We compared our results using (8) and (9) (when no DC
voltage was applied) with conventional coaxial line technique using (2) and (3) and the
accuracy in measurement is 2%.
3. Experimental Measurements
A toroidal shaped sample in a coaxial line was inserted (the material was a hexaferrite
Z-type, Sr3Co2Fe24O41 [1]). One side of the toroid was shorted to the coaxial line
termination as well as to the DC ground voltage. The other side of the toroid was coated
with a thin film of silver paint and then connected to a high DC voltage power supply,
shown in Figure 3-4.
There are three precautions that need to be exercised: (1) the high DC voltage needed
to be isolated from the microwave signal of the Network Analyzer (NA) instrumentation,
(2) reduce antenna effects from dangling wires connected to the toroidal sample. The
VNA was used to measure the electrical scattering S-parameter. Antenna effects were
prevented by connecting high frequency capacitors to electrically short out any
56
microwave signals and connect the DC isolated plate to the grounded body of the coaxial
line, and (3) the thickness of the silver paint film was sufficiently small compared to the
skin depth(10µm- 200µm) so that the reflected signal from the toroid was notdominated
by pure metallic reflections from the silver paint. For example, initially we inserted the
toroidal sample without any wire attachments, silver paint and capacitors attached to any
wire. We then loaded the toroidal sample with all the attachments (silver paint, capacitors,
etc.), but no DC voltage applied and measured µ again. We were again able to obtain the
same µ curve within 3% accuracy. At this point we applied the DC voltage to the toroidal
sample and measured changes in µ due to the DC voltage.
The fabricated coaxial line assembly is shown in Figure 3-5. High resistivity is critical
in order to minimize current flow through the hexaferrite sample in the presence of high
electric fields. The I-V curve of the hexaferrite material is shown in Figure 3-6 The
resistivity estimated from the experimental linear I-V characteristic measurement, shown
in Figure 3-6, was ρ = 1.4×109 Ω.cm for a toroid with 1mm thickness. The real and
imaginary parts of µ versus frequency for E=0 kV/cm are shown in Figure 3-7. For E≠0
(application of DC voltage) the theoretical calculation and experimental measurements
for the change in permeability is shown in Figure 3- 8. The calculated formula for the
changes in µ (∆N ) is:
57
∆N
@ PQ
0
RS R
RS R U
T
∆VN
X!"
W
VN 1 Y 10
with respect to the direction of E to M, direction of magnetization.
Figure 3-5 Coaxial line parts and assembled device.
The plot in Figure 3-8 is for E=500 kV/cm and similar curve may be obtained for any
electric field. The material is anisotropic and it is expected that ∆N to reflect the relative
directional dependence on E. Since we cannot change the mechanical structure of the
designed device, shown in Figure 3-5, the ferrite sample was magnetically poled before
applying the DC voltage or E. We chose Mr to be parallel, anti-parallel, and
perpendicular to the applied electric field direction, E . For E-field parallel and
perpendicular to the magnetization ∆N plots are given in Figures 9 and 10, respectively.
The FMR frequency is about 3GHz and also ∆N
is about zero for frequencies above
3GHz. However, this technique is applicable for frequencies up to 10GHz and DC
58
voltage up to 2000V.
Figure 3-6 Measured I-V characteristic of polycrystalline Sr Z-type hexaferrite.
Figure 3-7 Measured real and imaginary parts of the ME ferrite permeability versus frequency for
E=0KV/cm.
59
Figure 3-8 The theoretical calculation and experimental measurement of magnetic permeability change
versus frequency for E=5KV/cm.
Figure 3-9 The magnetic permeability change versus electric field and frequency when Mr is parallel and
anti-parallel to E.
60
Figure 3-10 The magnetic permeability change versus electric field and frequency when Mr is
perpendicular to E.
Figure 3-11 Phase change versus electric field and frequency when Mr is parallel to E.
61
Figure 3-12 Phase change versus electric field and frequency when Mr is anti-parallel to E.
4. Conclusions
A coaxial line measurement technique was presented to measure the constitutive
parameters of the magneto-electric ferrite materials in the presence of high DC voltage
(Z 2000V) and for frequencies up to 10GHz. The measurement technique yields
measurements of µr versus frequencies which are in general agreement with theory. This
technique can be equally applied in measuring the dielectric constant as a function of
frequency in the presence of DC voltage or magnetic field.
62
References
[1]
K. Ebnabbasi, Y. Chen, A. Geiler , V. Harris, and C. Vittoria, Magnetoelectric
effects on Sr Z-type hexaferrite at room temperature, Applied Physics 111,
07C719 (2012).
[2]
Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura and T. Kimura,
Low-field magnetoelectric effect at room temperature, Nature Mater. 9, 797
(2010).
[3]
C. Vittoria, Elements of Microwave Networks, World Scientific (1998).
[4]
C. Vittoria, "Magnetics, dielectrics, and wave propagation with MATLAB codes",
CRC press, New York (2011).
[5]
M. Soda, T. Ishikara, H. Nakamura, Y. Wakabayashi, and T. Kimura, Magnetic
Ordering in Relation to the Room-Temperature Magnetoelectric Effect of
Sr3Co2Fe24O41, Physical Review Letter, 106, 087201 (2011).
63
Chapter 4. Converse Magnetoelectric Experiments on a
Room-Temperature Spirally Ordered Hexaferrite
1. Introduction
In this chapter magnetoelectric properties of room-temperature spirally ordered
Sr3Co2Fe24O41 hexaferrite slabs have been measured. A physical model in this paper
referred to as the “slinky helix” model is presented to explain the experimental data. The
measured properties include the magnetic permeability and the strain, all as a function of
the electric field E. Upon application of an electric field to slabs of Sr Z-type hexaferrite,
it exhibits broken symmetries for time reversal and parity. This is the central feature of
these magnetoelectric materials.
There has been considerable recent interest in the nature of magnetoelectric (ME)
materials [1]. Of interest in this work is spirally ordered hexaferrites [2–5] which have
strong ME effects at room temperature. Neutron scattering experiments [5,6] revealed a
spiral spin configuration responsible for the ME effect at room temperature in
Sr3Co2Fe24O41 hexaferrite. Sr3Co2Fe24O41 is identified as a Z-type hexaferrite consisting
of S, R, and T “spinel” blocks [4,5]. It was further revealed that in the T block the
Fe-O-Fe bond angles were slightly deformed to affect the superexchange interaction
between the Fe ions and induce the spiral spin configuration [7] in Sr3Co2Fe24O41 as
shown in Figure 4-1. Changes in the spin spiral configuration in the presence of an
electric field E induce changes in the magnetization M. In a polycrystalline sample such
64
as ours it induces changes in the remanent magnetization. This physical mechanism for
the ME effect is very different from the mechanisms applicable to multiferroic materials
in the past. This new mechanism opens up new properties or opportunities in the physics
and applications of ME materials.
Figure 4-1 (a) Crystal structure of a part of the hexagonal unit cell. (b) Spiral spin order.
The previously most used technique to explore ME effects was ferromagnetic
resonance (FMR). In the past FMR frequency shifts were measured with an applied E.
There has never been a report on permeability measurement in ME material with
65
application of an electric field, although there are many reports on FMR shifts. The
measurement of FMR frequency shifts is ineffectual in our case, because (a) the shifts are
extremely small and (b) they are strongly damped in the new mechanism. Hence, we have
devised a new measurement method whereby the permeability of our material is
measured directly via a modified coaxial line technique. We refer to these measurements
as “converse” ME measurements.
Although previous authors [1–5] have established a strong correlation between the
spiral configuration and the ME effect, we provide a physical picture, i.e., model for the
effect. Our measurements reveal that Sr3Co2Fe24O41 is electrostrictive. As such, the
application of E strains the material, thereby changing the physical structure of the spiral
spin configuration. It is this physical motion of the spiral response to E that induces a
change in magnetization M. We refer to this model as the “slinky helix” model. Our
model should be contrasted with the model for the ME effect in multiferroics as well as
ferromagnetic metal films wherein the band energies of the up and down spin are
modified by the electric fields at the interface between phase separated ferromagnetic and
ferroelectric films. The change in band splitting leads to a change in surface
magnetization [8].
The thermodynamic enthalpy per unit volume ω(s, E, H, σ) determines all of the
spirally ordered hexaferrite thermodynamic equations of state [9] via the thermodynamic
minimum principle:
66
, , , min
, , , . . ,
. . : (1)
Here, T, P, M, and e represent, respectively, the temperature, polarization,
magnetization, and strain, while s, E, H, and σ represent, respectively, the entropy per
unit volume, electric field, magnetic intensity, and stress. Other thermodynamic quantities
of interest include the adiabatic dielectric constant tensor
1
4" #
the adiabatic permeability tensor
*1
4" #
and the adiabatic ME tensor
,#
$
%
1
$ &,,'
$
%
1
$ &,,'
4"( ,
2
4"( ,
3
$
$
%
# %
.
$ &,,'
$ &,,'
4
Conventional experiments probing ME effects measure elements of the ME tensor αij
= (∂Mi/∂Ej )s,H,σ. In the converse experiments reported in this work, the ME effect is
probed by measuring elements of the magnetic permeability tensor µ and the strain tensor
e, while noting the manner in which these tensors depend on E and H. Direct
measurements of the magnetization M were also employed.
67
2. Experimental Results
2.1 Experimental Material Growth
In chapter 2, the material growth procedure was presented. We have adopted a
procedure similar to that in Ref. 5 to prepare a single phase of Sr3Co2Fe24O41 except for
the following preparation steps. In order to prevent the formation of other impurity
phases, including W-, M- and/or Y-type phases, it was found most favorable to quench
the sample immediately to room temperature after annealing. Our x-ray data are
consistent with a Z-type hexaferrite structure [11]. Also, for the ME measurements it is
important to minimize conductance current flow or heating effects through the sample in
the presence of high electric fields. As such, the resistivity was increased by annealing the
samples at 600 ◦C in an oxygen atmosphere for 6 hours. The resistivity estimated from
the experimental linear I-V characteristic was ρ = 1.43 × 109 Ω cm for samples of 1-mm
thickness. The preparation in oxygen leads to an Fe2+ concentration reduction, which then
lowers the hopping of electrons between Fe2+ and Fe3+ ions [5,10].
2.2 Magnetoelectric Measurement Technique
Typically, coaxial lines are used to measure permeability and dielectric constants as a
function of frequency, but never in the presence of an electric field or a dc voltage as high
as 2000 V.
68
Figure 4-2 Real and imaginary parts of the polycrystalline Sr Z-type permeability versus frequency.
In chapter 3, the measuring fixture apparatus was presented. In order to minimize the
risks to the instrumentation, the termination of the coaxial line was electrically separated
from the rest of the coaxial line by ∼10 mil. Software was developed in order to calculate
the effects of the separation on the measurement of µ. The technique was calibrated or
standardized against well-known coaxial line results where the line was not split. We
inserted a toroidal-shaped sample in a coaxial line. One side of the toroid was shorted to
the coaxial line termination as well as to the dc ground voltage. The other side of the
toroid was coated with a thin film of silver paint and then connected to a high dc voltage
power supply. Three precautions need to be exercised, as follows. (i) The high dc voltage
must be isolated from the microwave voltage of network analyzer instrumentation. (ii)
Antenna effects from dangling wires connected to the toroidal sample must be reduced.
The vector network analyzer was used to measure the electrical scattering S-parameter.
69
Antenna effects were reduced by connecting high-frequency capacitors to electrically
short out any microwave signals in the dangling wires. (iii) Finally, the thickness of the
silver paint film must be sufficiently small compared to the skin depth (10 µm < 200 µm)
so that the reflected signal from the toroid is not dominated by pure metallic reflection
from the silver paint. For example, initially we inserted the toroidal sample without any
wire attachments, silver paint, or capacitors attached to any wire. In short, a conventional
coaxial line measurement was performed to measure µ as a function of frequency (see
Figure 4-2). We then loaded the toroidal sample with all the attachments (wires, paint,
capacitors, etc.) but no dc voltage applied and measured µ again. We were again able to
obtain the same µ curve as in Figure 4-2. At this point we applied the dc voltage to the
toroidal sample so we measured changes in µ due to the dc voltage. Using conventional
scattering S-parameter analysis, µ may be calculated from the reflection coefficient, S11
(see Figure 4-3). The analysis is simplified considerably if the thickness of the toroidal
sample is less than the wavelength in the sample (1 mm . 6cm). The calculated S11
scattering coefficient was calculated as follows [14]
&
1
/00
23 cos78 92:;78
<
23 cos78 92:;78
where 2 ?*/ and 7 √*.
70
928=;78.
5
Figure 4-3 Coaxial line schematic.
&
is the reflection coefficient for the shorted port of the coaxial transmission
Here /00
line; Z is the coaxial line characteristic impedance of the sample; k is the propagation
constant, which is equal to 2π/λ; t is the sample thickness; and Z0 is the characteristic
impedance of the coaxial line, which is 50Ω. The permeability may then be determined
from
* B 23 #
&
1
1 /00
%1
& <,
98 1 /00
6
where ω is 2πf and f is the frequency. Note that this formula is an approximate formula
and it is valid as long as kt . 1. The sample thickness was 1mm and the approximation
is valid up to 3 GHz. The advantage of our approach or calculation technique is that the
permittivity, ε, does not enter into the analysis in this limit of approximation. This is an
extremely important point in that dielectric changes cannot influence the changes in µ as
measured by this technique, as there is no dependence on ε in Eq. (6).
71
Microwave experiments were performed under the following conditions: for a given
direction of the remanent magnetization, Mr, the electric field was applied parallel,
anti-parallel, and perpendicular to Mr. Prior to the experiments the remanence direction
was poled with a permanent magnet. The direction of the remanence magnetization, Mr,
is fixed by applying a DC magnetic field in the direction perpendicular or parallel to the
sample’s slab plane prior to the application of a static electric field as shown in Figures
4-4 (a) and (b). The removal of the DC magnetic field leaves the ferrite in the remanence
state, Mr, or simply magnetically poled.
In Figure 4-2, we illustrate the complex relative magnetic permeability µ(ω-j0+) for
low microwave frequencies, on the scale of the ferromagnetic resonant frequency. In the
limit ω→0, we expect the permeability, µ(0), to be of the order of [14]
* 0 1
1
4"EF
<,
GH
7
where Mr is the remanence magnetization and Hφ is the six fold magnetic anisotropy field.
We measured 4πMr = 105 G and thereby Hφ ≈ 40 Oe, as in Figure 4- 2. This result is
typical of Z-type hexaferrite [7]. The permeability µ(ω) as a function of the frequency is
given as [14]
* 1
#
4"EF G0
%,
G0 GJ J /K J
72
8
where 4πMr is the remanence magnetization, H1 = H + Hφ + 4πMr + Hθ , H is the external
magnetic field, Hφ is the six-fold magnetic anisotropy field, Hθ is the polar angle uniaxial
magnetic anistropy field, H2 = H + Hφ, γ = g(JNO ) P 1.4g × 106, and g ≈ 2.
M
∆R
Magnetic damping may be included by making ω complex for example ( S ) ≈ 100
Oe at X-band frequencies for Z-type hexaferrites, where ω → ω -jω (magnetic damping)
and for H > 0 such that magnetization saturation occurs, 4πMr is replaced by 4πMs, Ms
saturation magnetization.
Figure 4-4 Static electric and magnetic fields bias conditions of the hexaferrite slab in (a) E parallel or
anti-parallel to Mr and in (b) E perpendicular to Mr.
73
In our experiments H = 0 and thus there is no magnetic saturation. All of the magnetic
parameters in Eq. (8) were measured by us in Ref. 11. This means that for a given value
of 4πMr, µ may be plotted as a function of frequency. The plot in Figure 4-2 applies for H
= 0 and E = 0. However, as E was varied in our experiment, 4πMr also varied. This
implies that from the knowledge of 4πMr alone as determined at zero frequency, one may
indeed infer µ as a function of frequency. Hence, a family of curves of µ versus frequency
may be plotted where 4πMr or E is the third variable parameter, since 4πMr is related to E
via the ME effect of these materials. This was an important clue in the performance of
our experiment at microwave frequencies. We chose to measure the change in µ, ∆µ,
relative to the value of µ at E = 0 and H = 0, as a function of frequency. We do not report
the imaginary component of µ, since there is no FMR line width measurement on these
materials.
2.3 Experimental Magnetoelectric Measurements
Figures 4-5 and 4-6 show the changes in permeability when an electric field is applied
parallel or antiparallel and perpendicular to the magnetization, respectively. Under a
change in parity, E→−E and Mr → Mr. Under time reversal, E → E and Mr →−Mr the
data indicate both broken parity and broken time reversal symmetry. This represents the
fundamental broken symmetry expected of ME effects. The measurements in Figure 4-5
correlate very well with the vibrating sample measurements whereby Mr scales as E,
changing polarity with the direction of E [11]. The quadratic ME interaction in the
74
conjugate enthalpy of Eq. (1) is given by
T
U V. V. ,
9
where n is a unit vector in along the spiral axis.
(a)
(b)
Figure 4-5 Magnetic permeability change versus electric field over a microwave frequency range when M
is parallel and antiparallel to E. (a) Theoretical calculation and (b)experimental measurement for E = 5
KV/cm.
75
Figure 4-6 Magnetic permeability change versus electric field over a microwave frequency range when M
is perpendicular to E.
The total driving fields Ed and Hd have a reversible and an irreversible thermodynamic
part [12,13]. There are two ways to calculate the change in µ with frequency and E. One
way is to apply Eq. (8) for different values of Mr of E. It is somewhat tedious but possible.
The other way is to go back to the magnetic dynamic equation of motion (after
linearization).
1 XY
K dt
\ ] ^
Y ] \
10
where m is the microwave dynamic magnetization, M0 is the average static internal
magnetization =Mr , h is the microwave magnetic field, and H0 is the static internal field
=Hφ. The ME coupling to the magnetic motion modifies the above equation
76
1 XY
K dt
\ ] ^ #1
αχa ωZ3
%
χa 0χd 0
Y × \
11
where α is the ME coupling ≈0.5 × 10−2 [5], χe(0) is the dc electric susceptibility, χm(0) is
the dc magnetic susceptibility, and Z0 is the characteristic impedance of the medium.
(a)
(b)
Figure 4-7 (a) Applied electric field over the slab to measure strain, (b) Electrostriction strain of
polycrystalline Sr Z-type versus electric field.
77
The ME effect manifests itself as a change in the dynamic magnetic field at microwave
frequencies. After much algebra as developed in Ref. 14, we obtain
T*Fe
χeN f ∆Mh χeM f
B1
.
<1
. ,Z3 <,
*0
χd 0 Mh
χa 0
12
where χeN f and χeM f are the real parts of the magnetic and electric susceptibilities,
respectively. For example, the complex magnetic susceptibility is defined as [14]
(N f χeN f 9χeeN f 4"EF G0
G0 GJ J /K J
13
where H1 = Hφ + Hθ, γ = 2π g 1.4×106 Hz/Oe, ω=2πf, and Mr is the remanence
magnetization. Magnetic damping may be included in the expression for (N f by
assuming ω to be complex. Mr, Hθ (uniaxial magnetic anisotropy field), Hφ (six-fold
magnetic anisotropy field), and i factor were measured [11] and their corresponding
values were 105 G, 25 kOe, 40 Oe, and ~ 2, respectively. The zero magnetic field FMR
frequency, f0, may be easily deduced from the expression for (N f as f0 = i1.4 ]
10j ?GH GH
Gk B 2.51 GHz. Clearly, f0 is well above the frequencies where T*Fe is
maximum (l 0.5 GHz). Thus, there is no correlation between the zero magnetic field
FMR and Δ*Fe , but according to Eq. (7) there is a direct correlation between Δ*Fe and
ΔMr induced by the application of an E field [11]. The relationship between E and ΔMr
is given as TMr = α E, where α is the linear ME coupling.
78
Mr also implies an internal
change in magnetization via the spin spiral reconfigurations. Since Δ*Fe is maximum at
relatively low frequencies compared to f0, we can approximate Eq. (7) by neglecting
magnetic damping. Magnetic loss or damping is the maximum at FMR frequency,
GH G0
T*Fe
∆EF
,23
o
Bn
.
%,
#
*0
GH G0 J /K J EF 1 J p J
14
where ω is real (no magnetic damping), τ is the electric relaxation time, and Z0 is the
characteristic impedance of the ME medium (~250). Thus, Eq. (8) is applicable for
frequencies below f0. From Eq. (8), it is predicted that the decrease or "roll-off" of Δµeh
with frequency is due to electric damping or relaxation rather than magnetic damping.
The experimental data in Figure 4-5 are compared with the theoretical plot of Δµeh as a
function of frequency and E = 5kV/cm. Other theoretical plots scale the same with
frequency at other values of E. The relaxation parameter τ was assumed to be 3.2 × 10-10 s,
which compares with the τ ≈1.5 × 10-10 s deduced from the measured frequency
dependence of ε (see data in Refs. 4 and 11). Assuming that , 60 ] 10rs , Z0 ≈250 ,
and ∆EF /EF= 0.16, we estimate ∆EF = 0.96, compared to the experimental value of 1.2
at E = 5 kV/cm. Finally, in Figure 4-7 the strain induced by an electric field is exhibited
as a function of the electric field. The strain is quadratic in the electric field strength,
which indicates that Sr3Fe24Co2O41 is neither ferroelectric nor piezoelectric material.
Hence, the material exhibits electrostriction, and therefore, it may not be classified
79
strictly as a multiferroic material.
Figure 4-8 Spin spiral configuration for different directions of E. (a) E = 0, (b) E parallel to M, and (c) E
antiparallel to M.
3. Conclusions
The material hexaferrite Sr3Fe24Co2O41 exhibits broken symmetries for both time
reversal and parity. This is a central feature of these ME materials. Measurements have
been made in order to verify this feature, but in a novel manner. The measurements
involve the magnetic permeability and strain, both as a function of the electric field E.
The field dependence on strain indicates that the material is electrostrictive, which
distinguishes this material from a pure multiferroic material. The application of an
electric field induces a change in the spin spiral configuration of the hexaferrite via
80
electrostriction. This spin reconfiguration manifests itself as a change in the remanence
magnetization Mr and, therefore, as a change in the permeability. The changes in Mr were
confirmed by vibrating sample measurements, and changes in permeability were
measured using a modified coaxial line technique. This physical picture may be detailed
in a sketch we refer to as the “slinky” model (see Figure 4-8). With the application of E
the angle θ or the angle of the spin within the cone is affected by the direction of E. As
the angle θ is varied with E, the size of the “slink” changes, as well as the “net” internal
magnetization along E and, therefore, Mr. It is well known that hexaferrites are
mechanically hard along the c-axis and easier to strain in the azimuth plane
(perpendicular to the C axis). Figure 4-7 represents the average strain along the
component of E in the azimuth plane rather than along the c-axis, since the hexaferrite is
polycrystalline. Figure 4-8 shows the average change in magnetization along the
component of E in the c-axis of each crystallite, in agreement with Figure 4-5. Hence, the
strain along the c-axis or the change in magnetization is not at all correlated with the
strain as measured in Figure 4-7. As such, from practical considerations this simplifies
the design of ferrite devices and applications, since µ is the principal quantity that
governs the performance of a microwave ferrite device, for example. Hence there would
be less need for permanent magnets in microwave device applications, since only E is
applied.
81
4. Appendix
In this section the theoretical calculation derivation of equation (8)-(12) are presented.
(I) FMR condition may be derived from magnetic dynamic equation of motion (after
linearization):
ttttttu
1 dm
tttu ] H
ttu wM
tttttu3
M
K dt
ttttttu
1 dm
tu
tttttu3 ] h
M
K dt
ttttu3
m
tttu ] H
ttttu3
m
tttux ] H
tu
h
where H3 B H{ and M3 , is average static magnetization.
I
(II) Assuming shape of particle as polycrystalline, µ may be calculated as
* 1
|€
s}~ €
 €‚ rR
‚ /S ‚
ƒ ; G0 GH
Gk ; GJ GH
II
(III) Introducing magnetoelectric effect,
tu , e M
tttu. P
tu
…~† , ttu
H. E
, e (3N ttu
H. (3M tEu , 3 1 ‰
(3 is the DC susceptibility.
ttuŠ
(IV) Calculation of internal magnetic field, H
, , e (3N
e tu
e tttu
ttuŠ ‹
tttttu
H
Œ FŒŽ , P , P3
82
p
tu
(III)
(IV)
P3  Static polarization
p  Dynamic polarization
--------------------------------------------------------------------------Considering (I), (II), (III) and (IV) the equation of motion becomes
yielding
ttttttu
1 dm
tu1
tttttu3 ] h
M
K dt
* f 1
αχa Z3 4"EF G0 1
, e χa Z3 ; EF EF3
J
G0 GJ J
K
‰ * f *3
hence,
ttttu3
m
tttu ] H
T*F
TEF
T*F f 4"TEF G0 , e χa Z3 J
* 0
G0 GJ J
K
tttu ‹
tttttu
tu
where from M
Œ FŒŽ αE or simply TEF ,‘. Thus,
TEF
e
T*F f 4"TEF G0 , χa Z3 EF
;
J
* 0
G0 GJ J
K
’
TEF ,‘ .
T*F f
,‘3
,23 (Me f
e (N
f
e
* 0
EF (N 0 (Me 0
T*F f
* 0
or
e (N
f ,‘3 (Me f
on
n e
,23 o
(N 0 EF (Me 0
83
V
e (N
f
e
(N 0
Replacing in (V),
GH G0
and
J
G0 GJ J
K
T*F f
•–
* 0
(Me f
(Me 0 1
1
J p J
GH G0
,‘3
,23
˜
—
%.
#
J EF 1 J p J
G0 GJ J
K
84
References
[1]
M. Fiebig, J. Phys. D 38, R123 (2005).
[2]
G. Srinivasin, V. Zavislyak, and A. S. Tatarenko, Appl. Phys. Lett. 89, 152508
(2006).
[3]
T. Kato, H. Mikami, and S. Noguchi, J. Appl. Phys. 108, 033903 (2010).
[4]
M. Soda, T. Ishikura, H. Nakamura,Y.Wakabayashi, and T.Kimura, Phys. Rev.
Lett. 106, 087201 (2011).
[5]
Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,
Nature Mater. 9, 797 (2010).
[6]
Y. Takada, T. Nakagawa, M. Tokunaga, Y. Fukuta, T. Tanaka, and T. A. Yamamoto,
J. Appl. Phys. 100, 043904 (2006).
[7]
W. Martienssen (ed.), Landolt-B¨ornstein: Numerical Data and Functional
Relationships in Science and Technology (Springer-Verlag, Berlin, 1970).
[8]
C.-G. Duan, J. P. Velev, R. F. Sabirianov, Z. Zhu, J. Chu, S. S. Jaswal, and E. Y.
Tsymbal, Phys. Rev. Lett. 101, 137201 (2008).
[9]
L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media
(Pergamon Press, Oxford, UK, 1984).
[10]
O. Kimura, M. Matsumoto, and M. Sakakura, J. Am. Ceram. Soc. 78, 2857
(1995).
[11]
K. Ebnabbasi,Y. Chen, A. Geiler, V. Harris, and C.Vittoria, J. Appl. Phys. 111,
07C719 (2012).
85
[12]
A. Widom, S. Sivasubramanian, C. Vittoria, S. Yoon, and Y. N. Srivastava, Phys.
Rev. B 81, 212402 (2010).
[13]
L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Elsevier
Butterworth-Heinemann, MA, 1984).
[14]
C. Vittoria, Magnetics, Dielectrics, and Wave Propagation with MATLAB Codes
(CRC Press, New York, 2011).
86
Chapter 5.
Strong Magnetoelectric Coupling in Hexaferrites
at Room Temperature
1. Introduction
In this chapter, the magnetoelectric effect in single-crystalline Sr Z-type hexaferrite
materials is presented. The measurements include material characterization and change in
remanence magnetization (Mr) versus electric field. In a very low electric field equal to
3.75 V/cm, 14% change in Mr was observed. We deduced a magneto-electric coupling of
55.4 in CGS units or 2.32×10-6 sm-1(SI units) which is the highest value measured to date.
There have been a number of publications dealing with the magneto-electric properties
of M- and Z- type hexaferrites [1-6]. These hexaferrites are special ferrite materials,
because they exhibit high magneto-electric coupling coefficient at room temperature. This
means that the application of an electric field or DC voltage induces magnetization changes
and the application of a magnetic field induces electric polarization changes. The common
denominator of recent publications was that the tested materials were poly-crystalline. The
application of these types of materials still is not possible along with semiconductors.
And converse measurements have shown that very high voltage or electric field in the
range of 1-5 kV/cm is required for high magneto-electric coupling effect [3].
The magnetic properties of single crystals of Z-type hexaferrites, Sr3Co2Fe24O41,
exhibiting the strongest magnetoelectric effect at room temperature is presented. High
87
ME coupling, α, at very low voltage or electric field was observed in converse
measurements. This is quite promising in terms of being able to induce magnetization
changes with as little as 15 mV compared to polycrystalline materials requiring hundreds
of volts affecting the same change in magnetization. We believe that changes in
magnetization at low voltages places ferrite and semiconductor devices in the same range
of required voltages for modern multi-functional applications.
2. Experimental Measurements
SEM (Scanning Electron Microscope) photograph, XRD (X-ray Diffraction) material
characterization, and FMR (Ferromagnetic Resonance) measurements are shown in
Figures 5-1, 5-2, and 5-3, respectively, consistent with a hexagonal crystal structure.
From VSM measurements we measured 4πMs≈3100 G and Hc=14.14 Oe. From FMR
measurements, we deduced the following parameters: g = 2, ∆H=750 Oe (9.53 GHz),
Hθ=12 kOe, and Hφ=60 Oe where 4πMs, Hc, ∆H, Hθ, and Hφ are the saturation
magnetization, coercive field, the FMR linewidth, the uniaxial magnetic anisotropy field,
and the azimuth anisotropy field (six fold symmetry), respectively.
88
Figure 5-1 SEM micrograph of single crystal of Z-type hexaferrites, Sr3Co2O24O41.
Figure 5-2 Room-temperature X-ray diffraction pattern.
89
Figure 5-3 Ferromagnetic resonance at room-temperature (derivative absorption versus Hext).
The internal field (Hi) is equal to HextNM, where Hext, N, and M are external applied
magnetic field, the demagnetization factor, and the magnetization, respectively. As it is
well known in the non-saturation regime (Hext NM ; Ms is the saturation magnetization)
Hi=0 and typically Hext is linear with M. In the saturation regime (Hext NM ) the internal
field is finite and pointing along the saturation magnetization direction. As shown in
Figures 5- 4 and 5-7, for external fields up to 700 Oe the measured magnetization scales
as the external field implying non-saturation of the magnetization and, therefore, zero
internal magnetic field.
90
Figure 5-4 Hysteresis loops change versus electric field with the magnetic field applied parallel (//)
and perpendicular (┴) to the slab plane.
The change in remanence magnetization versus DC electric field when the applied
magnetic field is parallel and perpendicular to the material slab in an electric field equal
to 3.75 V/cm, is given in Figure 5-4. The observed change in Mr, remanence
magnetization, is 14%. This is given in Figure 5-5 for the external magnetic field
perpendicular to applied electric field and parallel to slab plane. The change in Mr versus
electric field when it is applied parallel, anti-parallel and perpendicular to the
magnetization is given in Figure 5-6. The magnetoelectric phenomenon is explained in
terms of spin spiral order of the magnetic structure referred by us previously as the
"slinky helix model" in chapter 4 and [3].
91
Figure 5-5 Remanence magnetization change versus electric field with the magnetic field applied
parallel (//) to the slab plane.
Figure 5-6 Change in remanence magnetization versus electric field.
92
Figure 5-7 change in capacitance versus magnetic field.
These measurements show the ME effect at very low electric fields. The
magnetoelectric coupling was measured to be in the order of ~55.4 in CGS units or
2.32×10-6 sm-1 (SI units) at room teperature and there is no other material that exhibits
such high coupling at any temperatures. In poly-crystalline Sr-Z α was measured to be
1×10-10 sm-1 and at ~30 Oe reached a maximum value of 2.5×10-10 sm-1 [4]. In the convers
magnetoelectric this value was measured to be 7.6×10-10 sm-1 [7]. The ⁄
peak
values in single phase materials usully are small. For instance, α=4.1×10-12sm-1 (Cr2O3) at
307K, and ⁄
~10-9 sm-1 (Tb2(MoO4)3) [8-9]. Giant magnetoelectric effects equal to
α=2.3×10-7 sm-1 in single epitaxial interface in ferromagnetic 40 nm La0.67Sr0.33MnO3
films on 0.5 mm ferroelectric BaTiO3 substrate has been observed near room temperature
with low magnetization [10]. This is almost 10 times smaller than our measured value
93
reported here in single crystalline Sr-Z hexaferrite. Also, the magnetoelectric effect
observed by us was measured at very low electric fields ~3.75 V/cm.
3. Conclusions
We measured a magnetoelectric coupling, α, of 2.32×10-6 sm-1 in Sr3Co2O24O41 single
crystals. The α value measured by us represents the highest value measured at room
temperature. For example in La0.67Sr0.33MnO3 films α=2.3×10-7sm-1 at room temperature.
The implications of high values of α are immense especially at room temperature. It
means that one can affect significant changes in magnetization in the millivolt range
rather than hundreds of volts range (for thickness in the order of 1mm, for example). We
envision many applications in sensor and microwave devices.
94
References
[1]
K. Ebnabbasi,Y. Chen, A. Geiler, V. Harris, and C.Vittoria, J. Appl. Phys. 111,
07C719 (2012).
[2]
M. Soda, T. Ishikura, H. Nakamura,Y.Wakabayashi, and T.Kimura,Phys. Rev. Lett.
106, 087201 (2011).
[3]
K. Ebnabbasi, C. Vittoria, and A. Widom, Phys. Rev. B 86, 024430 (2012).
[4]
Y. Kitagawa, Y. Hiraoka, T. Honda, T. Ishikura, H. Nakamura, and T. Kimura,
Nature Mater. 9, 797 (2010).
[5]
L. Wang, D. Wang, Q. Cao, Y. Zheng, H. Xuan, J. Gao & Y. Du, Nature, 2, 223
(2012).
[6]
K. Ebnabbasi, Marjan Mohebbi, and C. Vittoria, Appl. Phys. Lett.
101, 062406
(2012).
[7]
K. Ebnabbasi, Marjan Mohebbi, and C. Vittoria, J. Appl. Phys., Accepted (2013).
[8]
Folen, V. J., Rado, G. T. and Stalder, E.W., Phys. Rev. Lett. 6, 607–608 (1961).L.
D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon
Press, Oxford, UK, 1984).
[9]
Ponomarev, B. K., Ivanov S. A. et al., Ferroelectrics 161, 43–48 (1994).
[10]
W. Eerensteini, M. Wiora, J. L. Prieto, J. F. Scott and N. D. Mathuri., Nature
Letters, 6, 348 (2007).
95
Chapter 6.
Microwave Magnetoelectric Devices
1. Introduction
Ferrite materials are widely used in passive and tunable electromagnetic signal
processing devices. In Figure 6-1, potential and current applications of ferrite materials and
devices in communication systems and their operating frequency range are shown. Due to
their excellent dielectric properties, ferrites possess the advantages of low loss and high
power handling relative to semiconductors. Magnetic fields are usually generated using
permanent magnets or current driven coils, leading to relatively large component size,
weight, and cost, as well as slow response time in comparison to semiconductor-based
technologies.
Magneto-electric materials can be a practical solution to control the magnetic
parameters of ferrites by electric field and/or voltage and would eliminate permanent
magnets and tuning coils to overcome most of the disadvantages in the use of ferrites for
microwave devices. A situation where ferrites are compatible with active components
based on semiconductors would become a reality. Furthermore, key advantages of ferrites,
including low insertion loss and high power handling capability could be exploited without
the penalty of added size, weight, and cost, as well as increased response time.
In this chapter a single layer of poly-crystalline magneto-electric Z-type,
Sr3Co2Fe24O41, which has strong ME effects at room temperature, is proposed to induce
magnetic parameter changes with application of voltage. It is very important that in this
96
type of material there is no need of an external magnetic field to control the parameters of
magnetic material and simplify the tune of device performance.
Figure 6-1 Potential and current applications of ferrite materials and devices in communication systems
and their operating frequency range.
Traditionally, most of ferrite devices and elements were used in defense and military
applications such as phase array systems and search and missile radars, shown in Figure
6-1. In these applications, phase shifters and circulators play key role. The magnetoelectric
material studied in this work has good performance in low frequencies (< 4GHz) with no
magnetic bias field and hence, very compact devices can be designed. This is quite
97
important since there are a lot of commercial applications like cellular mobile, medical
applications and GPR (Ground Penetration Radar) in this frequency range.
In terms of phase array in wireless communication systems, in L and S frequency bands,
phase shifter has found its way into applications such as digital television, mobile
networking, GPS (Global Positioning System), RFID (Radio Frequency Identification),
and even anti-collision systems. Additionally, phase shifters are utilized in high data rate
communication systems and test equipments to implement mixer, VCOs (Voltage
Controlled Oscillators), phased locked loops, frequency synthesizers, and etc.
There are different types of phase shifters with different materials and design
techniques. In most cases, phase shifting functions are realized using digital semiconductor
devices that offer small size, fast switching times, and low power consumption. These
devices, however, suffer from high insertion loss (> 5 dB), poor power handling
capabilities (<1 W), and high cost (GaAs substrate). Other technologies, including MEMS
and ferroelectric phase shifters, have emerged over the years but none of them deliver the
same exceptional insertion loss, power handling, and reliability as ferrite devices. One
issue with MEMS phase shifters is that packaging is perhaps more critical than with
alternative technologies. Hydrocarbon contamination may compromise MEMS reliability
so hermetic seals and careful processing are required. In Table I, a summary of different
technologies in the design of phase shifters are provided for comparison [1].
98
2. Multi-Phase Magnetoelectric Microwave Phase Shifter
Multi-phase and multiferroic composite materials have been proposed to generate
internal magnetic fields via voltage. These composites usually consisted of
magnetostrictive and ferroelectric or piezoelectric slabs in physical contact whereby
magnetic field sensors have been implied and fabricated so far. Also, small shifts in
ferromagnetic resonance (FMR) have been observed using magnetoelectric composites in
the presence of an electric field.
The ME effect is observed in two classes of materials: single phase multiferroic
materials possessing simultaneously both ferroelectric and ferromagnetic properties and
composites consisting of ferroelectric and ferromagnetic phases. The ME effect in the
single-phase materials [3] arises from the long-range interaction between the atomic
moments and electric dipoles in ordered magnetic and ferroelectric sublattices. In previous
single-phase materials the problem was the realizable ME coefficient is very small (1–20
mV/cm Oe) and not sufficient for practical applications. Moreover, ME effect in most of
these single-phase materials is observed only at low temperatures as either ferromagnetic
(or antiferromagnetic) or ferroelectric and transition temperature is very low.
Traditional ferrite phase shifter use magnetic tuning systems that are slow, demand high
power, and are not miniature in size. A desirable alternative is the latching ferrite phase
shifter that operates at the remanent magnetization for the ferrite element and requires
current pulses for switching the magnetization state [4].
99
Table I. Comparison of phase shifter technologies (The ferrite type is non-ME) [1].
Type
Feature
Cost
Ferroelectric
Semiconductor
/MMIC
Ferrite
MEMS
Low
Expensive
Very expensive
Low
6
Reliability
Power
handling
Switching
speed
Radiation
tolerance
DC power
consumption
RF loss
Good after 10 to
Very good (if
40V/µm bias cycle
properly packaged)
Good, >1W
Intrinsically fast
(~ns)
Excellent
Very Good, tens of
watts
Fast at low power
-9
(<10 S)
Excellent
Very high (kW)
Slow
(inductance 10
to 100µs)
Poor (good if
radiation hardened)
Linearity
billion cycles
Low power,<50mW
for high reliability
Slow (mechanical 10
to 100µs)
Excellent
Excellent
(mechanical; no solid
state junction)
Low (10mW:
High (large
diodes,~0: FETs)
current)~10W
~5dB/36o
2dB/bit @ Ka
<1dB/360o
~2.3dB/337.5o @ Ka
@K-band
band=8dB
@X-band
band
Low (<<1µA) µW
2
Size
Good after several
Very small (mm2)
Small (~10mm @
Ka band)
IMD interest
IMD intersect +35
+60dBm
to +40dBm
Large
--------
negligible
Smalle (compared to
MMIC)
IMD intersect
+80dBm
Phase shifts could also be realized through magnetostatic wave propagation or
ferromagnetic resonance FMR in planar ferrites in microstripline structures [5]. The MSW
wavelength and group velocity are two to three orders of magnitude smaller than that of
electromagnetic waves of the same frequency. This makes possible a phase shift of decades
of π for propagation distances of several millimeters. In the case of phase shifters operating
close to FMR, a rapid change in the permeability and phase shift can be achieved by tuning
the bias magnetic field [6]. But all of the above ferrite phase shifters, in general, require
100
high electrical power for operation and cannot be miniature in size or compatible with
integrated circuit technology. Ferroelectric phase shifters, on the other hand, can be tuned
with an electric field [7]. But such phase shifters are very lossy at frequencies above 1–5
GHz. With a ferrite-ferroelectric layered structure, it is possible to achieve both magnetic
and electric field tunabilities of the phase shift [8,9]. In [10], the design and
characterization of a new tunable electric field phase shifter based on ferrite-piezoelectric
layer composite has been published. The electrical control of the phase shifter is realized
through microwave magnetoelectric effect. The phase shifter is capable of rapid tuning and
compact size. However, the disadvantage of this design is the multi-layer of the device and
the required magnetic field to bias the material leading to heavier and bigger component.
Figure 6-2 Schematics of fabricated magnetoelectric nonreciprocal microwave phase shifter in [10].
101
In Figure 6-2, the schematics of fabricated ME microwave phase shifter and ME
resonator of YIG film on GGG bonded to PMN-PT is shown [2, 10].
The base of the phase shifter is a microstrip transmission line on alumina substrate (εr
= 9.8, thickness =1mm). Ferrite phase shifters maximize phase shift over a given
distance by producing circularly polarized microwaves to interact with the magnetic
dipole moments in. the biased ferrite material. In the past this was typically done by
placing a longitudinally (i.e., in the direction of propagation) biased ferrite rod in the
center of a waveguide. Although this technique produced the desired phase shift, it was
costly to manufacture because the cross-section of the structure was a fraction of the
operating wavelength. In [10], the designed phase shifter consists of a YIG-PZT resonator,
and microstrip loops of lengths λ/8 and 3λ/8 that produce a circularly polarized
microwave magnetic field in the resonator.
By this phase shifter the differential phase
shifts of 90°–180° could be obtained with nominal electric fields on the order of 5kV/cm.
The device shows an insertion loss of 1.5–4 dB at 5–10 GHz.
3. Single-Phase Magnetoelectric Microwave Phase Shifter
The design in [10] has two main disadvantages. First the multi-layer or multi-phase
structure of the device and second the required external biasing magnetic field. Both
make the device pretty big and non-compact. The design of the phase shifter in this
section is based on a single phase or single layer of the poly-crystalline Sr Z-type
hexaferrite which was presented in previous chapters and studied in detail in terms of
102
material characteristics change versus electric field with no external biasing magnetic
field. It was found that the change in remanence magnetization for E=5kV/cm is ~13%.
Here in our design we will refer to this change in permeability to design the phase shifter.
First the desirable structure of the phase shifter is analyzed and studied and then it is
simulated and compared to experimental results.
3.1 Meander Line Micro-strip
Here the meander line structure is studied to see if we can get reasonable phase shift. If
we suppose εr=8 and µr=3for the ME substrate, the phase constant at 1GHz for a
micro-strip with 1cm length will be:
360
360
3 10
6
1
60
6
√µε 10
By applying voltage if we have 10% change in both εr and µr, the phase shift will be:
∆φ = φ(E)- φ(0)≈7o
By utilizing meander line microstrip, shown in Figure 6-3, for 180o, we should use 25
lines which make the device big and for that number of lines the insertion loss will
increase and lossy devices is resulted.
103
Figure 6-3 Schematics of meander line microstrip.
A solution to use less number of meander lines is using high dielectric materials like
"D-100 Titania" as a substrate which has dielectric constant equal to 100. If sandwich
microstrip is designed, the overall permittivity will be between 32 and 100. And 10%
change in εr and µr will result in higher value in phase shift. For example, at 1GHz for
1cm length the phase shift will be roughly 90o. Although this is high value, the substrate
is expensive and fabrication of microstrip on that requires special fabrication process.
And also to get higher phase shift we need to use more microstrips and insertion loss gets
higher.
3.2 LC Phase Shifter Theory and Design
In this section a method is presented that prevents the big loss and size problems.
These disadvantages are resulted since the change in permeability in high frequencies
(>1GHz) is small and hence the phase shift by applying voltage is small. To achieve
higher shift we can use LC circuit in our design. L can be realized by the ME material
and microwave capacitors can be used in either of series or parallel with the L. And we
104
can design the L and C values to be set in the resonance frequency at required value and
by a small change in voltage the S21 phase change for ~180o. The series microwave
network is shown in Figure 6-4.
Figure 6-4 Microwave network consisting of elements connected in series.
S21 in this case is:
1
1
1 2
If Z is a pure inductor (Z=jLω) then
1
1 2
0%/ 5+%/ !"#
$
!"#$ '
/ 5+%/
!"#$ 2
0
'
(
2
2
02)×10
!"# '
(
100
5+%/
(
2
.
!"# '
0%/ !"#$ '
if 02)×100 1 1 then
105
0.902)×10
(
100
0.102)×100
(
1 0.902)×100 / !"#$ 2
1
3
0.902)×100
for an square spiral inductor with 2 turns with 1cm length the L(0) will be
0 4 5 # 6 6.28 10$0
which results in
/ 4.19:;.
Since L is proportional to µr any change in permeability is reflected in L. Considering
this and 10% change in L @ 1GHz the change in phase for a spiral inductor with 10 turns,
as shown, will be ~ 4 degrees.
For pure inductor the phase change is small. Instead of that a series LC is used where
Z=jLω+1/jCω. In this case one can calculates the S21 as:
2 <
< 2 <
3
2 < > ? @
1 2 < < > ? < ? 4
/ !"#$ =
1
Here L and L' are the inductance values in 0 and E (V/cm), respectively. The phase
shift is direct proportional to frequency and change in inductance.
In Figure 6-5, the change in phase for an example series LC is given (L=2.838µH,
C=15fF→fr= 0.77GHz). In this technique we can obtain more shifts in phase for small
changes in remanence magnetization of the ME material in microwave frequencies and
hence in inductance.
106
Figure 6-5 Phase shift by applying electric field or voltage.
L in the design is realized as spiral inductor. This is shown in Figure 6-6. CST
microwave studio was used to simulate the designed device. The problem with the
software simulators such as HFSS was there is no material in their component library to
be introduced to the software. The beauty with CST MWS is the user can model the
material such as Debye and Lorentz models. In this work we used Lorentz model and we
replaced the values by the experimentally measured results presented in previous chapters.
In the Lorentz model, as given below, it is required to put the resonance frequency and
static and relaxation permeability values.
107
5A 1 4)BA C
; D F D 1
C C D
G ,
G IJ KIL:6! 9M#"I N"6":!:6
C C CO 4)BA CP
C C CO
Here H=0.
If we re-write these equations
5A 1 4)BQ /C
5QSTSUV
F 5R 1 D 1
C C D
1
D In the simulation it was supposed 5QSTSUV 3.8, 5R 1 , W 2.51KCX and
2)W1
G .
(a)
(b)
Figure 6-6 Simulated phase shifter structure (a) without and (b) with the ME material introduced with
Lorentz model.
108
The simulation results for the S21 amplitude and phase in dB and degrees, respetively,
are given in Figure 6-7. As shown, the resonance frequency is close to 1GHz and there is
~180 phase shift. If the resonance frequency is shifted by applying voltage, this phase
change can be achieved. This is a reliable method to broaden the phase change for small
value change in permeability.
Figure 6-7 Insertion loss and phase simulation results.
The fabricated device and measure change in phase by applying voltage are shown in
Figures 6-8 and 6-9, respectively. We should notice that the measured values are for pure
inductor and without connecting the capacitor. The value is close to the calculation.
109
However in 300V it gets bigger and that is because by increasing voltage the permittivity
also changes and the overall change is bigger than what we expect for pure inductor. This
is required result and it can be an advantage because for a desire change we can apply
lower DC voltage.
Figure 6-8 The fabricated phase shifter.
Figure 6-9 Measured phase shift by applying voltage for the fabricated phase shifter with no capacitor.
110
4. Conclusions
In this chapter a compact DC voltage tunable microwave phase shifter with no external
biasing magnetic field was presented. It was shown that with a single phase
magnetoelectric poly crystalline Sr Z-type we can design an LC phase shifter with almost
180 degrees phase change although the change in permeability is not that big to
implement the design using the convention meander line microstrips. The designed
device is compact and small in the frequency range of L and S bands.
111
References
[1]
Robert R. Romanofsky, "Array Phase Shifters: Theory and Technology",
NASA/TM-2007-214906.
[2]
A. S. Tatarenko and M. I. Bichurin, "MicrowaveMagnetoelectric Devices",
Advances in Condensed Matter Physics vol. 2012.
[3]
M. I. Bichurin and V. M. Petrov, “Magnetic resonance in layered
ferrite-ferroelectric structures,” Soviet Physics -Technical Physics, vol. 33, p.
1389, 1989.
[4]
C. R. Boyd, Jr., IEEE Trans. Microwave Theory Tech. 18, 1119 (1970).
[5]
H. Chang, I. Takenchi, and X.-D. Xiang, Appl. Phys. Lett. 74, 1165 (1999).
[6]
H. How, W. Hu, C. Vittoria, L. C. Kempel, and K. D. Trott, J. Appl. Phys. 85,
4853 (1999).
[7]
H. Chang, I. Takenchi, and X.-D. Xiang, Appl. Phys. Lett. 74, 1165 (1999).
[8]
W. J. Kim, W. Chang, S. B. Qadri, H. D. Wu, J. M. Pond, S. W. Kirchoefer, H. S.
Newman, D. B. Chrisey, and J. S. Horwitz, Appl. Phys. A: Mater. Sci. Process. 71,
7 (2000).
[9]
Y. K. Fetisov and G. Srinivasan, Electron. Lett. 41, 1066 (2005).
[10]
A. S. Tatarenko, G. Srinivasan, and M. I. Bichurin, “Magnetoelectric microwave
phase shifter,” Applied Physics Letters, vol. 88, no. 18, Article ID 183507, 2006.
112
Chapter 7.
Discussion and Conclusion
In this dissertation we developed a new class of ferrite materials which exhibit the
highest magnetoelectric coupling ever measured at room temperature. The results gave
rise to the hope that magnetic materials along with semiconductors can be integrated
together in circuits and chips.
The material growth, characterization and converse ME effect in Z- and M- types of
hexaferrites were studied in chapter 2. The ME coupling coefficient at room temperature
were sufficiently high to explore the utilization of these new generation of ferrite
materials in applications such as phase shifter, filter, sensors, DC voltage variable
inductor, variable resonance frequency in printed antenna substrates and etc.
A coaxial device was developed to measure directly the microwave permeability
versus electric field which has been done for the first time. This was presented in chapter
3.
Chapter 4 covered the introduction of a physical model and theory of the converse ME
effects to explain and illustrate the ME coupling and it was referred to as the “slinky helix”
model. The application of ‫ܧ‬ሬԦ strained the material thereby changing the physical
structure of the spiral spin configuration. It is this physical motion of the spiral response
ሬሬԦ. Our model should be contrasted with
to ‫ܧ‬ሬԦ that induces a change in magnetization ‫ܯ‬
the model for the ME effect in multiferroics as well as ferromagnetic metal films wherein
the band energies of the up and down spin are modified by the electric fields at the
113
interface between phase separated ferromagnetic and ferroelectric films.
In chapter 5 the ME effect of single crystalline of single phase Sr Z-type hexaferrite
was presented and it was found that this material had the highest ME coupling coefficient
ever measured. Measurements were performed for both direct and indirect or converse
ME effects. This is quite promising in the use of magnetic materials in integrated devices
along with semiconductors. In addition to the compact devices advantages these materials
possess they can handle high power where semiconductor cannot.
In the last chapter a ME microwave phase shifter was designed and the compact
structure of the device was presented in L band. This is extremely important since this
gave rise to the hope to use these devices in commercial and personal applications where
a lot of those can be found in L and S bands.
This is the beginning of a new generation of microwave components for RF
communications and medical applications. Currently, research is in progress to develop
thin film of these types of materials and results have been obtained in ME M-type
hexaferrite growth to apply very small value of voltage to be comparable to
semiconductor biasing voltage and decreasing the DC power consumption. The materials
are currently bulk and can be utilized mostly in discrete circuits.
114
Документ
Категория
Без категории
Просмотров
0
Размер файла
9 087 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа