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Chapter 1:
Introduction
In this chapter I give an introduction to the thesis, and
describe how metallic-based spintronics has added new
possibilities in logic and memory devices to those
achievable with traditional semiconductor microelectronics.
In parallel to this development of classical information
processing,
practical
means
of
realising
quantum
computation are being sought. One approach uses low
numbers of superparamagnetic atoms to represent the
information carrying ‘qubits’. One of the main issues with
this approach is the positional control of these atoms and,
ideally, for their spacing to be varied controllably. To this
end this thesis investigates providing a way of trapping
and transporting paramagnetic atoms above domain walls
(DWs) in ferromagnetic nanowires. This chapter gives the
overall idea behind the research presented in this thesis.
Madalina Negoita
1.1. From semiconductor electronics to spintronics
In recent years the research focus in computational devices has broadened from purely
semiconductor microelectronics [1, 2] to now include ‘spintronics’ [3, 4]. Traditional
electronics uses simply the charge of electrons to operate [1, 2], but spintronic devices use
both charge and a quantum property of electrons named ‘spin’ [3, 4].
Over more than two decades researchers have focused their efforts into implementing devices
where the charge and spin of electrons can be used for a binary representation (the hard drive
read head is the first example of a spintronic device) [5]. The main purpose of using this kind
of devices is the low power consumption, high speed and non-volatile operating devices [6, 7,
8].
The research interest for ferromagnetic devices started along with the discovery of giant
magnetoresistive effect where alternate magnetic and non-magnetic layers showed an
increased resistance to an electric current that passes through the sandwich when the
magnetic layers have opposite orientation [9, 10]. After that ferromagnetic materials such as
Ni, Fe and Co started to be used widely in applications. A main characteristic of such
materials is that their magnetic structure represented by domains and domain walls (DWs)
can be changed easily by applying an external field or current so that the walls can be
transported in such materials. The main difference between transporting DWs in these two
ways is that with field one domain increases while the other decreases as the walls propagate
while a spin polarised current will interact with the spins in the material and exert a torque on
them known as spin transfer torque, so the walls tend to move in direction of current [6, 11].
For a better control of DW propagation, the magnetic materials are reduced to 1D, i.e.
nanowires. Magnetic nanowires are ferromagnetic stripes, usually of Permalloy (but other
materials can be used like Co), a few hundreds of nanometres wide, few tens of nanometres
thick and lengths that can go up to several micrometres. The first time the stripes were called
nanowires was by Nakatani et al. in [12] because the control of DWs in 3D nanowires with
cylindrical section is difficult. DW propagation in planar nanowires is influenced by wire
width, thickness, edge roughness, thermal stability and shape anisotropy [8].
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Domain walls in ferromagnetic nanowires for atom trapping applications
The behaviour of domain walls (DWs) in planar ferromagnetic nanowires is currently a topic
of great technological interest due to their proposed application in magnetic memory [6] and
logic [7, 8] technologies. The suitability of using DWs for these applications stems from their
particle-like properties, which allows them to be transported around complex networks of
nanowires [8] in a similar manner to that in which charge is transported in conventional
microelectronic devices.
While these applications primarily exploit the DWs’ dynamical properties, further utility is
promised by their monopole-like magnetic pole distributions [13] which allow the DWs to act
as nanoscopic, mobile sources of magnetic field. Previously it was shown how the field
emanating from a DW could be used to “trap” and transport ultra-cold paramagnetic atoms
[14, 15] and also magnetized micro-beads for biomedical applications [16]. When combined
with the intrinsic mobility of the DWs, such an approach could allow the creation of a
scalable platform for transporting and interacting atom-based qubits in quantum information
processing applications.
When under the influence of an applied field DWs rapidly accelerate to velocities as large as
several hundred m/s [17]. While there has been a general trend towards finding ways to
further increase these velocities, so as to enhance the operating speed of memory and logic
technologies [18, 19], the transport of trapped atoms presents the opposite challenge, i.e. that
the DWs must be slowed down. This is because there is a limit to the acceleration that an
atom may experience before it is lost from a trap. This effectively requires that DW velocities
are artificially limited to several cm/s [20] if the transport of trapped atoms is to be realised
experimentally. Achieving a reduction of this magnitude requires new approaches to
propagating DWs.
1.2. Atom trapping applications
The study of trapping and transporting ultra-cold paramagnetic atoms above magnetic
nanowires is motivated by the possibility of using the stray fields from DWs in nanowires
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[21, 22]. Ultra-cold atoms represent idealized quantum mechanical systems and have strong
potential as qubits in quantum information processing systems. It is possible to envisage that,
by coupling cold atoms to DWs, qubits could be transported above complex networks of
nanowires, allowing them to be written, read and interacted with each other [14]. There have
already been made strides experimentally towards this goal by demonstrating interaction of
ultra-cold atoms with an “atom-mirror” formed by a large array of DWs [21].
It was shown previously [14] how the field emanating from a DW could be used to trap ultracold (sub-milliKelvin) paramagnetic atoms (87Rb). These properties combined with the
intrinsic mobility of the DWs could be used to allow individual addressing of atoms and
atom-atom interactions which can perform logic gates, the basis of quantum information
processing applications. The atoms used are
87
Rb, paramagnetic atoms that have been
optically addressed into a low-field seeking state.
Such a trap is formed from the stray fields of the DW above the nanowire and applying a
field in the opposite direction to create the field minimum [21]. Trap parameters like
frequency, depth and adiabaticity are calculated in [21] as function of nanowire geometry and
type of DWs, while in [22] are presented some models to calculate stay fields from DWs at a
distance h above it.
Because the atom’s state is changed if the atom falls into a zero-field region, a top rotating
field is applied. The rotation frequency of this field must be higher than the trap’s frequency,
so that the atoms will respond to the time-averaged field modulus. The DW-cold atom
interaction has been demonstrated with a switchable atom mirror [21].
The harmonic nature of the atom traps limits the acceleration that the coupled DW-cold atom
system can experience without loss of the trapped atom. Although domain walls can
accelerate to their final velocity in under a nanosecond [17] the relevant time period over
which acceleration should be considered will be the harmonic period of the trapped atom. For
typical parameters, this will mean in practise that DW velocities should be limited to a few
cm/s. In [15] is presented a method of having low velocity DWs by placing them to
geometrically confined energy minima. This represents the basis of the study presented here.
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Domain walls in ferromagnetic nanowires for atom trapping applications
Another application that uses DWs in ferromagnetic nanowires as nanoscopic field sources is
trapping and transporting magnetized particles like beads [16, 23]. Manipulation of
superparamagnetic beads through water has been demonstrated [16, 24]. In this case, the
velocity of the coupled bead-DW system is self-limited by the hydrodynamic drag on the
bead as it travels through the fluid [25].
1.3. Thesis outline
In this thesis I present methods of propagating (DWs) through ferromagnetic nanostructures
at arbitrarily low velocities by confining them to geometrically defined energy minima. If the
applied field is then rotated, the minimum energy positions for the DWs move around the
nanowire, causing the DWs to propagate. As the field can be rotated arbitrarily slowly, DW
velocities can be easily reduced to the desired levels for transporting cold atoms.
Chapter 2 presents a theoretical introduction to magnetic materials, the various internal
energies relevant to ferromagnetic materials and how these combine to create and give
distinctive character to magnetic domains and DWs. Then, DWs that form in bulk and thin
film are presented, how they move in magnetic materials under applied fields. The study goes
further to lower dimensions, to nanoscale, where the DWs that form are transverse and vortex
walls. They move under applied fields in high velocities, the only limiting factors of the
speeds are edge roughness, impurities or notches. The discussion goes further to ring shaped
nanowires, where specific are two remanent states, vortex and onion states. In vortex state the
magnetization circulates around the ring clockwise or anticlockwise while in onion state the
magnetization circulates around half ring while in the other half it circulates in the opposite
direction, being separated by a head-to-head and a tail-to-tail DWs.
Chapter 3 presents the techniques that I have used to fabricate and characterise the samples.
Electron beam lithography was used to write the patterns in a polymer, thermal evaporation
was used to cover the sample with permalloy, the material used here, and then the polymer
was removed along with the permalloy deposited on top of it, leaving on the silicon substrate
just the wires to be investigated. Atomic force microscopy was used to check the structures
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for micron-scale defects and verify the width and thickness of the wires. Magneto-optic Kerr
effect magnetometry was used to characterise the magnetic response of the patterned
samples.
Chapter 4 presents a method of transporting DWs with applied fields at velocities less than 1
cm/s as required by our application by confining them to geometrically-defined energy
minima. The structures used are rings and several ring widths were analysed. First is shown
that it is possible to transport DWs around rings under a rotating applied field with a constant
velocity. Two parameters can be extracted from this kind of measurements: phase lag and
spot misalignment, after which the drive field, the actual field which drives the DWs in the
ring, can be calculated. The velocity of the DWs is given by the applied field frequency, so
several frequencies are analysed. There is also presented a method of calculating the local
velocity DWs experience when they depin from defects. This analysis is limited to the area
where the laser spot is placed. The effect of the applied field on the DWs shape is also
analysed. As the field increases, the walls become wider. Finally, several structures are
proposed which use ring shape nanowires to transport and interact DWs and atoms above
them.
Chapter 5 presents the analysis of a structure which allows linear DW transport at arbitrarily
low velocities. The transport of DWs in such structures is achieved for large distances, 80
μm. The structure is an undulating wire made of half rings. In order to drag the DWs in the
structure, a rotating field is applied. The field changes chirality every half-cycle clockwise to
anticlockwise and vice-versa. The analysis presented in this chapter shows that the walls can
be transported through this structure if the applied field is high enough to overcome pinning
by defects. Depending on the applied field amplitude is calculated the probability of
switching of each half-ring.
Chapter 6 presents the effect of transporting DWs in a correlated system comprising multiple
rings. Transporting DWs in such structures is affected by large periodic defects, the junctions
between rings. These systems act as statistical systems where the applied field has the effect
of temperature in statistical thermodynamics. A correlation is made between the remanent
states of rings, onion and vortex, and a number of particles in boxes. During low fields
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Domain walls in ferromagnetic nanowires for atom trapping applications
rotation, DWs can be created by splitting one wall in junction or annihilated. A calculation is
presented of DW population as function of probability of DW passage.
Chapter 7 presents the conclusions from the studies presented in this thesis.
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