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This is to certify that the

dissertation entitled

Spin Accumulation and Detection in Non-Magnetic Metals
Using Singh Domain Fermmagnet ic Metal Nanopart icles

presented by

CHARLES EDNARD IVDREAU

has been accepted towards fulfillment
of the requirements for

Ph . D ‘ degree in Physics

”mafia/1»

Major professor

N. Birge
Date 08/10/01

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6/01 c-JCIRC/DaieDuepGS-p. 15

SPIN ACCUMULATION AND DETECTION IN NON-MAGNETIC METALS
USING FERROMAGNETIC METAL NANOPARTICLES

B y

Charles Edward Moreau

AN ABSTRACT OF A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2001

Norman 0. Birge

ABSTRACT

SPIN ACCUMULATION AND DETECTION IN NON-MAGNETIC METALS
USING F ERROMAGNETIC METAL NANOPARTICLES

By

Charles E. Moreau

Linear arrays of 15nm thick, polycrystalline ComFeg nanoelements have been fab-
ricated using e—beam lithography, collimated sputtering and lift-off. The elements
have widths of 0.17 and 0.25pm, lengths from 0.5 to 4pm, pointed ends, and center-
to-center spacing of 0.5,um. Characterization by magnetic force microscopy shows that
in the virgin state these elements are single-domain and have magnetizations parallel
to their long axes. The field at which an element switches its magnetization direction
is shown to depend mainly on its width, and only slightly on its length. Fields of
about 440 and 6800e are needed to switch completely the 0.25 and 0.17pm struc-
tures, respectively. This separation in switching fields is adequate to allow elements
of different widths to be switched independently. Also, magnetic force microscopy
and super-conducting quantum interference magnetometry analysis show that a cap-
ping layer is necessary to protect the films from oxidation. Unprotected films show
an altered hysteresis loop and their associated nanostructures are not consistently
single-domain.

Using these nanoelements, we have measured the magnetoresistance (MR) of hy-
brid ferromagnetic/ normal (F/ N ) structures fabricated with a planar geometry, us-
ing multi-level electron beam lithography. The samples consist of two single-domain
nanofingers crossed by a 200nm wide Ag wire. The F elements have lengths of 2pm,
widths of 250 and 175nm respectively, and are placed parallel to each other with
a center-to—center spacing of 400nm. The different widths enable us to change the

magnetization direction of the fingers independently. When we apply the current

between two F elements via the N wire, the device is somewhat analogous to a tradi-
tional F / N / F perpendicular current (CPP) spin valve sandwich. Magneto-transport
measurements on our sample show the typical spin valve effect. Though the effect is
relatively small for these devices (% 2 4 x 10”), it is commensurate with theoretical
predictions.

There are several experiments we plan to perform in the near future using this new
approach to spin polarized transport. These include using multiple F elements to see

the dependence of the spin-dependent signal on the distance between the spin injector

and detector, as well as an experiment where the current leaves via the normal wire.

ACKNOW’LEDGEMENTS

During my time as a graduate student I’ve found that the assumption of people in
the greater world outside of academia is that graduate students eventually graduate.
Unfortunately, there are far to many ways not to finish a degree. Without support
from professional and personal sources, it would be all but impossible to accomplish
such an arduous task. As such, I would like to acknowledge the assistance of those
without whom this dissertation would not have been possible.

To begin I would like to thank my advisor, Norman Birge, for his time and patience
during my time at MSU. From him I have learned not just subject matter, but how
to function as a professional.

Second, it is imperative to give Juan Caballero proper credit for his role in this
work. During his post—doctoral work here at MSU, Juan worked closely with this
project and helped develop the rather involved fabrication processes used in this
work, as well as the design of the device. His efforts during the boot-strap phase of
this project were vital to its success.

Next I wish to thank Professors Jack Bass and William P. Pratt, Jr. for their role
as valuable resources of knowledge, and for providing substantial laboratory support
for this work, including the use of the sputtering system and the quick clippers.

The technical staff employed by the department have also been indispensable to
this work. There is Baokang Bi, who manages the Keck Microfabrication facility,
and who has provided constant education in lithographic fabrication techniques as
well as microscopy. Also, there is Reza Loloee, who manages the sputtering system
in particular, who has assisted me in the deposition and processing of the magnetic
materials. In addition to their prescribed jobs, both have lent to me their personal
and professional knowledge and expertise in many areas of science.

This work was supported by the National Science Foundation Center for Sensor

l\*laterials (DMR—9809688), the Ford Research Laboratories, the Keck Microfabrica-
tion Facility, and NSF Grant (DMR-9801841)

There must be mention of my fellow graduate students for playing their role
in this communal endeavor: David Hoadley, Matthew Miller, Barton Pritzl, Remo
DiFranceso, Robert Slater, Peter Peterson, Michael Davis, Ryan Kruse, Aaron La—
Cluyze, and Randy Yarger. I thank you all, and apologize for leaving anyone out.

Finally I would like to thank my family for their love and patience: my wife
Caryn, and my children, Riley and Elayna. They have accepted a husband and
father distracted by the toils of graduate school. I am greatly excited to return my
full attention to them. To my parents I send thanks for emphasizing the importance

of education.

Table of Contents

LIST OF TABLES
LIST OF FIGURES

1 Introduction
1.1 Short Introduction to Magnetism ....................
1.1.1 Electron Spin and Magnetic Moment ..............
1.1.2 Magnetic Dipole Interaction ...................
1.1.3 Ferromagnetism ..........................
1.1.4 The Spin Wavefunction ......................
1.1.5 Heisenberg Ferromagnetism ...................
1.2 Magnetism in Technology ........................
1.2.1 Hard Disk Drive Media ......................
1.2.2 Hard Disk Drive Read Heads ..................
1.2.3 Magnetic Random Access Memory ...............
1.3 Motivation for This Work ........................

2 Switching in Magnetic Structures: Background and Theory
2.1 Domain Structure .............................
2.2 Magnetization Direction .........................
2.2.1 Magnetocrystalline Anisotropy ..................
2.2.2 Strain Anisotropy .........................
2.2.3 Shape Anisotropy .........................
2.2.4 Comparison of Anisotropy Energies ...............
2.2.5 Acicular Nanoelements ......................

2.2.6 Meaning of Demagnetizing Factors ...............
2.3 The Switching Field ...........................

3 Switching in Magnetic Structures: Experimental Procedure
3.1 Electron Beam Lithography .......................
3.1.1 Specific Notes Regarding Electron Beam Lithography .....
3.2 Collimated Sputtering ..........................
3.3 Magnetic Force Microscopy ........................
3.3.1 Limitations of Magnetic Force Microscopy ...........
3.3.2 Specific Notes Regarding Magnetic Force l\/Iicroscopy .....
3.4 Sample Preparation and Measurement .................

4 Switching in Magnetic Structures: Experimental Results
4.1 Fabrication of Single Domain Elements .................
4.1.1 C091Fe9 Thin FllmS ........................

4.1.2 C091 F e9 N anostructures .....................

vi

viii

go

H
OOCDOOKIOUCfivbOwal-l

y—a

H
00

13
14
14
15
16
18
19
19
22

27
27
28
30
32
34
38
38

41
41
41
43

7

8

4.2 Controlling the Switching Field .....................

Spin-Polarized 'IYansport: Background and Theory

5.1 GMR Quickly ...............................

5.2 Two-Current Series-Resister Model ...................
5.2.1 Parallel Magnetizations ......................
5.2.2 Antiparallel Magnetizations ...................
5.2.3 Calculating the GMR Signal ...................

5.3 Application of AR ............................

Spin-Polarized Transport: Experimental Procedure

6.1 Multi—level Lithography ..........................
6.1.1 Photolithography .........................
6.1.2 Alignment .............................

6.2 Ion Milling .................................

6.3 The Quick Dipper .............................

6.4 Sample Mounting .............................

6.5 Low Noise Measurement Circuit and Techniques ............

Spin-Polarized Transport: Experimental Results

Conclusions

LIST OF REFERENCES

vii

48

55
56
58
60
61
61
63

65
65
65
68
70
70
71
74

77

85

89

1.1

2.1
2.2
2.3

3.1
3.2

4.1

6.1
6.2
6.3

7.1
7.2

List of Tables

Syrnmetrized Spin \Navefunctions .................... 6
Magnetocrystalline Anisotropy Constants, K1 ............. 15
Magnetization Energy Densities ..................... 18
Demagnetizing Factors for Limiting Cases ............... 22
Electron Beam Lithography Recipe ................... 27
JOEL EBL Parameters .......................... 28
Comparison of Stoner-W’ohlfartl‘l Prediction to Switching Results . . . 51
Photolithography Recipe ......................... 66
Step-by-step EBL Alignment ....................... 69
Ion Milling Parameters .......................... 70
Run Parameters for Additive Sample .................. 79
Run Parameters for Subtractive Sample ................. 81

viii

2.1
2.2
2.3

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9

5.1
5.2
5.3

6.1
6.2
6.3
6.4

7.1
7.2
7.3

8.1

List of Figures

Origin of the Demagnetizing Field ....................
Plot of the Total Energy of A Magnetized Ellipsoid ..........
Functional Dependence of Coercive Field for Acicular N anoelements .

Generalized EBL Process .........................
Undercut ..................................
Collimating Body .............................
AFM Tip .................................
AFM Tip Closer .............................
AFM Tip Closer Still ...........................
MFM Cartoon ...............................
MFM Example, Single-domain ......................
MFM Example, Multi-domain ......................
Solenoid ..................................

COglFeg Thin Film SQUID ........................
COglFeg Thin Films With Al Protection .................
C091Feg Collimated Thin Films .....................
MFM of COglFeg Fingers .........................
MFM of COglFeg fingers .........................
Switching of Fingers ...........................
Determining the Switching Field .....................
Results of switching experiment .....................
Results of switching experiment .....................

GMR Cartoon, Parallel Alignment ...................
GMR Cartoon, Antiparallel Alignment .................
Schematic Representation of a Planar Device ..............

Overview of Photomask .........................
Zoom of Photomask ...........................
Schematic of Quick Dipper ........................
Sample lVleasurement Circuit .......................

SEM Image of a Planar GMR Sample ..................
GMR Signal From Additively Patterned Sample ............
GMR Signal From a subtractively Patterned Sample .........

Improved Sample Design .........................

ix

21
24
26

29
29
31
33

33
35
36
37
40

42
44

46
47
50
52
53
54

59
59
64

78
8O
82

88

Chapter 1: Introduction

Magnetism and magnetic substances have been known to man since ancient
times. There are written accounts that date the knowledge of magnetism in
lodestone (magnetite) to at least 6OOB.C., and it is possible that the Chinese used a
compass as early as 2SOOB.C.[1] This early knowledge of magnetism can be
attributed to the existence of permanent magnets. Permanent magnets are
materials which posses a spontaneous magnetization, even at elevated temperatures.
It must have seemed quite extraordinary four thousand years ago to find a rock that
would attract objects through an invisible force. Since those ancient times,
permanent magnets and electromagnets have been used in myriad devices and
technological applications. From compass needles to cars, magnets are everywhere.
Magnetic fields, both from permanent magnets or generated by electricity, also have
been employed in everything from the medical profession to mall security. It is no
small wonder, then, that there should be a strong interest in investigating the
fundamental properties of magnetism.

But there is more than just credit cards and cellular phones to spur our efforts.
Magnetism as an intellectual pursuit has great intrinsic interest. Magnetism
represents a complex many-body ground state for electrons which, unlike another
such ground-state, the superconducting state, persists at high temperature.
Moreover, like superconductivity, magnetism is a purely quantum mechanical effect.
This fact is masked by the many historical explanations of magnetism, all of which,
as we shall see shortly eventually lead down the same blind alley: classically there is
no ferromagnetism. But even in the light of quantum mechanics, magnetism, like
many problems that involve electrons in materials, proves to be a difficult problem,

with many unanswered questions.

1.1 Short Introduction to Magnetism

So the real root of magnetism, like superconductivity, is the motion and spin of
the electron. The ground state of a BCS superconductor is made up of
quasi-particles that look like paired electrons[2]. The constituents of such a pair have
oppositely directed momenta and spins. In the case of magnetism, we have a ground
state that is described by electrons with net orbital and spin angular momenta. For

the purposes of this dissertation we will be primarily concerned with the latter.

1.1.1 Electron Spin and Magnetic Moment

The spin angular momentum of the electron was first devised to explain the
magnetic field induced splitting in atomic spectral lines that were observed by
Zeeman in 1896[3]. He suggested that an electron has a magnetic moment, [1, which
is the result of its intrinsic spin angular momentum. With the advent of relativistic
quantum mechanics, this spin was found to be an inherent property of the electron.
This spin may be completely described by two quantities: S, the total moment of
the particle, and Sz, the projection of the total moment onto the z-axis. Why the
z-axis? well, it need not be the z axis. In need only be an axis. Once the projection
of the spin is measured on one axis, then there is no information to be had about
projections onto the other two axes. The reason comes for the fact that in the
quantum mechanics formalism, the spin operators St, Sy, and 82 all commute with
the total spin-angular momentum operator, S2, but not with one another. This
implies that there is a Heisenberg uncertainty relation between values of the spin
along axis. By knowing one, we can forget about the others.

So, the magnetic moment of the electron can be written as follows[3]:

 

(a): (1.1)

Here, e is the charge of the electron, me is the mass of the electron, c is the speed of
light in vacuum, and :3 is the unit vector along the z-axis. For the electron, g has a

value of close to 2. 82 for the electron, which is a spin-% particle, may have values of
(52) = i—h. (1.2)

Substituting Equation 1.2 into Equation 1.1 gives

 

eh
T = 1.3
u $92,,“ ( )
or
.17 = HHBE (1-4)

where we have introduced the Bohr magneton #3.

1.1.2 Magnetic Dipole Interaction

In the subsequent discussion of magnetism, electrons will be treated as simply
magnetic dipoles whose moment is given by 1.4. A collection of moments that
spontaneously aligns is said to be ferromagnetic. But what causes the alignment?
The first logical place to begin looking is the dipolar magnetic interaction. The

magnetic field of a dipole is

 

where f is the vector between the dipole and the field point and fl is the unit vector
in the direction of :3. Here I have deliberately omitted the delta function term from

Equation 1.5[4]. When a second dipole is brought from infinity to a point 57' we may

calculate the energy from

Ez—fiBfi) um

Substituting equation 1.5 for moment 1 into Equation 1.6 for moment 2, we have

 

3072 - fiWI ’ [51) + fl2 471

 

 

E : - 1.7
|f|3 ( )
Neglecting the angular dependence of Equation 1.7, and substituting into it
Equation 1.3, we have
(9MB)2 e2 2 (10 3‘32 1 a0 3
E z , 5:: ——~ —— —— z — R’ 5 1.8
LL“ (he) (7‘) a0 (137)2(1') y[ i ( )

where a0 is the Bohr radius equal to -mh% = 0.529 x 10—80111, and Ry is the Rydberg
constant equal to 13.6eV. Using for the distance between spins, r, something on the
order of 2A, then Equation 1.8 gives a value of about 10‘4eV.

Comparing the above energy to thermal energy at room temperature
(300K),~ 10‘2eV, and the energy of the electrostatic (coulomb) interaction

(fractions of an eV) reveals that the magnetic dipole interaction cannot by itself

explain ferromagnetism. We must therefore seek out another explanation.

1 . 1.3 Ferromagnetism

It is apparent that lacking a classical argument for ferromagnetism, we will
require a quantum mechanical approach. The explanation for ferromagnetism, in
fact, comes about by way of symmetrizing the wave function for a many-electron
system. The discussion of this section follows from Ashcroft 85 Mermz'n [5]. In the

process of searching for a many-body ground state wave function for a collection of

electrons, we look for clues in the Hamiltonian of the form for two electrons

- h? , 2
I =——(V§+v§)+ 8

m (1.9)

The last term in Equation 1.9 represents the coulomb potential. This potential is
symmetric under exchange of the two particles. Therefore eigenstates of the
Hamiltonian will possess definite exchange symmetry. The Pauli exclusion principle
dictates that for electrons the total wave function is antisymmetric under exchange
of the particles. Next we notice that the Hamiltonian is independent of spin. This
allows us to separate the total wavefunction into a product of a spatial wavefunction
and a spin wavefunction:

\Il : \Ilspatialqlspin- (110)

1.1.4 The Spin Wavefunction

We begin by looking for the properly symmetrized wave functions, \Psmn. Using

the vector formalism we may write for a two spin system a state

I‘llspm) = lSz,1,Sz.2) = I 191)" lvl>ai l,T>a| Li) (1-11)

Where an up arrow indicates a spin up electron and a down arrow represents a spin
down electron. These states form a complete set of simultaneous eigenstates of S2
and S“, 82"" . Therefore, any linear combination of these states will also be
eigenstates. We build properly symmetrized wavefunctions out of the vectors in
Equation 1.11 by requiring that they be eigenstates of the exchange operator P12,
such that

pl.2|Sz,la 82,2) : ilSszSzJ) (L12)

The properly symmetrized (and normalized) wavefunctions are listed in Table 1.1

along with their various eigenvalues. The first wavefunction in Table 1.1is

 

 

 

State S 8,. P13
sum—m» 0 0 -1
NT) 1 1 1
fifltiH-ILU) 1 o 1
lid) 1 '1 1

 

 

 

 

 

Table 1.1: The properly symmetrized spin wavefunctions for a two particle system.
The first wavefunction, with spin=0 is antisymmetric under exchange of the particles,
while the next three, with spin=1, are symmetric under exchange of the particles.

antisymmetric under exchange of the particles. This is termed the singlet state, and
is nonmagnetic as it has total spin equal to zero. The next three are all symmetric

under exchange, and are called the triplet states. These are the magnetic states, as
they have total spin equal to 1.

If the total wavefunction is to be antisymmetric, we must build products like
Equation 1.10 using spatial and spin wavefunctions of Opposite symmetry. What is
required for ferromagnetism is to have the triplet state (spin=1) preferred over the
singlet state (spin=0). Such a triplet state would have an anti-symmetric spatial
wave function. Since the Hamiltonian is independent of spin, it is sufficient to show
that the anti-symmetric spatial wavefunction has lower total energy than the

symmetric.

1 . 1 . 5 Heisenberg Ferromagnetism

The argument that we’ve been pursuing follows from that of Heisenberg in
1928. [6, 7, 8, 9]. This was the first method that put ferromagnetism on a quantum
mechanical footing. The argument addresses the last point in Section 1.1.4 by
pointing out that the symmetric eigenstates of the spatial Hamiltonian will have
greater probability density of having r1 = r2 than do the antisymmetric eigenstates.

Since the potential energy of the problem is the coulomb interaction which goes as

the inverse of distance, the symmetric states might be expected to have higher
energy than the antisymmetric. Thus we may write for the ground state of the
problem a wavefunction that consists of an antisymmetric spatial wavefunction
multiplied by a symmetric (spin=1) spin wavefunction, as we wished to.

Well, just about as soon as the argument was formulated, it was realized that
there were problems with it. For instance, the ground state of the hydrogen
molecule (H2) is in fact a spin singlet, not a triplet. In fact, for the case of two
electrons just presented, it was shown that there is a fundamental theorem that
dictates just the opposite energy ordering, and thus the antiferromagnetic state is
preferred[5]. The proper formalism to prove the energy ordering for N electrons is, it
turns out, significantly more involved, and must be applied on a material by
material basis. In fact, there are a great many more antiferromagnetic materials
than ferromagnetic. The shortcoming in the Heisenberg formalism is that it only
takes into account first order perturbative corrections to the Hamiltonian. The
second order corrections, it turns out, aren’t negligible in general, and must be
calculated for each material. However, Heisenberg’s exchange approach, while not

complete, did show a path to a quantum mechanical description of ferromagnetism.

1.2 Magnetism in Technology

Magnetic materials certainly have played a vital role in all sorts of technologies.
However given the commercial importance of computer technology it is appropriate
to give some attention to how magnetic materials have and will continue to drive
technological innovations. Novel devices that employ magnets or the spin properties
of electrons are still being developed to expand upon current technology, or develop
new ones[10]. To illustrate this, consider three areas where the properties of

magnetic materials play a crucial role in current technology: hard disk read heads,

hard disk media, and magnetic random access memory (MRAM).

1.2.1 Hard Disk Drive Media

Current Hard disk drives utilize platters coated with a magnetic thin film,
typically CoCrPtTaB or CoCrPtTaNb[11]. Thin film technology suffers from a
fundamental bit density limit, which occurs when there is enough thermal energy
available to overcome the energy barrier to switching. In thin film recording, the
number of crystallographic grains that constitute a bit must remain constant in
order to maintain an adequate signal-to—noise ratio. In order to shrink the bit, then,
one must shrink the grain size. However, as the grain size shrinks, so too does the
energy required to flip them[12]. Thus as the density of the bits increases, and hence
the size of each bit decreases, so to does the energy barrier to switching. At some
critical size, the amount of thermal switching of bits becomes unacceptable, and the
information stored in the device is lost. This limit, known as the superparamagnetic
limit[13, 14, 15, 16] was estimated to occur at 40% [17]. To date, there are two
strategies for clearing this hurdle. The first continues using thin film media, but
substitues for the single metal layer a pair of layers sandwiched around an extremely
thin (z6A) layer of ruthenium[18, 19]. The result is that bits consist of two
antiferromagnetically coupled domains, one above the other and separated by the
ruthenium. Such media has been appropriately named antiferromagnetically
coupled (AFC) media. This technique is expected to reach 100%? . In addition to
this advanced thin film technology, there is a push to develop perpendicular
recording or patterned recording media. Here, the bits are comprised of, say,
columnar magnetic structures whose magnetization lies normal to the platter
surface, or single-domain nanometer size structures whose magnetization lies in the
plane of the structure. The uncompensated poles at the ends of such structures

represent the bits to be written and read. Here the density limit is a function of the

density of packing such structures on a planar surface, barring any interaction
effects[20, 21]. Methodologies have been suggested for producing such discrete

media with densities of up to 50C " [22, 23, 24].

171

 

1.2.2 Hard Disk Drive Read Heads

Hard disk read heads have also benefitted from magnetism research.
Historically, read heads were simple inductive devices which read and wrote data via
a coil wrapped around a magnetic pole piece. These were replaced in the early
1990’s by a design that relied on the anisotropic magnetoresistance (AMR) of the
head. The AMR of a magnetic material depends on the angle between the electrical
current and the internal magnetization of the read head, the latter being a function
of the external magnetic field from the bits. These head designs were more sensitive,
and hence could be made smaller than the previous inductive designs. However as
the bit density of the hard drive platters increased, the volume of magnetic material
and also the spatial extent of each bit decreased. So, in 1997 [12] IBM developed
the first giant magnetoresistance (GMR) read head. GMR, like MR, is a field
dependant resistance. In the case of GMR the value of the resistance is a function of
the angle between the magnetizations of two ferromagnetic thin films which are
separated by a thin spacer. These devices are often termed spin valves, and are
typical of a general class of devices which consist of four layers. There is the free
magnetic layer, which switches with the applied magnetic field, the spacer, the
pinned magnetic layer, and the pinning layer which is an antiferromagnet that
couples strongly to the pinned layer, preventing it from switching freely in the
external applied field. The development of the GMR heads allowed for even smaller

bits and higher bit densities.

1.2.3 Magnetic Random Access Memory

Historically, ferromagnetic structures were used as memory elements as early as
the late 1940’s[25]. These designs, though consuming little power, were quite slow
when reading and writing. So the computer industry developed random access
memory (RAM) designs that used capacitors (DRAM) and transistors (SRAM) as
the bit elements. These proved much faster, and could be made more dense, than
the ferromagnetic alternative. However, these newer types of memory required much
greater power (capacitors must be refreshed due to voltage leaks, transistors sink
current either in the on or off state), and are volatile, which means when the power
is removed from the device, all information is lost. Ironically, both of these problems
could be resolved by returning to magnetic elements. Improvements in fabrication
techniques now make it possible to produce dense arrays of magnetic elements which
can be addressed individually, and serve as RAM. This magnetic random access
memory (MRAM) would offer the features of low power consumption, non-volatility,
and fast switching speeds[26, 27, 28, 29]. Most of these designs involve a tunnelling

GMR effect using multi-layer stacks of ferromagnets separated by oxide layers[30, 31]

1.3 Motivation for This Work

It is easy to see that magnetic materials and spin-related transport phenomena
are the subject of intense study, due to their intrinsic interest and their
technological applications[10]. But there are a great many questions remaining
regarding the transport of spin in metals, such as the mechanism of spin memory
loss and the the spin diffusion length, and spin accumulation at interfaces[32], to
name a few. Early work in other spin—dependent transport areas like weak
localization theory and universal conductance fluctuations showed values of the spin

diffusion length on the order of 1;Lm[33]. Is this spin diffusion length the same in

10

each of these spin dependent phenomena?

In order to make these effects accessible to measurement, it is necessary to
design samples whose dimensions match these pm length scales. It is necessary then
to apply the experimental tools of mesoscopic physics to such problems. This work
develops a flexible technique for measuring spin related transport phenomena, and
presents the successful measurement of a GMR signal in a novel, planar geometry.
Moreover, this work explains some of the tools necessary for making such
measurements. Experiments such as these require magnetic elements with
controllable magnetic properties. For example, elements might be required to have
high spin polarization, be single domain with a known axis of magnetization, and
have switching fields that can be varied for different structures fabricated in the
same process step. These needs dovetail nicely with those of industry[34]. With
regard to the recording industry, it is important that the magnetic properties be
determined predominantly by the particle shape, thereby reducing
particle—to-particle variation due to factors such as grain structure or random
magnetocrystalline anisotropy.

In the first part of this work, we outline our approach to producing elements
with consistent, controllable magnetic properties. we have chosen an appropriate
magnetic material and then introduce a strong shape anisotropy. C091F€9 was
chosen due to its desirable thin-film properties: FCC crystal structure[35], low
crystalline anisotropy (hence in-plane magnetization), high moment, and moderate
coercivity (30 Gauss at 10 K). High-quality films can be produced by dc sputtering,
a process which can be made compatible with our e-beam lithographic
patterning[36]. Previous studies of other magnetic materials have shown that small,
acicular nanostructures with tapered ends are most likely to be single-domain, due
to suppression of the flux closure domains present in flat-ended structures[37]. In

this work, we employ magnetic force microscopy to determine the domain structure

11

and switching fields of C091Fe9 nanoelements of various sizes, and investigate the
fabrication steps necessary to produce consistently single-domain elements.

Injection of a spin-polarized current into a nonmagnetic metal and detection of
the spin polarization at a distant location dates back to the work of Johnson and
Silsbee in 1985. [32] Since that time, attention has shifted to the GMR effect
observed in ferromagnetic-nonmagnetic-ferromagnetic (F / N / F ) multilayers and spin
valve sandwiches.

In the second half of this work we study spin injection and detection in a planar
geometry, which allows more flexibility to perform spatially-resolved measurements
than is possible in the common sandwich geometries. To do this, we have fabricated
F / N / F devices consisting of two single-domain ferromagnetic (F) fingers crossed by
a submicron nonmagnetic (N) wire. We report here on the magnetoresistance (MR)
of these devices.

This dissertation will be divided into two distinct parts to reflect the two major
goals above . Chapters 2,3, and 4 will address the magnetic issues, while Chapters
5,6, and 7 will address the issues of spin-transport. The basis of the analysis in
Chapter 2 is the Stoner-Wohlfarth (SW) treatment of single domain particles[38].
Chapter 3 describes the steps taken to fabricate the structures with the desired
properties. Chapter 4 contains the experimental results. Chapter 5 will lay out the
basics of a spin-dependent transport theory. Chapter 6 will describe the fabrication
and measurement of the planar GMR device. Chapter 7 will discuss the results of
the transport measurement. Finally, Chapter 8 will include conclusions and

discussion of the results, as well as future plans for the experiment.

12

Chapter 2: Switching in Magnetic
Structures: Background and

Theory

Our primary concerns here are what will determine the domain structure of our
magnetic elements, what will determine the direction of magnetization of the
elements, and at what field will the direction of magnetization of an element switch.
The entire basis for this type of analysis dates back to a seminal paper by Stoner
and Wohlfarth [38]. Though this treatment is strictly classical, it holds surprising
validity for the behavior of magnetic particles whose dimensions approach the
characteristic length scales of spin-related phenomena. The Stoner-Wohlfarth
analysis (SW) follows an energy and geometric approach to solve the issues of
magnetization direction and switching field. It is this approach that we will follow

here.

2. 1 Domain Structure

Whether or not a magnetic element is comprised of a single or multiple
magnetic domains is determined by the domain wall energy. The domain wall
energy is a surface energy associated with the presence of regions separating the
individual domains, whose magnetizations are not parallel. The root of this energy
is the exchange energy, which is increased as the angle between adjacent magnetic
moments is increased. The domain wall energy competes with the energy of the

stray fields produced by the magnetic sample. In a single-domain sample, the stray

13

field energy is quite high, but there is no domain wall energy. In multi-domain
samples, there is an increase in domain wall energy along with a corresponding
decrease in stray field energy due to the formation of flux closure domain structures
within the sample which reduces the stray field. Both of these energies depend on
the sample dimensions, with larger samples favoring domain wall formation and
smaller samples favoring none. Kittel showed that. there is a critical dimension
below which the single domain structure will be preffered[39]. Using typical
numbers, he shows that for high aspect ratio needles (lengthzwidth = 20:1), the
critical width was 0.24pm and the critical length was 4.7/1m. Choosing sample

dimensions below these values should produce single domain features.

2.2 Magnetization Direction

The remnant state (zero field) magnetization of magnetic particles will be such
as to minimize the energy of the system. In this context, we do not need to
distinguish between the total energy and the free energy[38]. There are a number of
competing energies to be concerned with: magnetocrystalline, strain, and
demagnetizing energy. These energies are space dependent, and therefore give rise
to anisotropies, or preferred directions of magnetization referred to as easy axes[40].
In the absence of an applied field, the remnant. state magnetization will choose
between these easy axes. Hysteretic behavior of the resolved magnetization under

the application of an external magnetic field will reflect these anisotropies.

2.2.1 Magnetocrystalline Anisotropy

hv'lagiietocrystalline anisotropy is a result of, and contains in it, the symmetry of
the magnetic crystal. Or perhaps more correctly, it results from a breaking of

spacial symmetry by the presence of the crystal lattice. We have specifically chosen

14

for this experiment to look at ferromagnetic alloys with cubic crystal structures. For

cubic crystals the magnetocrystalline energy can be expressed as

EC 2 K1(a?a§ + (1303 + a'§a¥)[40], (2.1)

where an is the direction cosine between the magnetization vector and the in
direction unit vector. Typical values for the anisotropy constant K, are shown in

Table 2.1. For values of K1 > 0 the energy takes on a minimum at the [100], [010],

 

Alloy K1 high T K1 low T
MnFegO4 40 (290K) -20 (90K)
CUF€204 -6 (293K) -20.6 (77K)

Z110,30F€2_7004 -5.0 (290K) -21.3(90K)
C00,1F€0,9 34 (300K)
COO/11:80}; 3 (300K)
COO,5F€0.5 -11 (300K)
C00_7F€0_3 -42 (300K)

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2.1: List of the magnetocrystalline anisotropy constant for various Fe containing

magnetic alloys[40]. K1 are in units of 103 5'3

[001] directions, while for K1 < 0 the energy takes on a minimum at the [111], [1T1],

[111]. These energy minima correspond to the magnetic easy axes.

2.2.2 Strain Anisotropy

Strain anisotropy is the result of magnetostriction, the change of shape of a
magnetic specimen during the process of magnetization[40], and is mentioned here
only for completeness. Essentially when a sample becomes magnetized, the crystal
lattice becomes elongated in the direction of the magnetization. The amount of the
deformation, and the increase in strain energy associated with the crystal, will be a
function of the orientation of the magnetization relative to the crystal lattice. As

such, there will be easy axes associated with the crystal directions which yield

energy minima. In most cases, including this one, the energy scale of the
magnetostrictive effect is much smaller than the other energy scales of the problem,

and may be neglected.

2.2.3 Shape Anisotropy

Shape anisotropy is determined by the geometry of the magnetic structure. The
easy axes are determined by looking at the shape dependent demagnetizing energy.
This demagnetizing energy density, Ed, is determined by the scalar product of the
magnetization vector, 117(5), and the demagnetizing field [Ida-3'):

Eda?) —_— —%Hd(5) 471(5). (2.2)

Since we are dealing with the case of uniform magnetization, that is, single domain
particles, we may write

Mm=Mm am

where M is the magnetization per unit volume and fit is the unit vector parallel to
AI. The demagnetizing energy, in the absence of free currents, may be calculated

using a magnetic scalar potential, @(f), of the form:

rider) = —V<I>(:i:‘)[4] (2.4)
where
\7;‘.’-" GET”.
a.) . Hera... _ )Wa (2.5)
M-x1 M-$1

Since [if is constant inside the region of integration, the volume integral drops out,

and only the surface integral survives, and Equation 2.5 reduces to

M - 6'

If- an

 

(PC?) 2 dd. (2.6)

16

substituting Equations 2.6, 2.3, and 2.4 into Equation 2.2 gives
Ed(:r) = —-.u m . v f —,——;—da. (2.7)
2 [r — :r’l

We now have a form for the energy density as a function of position everywhere
inside an arbitrary shape for a uniform magnetization. It is proportional to the
square of the magnitude of the magnetization. Additionally there is a factor that is
completely geometric in nature. To continue, it is necessary to commit to a specific
geometry. However, general solutions to Equation 2.7 are not possible for all shapes.
In fact, only closed surfaces of the second kind (in particular, ellipsoids) are
possible. It turns out, however, that a great many shapes may be approximated
with good accuracy by these solutions. The mathematics of such a solution are
nonetheless complex, but are well known[41][42]. With these solutions we may write

the demagnetizing energy per unit volume as
1
E, = §.t12(Naa§+ Nbag + Nca‘j), (2.8)

where a, b, and c are the lengths of the semi-major axes of a general ellipsoid, on
are the direction cosines between the direction of magnetization and the principal
axes of the ellipsoid, and N n are called the demagnetizing factors along these

axes[38]. These demagnetizing factors obey the rule
1V1 + N2 + 1V3 Z 471'. (2.9)

The forms for N may be given as the following[42], using the reduced variables

5.
a.

,13=§and7=

Na_ .1537 , _
11—f—(1_72)%(1_m)[F(1.,9) E(k,6)] (2.10)

 

17

Nb 137' 1*“ “/2 “(I1 — 1’32)“ — ”/2lf
— 2 1 —F k,6 'i' "T—TE 57.6 ‘i‘ .
47r (1 — 7‘2)§(1—c2)[ ( ' ) (32 — 72 ( ) x3032 - 72)

 

 

] (2.11)

v, 5~ 1 — ~72 in
L 2 , I, [( I l , _ 50.72)] (2.12)
4.. <1— flaw? — )2) v

 

where E(k,6) and F(k,6) are elliptic integrals of the first and second kind, where

 

1 — .132
k2 = 1_ '72 (2.13)
and
sin2 6 = 1 — '72. (2.14)

2.2.4 Comparison of Anisotropy Energies

The energy scale of the magnetocrystalline anisotropy was set by the constant
K1 given in Table 2.1. The energy scale for the shape anisotropy is set by the value

of M in Equation 2.8, which are given in Table 2.2. If we compare the values in the

 

Alloy or Metal M
Fe 23.2
78 Permalloy 5.88

Supermalloy 3.14
CO50F€50 30.2

 

 

 

 

 

 

 

 

Table 2.2: List of the magnetization energy densities, M2[43]. Numbers are in units
of 103 ~17
m.

two tables, we see that the energy scales set by the two anisotropies are similar, with
the exception of the cobalt-iron oxide listed in Table 2.1, which possesses unusually
strong crystalline anisotropy. The suggestion here is, however, that careful choice of
material (low crystalline anisotropy, high saturation magnetization) and shape could

be used to fix the direction of magnetization in small magnetic structures.

18

2.2.5 Acicular Nanoelements

For structures in this work. we may use the forms for N in Equations 2.10.2.11,
and 2.12, and set a > b >> c, or 13 >> 7, 1 >> 7. In this case we may reduce the

arguments of the elliptic integrals to
k —+ m = 1 — 132 (2.15)

and

6—>

g. (2.16)
In this case F(k,6) and E(k.6) become K(m) and E(m), the complete elliptic

integrals of the first and second kind. Substituting them into the appropriate

equations along with the appropriate approximations, the demagnetizing factors

 

 

reduce to
N“ — "31 [M > E<- )1 (217)
47f — 1_ 132 m m ,
IV], _ (3’7 1 .
NC _ *y
4—,, —1 1,,E<m). (2.19)

W7 here the argument m:1-,:_32.

2.2.6 Meaning of Demagnetizing Factors

The physical origin of the demagnetizing factors comes from looking at the
demagnetizing field generated inside bodies with uniform magnetization. When a
body is uniformly magnetized, there will be on the outer surface free poles, whose
density is given by the numerator in Equation 2.6. These poles are analogous to the
charges on a capacitor, and generate a magnetic field inside the sample. For

instance, in the case of a flat sheet whose thickness is much less than the lateral

19

dimensions, we might see something like Figure 2.1. The magnitude of the

demagnetizing field is given as

HD = — X 0,11, (2.20)

where D,- are the demagnetizing factors, and are related to the N,- by

N,

Di (2.21)

We’ve already worked out the demagnetizing factors for the general ellipsoid,
which provides an excellent general form which provides a good approximation to
many shapes. It is instructive, however, to look at some limiting cases of the
ellipsoid. In fact, using the normalization of the demagnetizing factors given by
Equation 2.9 we may infer the values of D for some useful geometries.

Start with the case of a long, narrow cylinder. If we let the magnetization lie
parallel to the long axis, the poles are formed on the circular ends, but not on the
sides. Using the analogy of the charged capacitor plates we know that the field will
go as the inverse of the distance between the plates. So, if the length of the cylinder
goes to infinity, the field induced by the poles will go to zero, which implies that the
demagnetizing factor (HzDM) must go to zero. The remaining two factors lie in the
plane of the circular cross-section of the cylinder. The two factors must therefore be
equal, and therefore due to the sum rule each equal to %.

In the case of the infinite sheet shown in Figure 2.1, the directions in the plane
see poles way out at infinity, and therefore the demagnetizing factors must be equal,
and equal to zero. In the direction perpendicular to the plane, the sum rule dictates
that the remaining factor is equal to 1.

Finally, in the case of the the sphere, each of the factors must be equal, and the

sum rule dictates that they be equal to g. The demagnetizing factors for each of the

20

I
l
I
l
l
— —

 

. n -. - ~ .
. I ‘
. .
l : 1 -
- I . .
1
|
. I . n
. I c
i | l I l
: . _ l u 1 I
i . |
t I 1
I - - a I I
. 1
Ix
a . . A
4' . .
. . a o .
’ I
. ..
- Q t
‘ 1
. . n o l . I
x
l1 7
Q ~ » a u 1 .
1
, I i
1
- u
o \ - » a
l u
. , I r a
. 1 , 1
t. ‘. .3 ‘ .‘ ‘1',“
‘v I ‘ 7
, .. .

 

 

 

Figure 2.1: Schematic representation of the origin of the the demagnetizing field in
the case of the infinite sheet. The poles on either surface produce a magnetic field in
manner analogous to the electric field do to charges on the plates of a capacitor.

21

preceding limiting cases are listed in Table 2.3.

 

 

 

 

 

Da Db Dc
Long Cylinder 0 37 %
Flat Sheet 1 0 0
Sphere § .1: 15

 

 

 

 

 

Table 2.3: The demagnetizing factors for the limiting cases of the long cylinder, the
flat sheet, and the sphere.

So, apparently in the case of a magnetic sample, in directions where the sample
dimension is small, the demagnetizing factor is large, and from equation Equation
2.8 so to will be the demagnetizing energy. In a similar manner, where the
dimension is large, the demagnetizing factor is small, and so to will be the
demagnetizing energy. As an example, if one desired to control the magnetization
direction of the small sample, by choosing a metal with low crystalline anisotropy
and making the sample shape long and slender, it should be possible to force the

magnetization to lie parallel to the long axis.

2.3 The Switching Field

To calculate a form for the switching field we must look to the
Stoner-Wohlfarth method. We begin by looking at the total energy of a uniformly
magnetized ellipsoid in an external field. The total energy will have a term that
corresponds to the demagnetizing energy and a term that corresponds to the

external field and the magnetization:
Etol‘al : Eextcrnal '1' ED- (2'22)
Substituting Equation 2.8 into Equation 2.22 gives

- - 1
Em, = -11. H + §112(Naag + Nbaf, + N603). (2.23)

22

If c << (1, b then the magnetization will rotate in the plane of the sample, and we

may take ac = 0, on = cos 6, ab = sin 9, and
1 .
Etomlw, H) 2 H111 cosd + §AIQ{NQ cos2 6 + Nb(1 — cos2 6)}. (2.24)

The first term on the right hand side represents the field energy, where the field has
been applied parallel to the a—axis, but in the negative direction. The angle 0 is the
angle between the magnetization, M, and the positive a-axis. The two terms in the
energy compete, with the field energy wishing to flip the magnetization to the
negative direction, while the second term presents an energy barrier to such a
rotation.

Looking at the form of Equation 2.24, we know that when H is zero, the slope
of the function E(6, H) for small positive 0 will be positive (the magnetization sees a
hill to climb). As H is increased from zero, the hill is lowered, and the slope at (9 = 0
is reduced. At the critcial field, the slope of E(6, H = He) will equal zero. Moreover,
the second derivative of E(6, H = He) is negative, meaning that that the
magnetization is in an unstable equilibrium. At this point the magnetization may
spontaneously switch. Plots of Equation 2.24 in units of E/M2 for several values of
H are shown in Figure 2.2.

To calculate the value of HC it is only necessary to take the derivative of

Equation 2.24 with respect to 6 and set it equal to zero:

 

aEtotaf
, = 2.25
06 ( )
Solving Equation 2.25 for H and setting 0 = 0 gives
HG = M(Nb — Na). (2.26)

23

 

 

 

 

 

 

 

4
_ H: c
0.2
0.1 r
f. . 1
1‘ .7! 7r
4 2
-0.1
-0 2 H<Hc

 

 

 

 

Figure 2.2: Plots of the total energy as a function of 0 of a magnetized ellipsoid for
several values of the applied external magnetic field. The vertical axis is in units of

E/M2

Substituting in the forms of N from Equation 2.17 and Equation 2.18, gives

 

 

fl) 1 (37
He = 47r]\,[(—1—-_—@ 2135(m) — K(m)] — 1_ [B2[K(m) — E(m)]). (2.27)
This reduces to
_ , c (l + ,132)E(m) — 21’32K(m)
He — 47rMB[ 1 _ [32 ]. (2.28)

Rewriting Equation 2.28 in terms of m,

2 —— m)E(m) — 2(1— m)K(m)

m

 

H, = 47mg“ 1. (2.29)

(2—m)E(m)—2(l-m
m

 

The quantity )Kim) from Equation 2.28 is plotted in Figure 2.3. In
most samples considered in this work, a % 10b. This gives m=.99, for which the
quantity plotted in Figure 2.3 is essentially 1.

Thus the functional form for the ellipsoid of revolution with a > I) >> c reduces

24

for our samples to the simple form:
c
He 2 47ml]; (2.30)

It is not entirely unexpected that the energy barrier to switching would go as the
inverse of the width. This is because as the element becomes narrower, the
demagnetizing energy associated with the magnetization parallel to the b—axis grows
larger. What is surprising, perhaps, is the lack of dependence on a. In fact, it would
seem logical that the final result would have contained the quantity 3, which is the
aspect ratio of ellipsoid. However, we have essentially eliminated the a dependence
in our sample by letting the aspect ratio grow very large. Finally, there is the
surprising existence of c in the final form. The value of c is the thickness of the flat
ellipsoid. On first inspection it would have seemed that our requirement of rotation
in the plane would have eliminated any c dependence. This, however, is also a
natural consequence of the demagnetizing factors. Recall that the demagnetizing
factors must add to a constant value, and that the demagnetizing factor in a given
direction decreases as that corresponding length increases. So as the thickness of the
sample increases, its associated demagnetizing factor decreases, and returns some of
that to the total. Since the width is quite a bit less than the length, it evidently
absorbs the majority of that which has been returned, thereby increasing the

effective energy barrier to rotation.

 

 

 

 

(2—m)E(m)—2(l —m)K(m)

m

 

Figure 2.3: Plot of the quantity as a function of m.

26

Chapter 3: Switching in Magnetic
Structures: Experimental

Procedure

3.1 Electron Beam Lithography

In order to pattern elements of the required size (on the order of 100nm), we
required the use of electron-beam lithography (EBL)[44]. EBL is a form of
lithography whereby a thin polymer layer is exposed to an electron beam inside of a
scanning electron microscope. That resist layer is thereby made soluble to a
developer. The development process preferentially removes the exposed resist,
leaving a polymer layer that covers the surface of the substrate, with the substrate
uncovered in only the desired pattern. Figure 3.1 shows the process in a highly
generalized form. In principle, any new experiment will require some revision of the

general EBL procedure. Our specific procedure is indicated in Table 3.1.

 

 

 

 

 

 

 

 

 

 

 

 

Spin 9% P{MMA/MAA} 4000 rpm 403
Bake 150°C 60min
Cool
Spin 2% 450K PMMA 4000 rpm 40s
Bake 150°C 60min
Cool

Expose

Develop MIBKIIPA 1:3 23°C 608
Rinse IPA 20S
Rinse DI 203

Metalize

Liftoff Acetone 60°C 1 hour

 

 

 

 

 

 

Table 3.1: Recipe used to produce the EBL features.

27

Analysis of Table 3.1 indicates that two layers of resist are spun onto the
substrate. The first layer, a co-polymer of polymethylmethacrylate and
methylacrylic acid (P{MMA/MAA}), is more sensitive to the electron beam than is
the upper polymer layer of Polymethylmethacrylate (PMMA). The purpose of this
is to generate an undercut in the resist profile. After exposure, as development
commences, the developer begins to erode the pattern over which the beam has
been written. As the top layer clears, the developer begins to aggressively attack
the second layer at a rate much greater than that of the top. This leads to the
desired undercut. Figure 3.2 shows the result of the undercut produced by such a
bilayer. The purpose of the undercut is to ensure clean lift-off. Lift-off commenses
after the desired post-development processes. These are most generally
metalization. Were we not to use an undercut resist profile, the deposited metal
would climb the walls of the developed portion of the resist, resulting in a number of
undesired effects. These might include incomplete lift-off of the resist or sharp

vertical peaks along the edges of the resulting metal features.

3.1.1 Specific Notes Regarding Electron Beam Lithography

The EBL for this experiment was done using a JOEL JSM 840 equiped with a
tungsten hairpin filament. Typical operating parameters for the microscope are

listed in Table 3.2. In general, each batch of samples prepared will require a test

 

 

 

 

 

 

Accelerating Voltage 35keV
Course Beam Current 10pA
Measured Beam Current 5pA to 6pA
Line Dose 09-11%
Area Dose 150g];

 

 

 

Table 3.2: These are the operating parameters used in the JOEL J SM 840 scanning
electron microscope for a typical writing.

sample, where a variety of line and area doses are written, the sample developed and

28

   
  

Si chip'spim with
PMhAA/CofPMMA-h/M bil,

 

  
 

:IWBK remmesresisi 1h

, beam writes poflem
1: exposed to ’eledro

in resist layer '

    
 

ml”

 

lllllllllll
Snm

“vim. '— 4--, r». »‘,r. (fiv.—‘,——‘V— \" .—1 ,W __—~__.."

KMF 20.0kV 12.1mm x5.00k SE(U) 9i17l98 14:18 6.00um

 

Figure 3.2: SEM image showing the resist undercut of a developed bilayer of
P{MMA/l\‘IAA} and PMMA. The main image is the top View of a large box, be-
low which a series of lines have been written. The lines are left short of the box to
minimize widening of the undercut from proximity effect exposure due to the box
itself. The inset in the upper right corner is looking at the edge between the box and
the lines with the substrate tilted.

29

metallized, then imaged in the SEM to determine what doses yield the best features.

3.2 Collimated Sputtering

The refractory alloys required when using ferromagnetic materials may be
deposited by several methods. For this work we have chosen a technique known as
sputtering. Sputtering is a momentum-transfer process whereby a target made of
the species to be deposited is assaulted by argon ions which have been accelerated
at the target [45]. Excellent stoichiometric alloys can be produced using this
technique. There is a catch, however. Due to the relatively high pressure inside of a
sputtering chamber the sputtered species has a very short mean free path. As a
result, the substrate onto which we are sputtering sees an isotropic distribution of
incident momenta. If sputtering were performed in this manner the undercut
provided by the bilayer process would be insufficient to prevent coating of the side
walls. Therefore, a collimating body, pictured in Figure 3.3 is used. The collimator
is fabricated from stainless steel and is built to be compatible with the sputtering
chamber to be used. The critical dimensions of the collimator are the length of the
collimator, and the bore diameter of the long tube through which the sputtered
atoms will travel. For this particular collimator the inner bore is 0.08in and the
length is 0.40in. This body limits the momenta of incident momenta to those which
fall within some small range around the substrate normal. By doing so, the resist
undercut may adequately prevent deposited metal from coating the resist sidewalls.
It must be noted that the reduction in incident particles is accompanied by a
reduction in deposition rate at the sample. Longer sputtering times are therefore
necessary to produce desired thicknesses. Actual deposition rate is measured by

AFM topographic analysis (see Section 3.3).

30

 

Figure 3.3: Diagram of the collimating body used in the sputtering process. The
four smaller posts are for mechanical manipulation of the body inside the sputtering
chamber. The larger, single post has a hole bored parallel to the long axis which
limits the range of momenta of incident atoms that reach the substrate to a small
number around perpendicular.

31

3.3 Magnetic Force Microscopy

Magnetic force microscopy (MFM) is a modified form of atomic force
microscopy (AF M) where the tip has been coated with a magnetic alloy, and
Operates in a similar manner. In AFM, the microscope consists of a micromachined
silicon pyramid placed on the end of a cantilever. From Figure 3.6, one can deduce
that the pyramid itself has a height of roughly 10am. The radius of the tips, which
lie at the peak of the pyramid, is roughly 0.020um for ’standard’ AFM tips and
0.050/1m for coated MFM tips. From Figure 3.5, the cantilever itself is roughly
125pm long. During normal operation the tip is oscillated at its resonant
frequency, which for standard tips is between 100kHz and 300khz, and for magnetic
tips is between 50kHz and 100kHz. As the tip scans the surface, a laser reflected off
the tip monitors its oscillation. Interactions between the tip and sample surface
cause slight changes in the oscillation. In the case of standard topographic scanning
in the AFM mode, piezoelectrics in the tip holder alter the vertical position of the
tip to restore resonance. These changes in the tip height are recorded and mirror
the surface topography of the sample. In MF M mode, the phase of the oscillation is
monitored, and the piezoelectrics maintain a constant tip height. In fact, in order to
insure that the tip to sample distance remains constant throughout the scan, each
scan line is first made in topographic mode, then followed immediately by a phase
scan with the tip lifted to a height determined by the user. In this way, when the
phase of the oscillations shifts, it can be attributed solely to the magnetic
interaction between the tip and sample. This phase shift corresponds to changes in

the derivative of the perpendicular component of the magnetic field.

6H
Aooc - z (3.1)
Oz

 

32

,. -‘.‘...-'.

1 s_,- /

'. ." 2

. 3.- x 1'
I

llllllllll
75mm)

 

Figure 3.4: An SEM image of an AFM tip.

.11

\

 

Figure 3.5: An SEM image of an AFM tip, this time closer up.

lllllllllll
9.99.1"!

 

Figure 3.6: An SEM image of an AFM tip, really up close.

33

From Equation 3.1 we can deduce that in regions where the field points up, the
phase shift will be of opposite sign to those areas where the field points down.
Figure 3.7 shows a cartoon representation of the stray field from a magnetic sample
and the MFM tip.

A sample MF M image is shown in Figure 3.8. The left hand box shows a
topographic scan of a square 1,u.m on a side. The center box shows the phase
channel image acquired at a lift height of 50nm. The right hand side shows a
schematic view of the direction of magnetization. This square is single-domain.
Note in the center box that areas of light contrast correspond to uncompensated
north poles, while darker areas correspond to uncompensated south poles.

Figure 3.9 shows another square, this one 12pm on a side. Here there is
contrast all through the bulk of the square, indicating the presence of domain

structure throughout.

3.3.1 Limitations of Magnetic Force Microscopy

In principle, a phase channel map is not unique. Indeed there are an infinite
number of magnetic configurations that will yield any given magnetic scan.
However, in cases where symmetry dictate that only certain solutions are
appropriate, a unique solution can often be inferred. Also, the tip, also being
magnetized, exerts an equal force onto the sample. In cases of soft magnetic
materials, it is possible that the imaged phase map is not the actual remnant state
domain structure. Instead, as the tip scans the surface the local domain structure is
altered in the region of the tip, generally resulting in a net attraction between the

tip and sample.

34

 

Figure 3.7: A cartoon representation of the magnetic field from the sample and the
MFM tip.

35

 

 

 

 

 

 

 

 

 

Figure 3.8: A sample MFM image. The left hand box shows a topographic scan of a
square 1pm on a side. The center box shows the phase channel image acquired at a
lift height of 50nm. The right hand side shows a schematic View of the direction of
magnetization. This square is single—domain. Note in the center box that areas of light
contrast correspond to uncompensated north poles, while darker areas correspond to
uncompensated south poles.

36

 

Figure 3.9: This is a topographic/ magnetic image of a 12pm square. The left hand
image is the topographic, the right hand image is the magnetic. Here you clearly see
areas of contrast in the bulk of the square, indicating a multi-domain sample.

37

3.3.2 Specific Notes Regarding Magnetic Force Microscopy

The IMF M measurements presented in this work were made using a Digital
Instruments 3100 N anoscope with Extender Electronics. Topographic scans were
done using tapping mode, with an rms amplitude of 2.00 volts, 5% offset. It is also
important to note that in MF M all scans are made at zero applied field. In this
work we have employed MFM for magnetometry experiments in which an external
field is applied to a sample outside of the microscope, the sample is remounted and
the MFM image acquired. The magnetization images produced in this way are of

the remnant state magnetization.

3.4 Sample Preparation and Measurement

To fabricate the samples, we start with 3in (110) Si wafers, which are diced into
chips -;—in square. These chips are prepared for EBL using the recipe in Table 3.1. In
the SEM we write various arrays of elements, varying the length and width. After
development, C091Fe9 is sputtered using the collimator in Figure 3.3. Lifting off
reveals arrays of C091Fe9 fingers which are ready for characterization.

To measure the samples, a series of MFM images is acquired. Each image
shows the remnant state (zero field) magnetization of the arrays, after a field has
been applied using a small solenoid magnet, pictured in Figure 3.10. The solenoid is
made from light gauge copper wire, with as many turns as would be accomodated
by the teflon spindle. The inner bore of the spindle is slightly larger than the 0.5m
square Si substrates used in the experiment. The solenoid was calibrated using a
flux gate magnetometer and was found to have a coil constant of 220% The
field is applied parallel to the long axes of the fingers, and the magnitude is

incremented and decremented to various values. Continuing in this way we may

count the fraction of the fingers for each given size that have flipped as a function of

38

the field applied.

39

 

Figure 3.10: Representation of the homemade solenoid magnet used in the switching
field Characterization experiments. The inner bore of the magnet is 0.5111, and the
overall length is 3.0m.

40

Chapter 4: Switching in Magnetic

Structures: Experimental Results

4.1 Fabrication of Single Domain Elements

4.1.1 C091Fe9 Thin Films

In order to achieve the desired magnetic properties, we must choose an
appropriate magnetic material. We seek a material that will provide us with a good
spin polarization, but whose crystallographic properties won’t interfere with our
efforts to control the magnetization of the samples using shape anisotropy. Thin
films studies on films produced here at MSU suggested that C091Fe9 would be a
good candidate. C091Fe9 is a cubic crystal with low crystalline anisotropy. Contrast
this with, say, pure Co, which tends to grow as a hexagonal close-pack (hcp) crystal,
and possesses a strong magnetocrystalline anisotropy which encourages the
magnetization to point out of the plane of the film.

C091Fe9 thin films also show high saturation magnetization and large coercive
fields. Figure 4.1 shows a SQUID magnetometer measurement of a 30nm thick
C091Fe9 thin film.

A concern when using refractory metals is the effect of oxygen exposure. Many
magnetic alloys form oxides that can have perverse effects on the magnetization.
Often the oxide layer is anti-ferromagnetic, and causes anomalous hysteresis effects.
One way to combat this is to cap the ferromagnetic metal with a protective layer of
inert metal, such as Au, or a metal such as Al that forms a very thin native oxide
which protects itself from further oxidation. Figure 4.2 shows a series of C091Fe9

films with various thickness of Al capping layers. Those films with adequate

41

$300

a no:

 

 

 

 

 

 

 

 

8a 8a om. 8. 8 o 8. 8.. 8.. 8m. emu.
‘IflI-llddl-diqd-‘Idfl-dl‘d fill-‘4‘]dI-‘1‘lqlil‘dl-IHIHI
escaéxflecoaoaou .10.... . . .
‘ \OGO:QOO+OIOIIO . o T
. l
a .. .3.
O ._
\ 9o
0 H
a 1 ms
0 .
7.1.1.0053)... .. 3

 

 

W/W

Figure 4.1: A SQUID measurement of a 30nm C091Fe9 thin film.

42

protection, such as that with the 2.5nm thick Al layer, exhibit normal hysteresis,
with sharp transitions at the coercive fields. As the Aluminum becomes thinner, the
hysteresis curve becomes flatter, until the case where there is no Al at all, and the
unprotected film exhibits strong flattening.

One final concern is how will the thin film properties of C091Fe9 hold up under
collimation. This might not seem like a concern initially, however in all physical
vapor deposition processes, the exact conditions of the deposition play directly into
the quality and properties of the deposited film. The collimator itself not only
changes the distribution of incident momenta (see Section 3.2) but it will greatly
lower the sputtering rate as well. In order to verify the thin film properties, several
collimated films received SQUID analysis. Figure 4.3 shows two hysteresis curves for

collimated thin films. They show good hysteresis.

4.1.2 C091Fe9 Nanostructures

Now that we have a suitable thin film candidate, it is necessary to check that
the resulting nanostructures fabricated from C091Fe9 can indeed be made single
domain, and have a controllable direction of magnetization. Using the arrays
discussed in Section 3.4, we can image the virgin state magnetization in the MF M.
Figure 4.4 and Figure 4.5 show the Topographic and MFM images of protected and
unprotected C091Fe9 arrays, respectively. The fingers in both figures are 15nm thick.
The three distinct groupings represent different width fingers. The top group are
fingers with a width of 0.25pm. The middle group has fingers of 0.17pm, while the
last group has widths of 0.10pm. Within each grouping are fingers of lengths 0.5,
1.0, 2.0, and 4.0,um, except for the thinnest grouping, where the 4.0;1m length has
been omitted. Notice that Figures 4.4 and 4.5 are consistent with our thin film
data from Figure 4.2. Like the protected thin films, the nanostructures which have

been coated with gold are indeed single domain, while those left unprotected have

43

 

250

 

 

 

 

 

 

 

 

 

 

 

 

f 77'. AA .
l \ 2% :
“2‘0. .18
0 0\ g; I"
l o, as...-
o b EEEJB
g) \ 000*"
o 22.9.52.‘
\ ooo'
, u.u.u._-8
, r°o 666.—
O .l
\ be. 6157 ‘75“
0 O - (I)
0, 0 111.3 3
b .-- : o
1t \ —D‘-‘ . O
\\ 1° s—d
“,7 “a S 2
° ° 13.2
00 . LI—
(3 3o
0 o -2
\o I
\0 :2,
\0 :°
\ :o
O O :8
\ Lo
lllljlellll 00-1111 .m
c: “2 c. «a 9 °-'
'- O O O F'-

SW/ W

Figure 4.2: SQUID measurements of various thin films. Those films whose Al cap-
ping layer were inadequate suffered from environmental oxidation. This results in a
flattening out of the hysteresis curve.

44

 

250

 

 

 

 

' I .

l IE7 A I

‘ 2" A E '

' :1 E r: ' 8

0D A r- .—s -

:1 1. g g g 8 - N

f 9:. o 3’0 3’ -

. :1 O -:C O -( ' o

5 DO 92. \ Q \ - m

1 l1 .8 LE ‘ '-
- o O ‘

I [1"). U U 1

7 i>> "0 i I ‘ 8

i s D O " '-

I> Ou- ‘

i DD 7"---_0 i I 4

d> ‘D- 7"“... -

02 “on“ w- « 3

 

-50

if;

:1 I

' Y

I

V

$7! ‘.

0.
Fie|d(Ga uss)

llllllllllllll'lllllllll
450

-100

a

1?

 

 

 

 

 

I; O
? 8
1 I
I I I I I L I l I I I I I J I I l A I I l I a
o, «2 c. V: C: ‘1'
- ° ° 9 :-

’W/w

Figure 4.3: SQUID measurements of collimated C091Fe9 thin films. The films are
thinner than the amount in the legend by about a factor of 20, due to the collima-
tor. Actual thickness was determined via AF M topographic scan. The shape of the
hysteresis curves is good.

45

Data type
2 range

a»

9.
310
«a
C
NM
«S-

a
QN

#8004001.c0r

 

Figure 4.4: Topographic and MFM scans of 20nm thick C091Fe9 fingers of various
lengths and widths. These fingers have been protected with a thin layer of Au, and
are therefore protected from environmental oxidation. As such they are single domain,
with their magnetization parallel to their long axis, which is indicated by the light
and dark contrast on the ends, with no contrast interior to the fingers.

46

Phase
1.000 de

Data type
2 range

.-
-
——
_
—

-
~—

‘1'!
1111

1'
H

“W!

:80I3001.cor

 

Figure 4.5: Topographic and MFM scans of 20mm thick C091Fe9 fingers of various
lengths and widths. These fingers have been left unprotected, and therefore exhibit
the effects of environmental oxidation, which results in the domain structure interior

to the fingers.

47

formed domain structure interior to the fingers themselves. We interpret this as due
to the existence of a native oxide layer that forms in the unprotected case.

Figure 4.4 also confirms our expectation that the fingers that remain
single-domain indeed have their magnetization pointed parallel to their long axis.

One point of interest is that in the case of the unprotected fingers of Figure 4.5,
some of the fingers have remained single-domain in spite of the oxidation. Notice
too, that the effect of shape-anisotropy is actually dependent upon the aspect ratio
of the finger. However, the tendency to remain single domain actually correlates
with the width of the finger. Those in the bottom group, which are thinnest, are
almost all single-domain. Those in the progressively wider groups exhibit a

progressively greater tendency to break into domains.

4.2 Controlling the Switching Field

Through our judicious choice of material and geometry, we have shown that we
can indeed produce magnetic features which are single-domain with a known
direction of magnetization. Now the question is, what about when we apply an
external magnetic field? When will a finger decide to switch its direction of
magnetization? Can the shape of the fingers be made so that there are fingers with
different switching fields? Proceeding in the manner described in Section 3.4, we can
apply a series of external fields of different values to an array of such single—domain
fingers. The field is applied parallel to the long axis, and after each application, the
remnant state magnetization is imaged in the MFM. First, in Figure 4.6 the top
most image in each column is a topographic scan of two different width fingers. The
second row shows the corresponding MF M image of the virgin state magnetization.
The third row shows MFM images of the same fingers after application of an

800Gauss field parallel to the long axis of the fingers, and directed upward on the

48

page. In the virgin state images, the fingers have randomly oriented magnetizations.
After application of the field, all the fingers, in both widths, have aligned themselves
with the field (light contrast represents the north poles).

After application of the large field in the upward direction, we may now
continue and apply successively larger fields in the opposite direction. In Figure 4.7,
the top most image in each column shows MF M images of the same fingers from
Figure 4.6 after application of an 800 Gauss field parallel to the long axis of the
fingers, and directed upward on the page. The second row of pictures shows the
same fingers after application of an external magnetic field of 440 Gauss directed
downward on the page. The third row shows the same fingers after the field has
been increased to 570 Gauss. Notice that after application of the 440 Gauss field, all
of the wider fingers have reversed their magnetization, while only 1 of the narrower
fingers has. Furthermore, after the field is increased to 570 Gauss, several additional
narrow fingers have switched. Continuing in this way with more field values and
more widths and lengths, we may plot the average number of fingers of a given
length and width that have switched as a function of the applied field. The results
are shown in Figure 4.8. Here you see that the different widths separate themselves
into two distinct groups with different switching fields. This is consistent with
previous results[46, 47, 48, 49].

It is also of interest to compare the switching fields thus measured to the
theoretical prediction of Equation 2.30. The results are summarized in Table 4.1.
The table was constructed using a sample thickness of 15nm and a saturation
magnetization (M) of 1500 Gauss. Notice that the calculated numbers are larger
than the measured by about a factor of 3, but the ratio of measured switching field
between the wide and narrow samples agrees with the calculated ratio. That our
measured values deviate from those calculated from the mathematically perfect

ellipsoid is not discouraging. Our elements are nearly ellipsoidal when viewed from

40

0.17x2.0 micrometer

 

  

  
   

0.25x2.0 micrometer
Tammwv

.17 "WW

f

 

Figure 4.6: Example of how application of an external field can switch the magneti-
zation of a finger. The top most image in each column is a topographic scan of two
different width fingers. The second row shows the corresponding MFM image of the
virgin state magnetization. The third row shows MFM images of the same fingers
after application of an 800 Gauss field parallel to the long axis of the fingers, and
directed upward on the page. Note that all magnetic images are acquired at zero
applied field.

50

 

 

 

 

 

 

 

0.25pm width 0.17am width
c. / b 0.060 .088
47nll§ (Gauss) 1130 1658
HC measured (Gauss) 400 600

 

 

Table 4.1: Comparison of Stoner-Wohlfarth Prediction to Switching Results.

above. However when viewed from the side, they will be quite sharp. Moreover,
physical imperfections at edges further deviate our sample geometry from the
ellipsoidal ideal, and could lower the switching field.

Figure 4.9 shows the length dependence of the switching field. Here the
dependence of switching field on length is non-monotonic. This subtlety isn’t readily

accounted for in our simple Stoner-Wohlfarth picture.

   

      
 
   

    

and“? sin-1 E:

:i a ' 1 1 '

“It Wiw' ‘ f;

g ., ’.

a. j: . g1, .-

I; 's "I 333-3
- ' .21...
ti?“ “ii

0.17x2.0 micrometer
'- “Wan-try... '-
. u a}

 

 

0.25x2.0 micrometer

 

 

Figure 4.7: Example of the determination of the switching field. The top most image
in each column shows MF M images of the same fingers from Figure 4.6 after applica—
tion of an 800 Gauss field parallel to the long axis of the fingers, and directed upward
on the page. The second row of pictures shows the same fingers after application of
an external magnetic field of 440 Gauss directed downward on the page. The third
row shows the same fingers after the field has been increased to 570 Gauss. Note that
all magnetic images are acquired at zero applied field.

52

 

800

 

600

\E

_\ _
‘ up

  

 

400
Field (Gauss)

 

J

 

 

 

 

O

.- o

N
O. O O. 10. O °. O. 10. 11
uome z'o UOJOIUJ LL'O ‘

- O
O O O O O O O
F. O. h. It! O. F. F.
1- O O O O O 9

paddy” uonaeu

Figure 4.8: Plot showing the results of the switching experiment. The vertical axis
represents the fraction of fingers of a given size that have switched their remnant state
magnetization. The horizontal axis represents the applied external field. Notice that
the two sets of widths separate themselves into two distinct groups having different
switching fields.

 

 

 

 

+ Wlde
.__.._. narrow
l
3 o

 

 

 

 

E
.9
LI- A
C
a)
.s 9
c .2
:2 E,
(I) 1 N ‘5:
s ’ - ' s
O
a 1 - c
t 1 L192
LU ' v-
1’ 9.
:‘5 1' To an
8’ 0. I -..-
3 ‘\ \ *
IO
. I ”d
O
'I'I'T‘l I'T'I Irr'T'I'I'I' 0'
OOOOOOOOOOOOOOO
0&808000000000‘0
IN” I" QQGMNNPP

(ssnee) plaL-i SumouMs

Figure 4.9: Plot showing the results of the switching experiment. Again notice that
the two sets of widths separate themselves into two distinct groups having different
switching fields. The length dependence, however, is nonmonotonic.

Chapter 5: Spin-Polarized
Transport: Background and

Theory

The study of spin-related electronic transport in solids dates back several
decades. In 1970, Tedrow, Meservey, and Fulde performed tunneling experiments to
study the Zeeman splitting of the quasiparticle density of states in a
superconductor[50]. Tedrow and Meservey followed that by using the spin-split
density of states as a tool to study the spin-polarization in ferromagnetic metals[51].

Direct injection (as opposed to tunneling) of spin from a ferromagnet into a
nonmagnetic metal was pioneered by Johnson and Silsbee in 1985. Their sample
was a macroscopic slab of pure aluminum, with two long and narrow films of
permalloy evaporated on top to form the spin injector and detector. The current
passed from the injector into the aluminum slab and exited at the end opposite of
the slab from the detector, eliminating any IR voltage drop between injector and
detector. A net spin accumulation was present at the detector due to diffusion of
the nonequilibrium spin distribution from the injector to the detector. In addition
to the direct detection of spin accumulation, these authors measured the Hanle
effect, which is the rotation of the net spin in the presence of a magnetic field
perpendicular to the direction of the injected magnetization.

Later Johnson adapted the spin accumulation experiment to a thin-film
geometry, with injector and detector placed on opposite sides of the film[52, 53].
The interpretation of that experiment was questioned later by Fert and Lee[54], who

claim that the Johnson data require an abnormally large spin diffusion length.

Theoretical frameworks to discuss spin accumulation were developed both by
Johnson and Silsbee[55, 56] and by van Son, van Kempen, and Wyder[57, 58]. The
latter treat the space-dependent chemical potentials of spin-up and spin-down
electrons near interfaces between ferromagnetic and nonmagnetic metals. Those
macroscopic approaches were later validated by Valet and Fert[59], who showed that
the macroscopic approaches work as long as the mean free path is much shorter
than the spin diffusion (or spin memory loss) length. In this chapter we will discuss
a simplified approach to spin-polarized transport, which deals only with
spin-dependent electrical resistances.

The main focus in the field of spin—polarized transport shifted suddenly in 1988
with the discovery of giant magnetoresistance (GMR) in Fe/ Cr multilayers[60, 61].
At a certain Cr thickness, the magnetizations in nearest-neighbor Fe layers are
coupled antiferromagnetically, resulting in a high resistance of the multilayer. In the
presence of an external magnetic field parallel to the plane of the layers, the Fe
magnetizations are brought into alignment, causing the resistance to decrease
dramatically. As mentioned in the Introduction, GMR has attracted much attention
due to its strong technological applications. As the field has evolved, most of the
work is performed on ”spin valves” rather than multilayers. A spin valve consists of
only two ferromagnetic (F) layers separated by a nonmagnetic (N) layer thick
enough to avoid any magnetic coupling between the F layers. One of the F layers
has its magnetization pinned, usually by proximity to an antiferromagnet, while the

other F layer is free to rotate in the external field.

5. 1 GMR Quickly

A crude understanding of GMR can be obtained from the model shown in

Figure 5.1 and Figure 5.2. The underlying assumption is that the scattering rate of

56

a conduction electron within the F layer, and perhaps also at the F / N interface,
depends on the relative orientation of the electron’s intrinsic spin and the
magnetization of the material. Let us assume for argument that the scattering rate
is low for the spin parallel to M, and high for the spin antiparallel to M. In each
figure the balls with arrows represent electrons with either 5'; = +%h (arrow
pointing up) or S; = -——12—h (arrow pointing down). These will furthermore be referred
to as spin-up and spin-down electrons, respectively. Also in each picture are regions
of alternating shades of grey, which are labelled as either an F (ferromagnetic) or a
N (normal) metal. Also, each F layer is labelled with M (magnetization) and an up
arrow or a down arrow. These indicate the direction of magnetization in the F layer.
The long, horizontal arrows indicate fictitious independent current paths for the
electrons of different spin. In Figure 5.1 the spin-up arrow and corresponding
horizontal arrow, representing the spin-up current channel, passes from left to right
through the multi—layer without any scattering events, which would be represented
as a bend in the line. The spin-down channel, conversely, will experience a
scattering event in each of the F layers. According to this cartoon, then, when the
spin direction of a transport electron is anti-aligned to the direction of
magnetization in an F layer, it will experience a scattering event. These scattering
events will serve to increase the resistance of the spin channel. In Figure 5.2, the F
layers are antiparallel, and therefore each spin channel will be anti-aligned to one
layer. Consequently, each spin channel will experience a cartoon scattering event as
it traverses the multi-layer, and each will pick up an additional resistance. Recall
that in the parallel addition of resistances, two identical resistances in parallel give a
total resistance of one-half of the individual resistances. Furthermore, if a large
resistance is added to a much smaller one, then the total resistance favors the lesser.
The consequence for our cartoon depiction of GMR is that in the case where the F

layers are parallel (Figure 5.1) because there is a spin channel that experiences no

57

 

scattering events, the current will favor that channel, yielding a net lower resistance

than the case where both channels are experiencing scattering events (Figure 5.2).

5.2 Two-Current Series-Resister Model

The two—current series-resister model approaches the GMR problem by adding
up the macroscopic forms for interface and volume resistances for each spin channel
independently, then making the parallel combination of the tw0[62]. The case to be
analyzed here is depicted by the cartoon in Figure 5.3 and is analogous to the
cartoons depicted in Figures 5.1 and 5.2. The ellipses represent F nanoelements
similar to those of Chapter 2, and represent the F layers in the GMR cartoons. The
long rectangular box in Figure 5.3 represents an N wire which crosses on top of the
F elements, which is the analog of the N layer in the GMR cartoons . The line with
arrows that curves from the left ellipse into the box and out the other ellipse in the
sample cartoon represents a fictitious current path through the sample. With this
geometry, the experiment becomes a four terminal measurement with the current
leads being the portion of the F elements where the current is flowing, and the
voltage leads being the portion of the F fingers where the current is not flowing.
This is perhaps a crude approximation, as the current flow in such a complicated
geometry will be quite non-uniform. However, to improve the accuracy of this
estimate, a finite element analysis of the sample geometry would be necessary. For
the time being, it will be adequate to continue with the above description.

In the four terminal picture, the voltage measured is between points lying
within F near the interface between F and N. So the resistance that an electron
experiences will come from the interface resistances between F and N, and the
volume resistance in N. The interface resistances depend on the relative orientation

of the electron spin and the direction of M in F. So the case of the F fingers parallel

 

 

 

 

 

 

Figure 5.1: A cartoon representation of the GMR effect. This is the case of aligned
F layers, which yields a lower resistance than the anti—parallel case.

F FA
M

 

M

 

 

 

 

\A

Figure 5.2: A cartoon representation of the GMR effect. This is the case of anti-
aligned F layers, which yields a higher resistance than the parallel case.

 

59

magnetization will be treated separately from the antiparallel case.

5.2.1 Parallel Magnetizations

Assume that the F fingers have their magnetizations aligned, and parallel to the

spin up direction. The series resistance can be written for the spin up channel as

 

 

 

2;). 1t
_. IT A n _
and for the spin down channel as
2p, rt
_ ll 1‘ ll
In all discussion to follow, BLT/N = 21:; N represents the interface resistance of an

electron entering or leaving an F element whose magnetization is parallel to the

2HF/N
l—‘r

 

electron spin. Conversely, Rig/N 2 represents the interface resistance of an
electron entering or leaving an F element whose magnetization is antiparallel to the
electron spin. In each case, the second term represents the volume resistance. The
factor of 2 is chosen so that in the absence of spin-dependent interface resistance,
the parallel combination of the two resistances gives the volume resistance in the

normal wire without considering spin. The quantity 7 parameterizes the F / N

interface and obeys the relation

ll

RF/N_1+7
IT _ _ °
Rm 1 i

The parallel resistance of the case of parallel aligned magnetizations will be

1 1 1

—— = — + — 5.4
1111101111 31 R1 ( )

60

 

which yields
1 1 1

— +
RILtotal QRL‘T/N + 28.31 QRIFI/N + 22,?

 

 

 

which yields
11 ll v
(RF/N + BfilflfRF/N + 9&1)
R” +111];

1' {1' t
( F/N2 \)+e:\"_

 

RIT,total =

5.2.2 Antiparallel Magnetizations

Similarly, we may write for the antiparallel case for the spin up channel

2pNt

‘RTZZIEWN-f 14

and for the spin down channel as
2pNt

R1 = 1111,, + A + BLT/N. (5.8)

Which leads to a total resistance of

 

IT ll
RF/N + RF/N + PNt

-R 007:
11,121 2 A

5.2.3 Calculating the GMR Signal

The GMR signal measured will be related to the difference between the
resistance of the parallel and antiparallel magnetization states. Notice that no
assumption has been made a priori regarding the relative sizes of the interface
resistances, only that the resistance is determined by whether the electron spin is
aligned or anti-aligned to the magnetization at the interface. That is to say, there is
no distinction made in this case between an up electron entering a down

magnetization layer or a down electron entering an up magnetization layer. So, the

61

quantity to look to is

AB = 311,101.111— 1211.101111-

Substituting Equation 5.6 and Equation 5.9 into Equation 5.10 gives

 

If H ll 1"
RF F/N +Ri/v + flit. _ (RF /FN + LMRF/N + Fri—t)

 

AR— —
IT 11
2 A (Hp/v+ffF/\')+ m
2 A

Simplification yields
1 (RFT/N_ lel/A N)?

Rn +11.“

AR:
4 FlN: F/N +2.1L

 

This may be rewritten as

TI 11 2 II 112
(RF/N-I-RF/N) (RF/N-R my)

11
AR _ 4 (RF/N+RF /N)2

T1 ll
RFf'V'f'RFlN + HIV—t

 

 

Defining

RL‘T/zv RF/N
11

RF /N+RF/N

 

’7:

and
.. _ RivT F/N + RF/N_ _ RF/N
”N — 4 1 — 72

 

Equation 5.13 can be written as

(2712* /N)2t

113— —
212;), +

 

(5.10)

(5.11)

(5.12)

(5.15)

The form for AR in Equation 5.13 is positive definite, from which can be inferred

that the antiparallel resistance is larger that the parallel one.

5.3 Application of AR

The form for Equation 5.16 would apply to a multilayer stack where the current
flow is essentially uniform over the area of the sample (especially in cases where
superconducting leads are used), and will have to be amended to account for cases
of nonuniform current flow, such as that depicted in Figure 5.3.

Often in the literature the CPP GMR signal is given in units of AAR, where A
is the cross-sectional area of the multilayer stack, as it is a quantity that is sample
independent. In this case it is trivial to recast Equation 5.16 into this form by

multiplying everywhere by a factor of A such that

(2%?7 'F/N)2

AAR = .

 

(5.17)

However in the case of nonuniform current flow, there are two areas to note. One is
the interface area between F and N and the other is the cross-sectional area of the N

wire. This subtlety will be discussed in greater detail in Chapter 7.

63

 

Figure 5.3: Schematic of the GMR device to be analyzed. This geometry represents
a gross approximation to the devices used later in this work.

64

Chapter 6: Spin-Polarized
Transport: Experimental

Procedure

Building upon our work of the first part, it is our goal to employ the magnetic
elements we have developed for a transport experiment. we wish to fabricate a
sample using these nanostructures as injectors and detectors of spin, in a manner
consistent with the theory of Chapter 5. To do so, we will start with a series of
C091Fe9 fingers, placed parallel to one another, with a spacing on the order of
several hundred nanometers. Across this we will place a normal wire, perpendicular
to the fingers. Both the ferromagnets and the normal wire will be connected to the

macroscopic world via a series of lithographically patterned Au leads.

6.1 Multi—level Lithography

The samples are complex, and hence so is their fabrication. To produce the
desired features, we must perform a series of independent lithographic steps. To
start with, we make a set of large leads to which we will later connect wires to the

outside world. These leads are fabricated using photolithography.

6.1 . 1 Photolithography

Photolithography (PL) is a technique which is almost identical to EBL, but
which uses ultraviolet light to expose the polymer resist, rather than a focused

electron beam. A typical PL process is listed in Table 6.1. Notice that the sequence

of steps follows in parallel with that for EBL listed in Table 3.1. The difference here
is that in order to produce our undercut, we don’t employ a bi-layer. It is possible
to accomplish the undercut using a bi-layer by first spinning a layer of resist,
administering a blanket exposure of the entire layer, then spinning the top layer.
But for this experiment, we have employed a technique of soaking a single layer of
resist in Chlorobenzene. This serves to ’harden’ the top portion of the resist layer,

making it develop more slowly and hence producing the desired undercut.

 

 

 

 

 

 

 

 

 

 

Spin Shiplee 81805 4000 rpm 405
Bake 95°C 30min
Cool
Expose AB-M Mask Aligner 2.35ec
Soak Chlorobenzene 30°C 208
Bake 5min
Develop Microposit 452 23°C 458
Rinse D1 208
Metalize
Liftoff Acetone 60°C lhour

 

 

 

 

 

 

Table 6.1: Recipe used to produce the photolithographic leads.

The pattern to be printed by the exposure step is determined by a mechanical
mask. This is made from a piece of glass, typically quartz or soda-lime, which has
been coated with a layer of metal such as chrome or germanium. This metal layer
will be processed away, typically via a lithography of its own, to leave the mask
transparent in regions to be exposed. These masks are best purchased commercially,
and can be obtained by supplying the desired pattern in a computer drafting file to
the manufacturer. The file used to produce the mask for these leads is shown in
Figure 6.1. The overall size of the print area is 0.5inch on a side. The actual bonding
pads are 1.0mm on a side. Figure 6.2 shows a zoom of the area in which we will
write the sample using EBL. The vertical distance available for writing is 40pm and
the horizontal is 60pm. In Figure 6.1 are visible the short wires which connect each

of the contact pads. These are to prevent damage to the sample during handling.

66

 

 

 

 

 

 

 

 

 

Figure 6.1: An overview of the photomask used to to produce the photolithographic
leads to which current and voltage leads may be attached later.

a a
.13. :1:
"a 1,1

Figure 6.2: A closeup of the photomask used to to produce the photolithographic

leads to which current and voltage leads may be attached later.

67

These are then scratched to disconnect the pads just prior to measurement.

6. 1.2 Alignment

The real trick to achieving multi—level lithography is ensuring that the features
you produce in the various steps are aligned. In order to align the EBL steps with
the optical, there are a series of crosses placed in the photolithographic lead pattern.
These are visible in Figure 6.1 and again in Figure 6.2. These marks are placed for
several different magnifications of the EBL system. In this way, alignment may be
preformed step-wise, first aligning at low resolution, then increasing the resolution
and realigning. The computer software which controls the EBL system is designed
to accommodate such alignment. The size, shape and position of the alignment
marks that have been printed previously in the photolithographic step are supplied
to the software, as well as the area that will form windows around the mark. After
loading a set of Au leads into the EBL system, the alignment program is invoked.
What is presented to the user is a set of windows, each of which contains an outline
of a virtual alignment mark, as well as a live scan of the area of the alignment mark.
The user may then move the virtual mark about until it aligns with actual mark.
Once they are aligned, the software computes a matrix which contains information
about the displacement and rotation of the sample relative to the EBL system.
Such alignment is necessary because each time a sample is loaded, the position and
orientation of the sample will be different. The alignment process provides a way to
register the position and orientation of the sample for each lithography. Table 6.2
lists steps involved in the process. Proceeding in this way, alignment to within an

accuracy of better than 10011111 in successive EBL steps has been performed.

68

Table 6.2: Step-by-step description of the EBL alignment technique.

Start with sample prepared with An photolithographic leads
Spin EBL resist layer as per process

Load into EBL system (JOEL JSM 840 SEM)
Focus/Stigmate at high resolution

At 200X, center substrate roughly

blank beam, switch to external raster control

launch graphical interface program for EBL

invoke the alignment program from the graphical interface
use arrows keys on computer keyboard to align virtual marks with life scan
press space to calculate intermediate matrix

repeat arrow key /space bar to ensure good alignment

press enter to save matrix

increase magnification to 800X

continue alignment, using arrows/space bar, to align 800X virtual and actual
marks

save matrix
quit alignment
select write ’with alignment’ from the graphical interface

write the appropriate sample pattern

69

 

Base Pressure 3 x 10‘°Torr
Milling Pressure 3 x 10‘4Torr

 

 

 

 

 

 

 

Flow Rate 6 SCCM
Current 20mA
Voltage 500V

 

Table 6.3: Typical ion mill parameters for Au milling.

6.2 Ion Milling

An important part of this fabrication technique is the use of a short ion-mill just
prior to deposition of the normal metal. Ion milling is a momentum transfer process
whereby atoms or molecules from a sample are removed by the bombardment of the
surface with ions, hence the name. In our samples the ion milling removes the Au
protecting layer from the ferromagnetic elements in the area where the normal
metal will be placed (the patterned resist layer protects the remaining features from
the ion mill beam). We do so to ensure ohmic metal-to—metal contact between the
ferromagnetic and normal metals. In other experiments of this nature, the ion mill
has also been used to remove the native oxide layer that forms on unprotected

ferromagnetic elements[63]. Typical ion milling parameters for Au milling are listed

nm
111111

in Table 6.3. These parameters yield a sputter rate of 38.5

6.3 The Quick Dipper

For the purposes of measuring these samples, a ”quick dipper” system designed
and built by Prof. William P. Pratt, Jr. is utilized. The quick dipper consists of a
large mouth He dewar into which is inserted a sample probe. The probe has an
electronics and plumbing connections package at the top of a long skinny tube, with
superconducting solenoid magnet at the bottom. Samples are mounted onto a stage,
and wires are bonded to the samples leads using Ag conducting paint. The wires

then attach to a Bishop Graphics strip consisting of 6 Cu stripes on a

70

non-conducting backing. These wires are bonded to the Cu stripes using Rose’s
Alloy solder. The other end of the Cu strips attach to wire that travel through the
tube to the electronics package at the top. These connections to the Cu are made
using standard resin core solder. The reason for differing solders is that the melting
points are different. The standard solder connections are made first, then those
using the Rose’s Alloy. Because the Rose’s Alloy possess a lower melting point, the
first solder connections won’t be affected. Figure 6.3 shows a schematic
representation of the quick dipper sample area, including the sample (éinch on a
side), and the bishop graphics connectors for wire bonding. Over this entire
assembly is placed a brass cap which slides up from the bottom and completely
covers the sample area. The entire assembly then slides into a second tube
containing the superconducting magnet, and both tubes are lowered together into
the He dewar. To warm up and load a new sample, only the inner tube need be
removed. The outer tube containing the magnet need not be removed at this point.
This system design greatly improves sample throughput. Samples may be run

and switched quickly, with very little warm up/ cool down time.

6.4 Sample Mounting

Sample mounting is a subject of great concern. The samples involved in this
work have extremely small cross-sectional areas. Even a minute transient voltage
will produce exceedingly high current densities in the sample region. It is therefore
necessary to take great precaution in the mounting of the sample. The first and
most important thing is to make sure that everything that the sample will come
into contact with is grounded. A grounding strap from the body of the quick dipper
to a suitable place, such as the screened room into which the measurement system is

moved, which is itself grounded to the building transformer is recommended.

71

 

Figure 6.3: A schematic representation of the quick dipper apparatus used to measure
the samples in this experiment.

72

Anyone involved in the sample mounting procedure should also be grounded at all
times. Wrist straps are readily available for this purpose. Moreover, nothing which
is non-conducting should be used to contact the sample, as they will tend to build
up static charge and their voltage will float away from ground. Upon contact with
the sample, the charge will dissipate generating potentially dangerous transient
voltages. Finally, the mounting environment can have a great deal of influence on
the build up of static charge. Adequate humidity can help alleviate such static build
up.

The manner in which the electronics are connected to the sample is also of
great importance. There are grounding switches on the electronics box used to
connect the current and voltage leads from the dipper to the measurement
equipment. These switches are placed so as to connect each sample lead to ground
through a IMQ resister, providing a safe path for spurious voltages. The connection
is made immediately as the leads enter the electronics box from the dipper. The
switches are opened at the time of the measurement. As the electronics are added
to the circuit, it is important that they be powered on before bringing the
dipper/dewer assembly into the shielded room. At start up, large draw equipment
like power supplies can generate large line voltages that can couple through the
measurement circuitry to the sample. When connections are made, it is important
that the leads of the connector are grounded through the user to the dipper before
connecting. The large power supply used to power the superconducting magnet
should have its outputs shunted, and the low output grounded. The shunt is
removed during normal operation, however the ground remains intact.

Finally, it is possible to use various filters for the protection of the sample. For
instance, a simple RC filter on each lead consisting of a resistor in series with the
sample coupled with a capacitor to ground will act as a low pass filter, discouraging

high frequency transients from travelling down the leads to the sample.

73

Following these simple techniques cannot guarantee a successful mounting,

though they will greatly reduce the risk of catastrophic failure.

6.5 Low Noise Measurement Circuit and
Techniques

Measurement of low—level voltages requires specialized techniques for
amplification and elimination of noise. The basic circuit used is depicted in Figure
6.4. A Stanford Research Systems (SRS) D8345 Synthesized Function Generator is
used to excite the sample. In series with the sample is a ballast resistor whose
resistance is much greater than that of the sample. The combination of function
generator and ballast resister appear as a current source to the sample, which is

supplying

2 x Vrms,DS345

 

(6.1)

ISO‘UTCC :

Rballast
The factor of 2 in the above is an artifact of a mismatched impedance at the output
of the SRS function generator.

The voltage is measured in a four-terminal configuration to eliminate lead
resistances from the measurement. There is no current flow in the voltage leads, and
therefore no IR (current times resistence) drop. The voltage leads head into a SRS
Model SR552 Bipolar Pre—amplifier. The output of the preamp becomes one input
of a lock—in amplifier. The other is the output of a Singer Gertsch Ratio
Transformer. The lock-in used is an SRS Model SR530. The two inputs are
subtracted, and the ratio transformer is tuned to null out the background resistance
of the sample. By doing so, the dynamic range of the lock-in is available to measure
the change in sample resistance.

The output. of the lock-in is passed into a Keithley Dl\ll\l, which is under

74

Lon-m Arm

Prim

 

§ Balm! Rama
Sump.

 

 

 

 

RmTronflm
me

Figure 6.4: Diagram of the circuit used to measure the samples in the transport
experiment.

control from a personal computer via a GPIB interface. The software for the

experiment is written in Labview.

76

Chapter 7: Spin-Polarized

Transport: Experimental Results

To begin, a sample is mounted into the quick dipper. After mounting, it is
inserted into the He dewar. All measurements are made at liquid He temperature
(4.2K). Drive is applied to the sample, and the four-terminal resistance is measured.
Next the ratio—transformer is introduced, and the A-B signal is nulled by adjusting
the ratio. After nulling, the four-terminal resistance of the sample is measured as a
function of the applied magnetic field. In each case a large field was first applied in
the plane of and parallel to the long axis of the fingers. This field defines the
positive direction. This large field ensures that the magnetizations in the fingers are
parallel. The field is then returned to zero, and increased gradually in the negative
direction until first one, and then both fingers reverse their magnetization. The field
is returned again to zero, and then increased gradually in the positive direction.
ltleasurements are made in-situ with the field, which is held constant during the
measurement.

Of the many samples produced and measured in this experiment, many had
problems with contacts between the normal and ferromagnetic metals. Data from
the two best samples are presented here. The first sample which is shown in figure
7.1 is an additively patterned set of 15 nm thick gold-capped C091Fe9 fingers crossed
by a 30nm thick Ag wire. The four-terminal resistance measured between the pair
of adjacent F fingers labeled in Figure 7.1 was 1.2 Q.

The data presented represent a typical graph in which run parameters have
been optimized for best signal-to-noise ratio. The run parameters for this run are

summarized in Table 7.1. In all experiments, however, different drive currents were

77

 

Figure 7.1: SEM micrograph of a typical planar GMR sample.

78

tried. It was not possible, however, to increase drive current indefinitely as there is

fear of either destroying the sample or heating it excessively.

 

 

 

 

 

 

 

 

 

 

Drive Amplitude 2.5Vrm, (X2)
Drive Frequency 100Hz
Ballast Resister 100KB
Drive Current 5011A
Ratio 0.00117
PreAmp Gain 100
Lock-In Sensitivity 2011V
Lock-In Phase Shift 183°
Lock-In Band Pass Filter In
Lock-In Line Filter In

 

 

 

 

Table 7.1: l\leasurement parameters used in acquisition of data in Figure 7.2.

Figure 7.2 shows that the magnetoresistance of this sample displays a clear
spin-valve signal, with discrete jumps corresponding to magnetization reversal in
specific F fingers. As the field is increased in the negative direction, the wide finger
fiips anti-parallel to the narrow one at a field of approximately —1000 Oe. This gives
rise to the higher resistance magnetic state. At a field of approximately -1300 Oe
the resistance drops as the narrower finger switches and the fingers are again
parallel. This is repeated in the positive field direction. There are two curiosities to
note, one is that while the switching fields are symmetric, the MR response is
greater in the negative field direction than in the positive, possibly due to an
additional small magnetic domain that a subsequent MFM image has revealed.
However, this explanation also would require a non-zero MR in our data at fields
below ~1300 Oe, which does not appear to be the case. Also of interest is the narrow
negative MR response that occurs just before the larger, positive one. We do not
currently have an explanation for this feature.

The second sample is a subtractively patterned set of C091Fe9 fingers crossed by
a 30nm thick Cu wire. The subtractive patterning is achieved by first depositing a

thin film, patterning the fingers, putting down a mask metal, and lifting off the

79

 

 

1000 2000

 

Applied Magnetic Field (0e)

.2000 .1000. o

 

 

 

 

(%) HIEIV

Figure 7.2: The GMR response of a planar F / N / F structure. This sample was addi-
tively patterned C091Fe9 with a Ag wire.

80

resist. The mask metal is left only in the regions of the desired fingers. At this point
the sample is ion milled to remove the unwanted thin film material, leaving just the
fingers. As a final step the remaining mask material may be wet etched, unless the
ion mill time was large enough to completely remove the mask.

The 4-terminal resistance between adjacent fingers for this sample was 1.7 Q.
The run parameters are summarized in Table 7.2 Here the situation is less well
defined. Our MF M studies indicate that there may be a non-uniform magnetization
within the fingers, which is probably an artifact of the ion-mill patterning. The
ion-mill process introduces atomic disorder, which in turn influences the magnetic
structure. As the data show in Figure 7.3, there isn’t a well defined transition from
parallel to anti-parallel. Moreover, there is some additional structure to the field
dependence of the resistance that isn’t explained by the simple parallel/anti-parallel
model. Nevertheless, the relative size of the MR signal is similar to that of the first

sample shown in Figure 7.2.

 

 

 

 

 

 

 

 

 

 

 

 

Drive Amplitude 0.2Vrms (X2)
Ballast Resister lOKQ
Drive Frequency 100Hz
Drive Current 40aA
Ratio 0.01774
PreAmp Gain 100
Lock-In Sensitivity 50p.V
Lock-In Phase Shift 224°
Lock-In Band Pass Filter In
Lock—In Line Filter In

 

 

Table 7.2: Measurement parameters used in acquisition of data in Figure 7.3.

In order to estimate whether the size of the measured GMR signal for the data
shown in Figure 7.2 is reasonable, it is possible to use Equation 5.17 with some
amendment. Although parameters for the C091Fe9/Ag interface in our experiment
have not been measured, they are probably similar to the C091Fe9 / Cu interface, for

which 7 = 0.75 and AR‘COFC/CU = 0.52 fQ m2 [64]. With regard to the area problem,

81

 

 

 

 

 

 

Applied Magnetic Field (0e)

 

-3ooo-2ooo-1ooo 0 10002000

 

 

. 1 . 4 . n . L . 1 . 1
no <- N o N <- o
°. °. G! O. °. °. ‘2
o o o c c3 c3 9

(%) HIHV

Figure 7.3: The GMR response of a planar F / N / F structure. This sample was sub—
tractively patterned C091Fe9 with a Ag wire.

82

as discussed in Section 5.3, it is necessary to ask what is meant by the area on the
left hand side of Equation 5.17. In the case of multilayers where the current is
passed perpendicular to the planes, it is natural that the area would be the
cross-sectional area of the stack, as that is the area of the region active in current
transport. In our geometry, however, the F / N contact area is greater than the
cross-sectional area of the wire by about a factor of 6. It is not clear, then what the
appropriate area to use here is. However, for the purposes of estimating the value of
AR, we may use a range of areas bounded by the wire cross section on one end and
the total F / N contact area on the other. Using those values of the area, as well as for
this sample t N = 200 nm (the approximate distance between adjacent fingers) and
pN = 25 9 nm (obtained using the wire dimensions and the four-terminal resistance
of 1.20), we obtain 6x10“4 (2 3 AR 3 2x10-2 9, or 6x10-4 3 A?” g 2x10‘2.
That our value falls just outside the low end of the estimate may indicate the
presence of spin memory loss mechanisms not included in Equation 5.17, either at
the F / N interface or in the N wire. Estimates of the spin-orbit scattering length
from weak localization measurements in Ag wires similar to those used here are
about 500 nm[65], long enough not to cause significant spin memory loss on the
scale of this experiment. Further measurements as a function of the distance
between the F injector and detector fingers will be required to sort this out.
Additionally, it has become a question what effect the Au capping layer has on
the measured GMR signal. It is possible that Au forms a short circuit connecting
the current leads to the N wire. Given that the resistivity of Au at low
temperatures is several times smaller than that of C091Fe9 (p M = 5n§2m[5],
pCOpe = 70n9m[64]) means that a significant portion of the current is passing in
through the gold and in parallel with F. The result might be a reduced spin
polarization entering the N wire, and hence a lower GMR. One solution to this

problem is to eliminate the Au protecting layer, though it isn’t clear what effect the

83

oxidation of the C091Fe9 would have on the magnetic properties of the sample. In
that case, a different choice of F might be necessary. Jedema et. al have measured a
similar effect in unprotected permalloy/ Cu structures[63], and obtained
spin-dependent signals substantially larger than ours. Using permalloy without

protection could provide a starting point for testing this idea.

84

Chapter 8: Conclusions

This work lays out the ground work for a new type of spin-transport
experiment. By designing a new type of spin injector and detector that utilizes
carefully crafted single-domain ferromagnetic particles, we have opened up a
plethora of new experiments that probe spin-transport phenomena on the micron
length scale. This is accomplished by moving away from multi-layers into a planar
geometry. The multi-layers certainly provide a more simple case to study
analytically, but the planar geometry allows greater flexibility in experiment design,
as well as the increased length scale.

Though the primary thrust of this work has always been and remains
spin-transport, on the way to making such a measurement a myriad of technical and
scientific issues had to be addressed. This led into a long and intellectually fruitful
study of the magnetic properties of single—domain mesoscopic features. In the first
part of this work has been laid out a protocol for fabricating and characterizing
magnetic structures, with an emphasis on their applicability to spin-transport
experiments. This includes using shape-anisotropy to control the magnetization and
switching behavior of the magnetic features, as well as careful choice and processing
of the material. This work has shown one possible way to employ electron beam
lithographic techniques in using multiple metals deposited in separate stages, using
alignment, to produce complicated structures for this purpose. This fabrication
procedure, as defined in this work, is by no means trivial.

The spin-transport experiment chosen as the first attempt to test the validity of
the new geometry was a GMR measurement using one injector and one detector
crossed by a normal wire. This geometry has direct analogy to the CPP spin-valve

multilayer structure[66, 67]. Though the signal is relatively small for these devices

85

(9,73 = 4 x 10”), it is not unreasonable when compared to the two-current series
resister model. The analysis of these structures is quite a bit more complicated than
the case of multilayers, however, owing to the non-uniform current flow through the
sample. Further work will be necessary to analyze the exact nature of the current
flow, as well as adapt the transport equations to this geometry.

The possibilities for future experiments involving samples of this type are quite
exciting and varied. The current sample design can be extended employing an
improved design as shown in Figure 8.1. By adding more detectors along the wire, it
should be possible to map the GMR signal as a function of distance from the
injector. Information about the spin-relaxation length in the normal wire could be
extracted therefrom. It is also desirable to extend these measurements into new
metals. Though Jedema et al.[63] have measured a similar signal in permalloy and
Cu structures, they have failed in other combinations for reasons not yet clear. That
we have seen the signal in a different material combination is of significance.
Another difference between our technique and that of Jedema et a1. is that their
experiment requires the fabrication of different samples for each length measured,
where ours in principle will be able to measure the length dependence in a single
sample. Jedema et al. reported a very long spin diffusion length in Cu at low
temperature (1 pm). It is important to see if the spin-diffusion length measure by
our technique is consistently longer than that measure by other techniques, or if
these give commensurate results.

There are also other lead configurations available, such as letting the current
leave via the normal wire, rather than through the detector, which finds analogy in
the ”potentiometric” technique of Johnson et al.[32]. This case is of interest because
the non-equilibrium spin distribution developed by the spin-accumulation at the
injector can be measured in a region away from the actual current flow. It is of

interest to see if these techniques yield the same signal. There has not yet been an

86

experiment in which both configurations have been measured in the same sample.
Moreover, there is a. question as to what effect having a magnetic element present at
a position between the injector and detector would have. on the non-equilibrium
spin-distribution.

Finally there is the possibility of incorporating tunnel junctions between the
ferromagnetic and normal features, as well as incorporating superconducting

elements and wires into the device.

87

 

' ! I
15.0w 13.1mm mast: sale) 5118:2001 1626

Figure 8.1: An improved sample design. The inclusion of additional leads will allow
greater flexibility in designing future experiments.

88

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