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Novel microwave properties and “memory effect”in magnetic nanowire array

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NOVEL MICROWAVE PROPERTIES AND “MEMORY EFFECT” IN
MAGNETIC NANOWIRE ARRAY
by
Xiaoming Kou
A dissertation submitted to the Faculty of the University of Delaware in
partial fulfillment of the requirements for the degree of Doctor of Philosophy in
Physics
Winter 2011
Copyright 2011 Xiaoming Kou
All Rights Reserved
UMI Number: 3453237
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NOVEL MICROWAVE PROPERTIES AND “MEMORY EFFECT” IN
MAGNETIC NANOWIRE ARRAY
by
Xiaoming Kou
Approved:
__________________________________________________________
George C. Hadjipanayis, Ph.D.
Chair of the Department of Physics and Astronomy
Approved:
__________________________________________________________
George H. Watson, Ph.D.
Dean of the College of Arts and Sciences
Approved:
__________________________________________________________
Charles G. Riordan, Ph.D.
Vice Provost for Graduate and Professional Education
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
__________________________________________________________
John Q Xiao, Ph.D.
Professor in charge of dissertation
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
__________________________________________________________
Karl M. Unruh, Ph.D.
Member of dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
__________________________________________________________
Michael A. Shay, Ph.D.
Member of dissertation committee
I certify that I have read this dissertation and that in my opinion it meets
the academic and professional standard required by the University as a
dissertation for the degree of Doctor of Philosophy.
Signed:
__________________________________________________________
Matthew F. Doty, Ph.D.
Member of dissertation committee
ACKNOWLEDGMENTS
I would like to first thank my advisor, Professor John Q. Xiao, for his
expert guidance throughout the course of my Ph.D. study. Three things I learned from
Professor Xiao will benefit me in the rest my life: think hard, be confident, and take
the responsibility.
I also wish to thank all my collaborators in different projects: Dr. Kai Liu,
Dr. Randy Dumas, Dr. Wanfeng Li, Dr. Yan Ji.
I would also like to thank Dr. Karl Unruh, Dr. Michael Shay, Dr. Matthew
Doty, Dr. George C. Hadjipanayis, and Dr. Edward Nowak for their kind help and
enlightening discussions.
My sincere gratitude also goes to all my colleagues and friends for their
help and support: Dr. Hao Zhu, Dr. Xiaokai Zhang, Dr. Weigang Wang, Dr. Takahiro
Moriyama, Dr. Rong Cao, Dr. Lubna Shah, Dr. Xin Fan, Xing Chen, Qi Lu, Yaping
Zhang, Jian Shen, Chong Bi, Paul Parsons, Fariha Nasir, Jun Wu, Yunpeng Chen,
Yang Zhou, Yunsong Xie, Ryan Stearrett, Brian Kelly, Dr. Xiaojun Wang, Han Zou,
Shuhan Chen, Dr. Baozhi Cui, Hafsa Khurshid, Nilay Gunduz-Akdogan, Ozan
Akdogan, Dr. Qi Yao, Dr. Liyun Zheng
I would also like to thank my wife and my parents for their support and
encouragement.
iv
This work is dedicated to my loving wife, Lili Song. Her support and
encouragement made this work possible.
v
TABLE OF CONTENTS
LIST OF TABLES ........................................................................................................ ix LIST OF FIGURES ........................................................................................................ x ABSTRACT ................................................................................................................. xv
Chapter 1 INTRODUCTION ....................................................................................... 18 1.1 Soft Magnetic Material ............................................................................... 19 1.2 Tunneling Junction ..................................................................................... 23 1.3 Outline of Dissertation ............................................................................... 26 References ........................................................................................................ 28 Chapter 2 EXPERIMETNAL METHODS................................................................... 30
2.1 Thin Film Sample Fabrication .................................................................... 30 2.1.1 Magnetron Sputtering ..................................................................... 30 2.1.2 Ion Beam Etching ........................................................................... 34 2.1.3 Photolithography ............................................................................ 35 2.2 Magnetic Nanowire Array Fabrication....................................................... 36 2.2.1 Alumina Template Synthesis.......................................................... 37 2.2.2 Electrochemical Deposition ........................................................... 41 2.3 Structural Characterization ......................................................................... 42 2.3.1 X-ray Diffraction ............................................................................ 42 2.3.2 Electron Microscopy ...................................................................... 43 2.3.3 Polarized Neutron Reflectivity ....................................................... 47 2.4 Characterization of Magnetic Properties .................................................... 50 2.4.1 Vibrating Sample Magnetometer ................................................... 50 2.4.2 Hysteresis Loop Tracer .................................................................. 52 2.4.3 Cavity method ................................................................................ 53 Reference .......................................................................................................... 56 Chapter 3 NOVEL MICROWAVE PROPERTIES OF MAGNETIC
NANOWIRE ARRAYS .............................................................................. 58 3.1 Theoretical Background ............................................................................. 58 vi
3.1.1 Complex Permeability .................................................................... 58 3.1.2 Eddy Current Loss .......................................................................... 59 3.1.3 Landau-Lifshitz-Gilbert Equation and Ferromagnetic
Resonance .................................................................................... 60 3.1.4 Snoek’s Limit ................................................................................. 61 3.1.5 Apparent Permeability .................................................................... 62 3.2 Microwave Permeability of Magnetic Nanowire Arrays ........................... 63 3.2.1 Estimation of Permeability ............................................................. 64 3.2.2 Magnetic Nanowire Arrays with Negligible
Magnetocrystalline Anisotropy ................................................... 65 3.2.3 Cobalt Nanowire Array with Strong Magnetocrystalline
Anisotropy ................................................................................... 69 3.3 Tunable Double Ferromagnetic Resonance................................................ 75 3.3.1 NiFe Nanowire ............................................................................... 76 3.3.2 Co Nanowire................................................................................... 79 3.4 The Origin of Tunability and Double FMR ............................................... 81 3.4.1 A Dipolar Interaction Model .......................................................... 82
3.4.2 Model Improvement ....................................................................... 86
3.4.3 Potential Application ...................................................................... 87 Reference .......................................................................................................... 88 Chapter 4 MEMORY EFFECT IN MAGNETIC NANOWIRE ARRAY ................... 91 4.1 Memory Effect............................................................................................ 91 4.1.1 Demonstration and Irreversibility .................................................. 93 4.1.2 Switching Field Distributions in Magnetic Nanowire Array ......... 97 4.2 Electromagnetic Pulse Detector ............................................................... 100 4.2.1 Proposed EMP detector ................................................................ 100 4.2.2 Preliminary Test ........................................................................... 103 4.3 Practical Issues ......................................................................................... 105 4.3.1 Thermal Stability .......................................................................... 106 4.3.2 Surface Magnetic Field ................................................................ 110 4.3.3 Switching Speed ........................................................................... 112 4.4 Summary................................................................................................... 112 Reference: ....................................................................................................... 114 Chapter 5 HIGH TEMPERATURE ANNEALING INDUCED
SUPERPARAMAGNETISM IN MGO BASED MAGNETIC
TUNNELING JUNCTIONS ......................................................................... 117 5.1 Introduction .............................................................................................. 117 5.1.1 Symmetric Tunneling in MgO Based Tunneling Junction ........... 119 vii
5.1.2 Full Junction Structure ................................................................. 121 5.1.3 Synthetic Antiferromagnetic Pinning ........................................... 124 5.1.4 Rapid Thermal Annealing ............................................................ 125 5.1.5 Superparamagnetism .................................................................... 126 5.2 Time Evolution of MR Loop under High Temperature Annealing .......... 128 5.2.1 Magnetic Transport Measurement ............................................... 129 5.2.2 High Temperature Annealing Induced Superparamagnetism ...... 134 5.2.3 More evidence for superparamgneism ......................................... 140 5.3 Study of MgO/CoFeB Multilayer by Polarized Neutron Reflectivity ..... 141 5.3.1 Sample Fabrication and Characterization by XRD and VSM...... 142 5.3.2 Preliminary Result and Analysis .................................................. 145 References ...................................................................................................... 147 Chapter 6 ELECTROMAGNET DESIGN AND SIMULATION WITH
MAXWELL 3D .............................................................................................. 151 6.1 Introduction of Maxwell 3D ..................................................................... 151 6.2 Design of an Electromagnetic Assembly for Actuator ............................. 152 6.2.1 Preliminary Designs ..................................................................... 152 6.2.2 Design Improvement .................................................................... 157 6.2.3 Comparison between Simulation and Experiment ....................... 162 6.3 Simulation of Eddy Current Loss ............................................................. 170 Chapter 7 CONCLUSION .......................................................................................... 175 APPENDIX I .............................................................................................................. 179
List of patent, publications and presentations during Ph.D. study ................. 179
APPENDIX II ............................................................................................................. 182
Permission Letter for Figures 5.2 and 5.3 ...................................................... 182 viii
LIST OF TABLES
Table 2.1 Optimized conditions of the anodization process ........................................ 40 Table 2.2 Electrochemical deposition conditions of nanowires ................................... 42 Table 5.1 Parameters used in the fitting ..................................................................... 146 Table 6.1 Electric parameters with filling factor of 0.8 and current density of
1.5A/mm2 ................................................................................................... 162 Table 6.2 Comparison between experiment and simulation ...................................... 174 ix
LIST OF FIGURES
Figure 2.1 Incident ions with different energies leads to different outcome when
bombarding on material surface................................................................ 31 Figure 2.2 A schematic diagram of planar sputtering gun ......................................... 33 Figure 2.3 Sputtering chamber used in this study ...................................................... 34 Figure 2.4 Schematic diagram of Kauffman ion source ............................................. 35 Figure 2.5 Fabrication process of nanowire array. SEM micrographs show the top
view of the Al2O3 template (top left) and the cross-sectional view of
nanowire array (bottom right). The actual devices for anodization and
metal deposition only expose one side of the aluminum foil or AAT
template to the solution. ............................................................................ 39 Figure 2.6 AAT templates with thickness of 90 µm (left) and 50 µm (right), covered
with Cu layer as bottom electrode for nanowire deposition. .................... 41 Figure 2.7 X-ray diffraction scheme .......................................................................... 43 Figure 2.8 Schematic diagram of a typical SEM ........................................................ 45 Figure 2.9 JEOL JEM-3010 transmission electron microscope ................................. 46 Figure 2.10 Neutron reflectivity measurement examples. R++ and R-- are measured
[10]. ........................................................................................................... 50 Figure 2.11 A vibrating sample magnetometer (Lakeshore 7404) ............................... 51 Figure 2.12 The hysteresis loop is distorted by the diamagnetic signal from substrate
and sample holder, and a subtraction is necessary.................................... 52 Figure 2.13 Stripline cavity and required sample locations for measurement of
complex permittivity (axial mid-point) and complex permeability
(adjacent to end plate) [13]. ...................................................................... 54 Figure 3.1 (a) XRD pattern and (b) VSM measurement of Ni nanowire array. ......... 66 Figure 3.2 Permeability spectrum of Ni nanowire array (left) and NiFe nanowire
(right). The black lines are guide for eyes. ............................................... 67 Figure 3.3 Crystal structure (a) and hysteresis loops (b) of CoFe nanowire array .... 68 Figure 3.4 Permeability and loss tangent spectra for Fe50Co50 nanowire. The black
lines are guide for eyes. ............................................................................ 69 Figure 3.5 (a) Top view of an anodized alumina template, and (b) cross-section view
of a Co nanowire array with diameter of 50 nm and inter-pore distance of
90 nm......................................................................................................... 69 x
Figure 3.6 XRD patterns of Co nanowire arrays with different geometries: Sample 1,
d=35 nm, D=60 nm; Sample 2, d=35 nm, D=75 nm; Sample 3, d=50 nm,
D=90 nm. (100) and (110) peaks of the Co hcp structure dominates in all
three samples. ............................................................................................ 71 Figure 3.7 (a)-(c) Hysteresis loops of Co nanowire arrays with applied magnetic field
parallel to the nanowire (black dash line label with ||) and perpendicular to
wire (red solid line label with ). (d) Hysteresis loops (only low field part)
of sample 3 with different maximum applied field along the wire, showing
different stable remanent states. Entire loops are depicted in the insert. .. 73 Figure 3.8 The complex permeability =’-j” as a function of the frequency for Co
nanowire arrays with different geometries. .............................................. 74 Figure 3.9 Hysteresis loops (dashed lines) of Ni90Fe10 nanowire array with different
maximum field parallel to the nanowire and hysteresis loop (solid line)
with field perpendicular to the nanowire. The sample was demagnetized to
its initial state prior to each measurement................................................. 76 Figure 3.10 Dependence of complex permeability =’-j” on frequency for Ni90Fe10
nanowire array with different remanent magnetization. ........................... 78 Figure 3.11 Measured natural FMR frequency as a function of remanent magnetization
normalized to the saturation magnetization. The solid line is the
theoretical calculation based on proposed model. .................................... 79 Figure 3.12 Dependence of ” on the frequency of sample 3 with different remanent
magnetizations. ......................................................................................... 80 Figure 3.13 Measured FMR frequency shift as a function of remanent magnetization
normalized to the saturation magnetization. The solid line is the
theoretical calculation. .............................................................................. 81 Figure 3.14 (a) Calculate the field at point P by integrating contributions from
magnetic charges on both sides of the left wire (b) An array of nanowires
with magnetizations pointing at the same direction .................................. 82 Figure 3.15 Calculated dipolar fields versus n, and n is the number of wire along i axis
in Fig. 3.18 (b). Total number of wires is 6nn. ....................................... 84 Figure 3.16 Better fitting is achieved with the improved model .................................. 87 Figure 4.1 (a) Measured (open square) and calculated (solid line) hysteresis loops of
Ni90Fe10 nanowire array with magnetic field along the wire. The change of
the magnetization can only follow the direction of the arrows on the loop.
When the field is removed at point B, the magnetization returns to B’. If a
positive field smaller than 2Hc is applied at A, the magnetization moves
between A and A’ reversibly. The insert depicts the measured hysteresis
loop with magnetic field perpendicular to the wires (solid circle). (b) A
series of magnetic pulses applied parallel to the Ni90Fe10 nanowires. (c)
The magnetic moment of the nanowire array was measured during the
pulses. The negative pulses lower the magnetic remanent monotonically,
while the positive ones do not change the moment except the 800 Oe and
xi
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
900 Oe pulses. The arrows are guide for the eyes. (d) M-H plot of the
magnetic moment changes under the pulses (solid line). The major loop is
also included for comparison (open spare). .............................................. 94 (a) A family of FORCs for the Ni nanowire array with the applied field
parallel to the wires. The black dots represent the starting point of each
FORC. (b) The corresponding FORC distribution plotted in (HC, HB)
coordinates. The vertical black dashed line indicates the vertical line scan
shown in (c) at HC=750 Oe. (d) Projection of the FORC distribution onto
the HC-axis and Gaussian fit highlighting the mean switching field and its
distribution. ............................................................................................... 97 A novel magnetic field pulse detection scheme. (a) Saturated by applying
a strong positive field. (b) Maximum remanent state after removing the
field. (c) The strongest negative pulse is recorded. (d) Reading the surface
field with a magnetic field sensor to find the remanent moment. (e) Ready
for another measurement cycle. .............................................................. 101 Experimental setup for the demonstration of EMP detector ................... 103 (a)–(c), Three magnetic pulse series with various conditions. (d) the
remanent magnetization read from a Hall probe (blue, green, and red
points) and the remanent magnetization measured from hysteresis loop
(black line). ............................................................................................. 105 Time dependence of magnetization at different remanent state of a
Ni90Fe10 nanowire array. ......................................................................... 106 Magnetic viscosity of Ni90Fe10 nanowire array at different reversal fields.
................................................................................................................. 110 Estimation of surface magnetic field of a NiFe nanowire array in
saturation state. The surface field is in z direction ................................. 110 CoFeB amorphous layers become crystallized using MgO as a template
after annealed in magnetic field .............................................................. 118 Possible electron wave function symmetries in 100 direction [10]. ....... 119 Tunneling density of states in Fe (100)/MgO (100)/Fe (100) junctions for
different Bloch state with k║=0. Upper two graphs are for the parallel state
and lower ones for the antiparallel state [5]. ........................................... 120 Typical structure of an MgO based magnetic tunnel junction (left) and a
hysteretic loop with 300% MR (right). ................................................... 121 Hysteresis loop of a non-patterned MTJ sample annealed at 380 °C for 3
minutes. The arrows represent the direction of magnetic moments in the
four magnetic layers. ............................................................................... 124 Time evolution of TMR in an MgO based MTJ upon annealing. The
measurement is performed at room temperature. The sample is annealed at
360 °C in air [13]. ................................................................................... 125 Two methods to achieve linear and hysteresis free MR loop, (left) free
layer is set perpendicular to the pinning layer due to shape anisotropy;
xii
(right) free layer is composed of superparamagnetic CoFeB nanoparticles.
................................................................................................................. 128 Figure 5.8 Full MTJ structure (left) with a relatively thin 2 nm free layer and a thick
1.7 nm Ru layer. Schematic of a fully patterned MTJ and the four probe
method (right) ......................................................................................... 129 Figure 5.9 TMR ratio and coercivity as a function of annealing time for a single MTJ
junction annealed at 460 ºC .................................................................... 131 Figure 5.10 Measured MR loops of a MTJ junction annealed for different times at 460
°C ............................................................................................................ 133 Figure 5.11 The linear region in MR loops as a function of annealing time. The TMR
ratios are also labeled. ............................................................................. 134 Figure 5.12 Angle definitions used in Eq. 5.5~5.7 ..................................................... 135 Figure 5.13 Measured MR loops of an MTJ junction annealed for 20 minutes at 460
ºC, φ is the angle between the applied magnetic field and the pinning
direction. The solid line is the fitting based on the superparamagnetism
theory. ..................................................................................................... 137 Figure 5.14 Estimated particle volume evolutions during annealing ......................... 138 Figure 5.15 Conductances in parallel and anti-parallel states as a function of annealing
time of the MTJ used in Figure 5.9 annealed at 460 ºC. The inserted
picture shows the I-V curves of another MTJ junction annealed at the
same temperature for 1 minute and 40 minutes. ..................................... 139 Figure 5.16 MR loops at different temperatures shows different MR value and
coercivity................................................................................................. 141 Figure 5.17 XRD measurement of as prepared and annealed (MgO/CoFeB)10
multilayer samples. ................................................................................. 144 Figure 5.18 VSM loops (left) of the 1 hour annealed sample with different angle
between sample and applied field. The definition of the angle and the
direction of the easy axis and hard axis are also shown (right). ............. 145 Figure 5.19 (a) (b) Neutron reflectivity measurement results of spin up neutron and
spin down neutron for as prepared sample and (c) (d) for the sample
annealed for 1 hour ................................................................................. 147 Figure 6.1 Schematic of the rotation design. The attracting forces between the
permanent magnets and soft irons are controlled by rotation. ................ 152 Figure 6.2 Force and torque in z direction as a function of rotating angle. ............. 153 Figure 6.3 Simulated forces on soft irons in z direction when the PMs and soft irons
are facing each other (left), and rotated by 90° (right). .......................... 154 Figure 6.4 Schematic of the hybrid design. When currents are applied, both coils
exert forces on the PM in the same direction. ......................................... 154 Figure 6.5 Simulation result of the hybrid design and a uniform force over 5 mm is
achieved. ................................................................................................. 155 Figure 6.6 Schematic of the electromagnet design. The membrane (purple) can be
attached on the soft iron (green). ............................................................ 156 xiii
Figure 6.7 Simulation result of the electromagnet design. The force is uniform over 5
mm (left) and increases with current density (right) ............................... 157 Figure 6.8 Magnetic field distributions (xz plane) in the previous electromagnet
design without (left) and with (right) soft Fe. The soft iron is far from
saturation. ................................................................................................ 157 Figure 6.9 Improved electromagnet designs with larger coil ................................... 159 Figure 6.10 Relation between the force and displacement of the improved
electromagnet design .............................................................................. 160 Figure 6.11 The improved electromagnet design with 3 corners being cut off (left).
Force in z direction as a function of displacement when the moving soft
iron is center or shifted horizontally (right). Force in x direction is also
shown on the right when the moving iron is shifted horizontally........... 161 Figure 6.12 Force vs. Current Density with displacement of 5mm............................ 162 Figure 6.13 Magnetic field distribution inside the coil from simulation (top) and
measurements (bottom). the origin refers to the center of the coil ......... 163 Figure 6.14 Comparison of the field strength along the axial axis from the center
between measured (left) and simulated results (right) ............................ 164 Figure 6.15 Field strength distributions in the area of interest from the cross section
view of the electromagnet assembly. Magnetic field along the 3 lines were
experimentally measured. ....................................................................... 164 Figure 6.16 Magnetic field comparison in x and z directions between simulation
(line+data) and experiment (scattered data points) with circular wire (217
turns) at 5 A DC ...................................................................................... 166 Figure 6.17 Magnetic field comparison in x and z directions between simulation
(line+data) and measurement (scattered data) with flat wire (237 turns) at
5 A DC .................................................................................................... 167 Figure 6.18 Comparison between simulation and experiment of the force in z direction
for both circular and flat wire. ................................................................ 168 Figure 6.19 Initial magnetization curve of LTV steel and soft iron used in fabricating
the electromagnetic housing (left). Bz on line0 with different simulation
condition (right). ..................................................................................... 169 Figure 6.20 Fz on the moving soft iron under different conditions ............................ 170 Figure 6.21 Geometry of the loop tracer standard sample (left). Measurement of initial
magnetization curve of the standard sample at 50 Hz and 2000 Hz is
shown on the right. .................................................................................. 171 Figure 6.22 Simulated eddy current loss and coil current as a function of time ........ 173 xiv
ABSTRACT
Ferromagnetic nanowire arrays embedded in insulating matrices have attracted
great attention in recent years for their rich physics and potential as sensor and
microwave applications. Magnetic nanowires made of 3d transitional metals or their
alloys have the advantages of high saturation magnetizations, limited eddy current
loss, and guaranteed microwave penetration due to nanometer size. The nanowire
arrays can also have high ferromagnetic resonance (FMR) frequencies due to shape
anisotropy. In this work, the following new phenomena of magnetic nanowire arrays
are demonstrated and explained with a theoretical model.
(1) A simple theoretical analysis indicates that high permeability is possible in
nanowire arrays with the magnetocrystalline anisotropy comparable to the
demagnetization energy and its easy axis perpendicular to the nanowire. With proper
conditions, we have fabricated Co nanowire arrays with a crystalline easy axis
perpendicular to the nanowire. For Co nanowire arrays with certain geometries, high
permeability and low losses have been achieved.
(2) Magnetic materials with tunable FMR are highly desirable in microwave
devices. We demonstrate that the natural FMR of Ni90Fe10 nanowire array can be
tuned continuously from 8.2 to 11.7 GHz by choosing different remanent state.
xv
Theoretical model based on dipolar interaction among nanowires has been developed
to explain the observed phenomena. A double FMR feature caused by dipolar
interaction in magnetic nanowire array was predicted and verified in Co nanowires.
(3) A memory effect has also been demonstrated in magnetic nanowire arrays.
The magnetic nanowire array has the ability to record the maximum magnetic field
that the array has been exposed to after the field has been turned off. The origin of the
memory effect is the strong magnetic dipole interaction among the nanowires. Based
on the memory effect, a novel and extremely low cost EMP detection scheme is
proposed. It has the potential to measure magnetic field pulses as high as a few
hundred Oe without breaking down.
In the proposed EMP detector, a magnetic field sensor is required to measure
the surface field of the magnetic nanowire array. MgO based magnetic tunnel junction
(MTJ) is one type of magnetic field sensors. We investigated the evolution of the
magnetic transport properties as a function of short annealing time in MgO based MTJ
junctions. It is found that the desired sensor behavior appears in samples annealed for
17 minutes. The result can be well fitted by using the superparamagnetism theory,
suggesting the formation of superparamagnetic particles in the free layer during the
high temperature annealing. The control of MTJ properties with annealing time is
desirable in magnetic field sensor productions.
xvi
Electromagnet is one of the most important instruments in the magnetics
research. At the end of this work, an electromagnet design by using electromagnetic
field simulating software is presented.
xvii
CHAPTER 1
INTRODUCTION
Soft magnetic materials are broadly exploited for high frequency applications
from the radio wave to microwave frequency range. In many applications, such as
power transformer, DC-DC converter, patch antenna, etc., high permeability and low
loss are desired. Traditional metal-based materials comprised of lamination or of
ribbon are too lossy for these applications, due to eddy current. Traditional ferrites are
currently employed, but their ferromagnetic resonance (FMR) frequency is low and a
bias field is often required. Conventional composite material with metallic particles
embedded in an insulating matrix has higher resistivity compare to metal (lower eddy
current loss), but its permeability is limited by demagnetizing effect. In order to
explore for high frequency material with better performance, we systematically
studied the permeability spectrum of magnetic nanowire arrays and proved that they
are promising candidates with high permeability and with low loss. We also
demonstrated some interesting properties of magnetic nanowire arrays for their
potential applications in tunable microwave devices and electromagnetic pulse
detector.
Spintronic devices are widely adopted in modern magnetic industry for their
manipulation of the spin of the electron. Among them, magnetic tunnel junction is the
most important device used in magnetic hard drives, magnetic field sensors, and
magnetic random access memories. In sensor application, a linear and hysteresis-free
18
magnetoresistance loop is necessary. In this work, we developed an alternative and
more efficient method to satisfy this requirement.
In this following, we introduce briefly the background of soft magnetic
material development and magnetic tunneling junctions. The thesis outline is
described in the end.
1.1 Soft Magnetic Material
Soft magnetic materials play a significant role in modern societies. From
generators in a hydropower plant to motors inside a household washing machine. Soft
magnetic materials are widely used in both industries and our daily life. The global
market for soft magnetic materials is about 10 billion dollar per year [1]. In general,
soft magnetic materials require high permeability, high saturation magnetization, and
low loss. Material selection for particular application is a balance among those
attributes and cost. In this section, basic concepts and different soft magnetic materials
are briefly introduced. More attentions are focused on soft magnetic materials used in
high frequencies.
Carbon steel, due to its low cost, is used in the motors of consumer products
such as vacuum cleaners, refrigerators, fans and washing machines. In this case, since
consumers pays for electricity, loss is less of a concern. In other applications, one has
to handle loss more carefully, because loss not only brings energy waste but also
deteriorates the overall magnetic properties according to the Kramers-Kronig relations
[1]. In low frequency applications, loss mostly comes from hysteretic loss and eddy
19
currents. Hysteretic loss is proportional to the area enclosed by the DC hysteresis
loop, so very soft materials with low coercivity is favored to lower hysteretic loss [2].
Eddy current losses come from the induced current in metal or alloys under an
alternating magnetic field, which generates tremendous heat due to the Joules effect.
Eddy current losses can be reduced by adopting lamination structures and/or
increasing resistivity of the material. Eddy currents also limit the penetration of an
alternating magnetic flux. Skin depth describes the penetration depth in a material
when B is reduced by 1/e. It is proportional to square root of resistivity and inversely
proportional to square root of frequency and permeability [3]. Laminations of
magnetic material are used to guarantee infiltration of the AC field, where thickness of
sheets is smaller than the skin depth.
Electrical steel is a series of iron dominated alloys which contain a small
amount of Si. The addition of Si increases resistivity so that eddy current losses are
reduced. Si also makes the steel magnetically softer with a smaller coercivity,
resulting in higher permeability and a lower hysteretic loss. However, too much Si
makes the material brittle and difficult to manufacture. Electrical steel is mostly
produced into laminations, which not only assures the penetration of magnetic fluxes,
but also decreases eddy current losses. The direction of B is fixed in some applications
such as transformers, so loss can be further reduced by aligning the magnetocrystalline
easy axis of iron grains (100) in one direction inside the sheet [2].
20
A few other alloys have been broadly exploited due to their unique properties,
though they cost more than electrical steels [4]. NiFe alloys are used when better soft
magnetic performance is required. When Fe content is around 20%,
magnetocrystalline anisotropy and magnetostriction reaches zero. High permeability
can be acquired when Fe is 21.5%, and the alloy is named Permalloy. Supermalloys
with 5% Mo additions can have coercivities as small as 0.002 Oe. Co50Fe50 provides
the highest saturation magnetization (2.45 T) among magnetic materials although less
is used due to the high cost of Co. Amorphous magnetic ribbons produced by meltspinning have high permeability and can be wound into cores for applications up to
100 kHz [1].
At high frequencies, eddy current losses cannot be reduced by laminations,
since the skin depth becomes so small that the lamination thickness either cannot be
reached technically or too expensive. The other way to suppress eddy currents is to
increase resistivity. Soft ferrites are commonly employed at high frequencies due to
their high resistivity. Mn-Zn ferrites are used up to about 1 MHz, and Ni-Zn ferrites
up to 300 MHz or more [1]. At high frequencies, another source of loss is
ferromagnetic resonance (FMR). At resonance, magnetic materials largely absorb
magnetic radiation, leading to huge losses. Therefore, the working frequency of a high
frequency material has to be much lower than the FMR frequency, except that
microwave absorption is desired in some applications, such as stealth materials and
electromagnetic interference shielding. Dictated by Sneok’s limit [2], product of
21
permeability and FMR frequency is a constant which is proportional to the saturation
magnetization. So for materials working at high frequencies, high saturation
magnetization is favored. Unfortunately, soft ferrites have saturation magnetizations
lower than 0.5 T. The demand for both high saturation magnetization and resistivity in
the same material promotes extensive researches in magnetic composite systems,
which basically contain magnetic metal or alloy entities with high saturation
magnetization embedded in an insulating matrix [5, 6]. The insulating matrix
guarantees high resistivity. The magnetic entity can be a particle, flake, or nanowire.
The last one will be explored in detail in chapter 3.
For particle systems, the favored soft magnetic properties of magnetic particles
are severely deteriorated by a demagnetizing effect. In fact, composite materials
containing non-interacting magnetic particles cannot have permeability higher than 3
due to strong demagnetizing field inside the particle. However, when the particles are
reduced to nano-size and the particles are exchange coupled to each other, the
exchange coupling can overcome the demagnetizing field and the magnetic anisotropy
of the individual particles [7, 8]. In order to achieve exchange couplings among
particles, magnetic particles have to reach a certain concentration, which sacrifices
resistivity of the material. Another type of composite material has magnetic flakes
embedded in an insulating matrix [9]. The thickness of flake can be reduced to
submicrons. Sneok’s limit is enhanced in the flake system, where the product of
22
permeability and FMR frequency is increased by  '1 . μ’ is the real part of
permeability.
1.2 Tunneling Junction
Electron spins have been ignored by conventional electronics until the
discovery of the giant magnetoresistance (GMR) effect in 1988 by Fert and Grunberg
[10, 11]. Multilayers composed of repeating ferromagnetic (FM) layers and normal
metal (NM) layers show a few ten percent of resistance changes when the relative
orientation of the magnetic moments in FM layers vary. The effect is over ten times
larger than that of anisotropic magnetoresistance (AMR), which is due to spin-orbital
interaction in the ferromagnetic materials. The GMR effect can be understood using
Mott’s two-current model [1], which neglects spin flip scattering. In this model,
resistances from spin-up electrons R↑ and spin-down electrons R↓ are parallel and
independent from each other. Resistance in parallel states is given by RP1  R1  R1 ,
while in antiparallel state both spin-up and spin-down electrons experience the same
resistance RAP  ( R  R ) / 4 . Then MR is defined as MR 
RAP  RP
. The GMR effect
RP
was quickly commercialized and exploited in hard drive read heads and magnetic field
sensors. In practice, a spin valve structure is adopted [4], where two FM layers are
separated by a NM layer, and one of the FM layers is pinned unidirectionally by an
23
antiferromagnetic layer, while the other FM layer rotates freely with an applied
magnetic field.
Another type of spin dependent transport is tunneling. A magnetic tunneling
junction has two FM layers separated by an insulating layer, typically AlOx or MgO.
Tunneling resistance is high when magnetic moments in the two FM layers are
antiparallel and low when magnetic moments in the two FM layers are parallel. In
1975, for the first time Julliere observed the TMR effect in a Co/Ge/Fe sandwich
structure at a low temperature [12]. Julliere also developed a model to quantitatively
explain TMR effect. In the model, it is assumed that no spin flips during tunneling and
the tunneling probability is simply proportional to the product of the initial and final
density of states on Fermi level for both spin channels. Based on these assumptions,
MR can be calculated as MR 
2 P1P2
, where P1 and P2 are the polarizations of two
(1  P1P2 )
FM layers. Julliere’s model did not consider the symmetry filtering effect of the spinup and spin-down electrons and it is a fair model for the polycrystalline barrier such as
AlOx. In 1995, two groups independently achieved reproducible room temperature
TMR in CoFe/Al2O3/Co and Fe/Al2O3/Fe structures [13, 14]. The maximum MR value
observed in AlOx based junctions is about 80%. Predicted by symmetric filtering
theories [15, 16], over 200% TMR in MgO-based magnetic MTJs has been observed
independently by Parkins and Yuasa in 2004 [17, 18]. In MgO based tunneling
junctions, only electrons with Δ1 symmetry can tunnel through the (100) MgO barrier
in a MTJ with an epitaxial structure, which means the MgO barrier acts as a filter. In
24
Fe based FM layers, electrons with Δ1 symmetry only exist in one spin channel around
the Fermi level, and no Δ1 electrons in the other. Therefore 100% spin polarization can
be achieved in epitaxial Fe/MgO/Fe structures grown in the (100) direction. Due to the
high TMR ratio, MgO based MTJ is currently employed in many applications.
In magnetic hard drives, binary information is stored by millions of bits, each
bit containing several magnetic particles with magnetizations all pointing up or down,
representing “1” or “0”. A read head senses stray fields generated by a bit to
distinguish between up magnetization or down magnetization, and thus reads the
stored binary information. Spin valves based on GMR were implemented in 1997 and
TMR was used in read heads since 2006. Each revolution boosted the growth of
storage density by offering enough signal to noise ratio with a smaller device [1].
In magnetic field sensors, GMR or TMR based sensors can detect magnetic
fields in the range of 10-9~10-3 T. In these applications, the magnetization of free
layers is set to be perpendicular to that of a pinning layer, so a hysteresis free and
linear region can be used for sensing [4].
Another important application of MTJ is magnetic random access memory
(MRAM), which utilizes the high and low resistance states of MTJ to represent “0”
and “1”. It is nonvolatile since the magnetic state does not change when power is off.
In first generation of MRAM, free layer is switched by an orsted field given by a
current line. In currently developing MRAMs, magnetization in free layer is switched
by spin transfer torque (ST-MRAM) [19-21], based on the theory proposed by Berger
25
and Slonczewski [22, 23]. When spin polarized currents enter a ferromagnet with
magnetic moment different from the polarization direction, the current exerts a torque
on the ferromagnet so that the magnetic moment of the ferromagnet tends to align with
the polarization direction. In a ST-MTJ, electrons are first polarized by passing
through the pinning layer, and these polarized electrons exert torque on free layer so
that the magnetic moment in the free layer aligns parallel with the pinning layer.
When the current direction is switched, electrons are polarized by the free layer, then
some of the electrons with a spin antiparallel to the pinned moment are reflected back
from the pinning layer and they apply torque on the free layer moment, so the moment
in free layer aligns antiparallel with the pinning layer. Compared to other memory
types such as DRAM, SRAM and Flash, MRAM has the advantage of short write
times, unlimited reading and writing cycles, no volatility, and radiation hardness.
When a large external field is applied, the spin polarized current can no long
switch the magnetization in free layer, but drives magnetization to process along the
applied field and emit microwave. Nano-oscillators based on spin valve or tunneling
junction can generate microwave with frequency as high as 100 GHz, linewidth as
narrow as 2 MHz, and the frequency can be tuned by current [20].
1.3 Outline of Dissertation
Chapter 1 briefly reviews the development of high frequency magnetic
materials and magnetic tunneling junctions, covering the physics, principles, and
applications. Chapter 2 discusses the experimental techniques used in this dissertation,
26
including magnetic nanowire array synthesis, MTJ fabrication, and various
characterization methods. Chapter 3 first presents the physical principles behind high
frequency magnetic material development. Subsequently, an estimation of
permeability by solving LLG equation provides a guide to tailor magnetic properties
of magnetic nanowire arrays. After study of nanowire array made of different
materials, high permeability with low loss was achieved in Co nanowire arrays. In
Chapter 3, zero field FMR tunability is also demonstrated in magnetic nanowire
arrays. A double resonance feature is predicted and verified. A theoretical model
based on dipolar interactions was established to quantitatively explain the observed
tunability and double FMR features. In chapter 4, an analog memory effect was
demonstrated in magnetic nanowire arrays. The maximum negative field in a series of
magnetic pulses can be memorized as a remanent magnetization in nanowire array. A
novel, low cost and robust electromagnetic pulse detection method was proposed. A
time evaluation of MgO based MTJ with a relatively thin free layer was investigated
upon high temperature annealing in chapter 5. Reduction of MR and coercivity were
observed during annealing and a linear and hysteresis free loop was achieved. The
results can be well fitted by the superparamagnetism theory. Chapter 6 describes two
magnetic field simulation examples by using electromagnetic field simulation
software. One is a design of an electromagnet assembly for an actuator and the other is
a simulation of eddy current loss in a soft magnetic ring.
27
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S. Chikazumi, Physics of Ferromagnetism. Clarendon: Oxford, 1997.
D. M. Pozar, Microwave Engineering: Wiley, 1997.
R. C. O. Handley, Modern Magnetic Materials Principles and Applications.
New York: Wiley, 1999.
C. Brosseau, S. Mallegol, P. Queffelec, and J. Ben Youssef,
"Electromagnetism and magnetization in granular two-phase nanocomposites:
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034301, Feb 2007.
O. Acher and S. Dubourg, "Generalization of Snoek's law to ferromagnetic
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W. Wang, "Fabrication and study of Ni75Fe25-SiO2 granular films for high
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K. Ikeda, K. Kobayashi, and M. Fujimoto, "Multilayer nanogranular magnetic
thin films for GHz applications," Journal of Applied Physics, vol. 92, pp.
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X. K. Zhang, T. Ekiert, K. M. Unruh, J. Q. Xiao, M. Golt, and R. X. Wu,
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M. N. Baibich, J. M. Broto, A. Fert, F. N. Vandau, F. Petroff, P. Eitenne, G.
Creuzet, A. Friederich, and J. Chazelas, "Giant magnetoresistance of
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magnetoresistance at room-temperature in ferromagnetic thin-film tunneljunctions," Physical Review Letters, vol. 74, pp. 3273-3276, Apr 1995.
T. Miyazaki and N. Tezuka, "Giantmagnetic tunneling effect in Fe/Al2O3/Fe
junction," Journal of Magnetism and Magnetic Materials, vol. 139, pp. L231L234, Jan 1995.
W. H. Butler, X. G. Zhang, T. C. Schulthess, and J. M. MacLaren, "Spindependent tunneling conductance of Fe vertical bar MgO vertical bar Fe
sandwiches," Physical Review B, vol. 63, p. 12, Feb 2001.
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2001.
S. S. P. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant, and
S. H. Yang, "Giant tunnelling magnetoresistance at room temperature with
MgO (100) tunnel barriers," Nature Materials, vol. 3, pp. 862-867, Dec 2004.
S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki, and K. Ando, "Giant roomtemperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel
junctions," Nature Materials, vol. 3, pp. 868-871, Dec 2004.
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torques," Journal of Magnetism and Magnetic Materials, vol. 320, pp. 12171226, Apr 2008.
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and Magnetic Materials, vol. 320, pp. 1190-1216, Apr 2008.
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29
CHAPTER 2
EXPERIMENTAL METHODS
2.1 Thin Film Sample Fabrication
2.1.1 Magnetron Sputtering
Magnetron sputtering is one of the most important thin film fabrication
techniques in both industry and fundamental research. All the samples used in chapter
5 are fabricated by this method.
The sputtering process can be simply described as the following. In a chamber
with low Ar pressure, a large voltage is applied between two electrodes. When the
voltage exceeds the breakdown threshold, plasma is formed. Ar ions in the plasma
bombard the negatively charged cathode and generate secondary electrons, which are
accelerated by the electric field and strike on more neutral Ar atoms on the way to the
anode. If the electron energy is low, the Ar atoms are excited into a high energy state
and they return to the ground state by glowing. If the electron energy is high, more Ar
atoms are ionized and they strike on the cathode surface to give rise to the process of
sputtering. Ions bombarded on material surfaces with different energies yield different
results, shown in Figure 2.1. If the ion energy is very low, it simply bounces off the
surface. If the energy is less than 10 eV, the ions are absorbed into the material and its
30
kinetic energy turns into heat. If the energy is very high, above 10 keV, the ions
penetrate deeply into the cathode and change the physical structure of the material.
When the energy of ions lies in between, both processes can happen. Part of the
energy is turned into heat and part of the energy is transferred to the atoms inside the
material. When the energy transfer occurs within several atomic layers from the
surface, the atoms in the cathode are ejected from the surface with an energy of 10~50
eV. When a target material is used as cathode, atoms of the target material can be
deposited on a substrate to form a thin film.
Figure 2.1 Incident ions with different energies leads to different outcome when bombarding on
material surface.
A wide variety of materials can be deposited due to the physics nature of the
sputtering process. For metals, DC sputtering is favored for its high sputtering rates.
For insulating materials, RF plasma must be used. If the target is an alloy or composite
material, the deposit film has a similar composition with the target. The sputtering rate
31
depends on the following: ion flux to the cathode; the possibility that an incident ion
ejects an atom out of the surface; transport of the ejected atom through the plasma.
In magnetron sputtering, a magnetic field is applied by a set of permanent
magnets so that electrons spiral around the magnetic field direction due to the Lorenz
force. The orbital motion of the electron increases the possibility of a collision
between an electron and a neutral atom, thus boosting the ion flux bombarded on the
target surface and also allows lower plasma to form pressure in the chamber. The
magnitude of the magnetic field is a few hundred Oe.
A magnetron sputtering gun with a planar geometry is employed in this study,
shown in Figure 2.2. A set of NdFeB permanent magnets is placed radically
underneath the target so that a toroidally distributed magnetic field is parallel to the
surface of a circular target. The magnetic set consists of a ring magnet and a
cylindrical magnet at the center. The targets are usually hot pressed and sintered. Most
of the power in plasma goes to heat so cooling water is necessary to avoid excessive
heating.
32
Figure 2.2 A schematic diagram of planar sputtering gun
The sputtering chamber used in this study is shown in Figure 2.3. The system
is equipped with a dry diaphrahm-molecular drag pump and a cyropump, which can
provide a base pressure of 8×10-8 Torr. Seven sputtering guns are installed in the
chamber plus an oxygen plasma gun and an ion beam gun. Two DC and one AC
power supplies insures sputtering of both metal and oxides. 10 pieces of sample with
size about 2 inches can be mounted on 10 substrate carriers. A shutter is placed
between the targets and substrates, and the chimneys on the shutter allow desired
target material being sputtered onto the substrates. The rotation of the shutter and
substrate carriers can be controlled by a computer with the Labview program.
33
Figure 2.3 Sputtering chamber used in this study
2.1.2 Ion Beam Etching
Ion beam etching is frequently used in the micro-fabrication process. It shares
the same physical principle with sputtering technique, while the ion energy and ion
flux can be independently controlled. A Kauffman ion source is commonly used to
generate ion beams. A schematic diagram of the ion source is shown in Figure 2.4. A
voltage Vf is applied on the thermionic cathode filament. Electrons boiled off from the
filament fly toward the anode, which is held at a voltage of Vf+Va. The electrons hit
the neutral Ar atoms to ionize them. In order to maintain the plasma and also increase
34
the mean free path of the ions, the pressure is set at around 0.3 mTorr. The Ar ions are
subsequently accelerated by a grid with a voltage Vg and collimated before shooting
toward the target. The ion beam is also neutralized by a neutralizer so that the target
surface is not charged by Ar ions. To increase the ion density, magnetic field given by
a permanent magnet assembly is used in the ion sources. In this work, a Kauffman ion
source (Commonwealth Scientific Inc.) installed in the sputtering chamber is used.
Figure 2.4 Schematic diagram of Kauffman ion source
2.1.3 Photolithography
Photolithography combined with ion beam etching is commonly employed to
pattern desired shapes and structures from a continuous thin film in the
microfabrication process. Photolithography provides a layer of photo resist (PR) to
cover a desired area, and thus other areas can be etched off by ion beams. The PR can
35
be removed by chemicals after etching. A photo mask with a designed pattern is
necessary to transfer the pattern onto the sample. It is usually made of glass or quartz
plated. A typical photolithography process in this study is listed in the following:
1. Positive PR (Shipley S1811) is applied onto the sample by spin coating at a
speed of 4000 rpm.
2. The sample is soft baked on a hot plate for 1 minute at 110 °C. Most of the
solvents are removed during soft baking.
3. Covered by photo masks, the sample coated with PR is exposed to an UV light
(OAI HYBRALIGN SERIES 200) for a few seconds.
4. The sample is immersed into developer (Rohm Haas MF319) for 1 minute and
then washed with DI water. The PR in the exposed area is removed by
developer.
When negative PR (AZ 5214) is used, the PR is first baked at 90 C for one
minute after spin coating. Then the sample is aligned with the mask and exposed to
UV rays for 0.7 seconds. The sample is again baked at 110 C for 1 minute and
exposed under UV rays for 45 seconds without masks. Finally the exposed area is
removed by the developer (AZ 300 MIF).
2.2 Magnetic Nanowire Array Fabrication
A magnetic nanowire array is composed of magnetic nanowires of the same
size embedded in an insulating matrix. A commonly used method to fabricate
36
magnetic nanowire arrays is to electrochemically deposit magnetic materials into an
insulating template, such as anodized alumina templates, track-etched polymer
membranes, and copolymer-based templates [1, 2]. With different templates or
membranes, the diameter of the nanowires can vary from a few nanometers to a few
micrometers. The deposition time determines the length of the nanowire, which
typically ranges from hundreds of nanometers to hundreds of micrometers. This
section first illustrates the synthesis of porous anodized alumina templates and then
explains electrochemical deposition of magnetic materials into the template.
2.2.1 Alumina Template Synthesis
Figure 2.5 shows a typical fabrication process based on the high quality
aluminum foils and SEM graphs of the surface and cross section view of the newly
developed nanowire array. The fabrication conditions are listed in Table 2.1. The
detailed process is described as the following:
1. High purity aluminum foil (Alfa Aesar, 99.99%, 0.1 mm) is degreased in
acetone by sonication.
2. Place the aluminum foil into an anodization cell which contains acid. One side
of the foil contacts the acid. The foil is connected to the positive electrode of a
DC power supply, and the negative electrode is attached to another piece of
aluminum foil, which is immersed in the acid and facing the sample foil. The
37
anodization process is carried out at 1~2 ºC in a refrigerator. The template
thickness depends on the anodization time. The anodizing voltage determines
the inter-pore distance on the template, which is roughly 2.5 nm/V [1].
3. Take out the template from the cell and place it back upside down. Pour CuCl2
into the cell to remove the aluminum metal from the back of the template.
Clean the Cu residual with DI water after the reaction is finished.
4. 6 wt% phosphoric acid is used to etch away the alumina barrier developed
during the anodization on the bottom of the pores and widen the template. This
process is kept at 30 °C.
5. After rinsing the template with DI water, the template is placed into a vacuum
chamber for magnetron sputtering. A Cu layer of 400 nm is deposited on the
back of the template as the working electrode.
6. The magnetic material is electrochemically deposited into the template by
either a constant current or the constant voltage method.
7. The Cu layer, which is the working electrode, is removed by CuCl2.
38
Figure 2.5 Fabrication process of nanowire array. SEM micrographs show the top view of the
Al2O3 template (top left) and the cross-sectional view of nanowire array (bottom right). The
actual devices for anodization and metal deposition only expose one side of the aluminum foil or
AAT template to the solution.
Diameter/inter Acid
Voltage
Concentration
-pore distance
35nm/60nm
Anodizing
Etching time
time
Sulfuric
25 V
0.4 M
12 h
acid
Template
thickness
50 min from ~55 µm
top &1 h from
bottom
35nm/75nm
Oxalic
30V
0.5 M
18 h
acid
30 min both ~35 µm
sides
39
50nm/90nm
Oxalic
40V
0.5 M
18 h
acid
35nm/90nm
sides
Oxalic
40V
0.5 M
18 h
acid
25nm/90nm
Oxalic
40V
0.5 M
18 h
20 min both ~35 µm
sides
Oxalic
46V
0.5 M
12 h
acid
15nm/30nm
30 min both ~35 µm
sides
acid
60nm/105nm
40 min both ~35 µm
40 min both ~25 µm
sides
Sulfuric
10V
1.2 M
12 h
acid
20 min from ~55 µm
top & 20 min
from bottom
Table 2.1 Optimized conditions of the anodization process
In order to apply the nanowire array into practical microwave devices, the
thickness and flatness of the anodized alumina template have also been improved.
This is because in many applications, thick magnetic material is preferred, and the
flatness is crucial for the integration of nanowires into the devices.
To improve the flatness and achieve thick nanowire templates, we greatly
increased the anodization time. It has been observed that electrolyte leakage took
place in the reaction cell when the anodization time becomes longer than 18 hours
(The actual devices for anodization only expose one side of the aluminum foil to the
solution). The acid gradually leaks to the bottom of the aluminum foil through the
edge of the foil while the top of the foil is being anodized. The leaked acid underneath
the aluminum foil anodizes the foil and forms a thin alumina layer at the bottom,
which makes the further etching process less effective (as we mentioned in anodizing
40
process step 4). After a series of tests, we found that this problem can be solved by
replacing the etching CuCl2 solution with HgCl2 solution. The latter can easily etch
Al as well as the thin alumina layer that may form at the bottom. With this newly
developed process, we successfully increased the thickness of the template from 50µm
to about 90µm. The 90 µm template is shown in Figure 2.6 together with a 50µm thick
template for comparison. The new template shows significant improvement in flatness
and robustness than the thinner one.
Figure 2.6 AAT templates with thickness of 90 µm (left) and 50 µm (right), covered with Cu layer
as bottom electrode for nanowire deposition.
2.2.2 Electrochemical Deposition
Magnetic nanowires were deposited with a standard three-electrode
configuration with Pt as the counter electrode. The bath composition and growth
condition is summarized in Table 2.2. A potentiostat (Princeton Applied Research,
Model 263A) was used to provide a constant voltage or a constant current with respect
to a Ag/AgCl reference electrode [3].
41
Nanowire
Growth condition
Bath
Ni90Fe10
–1.2 V
FeSO4∏7H2O (6 g/L), NiSO4∏6H2O (120 g/L) and H3BO3 (45 g/L)
Co
–8 mA
CoSO4∏7H2O (252 g/L), H3BO3 (20 g/L) and NaCl (20 g/L)
Ni
-1.2 V
NiSO4∏7H2O (135 g/L), NiCl2∏6H2O (40 g/L) and H3BO3 (20 g/L)
Co50Fe50
–8 mA
FeSO4•7H2O(120g/l), CoSO4•7H2O(120g/l), H3BO4(30g/l), and
C6H8O6(1g/l)
Table 2.2 Electrochemical deposition conditions of nanowires
2.3 Structural Characterization
2.3.1 X-ray Diffraction
X-ray Diffraction (XRD) is the most commonly used technique that
characterizes the structure of various materials. X-rays have wavelengths around the
order of 1 A, similar to the lattice constant. The electric field component of x-rays
interacts with the electrons in a material and diffraction happens when k  G is
satisfied [4]. k  k s  ki is the difference between scattered wavevector ks and
incident wavevector ki. G is the reciprocal lattice vector. We only consider elastic
scattering, so ks and ki have the same magnitude, as shown in Figure 2.7. In XRD
measurement, one sweeps the angle θ to find diffraction peaks, which satisfy the
condition k  G . Another way to express the diffraction condition is Bragg’s law:
2d sin   n , where λ is the X-ray wavelength and d is the distance between two
adjacent crystallographic planes contributing to the diffraction peak. Once the peak
42
positions are found, together with the XRD data base, the crystallographic structure of
the material can be identified.
Figure 2.7 X-ray diffraction scheme
In our experiments, a Philips θ-2θ diffractometer is used, in which a x-ray is
generated by shooting a beam of fast-moving electrons to bombard a Cu target. XRD
data were collected with CuKα radiation and wavelength of Kα1 and Kα2 are 1.54050 Å
and 1.54434 Å respectively.
X-ray at low angles is used to determine thin film thickness (θ=1°~10°). A
series of peak positions reveals the constructive interference between beams reflected
from the surface of the film and substrate-film interface. Film thickness can be derived
from Bragg’s equation 2d sin   n , now d is the film thickness. If one plots 2sinθ/λ
against n, the slope of the fitting line is film thickness.
2.3.2 Electron Microscopy
Electron microscopy utilizes electrons to illuminate the sample and generate an
image of the microstructures. It shares the same principle with optical microscopy, but
43
has much higher magnification (up to 2,000,000x) due to the short wavelength of
electrons (~0.05 Å) [5, 6].
Scanning Electron Microscopy
A schematic diagram of a typical scanning electron microscope (SEM) is
shown in Figure 2.8 [6]. Electron beams are typically emitted from a tungsten filament
thermionically or by field electron emission, which provides better signal to noise
ratio and spatial resolution. The beam is accelerated by an electric field to boost
kinetic energy thus a short wavelength. It subsequently goes through a couple of
condenser lens to focus to a spot 0.4~5 nm. Pairs of scanning coil deflect the beam in
x and y direction so that it can scan in a rectangular area on the sample surface.
The electron beam interacts with the sample in a teardrop-shaped volume on
the surface. The interaction causes electrons to emit from the surface; high energy
electrons by elastic scattering, secondary electrons by inelastic scattering and also
emission of electromagnetic radiation. All these emissions can be collected by
specialized detectors. The information of secondary or backscattered electrons is
converted to the contrast in the SEM image and the topography of samples can be
resolved with fine detail. The resolution lies between the optical and TEM techniques.
Secondary electrons are more commonly used to form Images. Backscattered
electrons have high-energies due to the reflection or elastic scattering. Heavy elements
back scatter electrons more easily than light elements, so that heavy elements are
44
much brighter in the image. Therefore backscattered electrons are more used to detect
contrast between different elements.
As electrons may accumulate on the sample surface due to the electric field
generated by static charges, the surface of a SEM sample should be conducting and
grounded to avoid image distortion. For insulating samples, a thin layer of Au can be
deposited prior to the SEM test to assure a clear image.
Figure 2.8 Schematic diagram of a typical SEM
Transmission Electron Microscopy (TEM)
The generation, acceleration, and focus of electron beam in TEM are similar to
those of SEM. There are two commonly used modes in TEM operation: diffraction
mode (reciprocal space) and image mode (real space). In the image mode, if the direct
transmitted beam is selected, the resultant image is called a bright-field image; and if
the scattered electrons are selected, it is called a dark-field image. Bright-field
45
imaging is commonly used to image grains and defects in a sample, while dark-field
imaging allows one to link diffraction information with specific regions or phases in
the sample. The TEM set up used in this research work is shown in Figure 2.9.
Figure 2.9 JEOL JEM-3010 transmission electron microscope
Energy Dispersive X-ray Spectroscopy (EDX)
In both SEM and TEM, the bombardment of the energetic electron beams on
the sample surface produces fluorescence x-ray, which is characteristic of the element
in the sample. With an x-ray detector, material compositions can be analyzed. Since
windows in front of the detector absorb low energy x-rays, there is a detecting limit
for light elements with a low atomic number Z. For our system, the limit is at Z=5,
corresponding to boron.
46
2.3.3 Polarized Neutron Reflectivity
The interaction between neutrons and materials is very different from that of xrays or electrons. Neutrons are free of charge so that they can penetrate deep into
materials and interact with nucleus by short range forces instead of electromagnetic
interaction. Neutrons have magnetic moments which enables dipole-dipole interaction
between neutron and unpaired electrons, therefore neutron study can probe magnetic
structure of a material [7-9].
In a polarized neutron reflectivity (PNR) experiment, a beam of neutron is
reflected from the surface of a material. The intensity of the reflected beam is recorded
with respect to different neutron wavelengths and/or incidence angles. By fitting the
result, atomic and magnetic depth profiles of the sample can be evaluated. When the
surface is homogeneous, the angle of the reflected beam is equal to the incident angle
(specular reflection), which is the case in this work. We can decompose the incident
wave vector into two components, one normal to the surface and one parallel. In
specular reflection, only the normal component kz changes due to the potential U (z) in
the material. The potential can be expressed as
2
U ( z) 
N ( z )b( z )
2m
(2.2)
where b is the scattering length of the N constituent nuclei per unit volume. The
reflection process can be approximated by an interaction between neutrons with
 2 k z2
and the potential in Eq. 2.2. Solution of Schrodinger equation gives
energies of
2m
47
reflectance r and thus reflectivity R=|r|2. In the experiment, reflectivity R is measured
with respect to wave vector transfer Qz,
Qz  k zf  k zi 
4 sin 

(2.3)
where α is the incident angle and λ is the neutron wave length. The z-component of the
incident and reflected wave vector iskzi and kzf. Because Qz is the quantum
mechanical conjugate of position z, the reflectivity information R (Qz) can be
transformed into depth profile of b(z), which leads to the structural information of the
material.
In general, reflectivity is 1 up to a critical value of wave vector
transfer Qc  16Nb , which is in the order of 0.01 Å -1. After the critical value, Qz
decreases rapidly. When Qz>>Qc, using Born approximation,
L
1
R  4 4  [( Nb)l  ( Nb)l 1 ] exp(iQz d l )
Qz
l 1
2
(2.4)
where dl is the distance between the top surface of the lth layer and the surface of the
film.
In magnetic materials, potential U has an additional magnetic term originated
from the dipole interaction between neutrons and magnetic atoms,
U ( z)  U n ( z)  U m ( z) 
2
N ( z )b( z )  B  sˆ
2m
(2.5)
where s is the neutron spin operator. The neutron spins can have two directions with
respect to the field applied on the sample. In measurement, the neutron is first
48
polarized by a polarizer and examined by another polarizer after it is reflected. Four
quantities can be measured, R++, R--, R+-, R-+. The latter two represent the spin flipped
during the reflection. In a simple case (in this study), the sample is saturation by the
applied field so that the neutron can be either parallel or antiparallel to the magnetic
moment, and no spin flip happens, so R+-=R-+=0. A measurement example is shown
Figure 2.10. The small oscillation is due to interference between the neutrons reflected
from the film surface and the film-substrate interface. The large peaks in the bottom
graph are Bragg peaks from the periodic structure.
The purpose of reflectivity measurement is to infer an atomic density and
magnetization profile normal to the film surface. The measurement results are usually
fitted with a layer model. The fitting is not unique, but background knowledge of the
specific sample can make the model reliable. The measurement in this study is
performed in the Spallation Neutron Source of Oak Ridge National Lab (ORNL).
49
Figure 2.10 Neutron reflectivity measurement examples. R++ and R-- are measured [10].
2.4 Characterization of Magnetic Properties
2.4.1 Vibrating Sample Magnetometer
Vibrating sample magnetometers (VSM) measure magnetic moments with
respect to magnetic fields, time, or temperature. It was invented in 1955 by Simon
Foner at Lincoln Laboratory at MIT. The sample is driven by an actuator and vibrates
sinusoidally at frequency ω in a direction perpendicular to the applied field, which is
given off by an electromagnet. A pair of pick up coils is fixed on the poles of the
electromagnet.
The
flux
passing
through
the
pickup
coils
is   AH  BM cos t  CM cos 2t  ... . Due to Faraday’s law, an AC voltage at
50
frequency ω is induced in the coil, emf  
d
, which can be measured by the
dt
sensitive lock-in technique. The measured signal is linearly proportional to the
magnetic moment. The system is calibrated with a nickel ball with a known magnetic
moment. The voltage induced by the sample under testing is compared to the signal
given by the nickel standard, thus, the magnetic moment of the sample can be
determined. It should be pointed out that B depends on sample size and position, but it
can be considered as a constant when the sample is centered and fits the sample
holder.
Figure 2.11 A vibrating sample magnetometer (Lakeshore 7404)
VSMs can measure materials in various forms, such as thin films, powders,
plates, or liquids. Before each measurement, the sample needs to be properly centered
by applying a field and finding the minimum magnetic moments in the field direction
51
and the maximum moment in the other two directions perpendicular to the field.
Lakeshore 7404 is used in this thesis, displayed in Figure 2.11. When samples with
very small magnetic moments are measured, the contribution from the substrate and
sample hold needs to be subtracted, illustrated in Figure 2.12 [11].
Figure 2.12 The hysteresis loop is distorted by the diamagnetic signal from substrate and sample
holder, and a subtraction is necessary.
2.4.2 Hysteresis Loop Tracer
The hysteresis loop of a bulk soft magnetic material can not be accurately
measured by VSMs due to demagnetizing effect, and VSMs can only work in DC
magnetic fields. Hysteresis loop tracers measure hysteresis loops of a ring shape
sample at different frequencies without demagnetizing effects [12].
Before measurement, a primary coil and a secondary coil is winded uniformly
around a ring made of the material under test. A current I is applied in the primary coil
to produce a magnetic field H along the ring. H in the unit of A/m can be simply
calculated by
H  N1I / L
52
(2.6)
where N1 is number of turns in the primary coil and L is path length along toroid
circle. The current in the primary coil is determined by measuring the voltage across a
standard resistor. A voltage Vsecond is induced in the secondary coil, Vsec ond  
d
.
dt
Thus Vsecond is picked up by the secondary coil and integrated to determine the
magnetic induction B. B can be expressed by
B
1


Vsec ond dt
N2 A
N2 A 
(2.7)
where Φ is the magnetic flux and A is cross section area of the sample ring. N2 is the
number of turns in the secondary winding. This whole process is controlled by a data
acquisition (DAQ) board on a computer. In practice, a sinusoidal current is used for
the primary coil and the hysteresis loop at that frequency can be measured within a
cycle. In this dissertation, we use a commercial hysteresis loop tracer AMH-401
manufactured by Walker Scientific.
2.4.3 Cavity method
53
Figure 2.13 Stripline cavity and required sample locations for measurement of complex
permittivity (axial mid-point) and complex permeability (adjacent to end plate) [13].
In this study, a stripline cavity is employed to measure the complex
permeability spectrum. This technique is based on the perturbation method analyzing
the standing wave excited in the rectangular cavity. The resonance frequencies of the
standing waves depend on the real part of the permeability or permittivity of the
medium in the cavity. Q factors are correlated with the imaginary part of the
permeability and permittivity which dictates the dissipation properties of the medium.
The sample inserted into the cavity changes the harmonic frequency and Q factor, thus
the permeability and permittivity of the sample can be derived with Waldron’s
perturbation theory [13].
In the stripline cavity, the E component of the microwave is perpendicular to
the center stripe and the H component is along the center stripe. Both fields are
perpendicular to the propagation direction. This allows the anisotropic specimen to be
measured within the cavity, which is not possible in the coaxial airline due to its radial
54
field configuration. The disadvantage of this method is that it can only provide results
at a discreet harmonic frequency, up to 24 harmonics of the base frequency [14, 15].
A 30 cm long stripline cavity with a base resonant frequency of 0.5 GHz
(Damakos Inc.) is used in this work. The stripline cavity is illustrated in Figure 2.13.
The first or fundamental resonance is achieved when the cavity length is equal to a
half-wavelength of the exciting microwave, 0.5 GHz in our case. Additional
resonances occur at harmonic frequencies of the fundamental resonance, i.e. 1 GHz,
1.5 GHz, 2 GHz, etc. Based on the perturbation theory, the dielectric parameters are
derivable only when there is no magnetic field acting on the sample. Similarly, the
magnetic parameters are derivable only when there is no electric field influence.
Therefore, permeability can be measured for all harmonics by placing the sample at
the end of the cavity where the magnetic field is at a maximum and the electric field is
zero. Permittivity is measured only at odd harmonics by placing samples at the center
of the cavity where the electric field is maximized and the magnetic field becomes
zero.
Permeability and permittivity can be calculated by [14]
fs  fe j 1
1
 (  )  C ( r  1) ws hs t s
fe
2 Q s Qe
fs  fe j 1
2
1
 (  )  C ( r  1 
) w s hs t s
fe
r
2 Q s Qe
(2.8)
where fs and Qs are the harmonic frequency and quality factor with the sample in the
cavity and fe and Qe are those of the empty cavity without the sample, ws, hs, ts are the
55
width, height and thickness of the rectangular sample, μr and εr are the complex
relative permeability and permittivity of the sample, and C is a constant related to the
geometry of the cavity design. Calibration needs to be done before each measurement.
The accuracy of the cavity measurement depends on the sample position, size,
geometry and homogeneity, which may violate the assumption of uniform field
distribution in the vicinity of the sample required by the perturbation theory.
Instrument errors also contribute to the inaccuracy, which can be reduced by
averaging and use of a sensitive receiver. When the room temperature and conditions
are kept the same, an overall error of about 10% or less for the permeability can be
achieved with the stripline cavity purchased from Damakos Inc [14].
Reference
[1]
[2]
[3]
[4]
[5]
[6]
[7]
A. P. Li, F. Muller, A. Birner, K. Nielsch, and U. Gosele, "Hexagonal pore
arrays with a 50-420 nm interpore distance formed by self-organization in
anodic alumina," Journal of Applied Physics, vol. 84, pp. 6023-6026, Dec
1998.
H. Masuda, F. Hasegwa, and S. Ono, "Self-ordering of cell arrangement of
anodic porous alumina formed in sulfuric acid solution," Journal of the
Electrochemical Society, vol. 144, pp. L127-L130, May 1997.
T. Ohgai, L. Gravier, X. Hoffer, and J. P. Ansermet, "CdTe semiconductor
nanowires and NiFe ferro-magnetic metal nanowires electrodeposited into
cylindrical nano-pores on the surface of anodized aluminum," Journal of
Applied Electrochemistry, vol. 35, pp. 479-485, May 2005.
C. Kittel, Introduction to Solid State Physics: Wiley, 1995.
JEOL JSM6335F user manual.
"http://en.wikipedia.org/wiki/Scanning_electron_microscope."
J. F. Ankner and G. P. Felcher, "Polarized-neutron reflectometry," Journal of
Magnetism and Magnetic Materials, vol. 200, pp. 741-754, Oct 1999.
56
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
H. Zabel and K. Theis-Brohl, "Polarized neutron reflectivity and scattering
studies of magnetic heterostructures," Journal of Physics-Condensed Matter,
vol. 15, pp. S505-S517, Feb 2003.
M. Vadala, K. Zhernenkov, M. Wolff, B. P. Toperverg, K. Westerholt, H.
Zabel, P. Wisniowski, S. Cardoso, and P. P. Freitas, "Structural
characterization and magnetic profile of annealed CoFeB/MgO multilayers,"
Journal of Applied Physics, vol. 105, p. 113911, Jun 2009.
F. Klose, "Introduction to Polarized Neutron Reflectometry," Oak Ridge
National Laboratory Oct. 13, 2005.
Lakeshore 7404 VSM user manual.
AMH-401 Automatic hysteresis Graph Instruction Manual: Walker LDJ
Scientific Inc. .
C. M. Weil, IEEE Transactions on Microwave Theory and Techniques, vol.
48, 2000.
Cavity measurement manual: Damaskos Inc., 2009.
R. Cao, Doctoral Dissertation, University of Delaware
57
CHAPTER 3
NOVEL MICROWAVE PROPERTIES OF MAGNETIC NANOWIRE
ARRAYS
3.1 Theoretical Background
In order to develop better high frequency magnetic materials, we need to
understand the following physics principles.
3.1.1 Complex Permeability
Under AC magnetic field H  H 0e jt , magnetic induction responses
as B  B0e j (t  ) , where δ is the phase delay caused by loss. Permeability can thus be
expressed as

B B0
B

cos   j 0 sin    ' j "
H H0
H0
(3.1)
where μ' is from the in phase component of B with respect to H, and μ'' is from the out
of phase (90° phase delay) component of B with respect to H. Loss tangent is defined
as
58
tan  
"
'
(3.2)
Power loss of a material with unit volume can be express as:
T
Ploss
T
1
1
1
  H  dB    H 0 cos tB0 sin(t   )d (t )  H 0 B0 sin   f 0  " H 02
T 0
T 0
2
(3.3)
Apparently µ” is proportional to loss. Loss mainly comes from three mechanisms:
hysteretic loss, eddy current, and ferromagnetic resonance. Hysteretic loss is only
important at low frequencies (<10 MHz). It is introduced by irreversible domain wall
movement and/or irreversible magnetization rotation. Since it is proportional to the
area within the hysteresis loop, the hysteretic loss can be reduced by decreasing the
coercivity of the materials. In high frequency range, loss mainly comes from eddy
current and ferromagnetic resonance.
3.1.2 Eddy Current Loss
Vortex currents can be induced in materials with low resistivity by alternating
magnetic field, leading to eddy current loss. From the Maxwell equations, the eddy
current loss of a plate can be expressed as [1]
Peddy  k
B2d 2

59
f2
(3.4)
where d is the thickness of the plate, f is frequency, and ρ is the resistivity of the
material. k is a constant. It suggests that the eddy current loss is proportional to f2 and
B2, and thinner plate with high resistivity lowers the eddy current loss.
3.1.3 Landau-Lifshitz-Gilbert Equation and Ferromagnetic Resonance
Magnetic dynamics is governed by the Landau-Lifshitz-Gilbert (LLG) Equation,
which was introduced by Landau and Lifshitz in 1935:

   
 
dM
 M  H 
M  ( M  H ) (Landau-Lifshitz)
dt
Ms
(3.5)
In 1955, Gilbert modified it with an additional denominator (1+α2):

 

 
dM



M H 
M  ( M  H ) (Landau-Lifshitz-Gilbert)
2
2
dt
1 
(1   ) M s
(3.6)
It is equivalent to the form [1]


    dM
dM
 M  H 
M
dt
Ms
dt
(3.7)
where α is the Gilbert phenomenological damping parameter and γ=28 GHz/T is the
electron gyromagnetic ratio.
When magnetic materials are in the presence of a static magnetic field and
microwave radiation, magnetization of the material will precess around the direction
of the static magnetic field at a certain microwave frequency. This phenomenon is
referred to as ferromagnetic resonance (FMR) and this frequency as resonant
frequency. The static magnetic field is an effective field, which may include an
60
applied magnetic field, anisotropy field, demagnetizing field, and dipolar field. When
FMR occurs, magnetic material will largely absorb microwaves to sustain the
precessional motion of the magnetization.
The Kittel equation derived from the LLG equation describes the FMR
frequency of a uniformly magnetized ellipsoid [1],
res   [ H ex  ( N x  N z ) M s ][ H ex  ( N y  N z ) M s ]
(3.8)
where Hex is a static field, applied externally in z direction; Nx, Ny and Nz are the
demagnetizing factors of the ellipsoid. For a ball, Nx= Ny =Nz=1/3, ωres=γ Hex. For a
plate, res   H ex ( H ex  M s ) when Hex is in plane, and ωres=γ (Hex-Ms) when Hex is
out of plane. For a cylinder (for example a magnetic nanowire), res   ( H ex 
1
Ms)
2
when Hex is applied along the cylinder.
3.1.4 Snoek’s Limit
If we assume FMR is governed by internal magnetocrystalline anisotropy field,
the resonance frequency can be expressed by [1]
res  H a  
61
2 K1
Ms
(3.9)
where Ha and K1 are effective magnetocrystalline anisotropy field and
magnetocrystalline anisotropy constant, respectively. When magnetization rotation
dominates, permeability can be expressed by

2
Ms
3 K1  0
(3.10)
Combine above two equations, and one can have
 rev  
2M s
(3.11)
3 0
which dictates that product of permeability and FMR frequency is a constant
proportional to saturation magnetization. Therefore a limit is set for permeability, and
it is referred to as Snoek’s limit. It suggests high saturation magnetization may lead to
high permeability. In case of thin film or flake, Snoek’s limit is enhanced by a factor
of
  1 [2]
 res (   1) 

2
(4M s )   1
(3.12)
3.1.5 Apparent Permeability
The magnetic field inside a material can be significantly lower than the
external field due to demagnetization effect. Demagnetizing fields exist in samples of
62
finite sizes, leading to an apparent permeability  app 
intrinsic permeability  
B
, which is smaller than
H ex
B
. Using H in  H ex  NM , one can find the relation
H in
 app 

1  N (   1)
(3.13)
where N is the demagnetizing factor along the direction of the applied field. If N=1,
such as the applied field is perpendicular to a plate, no mater how large the intrinsic
permeability is, μapp is always close to 1. For a spherical ball, Nx= Ny =Nz=1/3, μapp
can not exceed 3. Therefore the demagnetizing effect needs to be minimized to
achieve high permeability. One way is to introduce exchange coupling or dipolar
coupling among isolated magnetic objects, for example exchanged coupled magnetic
nanoparticles embedded in insulating materials [3]. Alternatively, one can use
magnetic objects with special shape, thus N=0 in a certain direction, such as wires or
flakes.
3.2 Microwave Permeability of Magnetic Nanowire Arrays
A magnetic nanowire array is composed of magnetic nanowires of the same
size embedded in an insulating matrix. DC magnetic properties of the magnetic
nanowire array have been extensively studied for their potential applications in sensor
and magnetic recordings [4-9]. In recent years, more attention has been focused on the
microwave properties of magnetic nanowire arrays for high frequency applications
63
[10-14]. Magnetic nanowires made of 3d transitional metals or their alloys have,
compared with traditional high frequency ferrites, higher saturation magnetization,
which has potential for higher permeability according to Snoek’s limit. The small
diameter in nanometer limits the eddy current loss and eliminates the skin effect, both
of which commonly exist in metallic systems. In addition, large shape anisotropies due
to the nanowire structure may significantly increase the ferromagnetic resonant
frequency, allowing for a much higher operating frequency in the range of 1~30 GHz.
In this section, we will investigate the permeability spectrum of different magnetic
nanowire arrays by following a simple theoretical argument.
3.2.1 Estimation of Permeability
The easy axis of a single magnetic nanowire depends on its shape anisotropy
and magnetocrystalline anisotropy. We may simply categorize magnetic nanowires
into two groups according to the direction of the easy axis. One has its easy axis along
the wire. Nanowires made with typical soft magnetic materials such as Ni, NiFe, and
CoFe fall into this category. For nanowires with their easy axis perpendicular to the
wire, Co nanowires with strong perpendicular magnetocrystalline anisotropy are an
example.
The LLG equation has been applied to single nanowires to estimate high
frequency permeability. It is assumed that the single nanowire behaves as a macrospin
64
along the nanowire [15]. In the frequency range far from the ferromagnetic resonance,
the real part of permeability can be expressed by
' 
Ms
Ms
2
 Ha
1
(3.14)
where Ms is the saturation magnetization, and Ha is the magnetocrystalline anisotropy
field. The plus and minus signs correspond to the magnetic easy axis parallel and
perpendicular to the nanowire, respectively. The term Ms/2 in the denominator is from
the demagnetization energy of the nanowire. Equation (3.1) suggests that the value of
μ΄ is always less than 3 for negligibly smaller Ha << Ms/2. Therefore, nanowires made
of typical soft magnetic materials such as Ni, FeNi, and FeCo will not show
permeability larger than 3 because of the large effective demagnetization field [16].
On the other hand, Co nanowire array with high perpendicular Ha from the second
category is a suitable candidate.
This argument is rather tentative, since in the real situation, strong dipolar
interactions exist among nanowire, which may lead to results different from the
estimation of a single nanowire. We fabricated and characterized both types of
nanowire arrays to verify the above arguments.
3.2.2 Magnetic Nanowire Arrays with Negligible Magnetocrystalline Anisotropy
First, Ni nanowire arrays were studied. From XRD measurements, Figure 3.1(a)
shows a well crystallized structure of Ni nanowires. The hysteresis loops displayed in
65
Figure 3.1(b) indicate a well defined easy axis along nanowires. The microwave
spectrum was acquired by cavity method without external field at room temperature.
The sample under testing was in an as-prepared state with zero remanent
magnetization. Figure 3.2 (left) shows the frequency dependence of the complex
permeability in Ni nanowire array. Although no clear resonant peak is observed, the
decreasing µ’ and increasing µ” imply that it is reaching the resonant frequency,
which is supposed be around 9 GHz. The real part of the permeability stays close to 2
until the frequency is over 9.5 GHz. Loss increases from 0.035 at 1 GHz to 0.2 at 10
GHz.
0.004
2000
2
(220)
Ni nanowire
1500
1000
(002)
500
0
20
30
40
0.002
Ni nanowire
0.000
H II Wire
H  Wire
-0.002
(011)
50 60
2(deg.)
(b)
)
(a)
Moment (emu/mm
Intensity (a.u.)
2500
70
80
-0.004
90
-10000 -5000
0
H (Oe)
5000
10000
Figure 3.1(a) XRD pattern and (b) VSM measurement of Ni nanowire array.
66
8
4
Ni nanowire
2
0
-2
0
2
4
6
8
10
12
NiFe nanowire
2
0
0
2
4
6
8
10
12
10
12
0
10
Loss Tangent
Loss Tan
Loss Tan
4
-2
0
10
-1
10
-2
10
'
"
6
' & ''
' & ''
8
'
"
6
Loss Tangent
-1
10
-2
0
2
4
6
8
Frequency (GHz)
10
10
12
0
2
4
6
8
Frequency (GHz)
Figure 3.2 Permeability spectrum of Ni nanowire array (left) and NiFe nanowire (right). The
black lines are guide for eyes.
Based on the LLG equation, the calculation of FMR in single nanowire shows
smaller damping constant reduces the loss. Since NiFe alloy has a small damping
constant around 0.01, we synthesized NiFe Nanowire array. Characterization of NiFe
nanowire array will be discussed in next section. High frequency response was tested
by the cavity method at room temperature. Figure 3.2 (right) shows the dependence of
complex permeability on frequency in the range of 1-12 GHz. An FMR peak is
observed at 11.7 GHz, which is very close to predicted value (12.6GHz). The
magneto-crystalline anisotropy of NiFe nanowire is about 1.5 × 103 J/m3, which is
negligible compared to the large shape anisotropy of about 1.3 × 105 J/m3. As
expected, the real part of permeability is about 2 which persist over a broad frequency
up to 9 GHz. The loss remains to be around 0.03~0.04 up to 6 GHz.
To further increase the FMR frequency, Fe50Co50 nanowire arrays were
fabricated because of their higher saturation magnetization. The composition of the
67
nanowires is confirmed by Energy-dispersive X-ray Spectroscopy (EDX). As shown
in Figure 3.3, the XRD study indicates a sharp dominant (110) peak indicating a fully
crystallized structure. An easy axis along the nanowire is apparent in the hysteresis
loops.
0.015
(a)
Intensity (a.u.)
)
(110)
2
1250
Moment (emu/mm
1500
1000
750
0.010
(b)
CoFe
0.005
0.000
-0.005
500
(211)
250
0
20
30
40
50 60
2(deg.)
70
80
H II Wire
H  Wire
-0.010
-0.015
-10000 -5000
90
0
H (Oe)
5000
10000
Figure 3.3 Crystal structure (a) and hysteresis loops (b) of CoFe nanowire array
High frequency responses were measured by the cavity method, and the result
is shown in Figure 3.4. The real part of permeability is gradually increased from 1.9 at
1 GHz to 2.3 at 11 GHz. The permeability spectra implies that the FMR peak is well
above 11 GHz (f = 2Ms  30 GHz in this case). The loss first decreases from 0.06 at
1 GHz to 0.01 at 2 GHz and then slowly goes up to 0.036 at 11 GHz.
68
'
"
4
' & ''
3
CoFe nanowire
2
1
0
0
Loss Tan
10
0
2
4
6
8
10
12
4
6
8
Frequency (GHz)
10
12
Loss Tangent
-1
10
-2
10
0
2
Figure 3.4 Permeability and loss tangent spectra for Fe50Co50 nanowire. The black lines are guide
for eyes.
The permeability study of Ni, NiFe, and FeCo nanowire arrays agrees with the
prediction in the previous section, which stated that µ’ cannot exceed 3 in nanowires
with negligible crystal anisotropy.
3.2.3 Cobalt Nanowire Array with Strong Magnetocrystalline Anisotropy
Figure 3.5 (a) Top view of an anodized alumina template, and (b) cross-section view of a Co
nanowire array with diameter of 50 nm and inter-pore distance of 90 nm
69
From the simple theoretical argument, in order to have high permeability, the
magnetocrystalline easy axis must be perpendicular to the nanowire and the
magnetocrystalline anisotropy must be close to the demagnetization energy. We thus
choose Co, since bulk cobalt has large magnetocrystalline anisotropy of 4.1×105 J/m3
that is comparable to the demagnetizing energy of a Co nanowire of 6×105 J/m3.
Furthermore, the magnetocrystalline easy axis in Co nanowire array can be tuned to be
parallel or perpendicular to the nanowire by selecting different deposition conditions
[17-20].
Three Co nanowire samples with different geometries were studied: (1) pore
diameter d=35 nm, inter-pore distance D=60 nm, volume concentration (

d
( )2 )
2 3 D
V=30%; (2) d=35 nm, D=75 nm, V=20%; and (3) d=50 nm, D=90 nm, V=28%.
Figure 3.5 shows typical SEM graphs of an AAT surface before deposition and a cross
section view of a Co nanowire array. Electron back scattering technique was used in
Figure 3.5 (b). The brighter part represents elements heavier than Al, the Co nanowire
array in this case.
70
Figure 3.6 XRD patterns of Co nanowire arrays with different geometries: Sample 1, d=35 nm,
D=60 nm; Sample 2, d=35 nm, D=75 nm; Sample 3, d=50 nm, D=90 nm. (100) and (110) peaks of
the Co hcp structure dominates in all three samples.
XRD patterns of Co nanowire arrays are illustrated in Figure 3.6 (100) and
(110) peaks of Co hcp structure are observed for every sample. The easy axis of the
magnetocrystalline anisotropy in hcp Co is perpendicular to the nanowire.
DC hysteresis loops with an external applied field parallel and perpendicular to
the nanowire are depicted in Figure 3.7 (a) to (c). When the applied field is parallel to
the nanowire, all three samples show similar behavior. With an applied field
perpendicular to the nanowire, hysteresis loops of sample 1 and 2 indicate an effective
easy axis perpendicular to the nanowire. This is a result of competition among the
shape anisotropy, the magnetocrystalline anisotropy, the Zeeman energy, and the
dipolar interaction. The loop of sample 3 suggests a different magnetic behavior with
a small remanent and wasp-waisted shape. Materials bearing two magnetic phases
with different coercivity and remanent may give this type of wasp-waisted loop.
71
However, the single phase in the X-ray diffraction result makes it highly unlikely.
Another tentative explanation is the strong pinning of the domain walls in this sample,
due to stress or defects. When the magnetic field is large enough, domain walls jump
to a new position resulting in a sharp change in magnetization [21]. However, there
was no change in the hysteresis loop after sample 3 was annealed at 500 °C for an
hour in an H2 gas, suggesting the domain wall pinning is unlikely to be a cause.
Another possible reason for this wasp-waisted shape is the changing of magnetization
axis from parallel to the nanowire in a low field to perpendicular to the nanowire in a
high field. This is probable since the dipolar interaction is strong in the nanowire and
is a function of the applied field. The change between the two states gives rise to the
steep transition in the loop. This argument is supported by the following tunable FMR
studies.
72
Figure 3.7(a)-(c) Hysteresis loops of Co nanowire arrays with applied magnetic field parallel to
the nanowire (black dash line label with ||) and perpendicular to wire (red solid line label with ).
(d) Hysteresis loops (only low field part) of sample 3 with different maximum applied field along
the wire, showing different stable remanent states. Entire loops are depicted in the insert.
Figure 3.8 shows the complex permeability =’-j” as a function of the
frequency for as-prepared Co nanowire arrays at room temperature. No external field
was applied during the cavity measurement. Ferromagnetic resonance effects are
observed in all three samples. The resonance peaks are located at 9 GHz, 8.5 GHz, and
6.5 GHz respectively, much lower than other reported results [10]. This is because the
73
easy axis of the magnetocrystalline anisotropy is perpendicular to the nanowire and
competes with the shape anisotropy. As a result, the effective anisotropy field is
reduced, leading to lower resonant frequencies.
Figure 3.8 The complex permeability =’-j” as a function of the frequency for Co nanowire
arrays with different geometries.
Sample 1 and sample 2, with the same pore diameter, have similar
permeability spectra. The FMR frequency shifts slightly from 9 GHz toward 8.5 GHz
when the inter-pore distance increases from 60 nm to 75 nm. The reduction of dipolar
interactions among nanowires, due to increasing inter-pore distance, implies the
change in dipolar interaction has less of an effect on resonant frequencies than from
the change in wire diameter. The value of ’ for sample 1 is about 2.4 in the offresonance frequency range below 6 GHz, slightly higher than that for sample 2. This
is because a smaller inter-pore distance gives a higher volume concentration of Co,
which increases ’. Loss tangents of sample 1 and 2 are at 0.1 levels below 6 GHz.
74
Sample 3 has a similar volume concentration to sample 1, but has a larger pore
diameter and inter-pore distance. It has been reported that Co nanowire arrays with
different pore diameter have different crystalline anisotropies [22]. The low resonant
frequency of 6.5 GHz can be attributed to the change in crystalline anisotropy in
sample 3. The value of ’ gradually increases from 3.5 at 1 GHz to 4.8 at 4.5 GHz
before it reaches the resonance. The loss tangent remains around 0.045 between 1
GHz and 4.5 GHz. Compared to samples 1 and 2, this sample shows a significant
improvement in ’ and magnetic losses.
These results verify the argument in the previous section that, in order to have
high permeability, the magnetocrystalline easy axis must be perpendicular to the
nanowire and the magnetocrystalline anisotropy must be near the demagnetizing
energy.
3.3 Tunable Double Ferromagnetic Resonance
In the previous sections, we studied the permeability spectrum of different
magnetic nanowire arrays by cavity method and FMR are observed. All the FMR
measurements were performed on as-prepared samples with zero remanent
magnetization along wire direction. In this section, we will focus on the FMR property
of magnetic nanowire arrays in remanent states. A tunable double resonant feature was
observed and this new feature has potentials in novel microwave devices.
75
3.3.1 NiFe Nanowire
Figure 3.9 shows hysteresis loops of Ni90Fe10 nanowires that were exposed to a
different maximum field parallel to the nanowires (dash lines). The hysteresis loop
with the field perpendicular to the nanowires is also shown (solid line). Every loop
measurement was performed after the sample was demagnetized in an AC magnetic
field parallel to the nanowire. This procedure ensures the same initial state with zero
magnetic moment along the nanowire direction. The loop with a maximum applied
field of 1 T along the nanowire indicates a well-defined easy axis parallel to the
nanowire due to the shape anisotropy [15]. With different maximum applied fields
changing from 1 T to 1250 Oe, sample shows different remanent magnetizations from
0.54 Ms to 0.09 Ms, respectively, where Ms is the saturation magnetization. However,
the coercivity remains the same around 1100 Oe.
Figure 3.9 Hysteresis loops (dashed lines) of Ni90Fe10 nanowire array with different maximum
field parallel to the nanowire and hysteresis loop (solid line) with field perpendicular to the
nanowire. The sample was demagnetized to its initial state prior to each measurement.
76
Figure 3.10 shows the dependence of complex permeability =’-j” as a
function of the frequency for Ni90Fe10 nanowire arrays with different remanent
magnetizations at room temperature. Prior to each measurement, the sample was first
demagnetized as described above, and then magnetized along the wire with different
maximum fields to obtain the desired remanent magnetization according to the
hysteresis loops shown in Figure 3.9. No external field was applied during the
permeability measurement. As shown in Figure 3.10, the ferromagnetic resonance
effects are observed in all cases, with resonant frequency monotonically increasing
with decreasing remanent magnetization. The resonance frequency as a function of
remanent magnetization is plotted in Figure 3.11, where a linear behavior is apparent.
These results indicate that magnetic history greatly affects the zero field resonance
frequency, different from other reports [10]. The resonant frequencies with different
remanent magnetizations remain the same after three months, indicating good stability
of the samples.
It should be pointed out that the FMR line width of Ni90Fe10 nanowire arrays
increases with resonance frequency. There are three major effects contribute to the
FMR line width of the nanowire array in this case. First, it is reasonable to consider
that demagnetizing field from the magnetostatic interaction among nanowires (i.e.
Hstatic) has larger distribution at higher remanent state, and thus broader FMR peaks.
So the FMR line width would decrease with increasing frequencies. Second, by
solving LLG equation, FMR line width of a single nanowire can be expressed as 2f res ,
77
where  is the damping constant and fres is the resonance frequency. It shows that the
FMR line width naturally broadens when resonance frequency increases. Third, size
distribution of nanowires further broadens the resonance line width, but this
distribution is not frequency dependable. The trend of the line width change depends
on the competition between the first two effects. The observed decreasing FMR line
width with increasing remanent magnetization implies that the second effect
dominates in this sample.
Figure 3.10 Dependence of complex permeability =’-j” on frequency for Ni90Fe10 nanowire
array with different remanent magnetization.
78
Figure 3.11 Measured natural FMR frequency as a function of remanent magnetization
normalized to the saturation magnetization. The solid line is the theoretical calculation based on
proposed model.
3.3.2 Co Nanowire
The same experiment was performed on all Co samples by magnetizing the
samples with different magnetic fields that were subsequently removed. Only the
FMR in sample 3 (d=50 nm, D=90 nm, V=28%) can be tuned. Figure 3.7(d) shows
hysteresis loops of sample 3 that were exposed to different maximum fields parallel to
the nanowires. Every measurement was performed after the sample was demagnetized
in an AC magnetic field parallel to the nanowires. The remanent magnetization
changes from 0.085 Ms to 0.012 Ms when maximum applied field varies from 1 T to
1.5 kOe. Prior to each cavity measurement, the sample was first demagnetized again
and then magnetized along the wire with a different maximum field to obtain the
desired remanent state according to the minor loops in Figure 3.7(d) ” as a function
of the frequency with a different remanent state is shown in Figure 3.12. No external
79
field was applied during the cavity measurement. FMR is observed in all cases, with
resonant frequencies monotonically increasing from 4.5 GHz to 6.5 GHz with
decreasing remanent magnetization. The magnitude of the peak increases too. The
resonance frequency changes as a function of the remanent magnetization as plotted in
Figure 3.13. Interestingly, a small peak appears at 9 GHz and gradually shifts to
higher frequencies when the remanent magnetization increases.
Figure 3.12 Dependence of ” on the frequency of sample 3 with different remanent
magnetizations.
80
Figure 3.13 Measured FMR frequency shift as a function of remanent magnetization normalized
to the saturation magnetization. The solid line is the theoretical calculation.
3.4 The Origin of Tunability and Double FMR
Studies suggest that, in most cases, individual nanowires only have one
magnetic domain (single domain), meaning that each nanowire is like a single bar
magnet with a north and a south pole. In a non-rigorous way, each nanowire can be
viewed as a magnetic dipole. When two magnetic dipoles are close to each other, there
is an interaction between them, referred to as a dipolar interaction which is longranged in nature. Consequently, when millions of magnetic nanowires are assembled
together, dipolar interactions appear among nanowires. The magnetic field associated
with this interaction is the dipolar field. In this section, a theoretical model based on
dipolar interaction is proposed to explain the observed FMR tunability and double
resonance. The magnitude of the dipolar field is calculated and it depends on the
material and size of the nanowire, and the separation between the nanowires.
81
3.4.1 A Dipolar Interaction Model
Figure 3.14(a) Calculate the field at point P by integrating contributions from magnetic charges
on both sides of the left wire (b) An array of nanowires with magnetizations pointing at the same
direction
In order to explore the origin of tunability and double FMR, a model was
developed to study the magnetostatic interaction among nanowires. The model is
based on two assumptions. First, each nanowire is a single-domain cylinder with
uniform magnetization pointing up or down along the wire due to the large shape
anisotropy. Because of this large shape anisotropy, other anisotropies are negligible.
In this case, the zero field resonance frequency fres can be predicted by the Kittel
equation (3.8) with addition magnetostatic interaction term Hstatic,
f res   H static  H ex  ( N x  N z ) M s )( H static  H ex  ( N y  N z ) M s )
(3.15)
where Nx, Ny and Nz are the demagnetizing factors of a single nanowire that is parallel to the z direction.
Second assumption is that the number of nanowires with up magnetization (N↑) and down
magnetization (N↓) is determined by the total magnetization M (H), i.e. (N↑-N↓)/(N↑+N↓)=M (H)/Ms.
82
At zero magnetic field, M (H) reduces to remanent magnetization. This assumption is supported by the
magnetic force microscopy measurements for different remanent states of Ni nanowires [15]. Based on
this assumption, the wires switched by the external field will be randomly distributed among all the
nanowires.
According to the first assumption, magnetostatic fields given of by a single
nanowire can be calculated by integrating contributions of magnetic charges on both
sides of the wire, as shown in Figure 3.14(a).
H  M s r 2 L
1
3
L2
(R  ) 2
4
(3.16)
2
where r, R, and L are the radius, inter-pore distance, and length of the nanowire,
respectively. Shown in Figure 3.14 (b), assuming all the nanowires form a perfect
hexagonal array, when the magnetizations of all nanowires are aligned in one
direction, one can find the total magnetostatic field Hstatic by adding the field from all
nanowires. Due to the symmetry in nanowire array, Hstatic is along the wire axis and
can be written as
n
n
H static  M s    M s  6r 2 L
i  0 j 1
1
2
[(i 2  ij  j 2 ) R 2  L
4
]
3
(3.17)
2
where i, j are the coordinates of nanowires and the total number of nanowires is 6nn.
 is defined as a geometric factor. When n increases, Hstatic gradually saturates,
displayed in Figure 3.15.
83
2500
Hdip(Oe)
2000
108 Nanowires
2
0.6*0.6mm sample
1500
R=60nm
L=17um
Ms=0.8T
1000
500
r=17.5nm
0
1000
2000
3000
4000
5000
Number of n
Figure 3.15 Calculated dipolar fields versus n, and n is the number of wire along i axis in Fig. 3.18
(b). Total number of wires is 6nn.
Eq. 3.17 indicates that the Hstatic is only determined by the magnetization of the
sample and template geometry. Based on our second assumption, the Hstatic (0) in zero
magnetic fields can be written as
H static (0)  M r  
(3.18)
where Mr is the remanent magnetization that is achieved by removing the field from
different magnetized state. With this term and the fact that the demagnetizing factor in
Kittel equation is 0 along the wire and 0.5 perpendicular to the wire due to the high
aspect ratio of nanowires, the resonance frequency fres, in zero external fields can be
expressed as
f res   ( H static (0) 
1
1
M s )   ( M r   M s )
2
2
84
(3.19)
According to this equation, a linear behavior between fres and Mr is expected. Shown
in Figure 3.11, the fitting by Eq. (3.19) agrees very well with the experimental data.
The value of  is 3.79. Saturation magnetization is 0.8 T and no other parameter was
used in the fitting. The positive and negative signs of Hstatic (0) come from the fact
that, based on the first assumption, the sample is composed of two groups of
nanowires with magnetization pointing up or down. They are either parallel or antiparallel to the static field. Therefore Eq. 3.19 predicts another set of resonances at
higher frequencies corresponding to the positive sign. Although we are not able to
observe both resonant peaks in Ni90Fe10 nanowire array due to the limited frequency
range in our instrument, two sets of resonance peaks appear in the 3rd sample of Co
nanowire arrays.
In Figure 3.12, when the main resonance peak shifts toward a lower frequency,
a small resonance peak gradually shows up and moves toward the high frequency
regime. For the major peaks, after applying the same theory, the FMR frequency shift
in Co nanowire arrays can be expressed as
f res  M r 
(3.20)
The linear relation between Δfres and Mr according to Eq. (2) is plotted in Figure 3.13
(solid line). The experimental data and the theoretical calculation share the same
trend, suggesting a large amount of magnetic moments are indeed parallel to the wire
in a low field. This observation also supports our earlier explanation on the waspwaist shaped hysteresis loops (Figure 3.7c). The theoretical model is based on the
85
assumption that the shape anisotropy dominates and the easy axis is along the wire. In
Co nanowires, the situation is complicated by the strong perpendicular
magnetocrystalline anisotropy. At remanent states, not all magnetic moments are
along the wires, causing the discrepancy observed in Figure 3.13. For sample 1 and 2,
no tunable FMR is observed because most of the moments are perpendicular to the
wire at remanent states, as indicated from the hysteresis loops in Figure 3.7(a) and (b).
3.4.2 Model Improvement
In the above model, only the dipolar interaction in the direction along
nanowires was considered by adding an extra static field term into the Kittel equation.
A dipolar field in the perpendicular direction exists when the magnetizations are
processing under microwave field. A more precise description should also include the
dipolar interactions perpendicular to the nanowire. Since there are two groups of
nanowires with magnetizations pointing either up or down and process at the same
time, the perpendicular field acting on a single nanowire in one direction is
contributed by both groups of nanowires. The Kittel equation is not valid any more.
The resonance frequency needs to be derived from the very beginning, which
composed of two coupled LLG equations,
dM 
 dM 

 dt  M   H eff   M M   dt
s
 dM
dM 



M 
 M   H eff  
 dt
Ms
dt
86
(3.21)
where Heff includes microwave field, external field, demagnetizing field, crystal field,
dipolar field along the nanowire and dipolar fields along x and y directions,
1
1

 H eff   hrf xˆ  [ H ex   (n  n ) M s ]zˆ  2 (m x  n m x  n m x ) xˆ  2 (m y  n m y   n m y ) yˆ

1
1
 H eff   hrf xˆ  [ H ex   (n  n ) M s ]zˆ  (m x  n m x  n m x ) xˆ  (m y  n m y   n m y ) yˆ
2
2

(3.22)
The resonance frequency can be derived as
 res   [ H ex 
M
(5n  4  4   n 2  2 )]
4
(3.23)
The experimental result in Figure 3.11 is fitted again by Eq. 3.23, illustrated in Figure
3.16, and a better fitting is achieved.
Figure 3.16 Better fitting is achieved with the improved model
3.4.3 Potential Application
The FMR tunability study indicates that the zero field resonance frequency
depends on not only the saturation magnetization but also on the remanent
87
magnetization. The latter can be tuned with magnetizing fields. Due to the relatively
high coercivity, the designed remanent states with different natural resonance
frequencies remain stable and therefore, have the potential to be used in band stop
filter or other microwave devices [23-25]. Since, traditionally, the working frequency
of a microwave device can be changed by applying an external field; one particular
advantage of the tunability is that no external field is required during the operation.
The model and conclusion developed here should be applicable to nanowires with
other magnetic materials.
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A. Encinas, L. Vila, M. Darques, J. M. George, and L. Piraux, "Configurable
multiband microwave absorption states prepared by field cycling in arrays of
magnetic nanowires," Nanotechnology, vol. 18, p. 065705, Feb 2007.
90
CHAPTER 4
MEMORY EFFECT IN MAGNETIC NANOWIRE ARRAY
4.1 Memory Effect
Magnetic materials are widely used for information storage due to their large
capacity and low cost [1]. The storage medium technologies have evolved from
analog recording with magnetic tapes to high fidelity digital recordings with magnetic
hard disks. Nevertheless, both techniques use a magnetic medium consisting of
magnetic particles, whose sizes have also evolved from micrometers in magnetic tapes
to nanometers in modern hard disks. In analog, recording signals are converted into
magnetic fields which change the magnetization of a group of magnetic particles (bit).
The magnetization variations represent the stored information which can subsequently
be read out. The magnetization, and therefore the stored information, could be
changed by an external magnetic field and/or thermal effects. In digital recording, the
bit magnetization can be aligned either left or right in a parallel recording or up and
down in perpendicular recording [2]. The information is stable as long as the medium
is not subject to a magnetic field higher than the coercivity, or a temperature higher
than the superparamagnetic limit, of the constituent magnetic particles. To have a
clear “bit” information, it is advantageous to minimize the dipolar interaction among
91
magnetic particles, which is typically achieved by creating boundaries between
particles. Since the magnetic dipolar interaction exists in magnetic materials, and is
particularly pronounced in a collection of magnetic entities such as magnetic particles
and nanowires, it is scientifically interesting to question whether such a degree of
freedom can be controlled and used to create additional memory functions. To answer
this question, one needs a magnetic system with a sizable and preferably controllable
dipolar interaction. The magnetic nanowire array becomes an ideal system for this
purpose [3-6].
In a magnetic nanowire array, millions of nanowires share the same size and
are well organized in an insulating Al2O3 matrix. Nanowire size and interpore distance
can be controlled by fabrication process. When magnetocrystalline anisotropy is
negligible, the magnetization direction of nanowires is preferably aligned along the
nanowires due to shape anisotropy, which is the case in this chapter. When nanowires
are very close to each other (small interpore distance), dipolar interactions play a
significant role in the magnetic behavior of the nanowire array, leading to rich
physical phenomena and great application potentials [7-9]. In the previous chapter, we
have demonstrated that the dipolar interaction among magnetic nanowires can provide
a zero field FMR tunability, which has potential applications in tunable microwave
devices. A double FMR feature caused by the dipolar interaction in a magnetic
nanowire array was also predicted [10] and verified [11-14]. In this chapter, we
demonstrate how dipolar interactions can induce an analog memory effect in magnetic
92
nanowire arrays. Through this effect, the magnetic nanowire array has the ability to
“memorize” the maximum magnetic field that the array has been exposed to, after the
magnetic field has been turned off. A novel, low cost and robust electromagnetic pulse
detecting method is proposed based on this memory effect.
4.1.1 Demonstration and Irreversibility
Nanowire arrays of Ni90Fe10, Ni, and Co50Fe50 were synthesized by
electrodepositing magnetic metals into anodized alumina templates. The diameter,
center-to-center interpore distance, and length of the nanowires are 35 nm, 60 nm, and
30 μm respectively. Figure 4.1(a) shows the hysteresis loop of Ni90Fe10 nanowire array
with a magnetic field parallel to the wire (open squares). The coercivity is about 1080
Oe. The loop with the field perpendicular to the wire is shown in the inset. It can be
clearly seen that a well defined easy axis exists along the wire axis due to the
dominant shape anisotropy.
93
Figure 4.1(a) Measured (open square) and calculated (solid line) hysteresis loops of Ni90Fe10
nanowire array with magnetic field along the wire. The change of the magnetization can only
follow the direction of the arrows on the loop. When the field is removed at point B, the
magnetization returns to B’. If a positive field smaller than 2Hc is applied at A, the magnetization
moves between A and A’ reversibly. The insert depicts the measured hysteresis loop with
magnetic field perpendicular to the wires (solid circle). (b) A series of magnetic pulses applied
parallel to the Ni90Fe10 nanowires. (c) The magnetic moment of the nanowire array was measured
during the pulses. The negative pulses lower the magnetic remanent monotonically, while the
positive ones do not change the moment except the 800 Oe and 900 Oe pulses. The arrows are
guide for the eyes. (d) M-H plot of the magnetic moment changes under the pulses (solid line).
The major loop is also included for comparison (open spare).
The memory effect was demonstrated using a vibrating sample magnetometer.
The Ni90Fe10 nanowire array was saturated along the wire prior to the measurement.
The magnetic moment of the array was monitored as a series of magnetic field pulses
were applied parallel to the nanowires. Figure 4.1(b) displays the series of magnetic
pulses with different magnitudes and directions. The corresponding change of the
magnetic moment is illustrated in Figure 4.1(c). We find that the magnetic moment
decreases monotonically with the augmenting magnitude of the negative pulses; in
contrast, the moment remains the same after the positive pulses except for the 800 Oe
and 900 Oe pulses which will be explained later. This demonstrates that the pulse with
the maximum magnetic field in a negative direction is recorded in the magnetic
94
nanowire array. The result is also plotted in the M-H graph, displayed in Figure 4.1(d)
with the major loop. Similar properties are also observed in Ni and Co50Fe50 nanowire
arrays.
This phenomenon is attributed to the dipolar interactions among the nanowires.
In the previous chapter, we proposed a theoretical model based on two assumptions.
First, each nanowire is a single domain cylinder with a uniform magnetization
pointing up or down parallel to the wire. The second assumption is that the number of
nanowires with up magnetizations (N↑) and down magnetizations (N↓) is determined
by the total magnetization M (H), i.e. (N↑-N↓)/(N↑+N↓)=M (H)/Ms, where Ms is the
saturation magnetization. According to these assumptions, the dipolar field among the
nanowires can be written as [10]
H dipole ( H )  M ( H )  
(4.1)
where Hdipole and H are the dipolar field among the nanowires and the applied field,
respectively. β is a geometric factor, which depends only on the geometry of the
nanowires including their diameter, length, and separation.
Based on this model, when the positive applied field is reduced from the
saturation state, the first switching happens when Hdipole+H exceeds the switching
field of a single wire, Hsw. Subsequently, the magnetization M (H) decreases by a
small amount, and so does the dipole field Hdipole, according to Eq. (4.1). The
switching stops when Hdipole + H is decreased below Hsw. A stable state is reached at
the following condition
95
H dipole  H  H sw
(4.2)
The hysteresis loop can be reconstructed from Eq. 4.2 after substituting the Hsw by the
coercivity Hc, shown in Figure 4.1(a) (solid line). It can be inferred from this
argument, that the magnetic moment of the nanowire array remains unchanged as long
as the equation
H dipole  H  H sw
(4.3)
is satisfied. Hence, the change of the magnetization on the hysteresis loop is
irreversible at descending field directions below the saturation field, as indicated with
arrows in Figure 4.1(a). For example, if the sample is at state A, the magnetization
will change to B in a negative field and return to state B’ once the field is removed.
On the other hand, if the sample is at state A and subject to a positive field (along the
AA’ line), the sample will return to state A upon removal of the field reversibly as
long as Eq. 4.3 is satisfied. Therefore, a memory effect exists in the magnetic
nanowire array as there is a one-to-one correspondence between the remanent and the
negative field the sample was exposed to, as shown in Figure 4.1(a). In other words
the sample memorizes the maximum negative field in terms of remanent
magnetization. The memory remains provided the magnitude of a positive field does
not violate Eq. 4.3. In using Eq. 4.3, one typically uses the coercivity to represent the
switching field. It should be emphasized that there is local variation in switching fields
spread around the coercivity. Therefore, if the positive field pulse is close to the
coercivity, one must be careful in using Eq. 4.3. For example, as illustrated in Figure
96
4.1(b) and (c), the magnetic moment changes after the 800 Oe and 900 Oe pulses
applied in a positive direction (H>0). The dipolar field in this case is antiparallel to the
positive pulses, therefore H dipole  H is smaller than Hc=1080 Oe, and the magnetic
moment should stay unchanged, contradictory to the experimental observation. Such a
discrepancy is due to the distribution of the switching fields.
4.1.2 Switching Field Distributions in Magnetic Nanowire Array
Figure 4.2 (a) A family of FORCs for the Ni nanowire array with the applied field parallel to the
wires. The black dots represent the starting point of each FORC. (b) The corresponding FORC
distribution plotted in (HC, HB) coordinates. The vertical black dashed line indicates the vertical
97
line scan shown in (c) at HC=750 Oe. (d) Projection of the FORC distribution onto the HC-axis and
Gaussian fit highlighting the mean switching field and its distribution.
To further probe the interactions, switching field, and switching field
distributions of the nanowires, first-order reversal curve (FORC) [15-19]
measurements are performed on the Ni nanowire array. FORC measurements proceed
as follows: After positive saturation, the applied field is reduced to a given reversal
field, HR. From this reversal field the magnetization is then measured back towards
positive saturation, thereby tracing out a single FORC. This process is repeated for a
series of decreasing reversal fields thus filling the interior of the major hysteresis loop.
As shown in Figure 4.2(a), under increasing applied magnetic fields, each of the
FORCs traverses horizontally before conforming onto the major loop of the Ni
nanowire array; the stacking of the FORCs leads to the one-to-one correspondence
between the reversal field and the remanent magnetization.
The FORC distribution is then defined as a mixed second order derivative of
the normalized magnetization:
 (H , H R )  
1 2M (H , H R ) / M S
2
HH R
(4.4)
For our purposes here, the FORC distribution is plotted in (HC, HB) coordinates, where
HC is the local coercive field and HB is the local interaction or bias field. The
transformation from (H, HR) coordinates is accomplished by a simple rotation of the
coordinate system defined by: HB=(H+HR)/2 and HC=(H-HR)/2.
The FORC
distribution of the Ni nanowire array shown in Figure 4.2(b) is dominated by a broad
98
vertical ridge that runs parallel to the HB-axis and indicates the presence of strong
demagnetizing dipolar interactions. A line scan, indicated in Figure 4.2(b) with a
vertical dashed line, through this ridge is shown in Figure 4.2(c). The ridge begins to
deviate from zero at HB~2000 Oe, which indicates the maximum dipolar field, and is
consistent with a calculated value of 1830 Oe from Eq. 4.1. Furthermore, the FORC
analysis allows the switching behavior to be separated from the dipolar broadening.
We find that the vertical ridge is centered at HC~750 Oe, the coercivity of the major
loop. Quantitative analysis of the switching behavior is best illustrated by integrating
horizontal line scans, known as a projection along the HC-axis d/dHC, as shown in
Figure 4.2(d) (solid squares). A Gaussian fit of this FORC projection shows a peak at
758 Oe, with a full width at half maximum (FWHM) of 420 Oe. The peak location
indicates the mean switching field while the FWHM is a direct quantitative measure of
the distribution of switching fields among the ~109 nanowires measured. As there are
finite fractions of nanowires with switching fields less than 750 Oe, the Hsw in Eq. 4.3
is no longer a single value, but a distribution. Thus deviations from Eq. 4.3 occur first
in those wires. This can be clearly seen in a family of FORC curves in Figure 4.2(a) as
the individual FORCs begin to turn upward before reaching the ascending-field branch
of the major loop. The switching field distribution, which may be due to small
variations in wire length, diameter, etc., ultimately limits the working range of the
envisioned magnetic field pulse sensor.
99
4.2 Electromagnetic Pulse Detector
4.2.1 Proposed EMP detector
Based on the memory effect, we propose an electromagnetic pulse (EMP)
detection method. An EMP generated by nuclear or non-nuclear explosion poses a
threat to electronic and electrical devices by inducing a large current or voltage surge
[20]. The detection of an EMP is a challenging task because the detecting system must
be able to handle high peak field strengths. An optical method, measuring the
polarization change induced by EMP, might be one of the few operable methods that
can survive an EMP [21]. However, the optical system is usually expensive and bulky.
Magnetic nanowire arrays are robust against the EMP since they record the magnetic
pulses passively. Once the magnetic component is recorded and read out, the electric
component of an EMP can be readily calculated from the impedance of the
propagating media. In the following, the procedure of using magnetic nanowire arrays
to measure the magnetic field component of an EMP is described. The working
scheme is illustrated in Figure 4.3.
100
Figure 4.3 A novel magnetic field pulse detection scheme. (a) Saturated by applying a strong
positive field. (b) Maximum remanent state after removing the field. (c) The strongest negative
pulse is recorded. (d) Reading the surface field with a magnetic field sensor to find the remanent
moment. (e) Ready for another measurement cycle.
1. Before each measurement, the nanowire array needs to be initialized to the state
with the maximum remanent magnetization. This is achieved by saturating the
nanowire array with a large positive magnetic field (Figure 4.3(a)) and subsequently
removing the field (Figure 4.3(b)).
2. For simplicity, the magnetic field pulses are assumed to be always along the
direction of the nanowires. In cases of pulses in other directions, multiple pieces of
101
nanowire arrays can be combined together. When a series of magnetic pulses or EMP
is present, the nanowire array records the strongest negative pulse, Figure 4.3(c).
3. The nanowire array with a non-zero magnetization, behaves as a small permanent
magnet. A localized magnetic field of a few Oe exists at the surface of the nanowire
array and increases monotonically with the remanent moment of the nanowire array.
This field can be easily detected with a magnetic field sensor (Figure 4.3(d)). For
example, the surface field of a 5 mm by 5 mm Ni90Fe10 nanowire array is about 10 Oe
in the maximum remanent state, measured by a gaussmeter. After the surface field is
read, the array is ready to be initialized for another measurement (Figure 4.3(e)).
A unit in EMP detectors includes the following components: a magnetic
nanowire array, which is a passive element and does not require any power supply, a
reader that measures magnetic field at surface of the array, a movable permanent
magnet or a small electromagnet to initialize the nanowire array, and a control unit to
read the signal of the reader and translate into the field strength of the magnetic pulse.
Six units can detect an EMP in any direction. A magnetic field of 3500 Oe is enough
to saturate the Ni nanowire array. If an electromagnet is employed, only one magnetic
pulse is necessary to initialize the nanowire array, which lowers power consumption
and the cooling requirement, and reduces the size of the electromagnet. These parts
are easy to fit into a portable handheld device.
102
4.2.2 Preliminary Test
Figure 4.4 Experimental setup for the demonstration of EMP detector
A simple prototype has been set up to demonstrate the EMP detecting method,
shown in Figure 4.4. A piece of permanent magnet is mounted on a sliding frame to
initialize the sample and provide the magnetic field pulse. A 5 mm by 5 mm Ni
nanowire array is fixed on the Hall probe of a gaussmeter (Lakeshore 450). Placing
the probe on top of the magnet initializes the sample. The surface magnetic field Hr of
the sample is measured after initialization. Then the probe is placed under the frame.
Sliding the frame close to the probe simulates the magnetic pulses. The sliding
distance controls the magnitude of the pulses and rotating the probe by 180 degrees
changes the direction of pulse. The pulse magnitude can be read from the gaussmeter
and a timer records the duration of the pulse. After the pulse series, the surface
magnetic field Hr’ is measured again. Since the magnetization of the nanowire array is
proportional to the surface magnetic field, we can find out Mr’/Mr from Hr’/Hr. By
finding the corresponding magnetic field of the magnetic state Mr’ on the hysteresis
103
loop, one can know the maximum value of the magnetic field during the pulse series.
The experiment has been performed three times, each with a different series of pulses.
The pulses and the measurement results are depicted in Figure 4.5.
In Figure 4.5(d), three scattered dots correspond to the magnetization of the
nanowire array after the magnetic pulse series in three different trials. For
comparison, the remanent magnetization measured from the hysteresis loop (black
dots and line) is also presented. The reason that the scattered dots do not exactly fall
on the hysteresis loop is that we are using a crude way to simulate the pulses by
pushing the magnet close to the probe. A more precise method to generate magnetic
pulses is necessary. Nevertheless, the trend is clear that the sensor will only record the
negative field.
(a)
60
Magnetic Field (Gauss)
Magnetic field (Gauss)
80
Pulse series 1
40
20
0
-20
-40
-60
-80
0
5
10
15
20
25
30
Time (second)
200
160
120
80
40
0
-40
-80
-120
-160
-200
(b)
Pulse series 2
0
5
10
15
20
Time (second)
104
25
30
35
1.05
(c)
Pulse Series 3
0
5
10
15
20
25
Magnetic state (Mr'/Mr)
Magnetic Field (Gauss)
300
240
180
120
60
0
-60
-120
-180
-240
-300
30
Time (second)
1.00
0.95
Hysteresis loop
magnetic state after pulse series 1
magnetic state after pulse series 2
magnetic state after pulse series 3
(d)
0.90
0.85
0.80
0.75
-350 -300 -250 -200 -150 -100 -50
0
Applied Field(Oe)
Figure 4.5(a)–(c), Three magnetic pulse series with various conditions. (d) the remanent
magnetization read from a Hall probe (blue, green, and red points) and the remanent
magnetization measured from hysteresis loop (black line).
4.3 Practical Issues
Although the proposed EMP detector shows great potential, there are a couple
practical issues that need to the solved. How stable are the different remnant states?
How sensitive can the measurement be? How fast can the magnetization of a nanowire
switch or in other words, what is the shortest pulse the nanowire system can detect?
These issues are discussed in this section.
105
4.3.1 Thermal Stability
1.000
0.998
M/M0
0.996
0.994
0.54 Ms
0.49 Ms
0.43 Ms
0.24 Ms
0.09 Ms
0.992
0.990
0
1000
2000
3000
4000
Time (s)
Figure 4.6 Time dependence of magnetization at different remanent state of a Ni90Fe10 nanowire
array.
The proposed EMP detector records the magnitude of a negative pulse in a
remanent state, subsequently the pulse magnitude is read out by measuring the surface
field of the array, which is proportional to the remanent state. Thermal stability of the
remanent states is crucial to achieve an accurate reading. Displayed in Figure 4.6 is
time dependence of the remanent magnetization measured by VSM at room
temperature. Before each measurement, the sample is first demagnetized and then
magnetized to reach a remanent state. The maximum remanent magnetization with
0.54 Ms shows the largest decay, 0.8% in one hour. Projecting along this curve, 2%
reduction of the maximum remanent state is expected in two months. These results are
promising and indicate a high thermal stability of the remanent states. The small decay
can be compensated in the real application.
In term of physics, it is also interesting to study how the dipolar interaction
affects the thermal stability. The thermal stability of magnetic nanowire arrays can be
106
evaluated by magnetic viscosity, which is the relaxation of magnetization. The
magnetic viscosity has been intensively investigated in the field of recording media
and permanent magnetic materials, where the magnetization stability directly
influences the material performance [22, 23]. In the field of recording media, the
convoluted magnetic crystalline anisotropy, exchange coupling and dipolar
interactions among grains determine the bit stability. In the field of permanent
magnets, the magnetic crystalline anisotropy is a dominant term in determining the
magnetic viscosity [24, 25]. The effects due largely to the dipolar interaction have not
been systematically investigated. For a single nanowire, the large shape anisotropy
leads to two stable states for the magnetization. An energy barrier must be overcome
when the magnetization is switched from one direction to the other. When an applied
field is not high enough to directly switch the magnetization, the thermal activation
can still alter the magnetic state of the nanowire array, which is a time dependent
process. In the following, we first define the magnetic viscosity coefficient S and then
study how dipolar interaction plays a role on this coefficient.
The decay of magnetization M can be described by
dM
M
  M  
dt

(4.5)
where λ is decay constant and τ is mean life time or time constant. Integrating Eq. 4.5

t
with respect to time t, one can have M  M 0e  , which shows M has an exponential
decay. The delay constant is
107
  Ae

E
kT
(4.6)
where A is attempting frequency in the order of 109 and ΔE is energy barrier. Product
of Boltzmann constant k and temperature T is the thermal energy. When the
temperature is fixed, decay of magnetization depends on energy barrier. In the
previous section, we proved that the switching field has a broad distribution. Since
high switching field suggests a high energy barrier, ΔE has a broad distribution too.
Therefore Eq. 4.5 and 4.6 alone are not enough to explain the magnetization decay in
millions of nanowires and it is a superposition of many exponential decays with
different energy barriers. Time dependence of magnetization decay can be
experimentally approximated by a linear relation between magnetization and
logarithm of time [26],
M (t )  M 0 [1  S ln(t )] .
(4.7)
S is magnetic viscosity coefficient due to thermal activation, which depends on
temperature and magnetic field. By measuring the magnetization change over time at
different reversal fields, one can extract the viscosity coefficient S at different reversal
fields. Gao et. al. have performed viscosity measurements on FeCo and FePt nanowire
arrays [27, 28]. The viscosity coefficient S was extracted as a function of the reversal
field. In both systems, S peaks at a field close to Hc, which is common in magnetic
materials. The dipolar interaction in these studies is much weaker than that in our
samples, due to relative large nanowire separation in their samples.
108
For a dense magnetic nanowire array, a dipolar field term Hdipole modifies the
energy barrier according to
E  KV (1 
H  H dipole
Ha
)m
(4.8)
where K and Ha are the anisotropy energy density and anisotropy field, respectively, V
is the particle volume, and H is the applied field. The exponent m equals 2 in the
Stoner-Wohlfarth model. From Eq. 4.3, we addressed that for each state on the
hysteresis loop, Hdipole+H=Hsw is a constant. Therefore, even though the dipolar field
constantly changes depending on the magnetization, the magnetic field every
nanowire experiences under different reversal field is the same. Consequently, for an
ideal dense nanowire system, magnetic viscosity is same under different reversal
fields, while magnetic viscosity usually peaks around Hc in other magnetic materials.
The experimental result is shown in Figure 4.7. When applied field is between 750 Oe
and -1500 Oe, magnetic viscosity is a rather constant value. Beyond -1500 Oe,
viscosity peaks at -1700 Oe, even though far from Hc (-1100 Oe), violating our
argument above. In order to find the reason for this peak, we also plot susceptibility in
Figure 4.7, which indicates susceptibility and viscosity share the same trend. In an
ideal hysteresis loop of magnetic nanowire array as the red curve in Figure 4.1(a),
susceptibility is a constant. However, since the switching field has a broad distribution
as revealed by the FORC technique, susceptibility actually varies with applied field.
Higher susceptibility means nanowires are easier to be magnetized or switched,
leading to higher viscosity.
109
1.2
Susceptibility
Viscosity
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-0.2
-4500
-3000
-1500
0
1500
Normalized Viscosity
Normalized Susceptibility
1.2
-0.2
Magnetic Reversal Field (Oe)
Figure 4.7 Magnetic viscosity of Ni90Fe10 nanowire array at different reversal fields.
4.3.2 Surface Magnetic Field
900
Surface field (Oe)
800
1um
10um
50um
100um
500um
1000um
700
600
500
400
300
200
100
0
-100
1000
10000
n
Figure 4.8 Estimation of surface magnetic field of a NiFe nanowire array in saturation state. The
surface field is in z direction
The surface magnetic field of the magnetic nanowire array affects the
sensitivity of the proposed EMP detector. From previous sections, it is confirmed that
Ni90Fe10 nanowire arrays can record the largest negative magnetic pulse in a series of
magnetic pulses with a maximum magnitude smaller than 700 Oe. Assume 10 Oe
110
exists on the surface of a magnetic nanowire array which is in its greatest remanent
state. In order to detect a negative pulse of 0.7 Oe, the magnetic field sensor
measuring the surface field must have a sensitivity of 0.01 Oe. Therefore a large
maximum surface field is best for increasing sensitivity of the EMP detector.
The surface magnetic field of a Ni90Fe10 nanowire array is estimated by using
the dipolar field model developed in chapter 3. The nanowires are assumed to be in a
perfect hexagonal array, and all magnetizations are pointing up. After adding
contributions of 6n  n nanowires, z component of the surface magnetic field can be
expressed as
n
n
x
xL
1 n n
}
H  6  M s r 2 {


3
4 i 0 j 1 [(i 2  ij  j 2 ) R 2  x 2 ] 2 i 0 j 1 [(i 2  ij  j 2 ) R 2  ( x  L) 2 ] 3 2
(4.9)
x is the distance from the top of the nanowire array. The first term on the right comes
from contribution of positive magnetic charges on top of the nanowires, and the
second term comes from magnetic charges at the bottom. The calculation results are
shown in Figure 4.8 for different distance (x) above the surface. When x is larger than
50 μm, surface field has a peak value. This is because the first and second terms in Eq.
4.9 have opposite signs and different increase rates with respect to n. The sample size
is estimated to be 4.8 mm by 4.8 mm when n=40000. In section 4.2.1, we measured
the surface field of a 5 mm by 5 mm NiFe nanowire array with a Gaussmeter, and the
distance between surface of nanowire array and sensor in the Gaussmeter is about 0.8
mm. When the array is in its maximum remanent state, the measured surface field is
111
10 Oe, consistent with the estimation which is about 12 Oe at saturation state. A field
sensor closer to the surface of the array is needed to further verify the estimation in
Figure 4.8.
4.3.3 Switching Speed
The magnetization switching speed in nanowires determines the minimum
pulse width that the system can measure. A LLG micromagnetics simulator has been
employed to calculate the switching time of a single Ni nanowire. The computer
simulation shows the magnetic field pulse to switch the nanowire can be less than 100
picoseconds. Based on the simulation result, magnetic pulses longer than 100
picoseconds can be measured with the Ni system.
4.4 Summary
In summary, an analog memory effect in magnetic nanowire arrays has been
demonstrated for the first time. The maximum magnetic field in a series of magnetic
field pulses can be “memorized” in the array. The origin of the memory effect is the
dipolar interaction among the nanowires, which is modeled with two basic
assumptions. The deviation between the experimental result and the theory is clarified
by measuring the switching field distribution among nanowires with the FORC
technique. Based on the memory effect, a novel EMP detection scheme is proposed. A
few practical issues have also been discussed.
112
The magnetic nanowire based EMP detecting system has these advantages
compared to other methods:
1. The detector can capture a magnetic field pulse as short as 100 ps. For
electromagnetic pulse spectra consisting of random field strengths, the
detector records the maximum field strength.
2. The detector works in EM fields as high as 700 Oe (h field) and 1.6 MV/m (efield) without breakdown. Most detection methods based on RF diodes or
thermal couples breaks down in this EM field.
3. The nanowire arrays are detachable from the rest of the system. After the
initialization, the array probe alone can be attached to the testing object during
the detection. The maximum value of the magnetic field pulse is stored in the
array. After the test, the maximum value of the magnetic field pulse can be
read out by a magnetic sensor (reader). In this scheme, during the
measurement the magnetic field pulse under test does not affect any part of the
system except the array which can handle the extreme EM environment.
4. Antennae or electrodes are not needed in this application. The magnetic field
pulse or electromagnetic wave under detection will be much less disturbed.
This is also due to the much smaller size of the nanowire array compared to
the wavelength of the electromagnetic wave.
113
Reference:
[1]
[2]
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116
CHAPTER 5
HIGH TEMPERATURE ANNEALING INDUCED SUPERPARAMAGNETISM
IN MGO BASED MAGNETIC TUNNELING JUNCTIONS
5.1 Introduction
The basic structure of a magnetic tunneling junction (MTJ) has an insulating
layer sandwiched by two ferromagnetic layers (FM/I/FM). Tunneling resistance is
high when magnetic moments in the two FM layers are antiparallel, and low when
magnetic moments in the two FM layers are parallel. The ratio between the resistance
change and the lower resistance is referred to as tunneling magnetoresistance (TMR).
The TMR originates from spin dependent tunneling (SDT), which was first studied in
1970s in a Superconductor/I/FM structure by Tedrow and Meservey [1]. In 1975, for
the first time Julliere observed TMR effect in a Co/Ge/Fe sandwich structure at low
temperature [2]. In 1995, two groups independently achieved reproducible room
temperature TMR in CoFe/Al2O3/Co and Fe/Al2O3/Fe structures [3, 4].
After the prediction of symmetric filtering theory by Butler and Mathon [5, 6],
over 200% TMR in MgO-based magnetic MTJs has been observed independently by
Parkins and Yuasa in 2004 [7, 8]. In the same year, Djayaprawira developed a method
using CoFeB electrodes by magnetron sputtering, which worked surprisingly well [9,
10]. CoFeB electrodes are amorphous in as-prepared state and the smooth surface of
117
CoFeB bottom electrode promotes the growth of crystalline (100) MgO barrier. After
annealing, CoFeB layers crystallize in (100) direction using MgO as a template, which
is referred to as grain to grain epitaxy, shown in Figure 5.1. Symmetric filtering
produces large TMR in CoFeB/MgO/CoFeB structures despite the polycrystalline
nature of the MgO and CoFeB layers, and this method now is being widely used.
Figure 5.1 CoFeB amorphous layers become crystallized using MgO as a template after annealed
in magnetic field
In this section, symmetric tunneling theory is briefly introduced. Then
multilayer structure of a practical MTJ and a rapid thermal annealing method are
explained. Finally, theory of superparamagnetism is quickly reviewed.
118
Figure 5.2 Possible electron wave function symmetries in 100 direction [10].
5.1.1 Symmetric Tunneling in MgO Based Tunneling Junction
Pointed out by Butler and Mathon [5, 6], only electrons with a certain
symmetry can tunnel through the (100) MgO barrier in a MTJ with an epitaxial
structure. In such a system, atomic orbitals can be regrouped by symmetry in periodic
lattices; Figure 5.2 shows some possible wave function symmetries in (100) direction.
Along (100) direction, electrons with Δ1 symmetry decay in MgO barrier much more
slowly than electrons with other symmetries, which means the MgO barrier acts as a
filter and only electrons with Δ1 symmetry can tunnel through the barrier in an
epitaxial sandwich structure. However, the symmetry filtering effect alone is not
enough to generate large TMR; the symmetry filter needs to be transferred into a spin
filter effect. In other words, it is necessary to find a ferromagnetic material with Δ1
electrons only in one spin channel around the Fermi level, but no Δ1 electrons in the
other. From energy band diagram of bcc Fe in (100) direction [11], it can be clearly
119
seen there is only spin up Δ1 band at the Fermi level, and the spin down Δ1 band is 1.3
eV above the Fermi energy. Therefore 100% spin polarization can be achieved in
epitaxial Fe/MgO/Fe structure grown in the (100) direction. The same spin filtering
effect of MgO can be more dramatic with CoFe electrodes [12]. The tunneling density
of states in Fe (100)/MgO (100)/Fe (100) junctions for different Bloch states is shown
in Figure 5.3.
Figure 5.3 Tunneling density of states in Fe (100)/MgO (100)/Fe (100) junctions for different
Bloch state with k║=0. Upper two graphs are for the parallel state and lower ones for the
antiparallel state [5].
120
5.1.2 Full Junction Structure
In practice, an MgO based magnetic junction has a more complicated layer
structure than the sandwich discussed in previous section. As shown in Figure 5.4(a),
all layers are necessary and have their unique functions.
SiO2/Si: Prime grade (100) silicon wafer with 1 μm thick SiO2 is used as
substrate. The large resistivity of thick SiO2 layer insures that after the electrode pads
of a tunnel junction are wire bonded to a chip carrier, currents flow throw the junction
instead of Si wafer.
Ta: Ta is adhesive to silicon wafer. It wets the substrate, so the whole structure
is well bonded on the wafer.
Magnetoresistance (%)
350
300
460 C 7 min
250
200
150
100
50
0
-150 -100 -50 0 50 100 150
Field (Oe)
Figure 5.4 Typical structure of an MgO based magnetic tunnel junction (left) and a hysteretic
loop with 300% MR (right).
121
Ru: The 20 nm Ru layer provides a smooth surface for the rest of the structure
and also lower the sheet resistance to a few ohms because of its high conductivity.
Ta: The second Ta layer prevents diffusion of Ru into above layers during
annealing. Ta is a heavy element.
CoFe: The 1st CoFe layer is a seeding layer and promotes the growth of IrMn.
IrMn: IrMn is antiferrmagnetic and pins the 2nd CoFe layer after annealing and
magnetic field cool.
CoFe: The 2nd CoFe layer is pinned by IrMn. It also coupled with the CoFeB
bottom layer antiferromagnetically through a thin Ru layer.
Ru: This Ru layer is very thin (0.85 nm). It provides the antiferromagnetic
coupling between the 2nd CoFe layer and the bottom CoFeB layer. It also provides a
smooth surface for the grown of CoFeB layer.
CoFeB: It is antiferromagnetically coupled with the CoFe layer. The reasons
for the synthetic antiferromagnetic (SAF) structure are the followings: It lowers the
122
stray field by cancelling the magnetic moment of each other; the SAF slows down the
Mn diffusion during annealing, which is detrimental to the symmetric tunneling; third,
SAF promote the grain to grain epitaxial growth between MgO and bottom CoFeB,
otherwise, without SAF structure the CoFe crystallizes on top of IrMn, not in (100)
direction.
MgO: CoFeB is amorphous, so helps MgO grows in (100) direction.
CoFeB: The magnetization in this layer rotates freely. It crystallizes in (100) direction
during annealing using MgO as a template.
Ta: It prevents the oxidation.
Ru: The high conductivity of Ru provides good electric contact.
123
5.1.3 Synthetic Antiferromagnetic Pinning
0.0008
380 C 3min
(a)
(b)
M (emu)
0.0004
IEC = 360 Oe
(c)
0.0000
-0.0004
(d)
IEC + Pinning
= 960 Oe
350 Oe
(e)
-0.0008
-2000
-1000
0
1000
2000
H (Oe)
Figure 5.5 Hysteresis loop of a non-patterned MTJ sample annealed at 380 °C for 3 minutes. The
arrows represent the direction of magnetic moments in the four magnetic layers.
The effectiveness of SAF structures and the magnitude of pinning fields can be
tested by using VSM. Figure 5.5 shows the hysteresis loop of a non-patterned MTJ
sample annealed at 380 C for 3 minutes. The steps in the loop represent the
magnetization process of the four magnetic layers in the MTJ structure: CoFeB free
layer, CoFeB bottom layer, CoFe in the SAF, and CoFe seeding layer (labeled as four
arrows in Figure 5.5. In saturation state (a), magnetic moments of all four layers are
pointing in the same direction. Before the applied field decreases to zero, the bottom
CoFeB electrode is the first to rotate (b) because the field given off by the
antiferromagnetic exchange coupling is in the opposite direction of the applied field.
124
The strength of antiferromagnetic interlayer exchange couplings (IEC) between CoFe
and CoFeB layers can be extracted here as 360 Oe. The CoFeB free layer switches
when the applied field becomes negative (c). The next switched layer is the seeding
CoFe (d), which is slightly pinned by the IrMn on top of it and the pinning field is 350
Oe. The last one to rotate is the CoFe layer in the SAF structure (e). The reason for its
high switching field is that both the bias field given by IrMn layer and the exchange
coupling field from bottom CoFeB layer are acting in the direction opposite to the
applied field. From the total field, 960 Oe, the pinning field by IrMn on the CoFe layer
is 600 Oe.
5.1.4 Rapid Thermal Annealing
Figure 5.6 Time evolution of TMR in an MgO based MTJ upon annealing. The measurement is
performed at room temperature. The sample is annealed at 360 °C in air [13].
125
Annealing is an indispensable step to achieve high TMR in MgO-based
junctions. The reason is that, by magnetron sputtering CoFeB electrodes are
amorphous and need to be crystallized in (100) direction using MgO (100) as a
template. During annealing boron diffuses away. The annealing is usually hours long,
taking place in a strong magnetic field and under high vacuum. Recent research [1315] revealed that a high TMR can quickly develop at the early stage of annealing in air
or Ar, so the time-consuming annealing and expensive vacuum equipment becomes
unnecessary. Displayed in Figure 5.6 is a series of TMR loops measured after an MgO
based MTJ has been annealed for different time in air at 380 °C. The measurement
was performed in room temperature. It clearly shows the TMR develops to be over
160% after only 3 minutes of annealing, and over 200% for 10 minutes of annealing.
5.1.5 Superparamagnetism
In chapter 4, we discussed thermal stability of the magnetic moments in
nanowire arrays. The magnetic moment must overcome an energy barrier ΔE before
switching. The switching probability is expressed as
  Ae

E
kT
(5.1)
where A is attempting frequency in the order of 109. The switching probability
increases exponentially when the temperature increases. The same argument can also
be applied to magnetic nanoparticles except ΔE of nanowire originate from theshape
anisotropy and ΔE of nanoparticle comes from the magnetocrystalline anisotropy KaV.
126
For a group of small ferromagnetic particles with same volume V, when ΔE=KaV is
comparable to thermal agitation kT, magnetic moments of the particle become
unstable. Each particle is a giant magnetic moment and the whole group behaves
paramagnetically. This phenomenon is being referred to as superparamagnetism. If the
temperature is further increased passing by the Curie temperature Tc, the spontaneous
magnetization is lost and all the moments are paramagnetic on an atomic level. If the
temperature is decreased to KaV>>kT, the group acts as a ferromagnet. The
temperature when particles lose superparamagnetism is called blocking temperature
Tb. A conventional criteria for blocking is
E
 25
kT
(5.2)
The magnetization of a group of superparamagnetic particles under an applied field
can be calculated by projecting saturation magnetization along the field direction with
an average cos  . cos  can be calculated from [16]

cos  
 exp(
0
mH cos 
) cos  sin d
kT
(5.3)

mH cos 
0 exp( kT ) sin d
where m is magnetic moment of one particle, and H is the applied field. After
integration, magnetization of a group of superparamagnetic particles in an applied
field is
M  Nmcos   NmL( )  Nm(coth  
127
1

) (5.4)
where  
mH
, and L(α) is Langevin function.
kT
5.2 Time Evolution of MR Loop under High Temperature Annealing
Figure 5.7 Two methods to achieve linear and hysteresis free MR loop, (left) free layer is set
perpendicular to the pinning layer due to shape anisotropy; (right) free layer is composed of
superparamagnetic CoFeB nanoparticles.
Besides various applications such as hard drive read head [17], microwave
oscillators [18], magnetic random access memory (MRAM) [19], pressure sensors
[20], and microwave detectors [21], a great deal of attention has been focused on
applications in magnetic field sensors. The sensor application requires a hysteresis
free magnetoresistance (MR) loop and a linear response of TMR with respect to the
magnetic field. There are two strategies to achieve these features, shown in Figure 5.7.
One can use a perpendicular magnetization configuration between two magnetic
electrodes of rectangular or ellipsoidal shape with large aspect ratio [22-24].
Alternatively, one can introduce the superparamagnetic behavior in the free layer by
reducing its thickness [25-28]. The latter has the advantage of a simplified fabrication
process, although a precise control of the free layer's thickness is necessary.
128
In this section, we fabricated CoFeB/MgO/CoFeB MTJ junctions with a
relatively thin free layer and studied the evolution of the magnetoresistance (MR)
loops over annealing times at high temperatures in Ar. We found that the MR loop
becomes almost hysteresis free after 17 minutes of annealing and that the linear region
gradually increases with annealing time and a tradeoff in TMR values. The hysteresis
free loops can be well fitted by using the theory for superparamagnetism. This implies
the formation of superparamagnetic particles in the free layer during high temperature
annealing.
5.2.1 Magnetic Transport Measurement
Figure 5.8 Full MTJ structure (left) with a relatively thin 2 nm free layer and a thick 1.7 nm Ru
layer. Schematic of a fully patterned MTJ and the four probe method (right)
129
The MTJ samples were deposited in a magnetron sputtering system with a base
pressure of 8 x 10-8 Torr. The structure was Si/SiO2/Ta 7/Ru 20/Ta 7/CoFe 4/IrMn
15/CoFe 2/Ru 1.7/CoFeB 4/MgO 1.5-3/CoFeB 2/Ta 8/Ru 10, where the numbers are
the layer's thickness in nanometers. A thick Ru layer of 1.7 nm was used in the
synthetic anti-ferromagnetic structure for better stability at high annealing
temperatures [13]. A combinational technique was used to form a wedge-shaped MgO
barrier layer on the wafer. MTJ junctions with diameters from 25 to 100 μm were
defined by standard photolithography and ion-beam etching. The annealing was
performed in an Ar atmosphere on a specially designed sample stage allowing for
annealing temperatures up to 500 ºC. The oxygen level is lower than 5 ppm and the
H2O level below 0.5 ppm. After being annealed for a certain time duration, the sample
was cooled down to room temperature under a magnetic field of 2 kOe to establish the
exchange pinning. Subsequently, the TMR ratio of the junctions was measured at
room temperature in air by a conventional 4-probe method. The same annealing and
TMR measurement procedures were repeated several times on the sample in order to
study its evolution over its annealing time. The magnetic property of the sample was
measured by a vibrating sample magnetometer (VSM, Lakeshore 7404).
Figure 5.9 illustrates the TMR ratio and coercivity as a function of annealing
time for a single MTJ junction, which was annealed at 460 ºC. The TMR ratio in this
manuscript is calculated using (RAP-RP)/RP, where RP is the resistance of the parallel
state, in which the magnetizations of the free layer and the pinned layer are parallel.
130
RAP is the resistance in the antiparallel state. The TMR for the as-prepared MTJs were
only 5-8 %. The TMR quickly developed to 128% with only 1 minute of annealing,
similar to other reported results [13]. Interestingly, contrasting reported results, the
TMR ratio gradually decreases from 128% to 17% after 70 minutes of annealing. The
coercivity also shows a very different behavior. Little change in coercivity was seen in
the first 4 minutes of annealing. Then the coercivity decreases rapidly from about 17.2
Oe to 2.7 Oe in the next 12 minutes of annealing. The coercivity remains around 2 Oe
for the rest of the annealing. We attribute this unique property to the formation of
superparamagnetic particles in the free layer during the annealing, which will be
explained in detail later. More than 20 junctions from the same wafer with different
barrier thicknesses have been measured and they all show similar results.
Figure 5.9 TMR ratio and coercivity as a function of annealing time for a single MTJ junction
annealed at 460 ºC
131
Selected MR loops of the same junction at different annealing times are
depicted in Figure 5.10. As shown, the hysteretic behavior nearly disappears in
samples annealed for longer than 17 minutes. The linear region gradually expands
upon annealing. The dependence of the linear region on the annealing time is
displayed in Figure 5.11, with the decreasing TMR ratio. The linear region at 70
minutes ranges from –47 Oe to 68 Oe, more than 10 times larger than that at 17
minutes, from –3.1 Oe to 5.3 Oe. The growth of the linear region accompanied by the
decreasing TMR value which was also observed in other studies by systematically
reducing the free layer thickness [26]. The advantage in our sample is that, in sensor
fabrication, controlling of annealing time is much easier than tuning the free layer
thickness in the range between 0.8 to 1.5 nm.
132
Figure 5.10 Measured MR loops of a MTJ junction annealed for different times at 460 °C
133
Figure 5.11 The linear region in MR loops as a function of annealing time. The TMR ratios are
also labeled.
5.2.2 High Temperature Annealing Induced Superparamagnetism
In order to explore the origin of the MR loops without hysteresis, blank
samples without patterning were annealed for different durations at 460 ºC and
measured by the VSM. The magnetic field was applied in plane, perpendicular to the
pinning direction. The results indicate that no easy axis in the free layer was induced
in the direction perpendicular to the pinning field by annealing. This rules out the
possibility of a perpendicular magnetization configuration between two ferromagnetic
electrodes formed during annealing, which may eliminate the hysteretic behavior.
Another MTJ sample with the same structure but a thicker free layer of 3 nm was
fabricated. Annealed at the same temperature, the sample shows 200% MR with little
change in the first 15 minutes of annealing. After that, the TMR decreases and the
134
coercivity remains at about 17 Oe. The reduction of the TMR can be attributed to the
Mn diffusion during the high temperature annealing [29]. The same mechanism may
also contribute to the TMR decrease in the sample with a thin free layer of 2 nm.
However, it cannot explain the sudden change in coercivity. This comparison suggests
the thickness of the CoFeB free layer is important to the unique property observed
here.
In the aforementioned strategy of reducing the free layer thickness, a critical
thickness exists, below which the free layer becomes superparamagnetic. The critical
thickness is usually about 1.4 nm, smaller than the 2 nm in our junctions.
Nevertheless, the annealing temperature of 460 ºC is much higher than the
temperatures used by other groups. It is reasonable to consider that the high thermal
energy changes the critical thickness, leading to superparamagnetic behavior in a
relatively thick free layer.
Figure 5.12 Angle definitions used in Eq. 5.5~5.7
The superparamagnetism theory is used to study the MR loops of the junction
with 2 nm thick free layer. The junction was annealed for 20 minutes at 460 ºC. The
135
MR loops were measured with different angles between the applied field and the
pinning direction, illustrated in Figure 5.13. The applied field was in the film plane.
For MTJ, the conductance of a junction can be expressed as [25]
G  G0 [1  P 2 cos( F   P )]
(5.5)
where P is a constant, and G0 is the conductance when the magnetizations of the free
layer and pinning layer are perpendicular to each other. θF (θP) is the angle between
the magnetization of the free (pinning) layer and the applied field. After rearranging
the equation, the change in the conductance becomes
G  G  G0  cos( F   P ) (5.6)
The theoretical calculation [25] shows that the superparamagnetic particles in the free
layer have a pancake shape. Thus, it is reasonable to assume that the magnetic
moments stay in the film plane due to the shape anisotropy. Therefore we simplify the
Langevin equation into a two-dimensional case. For an assembly of paramagnetic
particles, the cos(θF-θP) can be written as
2
G  cos( F   P ) 
 cos(
0
F
2
  P )e
e
HM sV cos  F
kT
HM sV cos  F
kT
d F
(5.7)
d F
0
where Ms, k and T are the saturation magnetization (860 emu/cc) of CoFeB [25], the
Boltzmann constant, and the temperature (300 K), respectively. H is the applied field.
The particle volume V is used as a fitting parameter, which is set to be 1100 nm-3.
Another fitting parameter, the pinning field (240 Oe) is used for the loops measured at
136
φ=π/6, π/3, and π/2. The fitted results are also shown in Figure 5.13, which match the
experimental results very well.
Figure 5.13 Measured MR loops of an MTJ junction annealed for 20 minutes at 460 ºC, φ is the
angle between the applied magnetic field and the pinning direction. The solid line is the fitting
based on the superparamagnetism theory.
137
Particle Volume (nm3)
5000
Assume Ms=1.3 T
4000
CoFeB 2 nm
Ru 1.7 nm
3000
2000
1000
0
10
20
30
40
50
60
70
Annealing Time (min)
Figure 5.14 Estimated particle volume evolutions during annealing
Although the argument about the critical thickness altered by the high thermal
energy is tentative and the underlying mechanism has yet to be elucidated, the
excellent fitting implies that the formation of superparamagnetic particles during the
annealing is highly plausible. The same analysis was applied to the MR loops
annealed for different durations with φ=0. It was found that the fitting parameter,
particle volume V, quickly decreases with the annealing time, which seems counterintuitive, displayed in Figure 5.14. It has been known that the boron diffuses during
the crystallization of the CoFeB layer [30]. One scenario to explain the decreasing
particle size is that the initial continuous free layer keeps breaking down into small
pieces during annealing because of the boron diffusion. It should be mentioned that
we also annealed the 2 nm free layer sample at 420 ºC. The time dependent study
shows a slow decay of TMR from 180% to 148% in 60 minutes and no coercivity
138
changes, suggesting that the high annealing temperature is crucial for the observed
superparamagnetic behaviors.
Figure 5.15 Conductances in parallel and anti-parallel states as a function of annealing time of the
MTJ used in Figure 5.9 annealed at 460 ºC. The inserted picture shows the I-V curves of another
MTJ junction annealed at the same temperature for 1 minute and 40 minutes.
The formation of the superparamagnetic particles and the decrease of the
particle size upon annealing may make the magnetic moments in the free layer more
difficult to be aligned. Therefore, as long as the same measurement fields are used
(±150 Oe), the parallel conductance GP decreases with annealing while the antiparallel conductance GAP increases, leading to the reduction of the MR value. The
evolution of the parallel and anti-parallel conductance of the same MTJ junction used
above as a function of the annealing time is illustrated in Figure 5.15. The
139
conductance in both configurations reduces with the annealing time. The decrease of
the conductance was also observed in the previous study [14], where the decrease of
GP has been attributed to the impurities diffusion during annealing. However, in the
present case the anti-parallel conductance decreases slower than the parallel
conductance, supporting the above argument that magnetic moments in the free layer
become more difficult to be aligned with annealing, indicating the reduction of TMR
is not due to the change of barrier/electrode interface properties caused by annealing.
The I-V curves of another MTJ annealed at 460 ºC with different durations are shown
in the insert of Figure 5.15. The I-V curves of parallel and anti-parallel states almost
overlap each other after long annealing due to the superparamagentic nature of the top
electrode.
5.2.3 More evidence for superparamgneism
140
MR=170%
Resistance (k)
30
25
20
105 K
300 K
MR=120%
15
10
-15
-10
-5
0
5
H (mT)
10
15
Figure 5.16 MR loops at different temperatures shows different MR value and coercivity
Magnetic transport properties of tunnel junctions were studied at low
temperatures in order to find more evidence for superparamagnetism in free layer. MR
loops were measured at 105 K and room temperature, as displayed in Figure 3.16. The
sample was annealed for 10 minutes at 460 °C and shows a coercivity of 4 Oe and a
MR of 120% at room temperature. At 105 K, the coercivity decreases back to about 25
Oe and the MR increases to 170%, indicating the suppression of superparamagnetism
due to the low thermal activation. It clearly demonstrates that superparamagnetism is
the reason for the reduction of coercivity and MR value.
5.3 Study of MgO/CoFeB Multilayer by Polarized Neutron Reflectivity
The crystallization of the CoFeB layer plays a significant role in the formation
of spin dependent tunneling in MgO based MTJs, leading to MR larger than 200%.
141
The understanding of the crystal structure and magnetic property evolution of CoFeB
layer during annealing is crucial for the explanation of high MR. Recently, the fast
crystallization rate of CoFeB is characterized by in-situ and time-resolved
synchrotron-based X-ray diffraction at beam line X-20C of the National Synchrotron
Light Source [15]. However the change of the magnetic structure remains unknown. In
the polarized neutron reflectivity measurement, one can infer not only a nuclear
density profile, but also a magnetization profile perpendicular to the film surface, so it
is possible to probe both the structural and magnetic property change of
CoFeB/MgO/CoFeB junction upon annealing at the same time [31-33]. Polarized
neutron reflectivity (PNR) study was performed on (CoFeB/MgO)n multilayer samples
before and after annealing in Oak Ridge National Lab. The reason of choosing a
multilayer structure instead of a real MTJ sample is that periodic structure reinforces
PNR signal and easier to be analyzed. After we obtain useful structural and magnetic
information, we can move on to the real MTJ structure.
5.3.1 Sample Fabrication and Characterization by XRD and VSM
Three multilayer samples were fabricated by magnetron sputtering in Brown
University. All samples have the same structure: Glass/CoFeB (8 nm)/ [CoFeB (3.5
nm)/MgO (2.5 nm)] 10 /Ta (5 nm). Rapid thermal annealing was performed on two
samples, one for 30 seconds, and another for 1 hour at 420 °C.
142
The thickness of the periodic structure was verified by small angle X-ray
diffraction. Regular XRD measurements were performed on the samples with different
annealing conditions. Illustrated in Figure 5.17, MgO (200) peaks appear in all three
samples. Through annealing, the peak becomes clearer, suggesting improvement of
MgO quality. A CoFe (200) peak was not found in the as-prepared sample, since the
as-prepared CoFeB is amorphous. A small and broad CoFe peak was observed in the
sample annealed at 420 °C for 30 seconds, while a clear sharp peak is found in the
sample annealed for 1 hour at the same temperature. The structure evolution study
shows the gradual change of CoFeB layer from amorphous to crystallized in (100)
direction. Peak of Ta capping layer is observed in all three samples.
143
40
As-prepared
20
CPS
0
40
20
0
40
MgO (200)
Annealed 30 seconds
MgO (200)
CoFe (200)
Ta (220)
Annealed 1 hour
20
0
20
Ta (220)
CoFe (200)
MgO (200)
30
40
50
60
70
Ta (220)
80
90
2 (degree)
Figure 5.17 XRD measurement of as prepared and annealed (MgO/CoFeB)10 multilayer samples.
VSM measurement was performed on the 1 hour annealed sample to find out
the saturation field and easy axis. From Figure 5.18, it is interesting to see that the
easy axis lays in the direction 45 degrees from the edge of the rectangular sample,
which may be due to the sample rotation and rocking during the fabrication process.
The other two samples show similar properties.
144
Normalized Magnetization
1.0
45
135
0
0.5
420 C 1 h
0.0
-0.5
-1.0
-60
-40
-20
0
20
40
60
H (Oe)
Figure 5.18 VSM loops (left) of the 1 hour annealed sample with different angle between sample
and applied field. The definition of the angle and the direction of the easy axis and hard axis are
also shown (right).
5.3.2 Preliminary Result and Analysis
The neutron reflectivity of up spins and down spins as a function of wave
numbers are shown in Figure 5.19 (a)-(d) for both as prepared sample and the sample
annealed for 1 hour. A magnetic field of 1 T was applied along the easy axis to
saturate the samples during the measurement. In both samples, the clear differences
between the reflectivity of up spins and down spins come from the magnetic moments
in CoFeB layers. The oscillations are due to total film thickness. In all the
measurement, a large peak around 0.1 Å -1 was observed, which corresponds to the
first Bragg peak of the periodic multilayer structure.
145
The fitting was performed by a research team in Physics Institute of Chinese
Academy. Based on the fitting, nuclear and magnetic scattering length, the density of
different layers was extracted and displayed in Table 5.1. After one hour of annealing,
the nuclear scattering length density (SLD) of the MgO layer increases from 5.72  106
Å -2 to 5.96 10-6 Å -2, close to the nominal value, indicating improvement of MgO
quality through annealing. The same trend was also observed in the XRD study.
Because boron diffuses away during the crystallization of CoFeB layer, the magnetic
SLD of CoFeB layer increases close to the nominal value after annealing. Interestingly,
an extra thin layer is necessary to fit the reflectivity curve of the annealed sample. In
this layer, the nuclear SLD is rather small. Since the nuclear SLD of both CoFe and
MgO is much larger than 2.46 10-6 Å -2, it is reasonable to speculate the interface of
CoFe and MgO is rough and discontinuous. The small magnetic SLD of this thin layer
also supports this argument. In order to identify how this rough interface affects the
spin dependent tunneling, further PNR study on full MTJ structures is necessary.
Table 5.1 Parameters used in the fitting
146
Figure 5.19 (a) (b) Neutron reflectivity measurement results of spin up neutron and spin down
neutron for as prepared sample and (c) (d) for the sample annealed for 1 hour
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150
CHAPTER 6
ELECTROMAGNET DESIGN AND SIMULATION WITH MAXWELL 3D
Electromagnets are important tools in the study of magnetism and magnetic
materials. Computer simulations can visualize and significantly simplify the
electromagnet design process. In this chapter, electromagnet designing and analysis by
using the program Maxwell 3D are introduced with two examples, one at DC
condition and the other at AC.
6.1 Introduction of Maxwell 3D
Maxwell 3D is a commercial electromagnetic field simulation software for
designing and analyzing electromagnetic or electromechanical devices. Based on the
finite element method, the software can solve static magnetic or electric field
problems and transient problems [1]. The design and analysis process is highly
automated. After specifying the geometry, material property, and desired output
quantities of the design, the software automatically generates a mesh for solving the
problem. After the processing, desired output quantities can be presented in various
forms. Maxwell 3D can also be combined with a thermal analysis software “ephysics”
to simulate the thermal properties of the design.
151
6.2 Design of an Electromagnetic Assembly for Actuator
The objective in this example is to design a permanent magnet or
electromagnet assembly which can exert a 50~60 N force on a movable soft iron. The
force on the soft iron needs to be uniform in a 9 mm range and also removable. The
soft iron is attached on a membrane which is part of an actuator. The size of the
assembly is limited to 120 mm in diameter.
6.2.1 Preliminary Designs
1. Rotation Design
Figure 6.1 Schematic of the rotation design. The attracting forces between the permanent
magnets and soft irons are controlled by rotation.
In the rotation design, permanent magnets (PMs) and soft irons are being used.
The model is shown in Figure 6.1. When irons face the PMs directly, large forces exist
152
and they move toward each other by attraction. Assuming a motor can rotate the soft
irons by 90°, the magnetic forces are minimized and the irons can be moved apart. The
membrane is bonded to the soft irons.
Force in z direction (N)
Force acting on 2 soft irons in z direction
Torque acting on PMs in z direction
150
Distance between PMs
and irons are 1 mm
125
0.1
0.0
-0.1
100
-0.2
75
-0.3
50
-0.4
25
-0.5
0
0
20
40
60
80
-0.6
100
Torque in z direction (N*m)
0.2
175
Rotation angel of PMs around z axis (Degrees)
Figure 6.2 Force and torque in z direction as a function of rotating angle.
Solved by using Maxwell 3D, the torque and force on the soft irons in z
direction are shown in Figure 6.2 with different rotating angles. The distance between
the PMs and soft irons is 1 mm. The absolute value of the torque peaks at 45°. As we
expected, the attracting force is at its maximum when the PMs and soft irons are
facing each other. When the soft irons are rotated by 90°, the forces drop close to zero.
Figure 6.3 shows the attracting forces in z direction as a function of distance between
the PMs and soft irons, at 0° (left) and 90° rotation (right). In the 0° case, the
attracting force decreases dramatically from 130 N to 20 N when the soft irons are
moved away from PMs by 5 mm. The sudden reduction of the force is undesired and a
153
required motor to rotate the soft irons complicates the design, hence this design is less
favorable.
Force acting on 2 soft irons
in z direction
150
1.2
Force in z direction (N)
Force in z direction (N)
200
PMs and soft irons are
directly facing each other
Thickness of soft iron=30mm
Thickness of PM=45mm
100
50
0
1
2
3
4
5
6
Force acting on 2 soft irons
in z direction
1.0
PMs have been rotated
90 degrees around z axis
0.8
Thickness of soft iron=30mm
Thickness of PM=45mm
0.6
0
1
2
3
4
5
6
Distance between PM and soft iron (mm)
Distance between PM and soft iron (mm)
Figure 6.3 Simulated forces on soft irons in z direction when the PMs and soft irons are facing
each other (left), and rotated by 90° (right).
2. Hybrid Design
Figure 6.4 Schematic of the hybrid design. When currents are applied, both coils exert forces on
the PM in the same direction.
154
In the hybrid design, both PMs and electromagnets are adopted. A PM is
placed inside two coils, as displayed in Figure 6.4. The membrane is attached in the
middle of the PM which lies inside the gap between the coils. Whena current with the
same magnitude but in opposite directions is applied in the two coils, the lower coil
exerts a force on the PM to push it up, while the upper coil attracts the PM to pull it up.
The force is removed as soon as the currents are turned off. A displacement of 5 mm
in z axis is allowed in this design.
The simulation result is shown in Figure 6.5. Uniform force is achieved with
different displacements of the PM. The force is 45 N at 2 A/mm2 and the force
magnitude is proportional to the current density in the coil. From our experience,
when the current density in the coil is higher than 2 A/mm2, water cooling becomes
necessary, which is undesirable in this project. The hybrid design can successfully
generate enough force with uniformity, however, since the PM is adopted, magnetic
materials must be avoided in the rest part of the actuator and also the PM is relatively
more expensive than soft iron.
100
Fz (N)
80
J=1 A/mm2
J=2 A/mm2
J=4 A/mm2
60
40
20
0
0
1
2
3
4
Displacement (mm)
5
Figure 6.5 Simulation result of the hybrid design and a uniform force over 5 mm is achieved.
155
3. Electromagnet Design
Figure 6.6 Schematic of the electromagnet design. The membrane (purple) can be attached on the
soft iron (green).
In the electromagnet design, a copper coil is placed inside of a fixed
soft iron housing, shown in Figure 6.6. The membrane can be attached on top of the
moving soft iron which lies above the coil. When the current is on, the moving soft
iron is attracted in -z direction, when the power is off, the force is removed. The
weight of the soft iron is about 1.1 kg. The simulation results are displayed in Figure
6.7. The force is about 20 N when current density of 1.5 A/mm2 is applied, and the
force is uniform over 5 mm. The right side of Figure 6.7 indicates the force increases
with current density and so does the estimated temperature rise.
156
Obviously, this design is more advantageous than the previous ones. Only one
coil and soft iron housing is required, which is cheap and sufficient to exert a large
uniform force. The magnetic flux is confined inside the soft iron pieces, so there is no
requirement for the materials in the rest of the actuator.
6
25
Force in -z direction
Temp. Rise per Min.
J=1.5A/mm2
15
10
4
3
40
2
20
5
0
5
60
Fz (N)
Fz (N)
20
0
1
2
3
4
0
5
1
1
2
Current
Displacement (mm)
3
Density (A/mm2)
4
Temp. Rise (Degree/Min)
80
0
Figure 6.7 Simulation result of the electromagnet design. The force is uniform over 5 mm (left)
and increases with current density (right)
6.2.2 Design Improvement
Figure 6.8 Magnetic field distributions (xz plane) in the previous electromagnet design without
(left) and with (right) soft Fe. The soft iron is far from saturation.
157
The electromagnet design was adopted for the above advantages and several
improvements were made. First, we focus on increasing force from 20N over 5 mm
displacement to 60N over 9mm. The attractive force can be simply expressed as
F  m  B
(1)
where B is the gradient field, and m is the magnetic moment of the soft magnetic
material. We managed to increase both terms, which are all related to the magnetic
induction. Magnetic induction distributions in the previous design without soft iron
(left) and with soft iron (right) are shown in Figure 6.8. The largest magnetic
induction occurs at the tip of the housing, which quickly reduces in free space and
forms a gradient field. It can be clearly seen that the magnetic induction of both soft
iron housings and moving iron pieces are still far from the saturation magnetization
2.2 T. Increasing the magnetic induction would lead to a larger gradient field and
larger magnetic moment in the moving iron, thus stronger force. Therefore magnetic
driving fields need to be enhanced to saturate the device by increasing the current in
coil. The total current in the coil can be written as:
Itotal = Acoil  Filling Factor  J
(6.2)
In which Acoil is the cross section area of the coil, and J is the current density. Filling
factor is the ratio between the total wire cross section area and the total coil area. We
assume the filling factor is fixed to 0.8 for round copper wire. J is constrained by the
temperature rise in the magnet. Therefore, in order to significantly increase the force,
158
Acoil will have to be increased, leading to an enlarged overall size of the electromagnet,
shown in Figure 6.9. The outer diameter is 120 mm. The weight of the moving soft
iron is reduced to about 0.5kg.
Even though an extra thin layer was added on top of the moving soft iron to
reduce the attracting force at its maximum displacement, a 2 mm thick spacer should
be provided between the moving iron and magnetic housing to avoid strokes larger
than 9mm where the force will quickly become larger than 130 N. Figure 6.10
illustrates the relation between the force and displacement of the enlarged design. It is
quite clear that the force has been considerably increased but the uniformity become
worse, so the enlarged design has to be further modified to regulate the force.
Figure 6.9 Improved electromagnet designs with larger coil
159
120
100
Force (N)
80
60
40
20
0
0
2
4
6
8
10
Displacement (mm)
Figure 6.10 Relation between the force and displacement of the improved electromagnet design
Through analyzing the magnetic induction distribution in the yoke when
moving soft iron at different locations, we found that the magnetic flux leakage may
give rise to the decreased force when the displacement is around 5 mm. In general, the
magnetic flux can never make a sharp turn and it always prefers to turn gradually and
smoothly. Wherever there is a sharp turn on the soft magnetic yoke, a leakage of
magnetic fluxes will occur, which means a yoke with smoother corner should have
better performance. However, a curved corner on yoke will inevitably boost the
requirement for fabrication, which resuls in a trade-off. We found the magnetic flux
could be better conducted by simply cutting off three corners on the iron housing
(Figure 6.11 left), leading to much more uniform forces (Figure 6.11 right) with
magnitude larger than 60N. The electric parameters are listed in Table 6.1.
160
120
Fz when moving soft is centered
Fx when shifted 0.1mm along x
100
Fz when shifted 0.1mm along x
Fz (N)
80
60
40
20
0
0
2
4
6
8
10
Displacement (mm)
Figure 6.11 The improved electromagnet design with 3 corners being cut off (left). Force in z
direction as a function of displacement when the moving soft iron is center or shifted horizontally
(right). Force in x direction is also shown on the right when the moving iron is shifted
horizontally.
The clearance in the design is set to be 1mm. A ring with non-magnetic
materials can be stuffed in the clearance with lubricant. The simulation in Figure 6.11
shows that when the moving soft iron is shifted 0.1 mm away along x axis, there will
be a normal force lower than 60N again the wall, resulting in friction in z direction to
hinder the movement of the moving soft iron. The red line and the blue line represent
the forces in z and x directions respectively. If by assumption the ring is made of
Teflon, then by using the coefficient of friction between steel and Teflon, the friction
is calculated to be as large as 12 N. Therefore, the moving iron piece has to be
properly guided to avoid large transverse forces.
161
Table 6.1 Electric parameters with filling factor of 0.8 and current density of 1.5A/mm2
Figure 6.12 displays how the force varies with the current density when the
displacement is 5 mm. When the current density increases to 2 A/mm2, the force
quickly goes up to 106 N, after which the yoke is gradually saturated. Further
increasing current density has little effect on the force.
Figure 6.12 Force vs. Current Density with displacement of 5mm
6.2.3 Comparison between Simulation and Experiment
162
After manufacturing, the electromagnet was tested to compare with the
simulation result. In the experiment both round wires and flat wires were studied,
since a flat wire with a square cross section provides higher filling factor. First
magnetic field strength from only the coil has been measured and compared to the
simulation. The results are shown Figure 6.13. The origin refers the center of the coil.
It is apparent the simulation agrees with experiments very well.
Simulation
Experiment
Figure 6.13 Magnetic field distribution inside the coil from simulation (top) and measurements
(bottom). the origin refers to the center of the coil
The comparison of the field strength along the axial axis is shown in Figure
6.14. Again an excellent agreement has been achieved.
163
Figure 6.14 Comparison of the field strength along the axial axis from the center between
measured (left) and simulated results (right)
Magnetic fields in the electromagnet without moving soft irons were measured
along selected lines in horizontal directions. Both circular wires (217 turns) and flat
wires (237 turns) were used at a 5 A DC current. The flat wire has a square cross
section, so higher filling factor is allowed.
Figure 6.15 Field strength distributions in the area of interest from the cross section view of the
electromagnet assembly. Magnetic field along the 3 lines were experimentally measured.
164
Figure 6.15 shows simulated magnetic field distributions under the same
conditions. Magnetic field strengths in x and z directions along all 3 dotted lines in
Figure 6.15 has been calculated and compared with the experimental results, while the
field in y direction is zero due to the symmetric configuration. The results are
displayed in Figure 6.16 and Figure 6.17, for circular and flat wire respectively. The
gradient of Hz (z) is proportional to attractive force in z direction, and the gradient of
Hx(x) determines the force on the moving iron along the x direction, which could give
rise to frictional force if the moving iron is in contact with electromagnet housing. The
friction will decrease the total force along z direction.
Simulated Hz
0.3
Simulated Hz
Simulated Hx
Measured Hz
0.2
0.1
0.0
-0.2
-10
0.08
0.04
HZ
-0.1
Measured Hz
Measured Hx
HX
H (T)
H (T)
Measured Hx
Simulated Hx
0.12
0.00
-5
0
Line 0 (mm)
5
10
-10
165
-5
0
Line -5 (mm)
5
10
0.14
Simulated Hz
H (T)
0.12
Simulated Hx
0.10
Measured Hz
0.08
Measured Hx
0.06
0.04
0.02
0.00
-0.02
-10
-5
0
5
10
Line -9 (mm)
Figure 6.16 Magnetic field comparison in x and z directions between simulation (line+data) and
experiment (scattered data points) with circular wire (217 turns) at 5 A DC
0.16
0.3
Simulated Hz
Simulated Hz
Simulated Hx
0.2
Simulated Hx
0.12
Measured Hz
Measured Hz
Measured Hx
0.1
H (T)
H (T)
Measured Hx
0.0
0.08
0.04
-0.1
-0.2
-10
0.00
-5
0
5
10
-10
-5
0
Line -5 (mm)
Line 0 (mm)
166
5
10
0.16
Simulated Hz
Simulated Hx
0.12
Measured Hz
H (T)
Measured Hx
0.08
0.04
0.00
-10
-5
0
Line -9 (mm)
5
10
Figure 6.17 Magnetic field comparison in x and z directions between simulation (line+data) and
measurement (scattered data) with flat wire (237 turns) at 5 A DC
From Figure 6.16 and Figure 6.17, the simulation successfully reproduces the
trend of field distribution, although the local deviation can be as large as 100%. The
reasons for the deviation are the following:
1. Magnetic properties of housing materials are different from materials used in
the simulation.
2. Measurement error. The experimental results along line-5 for round and flat
wires are very different, which is unreasonable since the field pattern is not
expected to depend on the wire shape unless the winding uniformity is
significantly different in two cases.
The force exerted on the moving iron along z-axis at different location was
experimentally measured and compared with the simulation (Figure 6.18). While the
trend is correctly predicted (except at 9mm distance), the measured force is about 20
to 35 N below the simulation.
167
120
Circular Wire Simulated
Circular Wire Measured
Flat Wire Simulated
Flat Wire Measured
100
Fz (N)
80
60
40
20
0
0
2
4
6
8
10
Displacement (mm)
Figure 6.18 Comparison between simulation and experiment of the force in z direction for both
circular and flat wire.
The discrepancies arise from the following sources. First the initial
magnetization curve used in the simulation is from laminated LTV steel at 50 Hz,
while bulk soft iron was used at DC condition in the prototype of the actuator. The
initial magnetization curve of the actual electromagnet housing material was measured
at 50 Hz (Figure 6.19 left) by using a loop tracer. Subsequently it was used in the
simulation to find Bz on line 0. The result was compared with the previous simulation
using laminated LTV steel, as shown in Figure 6.19 right. It can be seen that at the
position close to the iron housing (x< –6 and x > 6), the field calculated using the
actual material curve gradually becomes smaller than the laminated LTV steel by up
to 56%. Consequently, the smaller field induces a smaller magnetic moment in the
moving soft iron as it enters into the gap. The attracting force is determined by Eqn. 1.
Smaller magnetic moments will lead to a smaller force, resulting in the discrepancy
between the simulation and experiment.
168
To support this argument, the force along the z-axis exerted on the moving soft
iron was calculated using actual material data and results are shown in Figure 6.20.
The force was apparently decreased to around 40N, consistent with the measured
force. Although the initial magnetization of the bulk soft iron is measured at 50 Hz,
which may give result different from the real experiment since it is performed at DC,
it is clear that that initial magnetization curve has a significant effect on the attracting
force.
2.0
0.3
0.2
Soft Iron
LTV Steel
1.0
Bz (T)
B (T)
1.5
0.5
Using LTV Steal Curve
Using Measured Soft Iron Curve
0.1
0.0
-0.1
0.0
0
20
40
60
80
100
120
-10
H (Oe)
-5
0
5
10
Position on Line0 (mm)
Figure 6.19 Initial magnetization curve of LTV steel and soft iron used in fabricating the
electromagnetic housing (left). Bz on line0 with different simulation condition (right).
Another possible reason is the friction between the housing and the moving
soft iron. As we discussed previously, when the moving soft iron is shifted 0.1 mm
away along x-axis, there will be a normal force of about 60N, resulting in friction of
about 12 N along z-axis. The friction will increase when the moving soft iron shift
more along the transverse direction.
169
120
Simulation using measured soft iron
Simulation using LTV steel
Experimental result
100
Fz (N)
80
60
40
20
0
0
2
4
6
8
10
Displacement of the moving soft iron (mm)
Figure 6.20 Fz on the moving soft iron under different conditions
6.3 Simulation of Eddy Current Loss
In Maxwell 3D, loss simulation has two modes:
1. Eddy current loss calculation can evaluate the eddy current loss in general soft
magnetic objects with any shape. Material conductivity and initial
magnetization curves are required for an accurate calculation.
2. Core loss calculations evaluate the core loss in electrical lamination steel or
power ferrites. The core loss includes eddy current loss, hysteresis loss and
excessive loss. For laminations, the core losses can be expressed as
Pcore  Ph  Peddy  Pexc  k h fB 2  k eddy ( fB ) 2  k exc ( fB)1.5 (6.3)
where Ph, Peddy, Pexc are the hysteresis loss, eddy current loss and excessive
loss respectively. f is the working frequency and B is the maximum magnetic
induction in a AC cycle. The core loss coefficients kh, keddy, and kexc can be
extracted by Maxwell 3D from characteristic BP curve provided by material
170
manufacturer. BP curve describes the core loss as a function of magnetic
induction at a testing frequency.
Both modes are calculated in the post process based on the already solved transient
magnetic field quantities. Desired mode can be set from the tool bar, “Maxwell 3D”→
“Excitation”→ “Set Eddy Effect” or “Set Core Loss”. Two modes can not be selected
at the same time.
20000
Loop tracer standard sample
15000
B (Gs)
50 Hz
2000 Hz
10000
7.28 Oe ~ 3 kGs
216 Oe ~ 3 kGs
5000
0
0
50
100
150
200
H (Oe)
Figure 6.21 Geometry of the loop tracer standard sample (left). Measurement of initial
magnetization curve of the standard sample at 50 Hz and 2000 Hz is shown on the right.
In this section, the eddy current loss of a loop tracer standard sample is
simulated and compared with experimental results. The loop tracer standard sample is
a bulk ring made of a soft magnetic material: Hiperco27. The geometry of the ring and
the simulation model are shown in Figure 6.21(left). The initial magnetization curves
at 50 Hz and 2000 Hz were measured by a loop tracer, which is a required input for
the simulation setup, shown in Figure 6.21(right). Experimentally, the core losses of
the standard sample were measured at 50 Hz and 2000 Hz by using a loop tracer. In
order to separate the eddy current loss from the total loss, the core losses of the sample
171
ring were acquired at a series of frequencies between 50 Hz and 2000 Hz.
Subsequently, the core loss Pcore/f is plotted against frequency f, according to the
expression,
Pcore
 Ph  k eddy B 2 f (6.4)
f
where B is the magnetic induction and keddy is eddy current coefficient. Equation 6.4 is
derived from Eqn. 6.3 by neglecting the excessive loss. By fitting the plot, the slope
keddyB2 can be extracted and the eddy current loss at a frequency f equals the slope
multiplied by f2. At 50 Hz, the eddy current loss extracted from experiment is 0.014 W,
which counts for 11.2% of the core loss. At 2000 Hz, the eddy current loss is 21.9 W
and counts for 83.4% of the total loss.
During the measurement, the stranded sample was driven up to 3 kGs at both
50 Hz and 2000 Hz, corresponding to maximum AC magnetic field H of 7.3 Oe and
216 Oe respectively from Figure 6.21(b). The currents in the coil are estimated to be
0.3 A at 50 Hz and 9.5 A at 2000 Hz by using I=dπH/N, in which d is diameter and N
is number of turns. In the simulation, the applied AC voltage is set so that the current
in the coil matches with the experiment. The conductivity of the material is set to be
2.5×106 S/m and sinusoidal wave is used in the simulation. The eddy current loss and
coil current are shown in Figure 6.22 as a function of time at 50 Hz and 2000 Hz
respectively. Table 6.2 illustrates the eddy current loss comparison between the
simulation and experiment. The 30% discrepancy may come from the followings: The
172
conductivity of the material is found from literature, not the manufacturer of the ring.
The winding of the standard sample ring may not be perfectly uniform.
Figure 6.22 Simulated eddy current loss and coil current as a function of time
173
Table 6.2 Comparison between experiment and simulation
Reference
[1]
Maxwell 3D user manual
174
CHAPTER 7 CONCLUSION
This dissertation has been mostly focused on ferromagnetic nanowire arrays
embedded in insulating matrices and their potential applications as magnetic pulse
sensor and microwave materials. In chapter 3 and 4 of this dissertation, a few new
phenomena of magnetic nanowire arrays are demonstrated and explained with a
theoretical model.
First, in order to develop better high frequency soft magnetic material, we
studied the permeability spectrum of various nanowire arrays. Ni, NiFe, and CoFe
nanowire arrays all showed limited permeability, which is consistent with a simple
theoretical analysis. The analysis also indicates that high permeability is possible in
nanowire arrays with the magnetocrystalline anisotropy comparable to the
demagnetization energy and its easy axis perpendicular to the nanowire. Both
conditions can be satisfied in Co nanowire arrays. With proper fabrication conditions,
we have fabricated Co nanowire arrays with crystalline easy axis perpendicular to the
nanowire. For Co nanowire arrays with diameters of 50 nm and inter-pore distances of
90 nm, the real part of the permeability is about 3.5 and the loss tangent is about 0.045
below 4.5 GHz.
175
Second, magnetic materials with tunable FMR are highly desirable in
microwave devices. When the magnetocrystalline anisotropy is negligible, the
magnetization direction of nanowires is preferably aligned along the nanowires due to
the shape anisotropy. When nanowires are very close to each other, dipolar
interactions play a significant role in the magnetic behavior of the nanowire array,
leading to zero field FMR tunability in magnetic nanowire arrays. We demonstrate
that the natural FMR of Ni90Fe10 nanowire array can be tuned continuously from 8.2 to
11.7 GHz by choosing different remanent state. In a similar fashion, natural FMR
frequency of Co nanowires can be tuned between 4.5 GHz and 6.5 GHz. Theoretical
model based on dipolar interaction among nanowires has been developed to explain
the observed phenomena. A double FMR feature caused by dipolar interaction in
magnetic nanowire array was predicted and verified in Co nanowires.
Thirdly, a dipolar field induced memory effect has been demonstrated in
magnetic nanowire arrays. The magnetic nanowire array has the ability to record the
maximum magnetic field that the array has been exposed to after the field is turned
off. The origin of the memory effect is the strong magnetic dipole interaction among
nanowires. A theoretical model is employed to explain the phenomenon. Switching
field distribution among nanowires was studied with first order reversal curve
technique to elucidate the discrepancy between the experimental result and the
theoretical prediction. Based on the memory effect, a novel and extremely low cost
magnetic field pulse detection scheme is proposed. It has the potential to measure
176
magnetic field pulse as high as a few hundred Oe without breaking down. Finally, a
couple of issues are pointed out for further development of the proposed detection
method.
In the proposed EMP detector, a magnetic field sensor is required to measure
the surface field of the magnetic nanowire array. MgO based magnetic tunnel junction
(MTJ) is one type of magnetic field sensors. The sensor application requires a
hysteresis free magnetoresistance loop and a linear response of TMR with respect to
the magnetic field. There are two strategies to achieve these features. One can use a
perpendicular magnetization configuration between two magnetic electrodes of
rectangular or ellipsoidal shape with large aspect ratio. Alternatively, one can
introduce the superparamagnetic behavior in the free layer by reducing its thickness.
The latter has the advantage of a simplified fabrication process, although a precise
control of the free layer's thickness is necessary. In chapter 5, we fabricated
CoFeB/MgO/CoFeB MTJ junctions with a relatively thin free layer and studied the
evolution of the magnetoresistance loops over annealing times at high temperatures in
Ar. We found that the MR loop becomes almost hysteresis free after 17 minutes of
annealing and that the linear region gradually increases with annealing time and a
tradeoff in TMR values. The hysteresis free loops can be well fitted by using the
theory for superparamagnetism. This implies the formation of superparamagnetic
particles in the free layer during high temperature annealing. The control of MTJ
properties with annealing time is desirable in magnetic field sensor productions.
177
At the end of this work, an electromagnet design by using electromagnetic
field simulating software is presented.
178
APPENDIX I
List of patent, publications and presentations during Ph.D. study
Patent
Xiaoming Kou, Xin Fan, Hao Zhu, John Q Xiao, “Tunable ferromagnetic resonance
and memory effect in magnetic composite materials” 2009, University of Delaware,
Provisional patent, U. S. Serial No.: 61/248,632
Publications
Published or in press:
1. Xiaoming Kou, Xin Fan, Randy Dumas, Qi Lu, Yaping Zhang, Hao Zhu,
Xiaokai Zhang, Kai Liu, John Q Xiao, “Memory effect in magnetic nanowire
array” Advanced Materials, in press
2. Xiaoming Kou, Weigang Wang, Xin Fan, Lubna Shah, Rae Tao, John Q Xiao,
“High temperature annealing induced superparamagnetism in
CoFeB/MgO/CoFeB tunneling junctions” Journal of Applied Physics, 108,
083901 (2010)
3. Xiaoming Kou, Xin Fan, Hao Zhu, Rong Cao, John Q Xiao, “Microwave
permeability and tunable ferromagnetic resonance in cobalt nanowire arrays”
IEEE Transactions on Magnetics, 46, 1143 (2010)
4. Xiaoming Kou, Xin Fan, Hao Zhu, John Q Xiao, “Tunable ferromagnetic
resonance in NiFe nanowires with strong magnetostatic interaction” Appl.
Phys. Lett. 94, 112509 (2009)
5. W.G. Wang, C. Ni, C.X. Miao, C. Weiland, L.R. Shah, X. Fan, P. Parsons, J.
Jordan-sweet, X.M. Kou, Y.P. Zhang, R. Stearret, E.R. Nowak, R. Opila, J.S.
Moodera and John Q Xiao, “Understanding the tunneling magnetoresistance
during thermal annealing in MgO-based junctions with CoFeB electrodes”,
Phys. Rev. B, 81, 144406 (2010)
6. Huanhua Wang, Xiaoming Kou, Zhiguo Pei, John Q. Xiao, Xiaoquan Shan,
Baoshan Xing, “Investigation into impact of magnetite nanoparticles on
plants” Nanotoxicology, in press
179
7. Jun-Dong Hu, Yuniati Zevi, Xiao-Ming Kou, John Xiao, Xue-Jun Wang, and
Yan Jin, “Effect of dissolved organic matter on the stability of magnetite
nanoparticles under different pH and ionic strength conditions” Science of
The Total Environment, 408, 3477 (2010)
8. Lubna R. Shah, Xin Fan, Xiaoming Kou, Weigang Wang, Yaping Zhang, Jing
Lou, Nian X. Sun and John Q. Xiao, “Effect of rapid thermal annealing on
microstructural, magnetic, and microwave properties of FeGaB alloy films”
Journal of Applied Physics, 107, 09D909 (2010)
9. Xin Fan, Kim Sangcheol, Xiaoming Kou, James Kolodzey, John Q. Xiao,
“Microwave phase detection with a magnetic tunnel junction” Applied Physics
Letter, 97, 212501 (2010)
10. Xin Fan, Yaping Zhang, Xiaoming Kou, Rong Cao, Takahiro Moriyama, John
Q. Xiao, “On chip detection of magnetic dynamics for single microscopic
magnetic dot” IEEE Transactions on Magnetics, in press
11. Yaping Zhang, Xin Fan, Weigang Wang, Xiaoming Kou, Rong Cao, Xing
Chen, Chaoying Ni, Liqing Pan, and John Q Xiao, “Study and tailoring spin
dynamic properties of CoFeB during rapid thermal annealing” Applied
Physics Letters, 98, 042506 (2011)
Under review or in preparation:
12. Lubna R Shah, Jing Lou, Xin Fan, Xiaoming Kou, Weigang Wang, Yaping
Zhang, Nian X. Sun and John Q Xiao, “Effect of interstitial addition (Boron)
on FeGa alloy film properties: microstructural, magnetic, magnetostriction
and microwave” submitted to Nanotechnology
13. W. G. Wang, C. Ni, A. Ozbay, L. R. Shah, X. Fan, X.M. Kou, A. Chen, E.R.
Nowak, C. L. Chien, and J. Q. Xiao, “Spin-polarized transport in magnetic
tunnel junctions with ZnTe barrier”, submitted to Applied Physics Letters
14. W. G. Wang, C. Ni, X. Fan, X.M. Kou, L. Shah and J. Q. Xiao, “Enhanced
tunneling magnetoresistance at large bias voltage in MgO-based double barrier
symmetric junctions”, in preparation
15. Jun-dong Hu, Xiao-Ming Kou, Yuniati Zevi, John Xiao, Xue-Jun Wang, Yan
Jin, “Effect of humic acid on transport and deposition of magnetite
nanoparticles in saturated porous media”, in preparation
16. J. Shen, S. Liu, S. T. Chui, Z. Lin, X. Fan, X. Kou, H. Zhang, J. Q. Xiao,
“Robust and tunable one-way magnetic surface plasmon waveguide”, in
preparation
17. Qi Lu, Michael W. Lattanzi, Yunpeng Chen, Xiaoming Kou, Wanfeng Li, Xin
Fan, Karl M. Unruh, Jingguang G. Chen, John Q. Xiao, “Advanced
supercapacitor electrode prepared from monolithic NiO/Ni nanocomposite”, in
preparation
180
Presentations
1. “Memory effect in magnetic nanowire array”, APS March Meeting 2011,
Dallas TX, March 21st~25th, 2011 (oral presentation)
2. “Microwave permeability and tunable ferromagnetic resonance in magnetic
nanowire arrays”, 55th Conference on Magnetism and Magnetic Materials
(MMM), Atlanta, GA, Nov. 14th-18th, 2010 (oral presentation)
3. “High temperature annealing induced superparamagnetism in
CoFeB/MgO/CoFeB tunneling junctions”, 55th Conference on Magnetism and
Magnetic Materials (MMM), Atlanta, GA, Nov. 14th-18th, 2010 (poster)
4. “Tunable ferromagnetic resonance in NiFe nanowire with strong magnetostatic
interaction”, 2010 International Conference on Microwave Magnetics, Boston,
MA, June 1st-4th, 2010 (oral presentation)
5. “High temperature annealing induced superparamagnetism in
CoFeB/MgO/CoFeB tunneling junctions”, APS March Meeting 2010, Portland
OR, March 15th-19th, 2010 (oral presentation)
6. “Tunable FMR frequency in Ni90Fe10 nanowire array”, IEEE Magnetics
Society Summer School, Colorado Springs, CO, Aug. 3rd-8th, 2008 (poster)
181
APPENDIX II
Permission letter for Figures 5.2 and 5.3
William Butler <wbutler@mint.ua.edu> Tue, Feb 8, 2011 at 4:29 PM
To: Xiaoming Kou <kouxm@udel.edu>
Xiaoming,
You have my permission to use the figures. I attach a review article that you may find interesting. It
contains color versions of both figures.
Bill
William H. Butler
Center for Materials for Information Technology
and Department of Physics
University of Alabama
Currently on Sabbatical
303 997 6780 (home)
205 246 9913 (cell)
303 497 3440 (NIST office)
182
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