Study of spin configuration of hexagonal shaped ferromagnetic structures

For the latter, hexagonal ferromagnetic structures were investigated due to its uniqueness of having a vortex state with well-defined, symmetric and moderate stray field for desirable ma

Study of Spin Configuration of Hexagonal

Shaped Ferromagnetic Structures

LUA YAN HWEE, SUNNY

(B Eng (Hons.), NUS)

A THESIS SUBMITTED FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

NUS Graduate School for Integrative Sciences and Engineering

National University of Singapore

2008

ABSTRACT

This thesis work consists of two distinct parts: the set-up of a unique characterisation system and the study of spin configurations in hexagonal ferromagnetic structures The

characterisation system developed is able to perform in-situ magnetic imaging,

structural modification and electrical transport measurement on ferromagnetic structures For the latter, hexagonal ferromagnetic structures were investigated due to its uniqueness of having a vortex state with well-defined, symmetric and moderate stray field for desirable magnetostatic interaction, which is not found in the vortices of

circular disk structures Systematic thickness reduction by in-situ FIB confirmed that

the vortex structure in hexagonal elements is stable over a wide thickness range The combined SEMPA and MFM characterisation makes it possible to determine the chirality of individual vortices By arranging the hexagons in ring networks, we found that there is an occurrence of alternating chirality configuration in the vortices when the inter-element spacing is small However, such alternating chirality distribution disappears in rings with either large inter-element spacings or additional / removed elements as well as in linear chains The results imply that, in addition to the strength, the symmetry of the stray field also plays an important role in determining the relative chirality of individual hexagons In order to explore potential applications of hexagonal elements, composite structures consisting of hexagons and a nanowire were also investigated by both magnetic-field and current-pulse induced domain wall motion measurements The results show that it is possible to cause magnetisation reversal in the composite structures by spin-transfer torque effect

CONTENTS

ABSTRACT I CONTENTS II LIST OF SYMBOL AND ABBREVATION XII ACKNOWLEDGMENTS XIII

1 INTRODUCTION 1

1.1 Ferromagnetic Elements with Different Shapes 2

1.1.1 Disks 2

1.1.2 Ellipses 5

1.1.3 Rings 6

1.1.4 Squares and rectangle elements 7

1.1.5 Wires 9

1.1.6 Other shapes 10

1.1.7 Dynamics study of ferromagnetic structures 11

1.2 Potential Applications 13

1.3 Motivation and Objectives 15

1.4 Organisation of this Thesis 17

Chapter 1 References 18

2 MICROMAGNETIC MODELLING AND MAGNETIC CHARACTERISATION TECHNIQUES 22

2.1 Introduction 22

2.2 Domain Walls in Ferromagnetic Material 23

2.2.1 Bloch wall 23

2.2.2 Neél wall 24

2.2.3 Domain walls in ferromagnetic nanowires 25

2.3 Magnetic Energy Terms in Micromagnetism 27

2.3.1 Magnetostatic self- energy 27

2.3.2 Magnetocrystalline anisotropy energy 28

2.3.3 Exchange energy 29

2.3.4 Zeeman energy 30

2.4 Micromagnetic Simulation with LLG Equation 31

2.5 Magnetic Imaging Techniques 33

2.5.1 SEMPA 34

2.5.2 MFM 39

2.6 Summary 43

Chapter 2 References 44

3 EXPERIMENTAL DETAILS AND DEVELOPMENT OF ADVANCED MAGNETIC CHARACTERISATION SYSTEM 47

3.1 Introduction 47

3.2 Fabrication Techniques 47

3.2.1 Electron beam lithography (EBL) 47

3.2.2 Thin film deposition process 48

3.2.3 Lift-off 49

3.3 Integrated Ultra High Vacuum Characterisation System Setup 49

3.3.1 FIB 50

3.3.2 Nanoprobe system 51

3.4 Experimental Set-up for Current-Induced Magnetisation Reversal Study 52

3.5 Summary 53

Chapter 3 References 54

4 STUDY OF HEXAGONAL ELEMENT ARRAYS BY SEMPA 55

4.1 Introduction 55

4.2 Experimental Details 55

4.3 Spin Configuration in a Hexagonal Element 56

4.4 Characterisation of Arrays with Various Inter-Element Spacings 60

4.5 Mechanism of Chirality Distribution 63

4.6 Correlation of SEMPA and MFM Imaging Results 64

4.7 Effect of Thickness Reduction by in-situ FIB on an Array of Hexagons 65

4.7.1 Thickness reduction by in-situ FIB 65

4.7.2 X-ray photoemission spectroscopy (XPS) 67

4.7.3 M-H curves 68

4.7.4 Micromagnetic simulation 70

4.8 Summary 72

Chapter 4 References 73

5 SPIN CONFIGURATION OF HEXAGONAL ELEMENTS IN DIFFERENT ARRANGEMENTS 74

5.1 Introduction 74

5.2 Hexagons in Artificial Arrangements 74

5.2.1 Ring network 74

5.2.2 Ring network with a missing element 78

5.2.3 Floral network 79

5.2.4 Linear chain network 83

5.2.5 Star network 84

5.2.6 Triangular network 85

5.2.7 Rhomboidal network 86

5.2.8 Pyramidal network 87

5.3 Summary 89

Chapter 5 References 90

6 MAGNETOSTATIC INTERACTION OF HEXAGAONAL ELEMENTS WITH A NANOWIRE 91

6.1 Introduction 91

6.2 Single Hexagon in Contact with a Nanowire 91

6.2.1 Nanowire 91

6.2.2 Nanowire with a notch structure 96

6.3 Six Hexagons in a Ring Network in Contact with a Nanowire 98

6.4 Six Hexagons in a Ring Network in Contact with Two Nanowires 102

6.5 Current Pulse Study on Hexagons with a Nanowire 106

6.5.1 Hexagon with a notched nanowire 107

6.5.2 Hexagons in a ring network with a notched nanowire 110

6.5.3 Hexagons in a ring network with a nanowire 113

6.6 Voltage-Pulse Injection Perpendicular to Ferromagnetic Structures 115

6.7 Summary 117

Chapter 6 References 118

7 CONCLUSIONS AND RECOMMENDATIONS 119

7.1 Conclusions 119

7.2 Recommendations for future work 121

LIST OF PUBLICATIONS 124

Journal papers: 124

Others: 124

Conferences: 125

Others: 125

LIST OF FIGURES

Figure 1.1 Magnetisation distribution in a circular disk obtained by micromagnetic

simulations for (a) a C-state and (b) S-state, respectively [After J K Ha,

2003, Ref 7] 3

Figure 1.2 Experimental observations of magnetic states in circular disk structures

together with the corresponding magnetisation distribution obtained by

micromagnetic simulation: (a) triangle state, (b) diamond state [After C A

F Vaz, 2005, Ref 10], and (c) vortex state [After T Shinjo, 2000, Ref

19] 4

Figure 1.3 Magnetic image of an elliptical structure at remanent state obtained

after an in-plane magnetic field applied along (a) long and (b) short axis,

with single domain and flux-closure state, respectively Arrows represent

the orthogonal magnetisation directions [After X Liu, 2004, Ref 32] 6

Figure 1.4 (a) MFM images of octagonal ring structures with corresponding

magnetisation distribution for SD and flux-closure states, respectively

[After S P Li, 2001, Ref 38] (b) MFM images of the square rings in a

horseshoe state, with magnetisation direction represented by arrows [After

P Vavassori, 2003, Ref 42] 7

Figure 1.5 Micromagnetic simulation of (a) a flower state and (b) a leaf state, in a

square nanomagnet of edge length 100 nm and thickness 20 nm [After R

P Cowburn, 2000, Ref 1] 8

Figure 1.6 (a) Foucault image of a rectangle in a S state [After J N Chapman,

1998, Ref 59] (b) Electron holography of a rectangle in a C state with its

corresponding magnetisation distribution in Co, and Ni and simulated

holography contours [After R E Dunin-Borkowski, 1998, Ref 52] (c)

Foucault image obtained for square and rectangle with a flux-closure state

and a seven-domain state [After K J Kirk, 2000, Ref 55] (d) Foucault

image of two rectangles with different width having a flux-closure state

and a partial flux closure [After K J Kirk, 1997, Ref 51] 9

Figure 1.7 (a) Foucault image of NiFe(26 nm thick) wires with two pointed ends in

an array [After K J Kirk, 1997, Ref 51] (b) A plot of the coercivity as a

function of the ratio of the spacing to the width when magnetic field

applied along the easy axis of the wire array [After A O Adeyeye, 1997,

Ref 70] 10

Figure 1.8 (a) SEM images of pentagon arrays in different sizes, 500 nm and 100

nm, respectively [After R P Cowburn, 2000, Ref 1] (b) SEM image of an

array of elongated hexagons, 1 mm long and 500 nm wide with its

corresponding Magnetic hysteresis loops obtained for easy and hard axis,

respectively [After G Xiong, 2001, Ref 74] 11

Figure 1.9 (a) Switching probabilities as a function of excitation current frequency

of NiFe disk used for vortex core polarity reversal by AC currents [After

K Yamada, 2007, Ref 81] (b) Schematic setup for the magnetic vortex core reversal by AC magnetic field which consists of the NiFe sample with

a flux-closure state and gold stripline [After B Van Waeyenberge, 2006, Ref 82] 12Figure 1.10 Schematics of (a) patterned media with higher storage density by

having smaller patterned elements and denser packing, and (b) MRAM, respectively 13Figure 1.11 (a) SEM image of a NiFe nanowire with a NOT function and its

corresponding magnetic signal response from a counterclockwise rotating magnetic field as a function of time [After D A Allwood, 2002, Ref 87] (b) SEM images of the left (A), center (B), and right (C) regions of two of the MQCA [After R P Cowburn, 2000, Ref 89] (c) A set of MQCA with single-domain states for majority logic gate application [After A Imre,

2006, Ref 90] (d) Schematic illustration of the shift-register operation Black squares and white squares represent head-to-head and tail-to-tail domain-walls, respectively [After M Hayashi, 2008, Ref 91] 14Figure 2.1 (a) Schematic of a ferromagnetic material containing a 180° Bloch wall

and (b) its spin orientations in a uniaxial material 24Figure 2.2 (a) Schematic of a ferromagnetic material containing a Neél wall (b)

Magnified sketch of the spin orientations of a Neél wall in a uniaxial material 25Figure 2.3 Schematic of spin orientation of a (a) transverse and (b) vortex head-to-

head domain wall in a soft ferromagnetic nanowire 26Figure 2.4 Schematic of the reduction of magnetostatic energy by forming flux

closure in a ferromagnet 28Figure 2.5 Comparison of different types of magnetic imaging techniques [After

A Hubert and R Schäfer, 1998, Ref 12] 34Figure 2.6 Schematic of the SEMPA Two of the four (2,0) LEED beams are

shown, together with the respective electron detectors 35Figure 2.7 The principle of the SEMPA: An incident beam from the SEM column

creates spin-polarised secondary electrons, from the surface of the ferromagnetic sample, which are subsequently spin analysed 37

Figure 2.8 Schematic of a typical MFM measurement in LiftMode 40

Figure 2.9 (a) Schematic of an interaction between a dipole and a magnetic

structure (b) A five-dipoles approximation of the tip used for the MFM contrast modelling 41Figure 3.1 Schematic of the flow of the fabrication process of the mesoscopic

sized ferromagnetic hexagonal elements 48Figure 3.2 Photographs of the integrated UHV system consisting of (i) FIB, (ii)

SEMPA, (iii) nanoprobe system 50Figure 3.3 SEM image of a network of NiFe hexagons created using FIB 51Figure 3.4 Secondary electron micrographs of (a) four nanoprobes positioned on

the contact pads of a device for nano-scale transport measurement and (b) a

nanoprobe on square element (it appears as a rectangle due to large tilt angle) for current-induced magnetisation switching study 52Figure 3.5 Schematic of a current-induced magnetisation reversal set-up integrated

with a MFM system 53Figure 4.1 Simulated magnetisation distribution for a permalloy (a) disk and (b)

hexagon at zero magnetic field, respectively [(c) and (d)] Calculated divergence of the magnetisation superposed with the stray field distribution (arrows), and [(e) and (f)] simulated MFM images of the corresponding elements (g) and (h) show MFM images of a permalloy hexagonal element with CCW and CW sense of rotation, respectively White (black) curved arrow represents the CW (CCW) chirality 59Figure 4.2 Simulated magnetisation orientation of the hexagonal element with a

diagonal length of 2 µm for (a) longitudinal and (b) transverse components Arrows represent the magnetisation directions 60Figure 4.3 SEMPA images of the in-plane magnetisation components: (i)

longitudinal (x) and (ii) transverse (y), as well as topographic images (iii),

of the hexagonal elements acquired simultaneously Each regular hexagonal element has a diagonal length of 2 µm, with edge-to-edge

separation s of (a) 100 nm, (b) 400 nm and (c) 2 µm, respectively 62

Figure 4.4 SEMPA images of the in-plane magnetisation components: (i)

longitudinal (x) and (ii) transverse (y), as well as topographic images (iii),

of the hexagonal elements with s = 200 nm 62

Figure 4.5 Schematic of a seven-element array with (a) same chirality and (b)

alternate chain of chirality distribution Curved arrows represent the magnetisation directions 63

Figure 4.6 (a) Topographic image of an array of hexagonal elements, with s = 100

nm, acquired by SEMPA Magnetic images of the corresponding area obtained by SEMPA, (b), and MFM, (c), agree with each other in terms of sense of rotation, as indicated by the white (CW) and black (CCW) curved arrows 65Figure 4.7 SEMPA images of the in-plane magnetisation components: (i)

longitudinal (x) and (ii) transverse (y), as well as topographic images (iii),

of the hexagonal elements acquired simultaneously The same sample with

s = 200 nm was imaged with different FIB trimmed thicknesses: (a) 30

nm, (b) 20 nm, (c) 12 nm and (d) 8 nm, respectively 66Figure 4.8 (a) Schematic of the area milled by FIB on a 30 nm thick NiFe film

XPS plot of the intensity against the binding energy of the FIB milled area over (b) a wide and (c) a narrow scan range 69Figure 4.9 Magnetic moment against magnetic field curves for (a) total NiFe film

with and without FIB milling, and (b) FIB milled region (extracted from the total measurement) 70Figure 4.10 A matrix of the simulated spin configurations of the regular shaped

hexagonal element with a diagonal length of 2 µm for different t and Ms 71

Figure 4.11 (a) SEMPA image (x component) of an array of hexagons with

diagonal lengths of 2 µm and s = 200 nm with a thickness of about 8 nm,

trimmed by in-situ FIB Elements with double vortex state were highlighted (b) A simulated magnetisation configuration in x component

of a hexagon with same diagonal lengths but lower Ms and thickness [Fig 4.8(h)] 72Figure 5.1 (a) A scanning electron micrograph of a ring network of NiFe hexagons

with diagonal lengths of 2 m [(b) – (h)] MFM images of the hexagons

with s ranging from 100 nm to 1 µm, respectively White (black) curved

dotted arrows represent the CW (CCW) chiralities 75Figure 5.2 Magnetisation configurations of hexagons in ring network with (a)

same (CCW) chirality and (d) alternating chirality, together with curved arrows outside of the hexagons representing the stray field 76

Figure 5.3 MFM images of a ring network of hexagons with s = 200 nm at

remanance after having a magnetic field of 10 kOe applied at angle θ, (a)

0°, (b) 180°, (c) 120°, and (d) 300°, respectively White (black) curved dotted arrows represent the CW (CCW) chiralities (e) and (f) show schematics of the alignment of the magnetisation to an applied saturation field Dotted lines with arrows indicate the direction of the magnetic flux emanating from the hexagons 78Figure 5.4 (a) A scanning electron micrograph of a ring network of NiFe hexagons

with diagonal lengths of 2 m and a missing element at the bottom right

corner.[(b) – (h)] MFM images of the hexagons with s ranging from 100

nm to 1 µm, respectively White (black) curved dotted arrows represent the

CW (CCW) chiralities 79Figure 5.5 (a) A scanning electron micrograph of a floral network of NiFe

hexagons with diagonal lengths of 2 m [(b) – (h)] MFM images of the

hexagons with s ranging from 100 nm to 1 µm, respectively White (black)

curved dotted arrows represent the CW (CCW) chiralities 80Figure 5.6 (a) A scanning electron micrograph of a floral network of NiFe

hexagons with diagonal lengths of 2 m and a missing element at the

bottom right corner [(b) – (h)] MFM images of the hexagons with s

ranging from 100 nm to 1 µm, respectively White (black) curved dotted arrows represent the CW (CCW) chiralities 81Figure 5.7 Plot of stray field distribution away from an edge of a hexagon obtained

by simulation 82Figure 5.8 Plot of stray field distribution away from a corner of a hexagon

obtained by simulation 83Figure 5.9 (a) A scanning electron micrograph of a linear-chain network of NiFe

hexagons with diagonal lengths of 2 m [(b) – (f)] MFM images of the

hexagons with s ranging from 100 nm to 1.5 µm, respectively White

(black) curved dotted arrows represent the CW (CCW) chiralities 84Figure 5.10 (a) A scanning electron micrograph of a star network of NiFe

hexagons with diagonal lengths of 2 m [(b) – (h)] MFM images of the

hexagons with s ranging from 100 nm to 1 µm, respectively White (black)

curved dotted arrows represent the CW (CCW) chiralities 85Figure 5.11 (a) A scanning electron micrograph of a triangular network of NiFe

hexagons with diagonal lengths of 2 m [(b) – (h)) MFM images of the

hexagons with s ranging from 100 nm to 1 µm, respectively White (black)

curved dotted arrows represent the CW (CCW) chiralities 86Figure 5.12 (a) A scanning electron micrograph of a rhomboidal network of NiFe

hexagons with diagonal lengths of 2 m [(b) – (h)] MFM images of the

hexagons with s ranging from 100 nm to 1 µm, respectively White (black)

curved dotted arrows represent the CW (CCW) chiralities 87Figure 5.13 (a) A scanning electron micrograph of a pyramidal network of NiFe

hexagons with diagonal lengths of 2 m [(b) – (h)] MFM images of the

hexagons with s ranging from 100 nm to 1 µm, respectively White (black)

curved dotted arrows represent the CW (CCW) chiralities 88Figure 5.14 (a) A scanning electron micrograph of a pyramidal network of NiFe

hexagons with diagonal lengths of 2 m and a missing elements at centre

[(b) – (h)] MFM images of the hexagons with s ranging from 100 nm to 1

µm, respectively White (black) curved dotted arrows represent the CW (CCW) chiralities 88Figure 6.1 Simulated magnetisation distribution of the composite hexagon-

nanowire structure without a notch: (a) vector form, (b) longitudinal and (c) transverse components at remanent state (d) Simulated MFM image of the composite structure 93Figure 6.2 Simulated magnetisation distribution of the composite hexagon-

nanowire structure with a separation of 60nm: (a) vector form, (b) longitudinal and (c) transverse components at remanent state (d) Simulated MFM image of the composite structure 94Figure 6.3 (a) A scanning electron micrograph of a NiFe hexagon with diagonal

lengths of 2 m, in contact with a wire of 400 nm width (b) – (d) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guides to the eyes 95Figure 6.4 Simulated magnetisation distribution of the composite hexagon-

nanowire structure with a notch: (a) vector form, (b) longitudinal and (c) transverse components at remanent state (d) Simulated MFM image of the composite structure 97Figure 6.5 (a) A scanning electron micrograph of a NiFe hexagon with diagonal

lengths of 2 m, in contact with a notched-wire of 400 nm width (b) – (f) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guide to the eyes 98

Figure 6.6 MFM images of a ring network of the hexagons with s = 200 nm at

remanance after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities 99

Figure 6.7 (a) A scanning electron micrograph of a ring network of NiFe hexagons

with diagonal lengths of 2 m and s = 200 nm, in contact with a wire of

400 nm width (b) – (g) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guide to the eyes 100Figure 6.8 (a) A scanning electron micrograph of a ring network of NiFe hexagons

with diagonal lengths of 2 m and s = 200 nm, in contact with a wire of

400 nm width (b) – (f) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guide to the eyes 101Figure 6.9 (a) A scanning electron micrograph of a ring network of NiFe hexagons

with diagonal lengths of 2 m and s = 200 nm, in contact with two wires of

400 nm width Bottom wire comes with a notch (b) – (g) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guide to the eyes 103Figure 6.10 (a) A scanning electron micrograph of a ring network of NiFe

hexagons with diagonal lengths of 2 m and s = 200 nm, in contact with

two wires of 400 nm width Bottom wire comes with a notch (b) – (g) MFM images of the hexagons after a magnetic field was applied White (black) curved dotted arrows represent the CW (CCW) chiralities Dotted white lines are drawn as guide to the eyes 105Figure 6.11 Schematic of the current-pulse experiment for a ferromagnetic

hexagon adjacent to a nanowire with a notched structure 107Figure 6.12 MFM images of the ferromagnetic hexagon adjacent to a nanowire

with a notch: (a) remanent state prior to current injection, and [(b)-(h)] magnetic states after injections of current pulses with pre-determined amplitude Dotted white lines are drawn as guide to the eyes 108Figure 6.13 (a) Topographic and (b) corresponding MFM images of a section of

the nanowire after a current-pulse of 5.6 mA was injected, causing electron-migration in the nanowire 109Figure 6.14 Schematic of the current-pulse experiment for ferromagnetic hexagons

in a ring network adjacent to a notched nanowire structure 111Figure 6.15 MFM images of the ferromagnetic hexagons in a ring network

adjacent to a nanowire with a notch: (a) remanent state prior to current injection, and [(b)-(h)] magnetic states after subsequent injections of pulsed current of constant amplitude of 3 mA Dotted white lines are drawn as guide to the eyes 112Figure 6.16 MFM images of the ferromagnetic hexagons in a ring network

adjacent to a nanowire without a notch, after a current pulse injection of (a) 3.2 mA, (b) 3.3 mA , and (c) -3.3 mA, respectively Dotted white lines are drawn as guide to the eyes 114Figure 6.17 (a) SEM image of a nanoprobe in contact with a NiFe square structure

at title angle SEMPA images of square structures: (b) before and (c) after a voltage-pulse of 0.3 V was injected 116

Figure 7.1 Proposed schemes to study the effect of current driven domain wall

motion using two nanoprobes for (a) a single hexagon-nanowire with systematic size reduction of the hexagon, and (b) different placement of hexagons along the nanowire 122

LIST OF SYMBOL AND ABBREVATION

NiFe Nickel Iron (permalloy)

OOMMF Object Oriented MicroMagnetic Framework

PEEM Photoemission Electron Microscopy

PMMA Poly-methyl-methacrylate

SEMPA Secondary Electron Microscopy with Polarisation Analysis

SQUID Superconducting Quantum Interference Detection

XPS X-ray Photoemission Spectroscopy

SD Single-Domain

Si Silicon

Ta Tantalum

W Tungsten

ACKNOWLEDGMENTS

I would like to first thank my supervisors Professor Chong Tow Chong, Associate Professor Teo Kie Leong and Professor Wu Yihong for providing numerous opportunities to learn and grow as a person as well as a scientist under their tutelage I

am deeply indebted to the strong support you have given my research, as well as your encouragement during this thesis work

At the same time, I would not have survived the Ph.D process without their unconditional support and understanding from my parents Equally noble and important

is my fiancée Janice, who always has the faith in me in everything I do Thanks also go

to my sister and brother for being have always provided their support and inspiration

I am also grateful to Associate Professor Liew Yun Fook, Thomas for his assistance and advice as a member of my thesis advisory committee

I would like to thank all my friends in DSI and ISML Special thanks go to Randall Law, Lim Boon Chow, Anthony Kay, Lim Sze Ter and Viloane Ko who have always provided me with not only technical and experimental assistance, but also company and entertainment that made the research process much more fun! Thanks also go to Dr Qiu Jinjun for his generous assistance in thin film deposition

Finally, I would like to thank Agency for Science Technology and Research (A*STAR) and Data Storage Institute (DSI) for their financial support, the NGS staff for being so efficient and friendly in handling our administrative issues, and all the staffs and students of DSI, and ISML for their friendship

C h a p t e r 1

Ferromagnetic structures of micro- and nanoscale dimensions are intensively studied due to their fundamental importance in nano-magnetism as well as their potential applications in data storage and logic devices Compared to electronic materials, the properties of magnetic materials are more sensitive to their shapes and size; this is mainly because the shape and dimension strongly affect the domain structures and their switching processes, which in turn determine the magnetic properties The length scale associated with this is on the order of domain wall width, ranging from a few to hundreds of nanometres In addition to fundamental physics, the surge in interest in magnetic nanostructures in the last one to two decades, is also stimulated by the fact that (1) the dimension of information bits and magnetic head in magnetic storage has already reached the domain wall width or even smaller, and (2) this length scale is easily accessible by modern nanofabrication techniques

Depending on its shape and dimensions, the typical domain structures of a patterned magnetic film includes single domain (SD), vortex and multi-domain states The SD state is formed in structures of various shapes in which the exchange energy is dominant in determining the total free energy, which occurs when the size of the structure is decreased to below a certain critical value Above this critical value, the magnetostatic energy term dominates, which favours the formation of flux-closure (FC) states The FC state usually consists of small domains with a nearly uniform magnetisation distribution The magnetisation only changes direction near the boundary

of neighbouring domains, forming the domain walls When a “circulating” type of

domain configuration is formed, it is referred to as a domain wall vortex state A

“perfect” vortex would be formed in circular dots because of its circular boundary which forces the spins to curl along it The vortex state, in particular, is interesting as it has curling in-plane magnetisation in its outer region and an out-of-plane magnetisation

at the centre, which is known as the vortex core As both the flux closure structure (characterised by sense of rotation) and vortex core (characterised by its polarisation) are doubly degenerated states, a magnetic vortex, in principle, can store two bits of information, in contrast to the single bit by a SD structure These properties make vortex state attractive for potential applications in both storage and logic devices In the rest of this chapter, we will give an overview of static magnetic domain structures formed in patterned magnetic films with different shapes, as well as the studies on their magnetisation dynamics We will then discuss the objectives of this study and why hexagonal structures were chosen as prime candidates for our research

1.1 Ferromagnetic Elements with Different Shapes

Advances in micro- and nano-fabrication techniques have made it possible to fabricate magnetic nanostructures with arbitrary shapes The mostly commonly investigated structures include circular disks, squares, rectangles, triangles, pentagons, ellipses, and rings [1] In this subsection, we will give an overview on the magnetisation behaviour exhibited by magnetic nanostructures with some of these shapes

1.1.1 Disks

The disk geometry is the simplest of the planar geometries Below a certain critical size, the exchange energy dominates and the disk exhibits a single domain state As the disk increases above a critical size, a vortex state develops With a further increase in the size of the disk, the magnetostatic energy becomes dominant over the exchange energy,

leading to the formation of multidomain states In addition to the vortex state [2]-[5], the typical types of multidomain states include C, S [6]-[8], triangle [9], [10], and diamond states [10], [11]

Figure 1.1 Magnetisation distribution in a circular disk obtained by micromagnetic simulations for (a) a C-state and (b) S-state, respectively [After J K Ha, 2003, Ref 7]

The C, S and triangle states have a relatively large remanence and are different from SD state, in order to accommodate the larger contribution of the magnetostatic energy The

C and S states, shown in Fig 1.1, have been predicted to be stable for small diameters between 200 to 400 nm by simulation [6]-[8] and are therefore difficult to be resolved experimentally The triangle state is a metastable state, which is characterised by a buckling of the magnetisation in the presence of two ‘edge vortices’ [Fig 1.2(a)] It is not the lowest energy state due to presence of the energy barriers The diamond state consists of two vortices in which the magnetisation is not uniform in any region except

in the inner part of the disk [see Fig 1.2(b)] The presence of the energy barriers makes the diamond state a metastable state but not the lowest energy state

Figure 1.2 Experimental observations of magnetic states in circular disk structures together with the corresponding magnetisation distribution obtained by micromagnetic simulation: (a) triangle state, (b) diamond state [After C A F Vaz, 2005, Ref 10], and (c) vortex state [After T Shinjo, 2000, Ref 19]

The vortex has gained much attention since it is the ground state of the disk elements over a large range of diameters and thicknesses [Fig 1.2 (c)] The phase boundary for ground state between the vortex state and the uniform single domain state, has been well studied both theoretically [12], [13] and experimentally [2] Moreover, there are schemes suggested to control the chirality of the magnetisation [ 14 ], [ 15 ] An interesting aspect of the vortex state is the core at the centre, where the large exchange energy cost due to the large twisting of the spins leads to a configuration where the magnetisation points along the out-of-plane direction, at a cost of magnetostatic energy The balance between these two contributions determines the size of the vortex core, which is of the order of the exchange length of the material [16]-[18] When the magnetisation is curling along a circumference, as in circular dots, the divergence of the magnetisation is equal to zero everywhere (besides in the core region) so there are no

volume magnetic poles are present that can generate a stray field This means that the stray field of the circular disk is weak, so the magnetostatic interaction among the circular disk will be small when they are arranged in large arrays The very small out-of-plane (vortex core) component of the magnetisation has been observed experimentally [19], [20]

The first step to the realisation of real application of vortex structure is to achieve perfect controllability of its sense of rotation, or chirality, and polarisation The approaches reported so far on chirality control centre on the ideas of introducing various types of asymmetry [21]-[24], defects [25], and / or using an external field [26], [27]

Recently, M Konoto et al have demonstrated that it is possible to control the chirality

with the use of a magnetic field gradient but without introducing geometric asymmetry

in the magnet shape [28] In all these reports, the emphasis was on the realisation of a specific type of chirality uniformly in a large array

1.1.2 Ellipses

By elongating one side of the disk, an elliptical shape can be easily formed The ellipse symmetry has been introduced to create magnetic shape anisotropy for reproducible magnetic switching Ellipses of micrometer and nanometer size, with large aspect ratio, show stable uniform magnetisations after the application of a magnetic field applied along the long axis [Fig 1.3(a)] On the contrary, when the magnetic field is applied along the short axis, different states may be formed [Fig 1.3(b)], such as the vortex, diamond, triangle, and SD states along the long axis [29]-[35]

Figure 1.3 Magnetic image of an elliptical structure at remanent state obtained after an in-plane magnetic field applied along (a) long and (b) short axis, with single domain and flux-closure state, respectively Arrows represent the orthogonal magnetisation directions [After X Liu, 2004, Ref 32]

1.1.3 Rings

The ring geometry is different from a disk geometry in that it has a lower energy vortex state due to the absence of the energetically costly vortex core [36], [37] Consequently, the vortex state is more stable as compared to the uniform state [13] Besides, it was observed experimentally that such structures are able to attain a high remanence state, called the onion state [37]-[39], in which the magnetisation in each half of the ring has

an opposite sense of circulation [see Fig 1.4(a)] The onion state is a metastable equilibrium state, which is made more stable from the energy barriers introduced by defects and irregularities, such as edge roughness Moreover, the switching field from the onion to the vortex state can be high [39]

In addition to circular rings, other toroidal structures were investigated [Fig 1.4(b)], such as elliptical rings [40], [41] and ‘window-frame’-type structures [42]-[45] The motivation of using elliptical rings, is explained in which it can creates easy direction of

magnetisation by shape anisotropy and therefore able to constrain the onion state to point in one direction [40] In the case of ‘window-frame’-type structures, the magnetic states resemble those observed for the ring structures, except for the presence of an additional horseshoe state [Fig 1.4(b)], with one head-to-head and one tail-to-tail wall

on one side of the square [42], [43]

Figure 1.4 (a) MFM images of octagonal ring structures with corresponding magnetisation distribution for SD and flux-closure states, respectively [After S P Li, 2001, Ref 38] (b) MFM images of the square rings in a horseshoe state, with magnetisation direction represented by arrows [After P Vavassori, 2003, Ref 42]

1.1.4 Squares and rectangle elements

For square elements and bars with length comparable to the width, equilibrium states like the flower and the leaf states occur with dimensions below 100 nm [46]-[48] (see Fig 1.5) Micromagnetic studies showed that a flower state will occur as an equilibrium state at larger thicknesses, whereas a leaf state will occur as an equilibrium state at small thicknesses [47] For more elongated structures, the equilibrium state is expected

to be a mixture of the flower and the leaf state, and resembles the S state found in larger elements [48], [49]

Figure 1.5 Micromagnetic simulation of (a) a flower state and (b) a leaf state, in a square nanomagnet

of edge length 100 nm and thickness 20 nm [After R P Cowburn, 2000, Ref 1]

For larger elements in which the magnetostatic energy dominates [Fig 1.6], besides the occurrence of the S and C states at remanence, there are also the occurrences of the flux closure quadrant [50] and / or the seven-domain states [51]-[55] These zero remanence states are characterised by the presence of uniform magnetic domains separated by 90° Neél domain walls Consequently, such states may be classified as multidomain states The high remanence states such as S and the C states have been studied numerically [9], [ 56 ]-[ 58 ] and experimentally [ 59 ]-[ 64 ] Another type of edge domain, which is observed in elongated rectangles after saturation in an applied field, consists of a constrained vortex which sits towards one corner of the element with the largest domain pointing in the direction of the average magnetisation [51]-[53], [61] In addition, cross-tie domain walls are observed in thick NiFe elements [53], [ 65 ] Multi-domain configuration typically sets in for elements larger than 5 µm [66], [67] These elongated elements have received much attention as their shape anisotropy and high thermal stability have shown to provide a desired condition for memory elements However, the presence of the edge domain does not result in the reproducibility of the magnetic switching Modification of the edge structures, such as pointed edge, has been proposed

to make switching more reproducible [51], [68]

Figure 1.6 (a) Foucault image of a rectangle in a S state [After J N Chapman, 1998, Ref 59] (b) Electron holography of a rectangle in a C state with its corresponding magnetisation distribution in Co, and Ni and simulated holography contours [After R E Dunin-Borkowski, 1998, Ref 52] (c) Foucault image obtained for square and rectangle with a flux-closure state and a seven-domain state [After K J Kirk, 2000, Ref 55] (d) Foucault image of two rectangles with different width having a flux-closure state and a partial flux closure [After K J Kirk, 1997, Ref 51]

1.1.5 Wires

Wires are defined as structures with lengths significantly larger than their width [Fig 1.7(a)] Consequently, the width and thickness of the magnetic wire becomes the relevant parameters Depending on the fabrication process, planar wires (typically lithographical process) or wires with circular cross-section (typically by electrodeposition) can be produced Wire arrays have been fabricated by standard lithography methods, with widths varying from about 100 nm to tens of micrometer

[69], [70] The coercivity is found to be lowered with increasing wire width, due to a buckling of the magnetisation perpendicular to the wire long axis, creating perpendicular domains which block the reverse domain propagation during magnetisation reversal Also, the magnetostatic interaction between wires becomes negligible for separation above wire width [see Fig 1.7(b)]

Figure 1.7 (a) Foucault image of NiFe(26 nm thick) wires with two pointed ends in an array [After K

J Kirk, 1997, Ref 51] (b) A plot of the coercivity as a function of the ratio of the spacing to the width when magnetic field applied along the easy axis of the wire array [After A O Adeyeye, 1997, Ref 70]

In addition, wires with constrictions [71], [72] and zig-zag wires [73] were also investigated to pin the domain wall specifically The depth of the constriction has a direct influence on the pinning field Furthermore, transverse and vortex domain walls can be pinned at the artificial sites and the types of domain walls formed are determined

by the dimensions of the ferromagnetic nanowires (details to be discussed in chapter 2)

1.1.6 Other shapes

Besides these common shapes, pentagons [1] and elongated hexagons [74] have also been investigated [see Fig 1.7] However, so far, only the magnetic properties of large

arrays have been studied The studies of the spin configuration and potential applications of these devices are still lacking

Figure 1.8 (a) SEM images of pentagon arrays in different sizes, 500 nm and 100 nm, respectively [After R P Cowburn, 2000, Ref 1] (b) SEM image of an array of elongated hexagons, 1 mm long and

500 nm wide with its corresponding Magnetic hysteresis loops obtained for easy and hard axis, respectively [After G Xiong, 2001, Ref 74]

1.1.7 Dynamics study of ferromagnetic structures

In addition to steady state spin configurations, much effort has also been devoted to the study of vortex switching dynamics Ferromagnetic resonance [75], [76], [77] and Brillouin light scattering techniques [77], [78], [79] have been employed in the study of the spectral and spatial components of the spin wave modes in the ferromagnetic structures The topography of the element has resulted in the existence of both azimuthally and radially excited modes [75], [76] Excitation at lower frequency modes indicates a correspondence to the resonant displacement of the vortex core of the disk [77] On the other hand, the gyrotropic mode corresponds to a spiral motion of the magnetisation at the vortex core as it approaches the equilibrium position [80]

Recently, it has been demonstrated that the polarity of the vortex core in the disk elements [see Fig 1.9(a)] can be switched by spin-transfer torque effect using AC currents [81] The switching probability is defined as the likelihood in which the polarity of the vortex core is switched It has also been demonstrated that the polarity of the vortex core of the square elements can be reversed [Fig 1.9(b)] by short burst of an alternating magnetic field [82] In both cases (whether magnetic field- or current-induced methods), the reversal of the polarity of the vortex core is effectively induced at resonant frequencies

Figure 1.9 (a) Switching probabilities as a function of excitation current frequency of NiFe disk used for vortex core polarity reversal by AC currents [After K Yamada, 2007, Ref 81] (b) Schematic setup for the magnetic vortex core reversal by AC magnetic field which consists of the NiFe sample with a flux-closure state and gold stripline [After B Van Waeyenberge, 2006, Ref 82]

J0,e =2.4×1011 Am−2

J0,e =3.5×1011 Am−2

J0,s =3.88×1011 Am−2

1.2 Potential Applications

In addition to fundamental studies, these ferromagnetic structures are useful for potential applications in data storage, magnetic random access memory (MRAM), and magnetic logic devices, as discussed briefly below

In patterned media, each magnetic dot is used to store one bit of information [83], [84]

by shape anisotropy [see Fig 1.10(a)] The bits can be oriented in-plane or perpendicular to the disk For this application, the magnetostatic interactions between adjacent elements have to be minimised because otherwise it would be difficult to achieve a high packing density As such, the shape, size and aspect ratio of the ferromagnetic nanostructures array have to be engineered to optimise the density and performance

Figure 1.10 Schematics of (a) patterned media with higher storage density by having smaller patterned elements and denser packing, and (b) MRAM, respectively

Figure 1.10(b) shows that patterned ferromagnetic structures are used as single-domain cell elements in MRAM [85], [86] A vortex state can store two bits of information; namely: its chirality and polarisation If nanostructures with vortex state are used, the storage densities of patterned media and MRAM can be doubled

So far, compared to patterned media, limited work has been carried out in magnetic

logic devices Allwood et al [87], [88] demonstrated that logic operations may be

performed in a submicron ferromagnetic structures of wires by field induced domain wall motion [Fig 1.11(a)] By making use of the ferromagnetic coupling effect at close proximity in the single domain elliptical elements in a predetermined arrangement, magnetic quantum-dot cell automata (MQCA) [89], [90] can behave as a logic gate [Fig 1.11(b, c)] Recently, a magnetic shift register [Fig 1.11(d)] is realised in a nanowire by spin–momentum transfer [91] These systems promise to offer a thousand-fold increase

in integration density and hundredfold reduction in power dissipation as compared to the current microelectronics technology

Figure 1.11 (a) SEM image of a NiFe nanowire with a NOT function and its corresponding magnetic signal response from a counterclockwise rotating magnetic field as a function of time [After D A

Allwood, 2002, Ref 87] (b) SEM images of the left (A), center (B), and right (C) regions of two of the

MQCA [After R P Cowburn, 2000, Ref 89] (c) A set of MQCA with single-domain states for majority logic gate application [After A Imre, 2006, Ref 90] (d) Schematic illustration of the shift- register operation Black squares and white squares represent head-to-head and tail-to-tail domain- walls, respectively [After M Hayashi, 2008, Ref 91]

1.3 Motivation and Objectives

From the overview, we can see that ferromagnetic structures of various types have been and are still being investigated intensively for both fundamental physics study and potential applications The vortex state is attractive because of its stability and multiple states represented by the same element When applying the vortex in real devices, it is most likely that one will require the following:

(1) the vortex has a negligible stray field so that a densely packed arrays can be formed such as in patterned media applications;

(2) the vortex has a moderate stray field so that it can interact with other elements in

a controllable way such as in logic circuit applications

The vortex formed in circular dots and rings are suitable for first category of applications because of their small stray field However, for logic circuit applications, elements with other shapes might be more suitable Among them, the hexagonal elements have attracted our attention because of their relatively high symmetry and moderate stray field, which will be the main objects of study in this work Although hexagons have lower symmetry as compared to circular disks, its symmetry is much higher than squares and triangles In addition, hexagons offer a closer packing when they are arranged into a hexagonal closed packed configuration With desirable thickness and dimensions, the vortex state formed in the hexagon can have controllable stray field of moderate strength and well-defined symmetry Therefore, ferromagnetic hexagons are promising for magnetic logic device applications

Based on these backgrounds, the objectives of this work are as follows:

a) To study the spin configuration of hexagonal ferromagnetic elements using both micromagnetic modelling and magnetic imaging;

b) To study the magnetostatic interaction of hexagonal elements in different arrangements by focusing on not only the effects of inter-element spacing but also the role of stray field symmetry in determining the chirality of vortices;

c) To explore the possibility of using both magnetic field and spin polarised current to switch the chirality of magnetic vortices in hexagonal elements

In addition to the study of hexagonal elements, another distinct part of this thesis work

is to set up a unique characterisation system which allows for both magnetic imaging experiment and modification of magnetic elements to be carried out in a same setup The integrated system consists of a scanning electron microscopy with polarisation analysis (SEMPA) for magnetic imaging, focused ion beam (FIB) system for structural modification and a nanoprobe system for electrical measurement In addition, an experimental set-up for studying current-driven domain wall motion is also incorporated into an existing magnetic force microscope (MFM) operating in ambient conditions These set-ups complement each other, therefore, helping us gain a better understanding of the experimental observations

1.4 Organisation of this Thesis

Chapter 2 provides an overview of the micromagnetic modelling for the understanding

of the experimental work presented in the thesis In addition, a brief review of various types of magnetic imaging characterisation techniques will be discussed

Chapter 3 describes the fabrication processes used in the research work A customised equipment setup for advanced magnetic characterisation, which includes SEMPA, FIB and nanoprobes, will be discussed A brief description of a commercial MFM system will be presented together with magnetic imaging modelling

Chapter 4 provides an investigation of the array of hexagonal elements with different

inter-element spacings In addition, the effect of thickness reduction by in-situ FIB will

be studied A model will be used to illustrate the formation of different chirality configurations formed in the array

Chapter 5 investigates the magnetostatic interaction of various types of arrangements of the hexagonal elements Moreover, a method to control of the relative chirality configuration as well as switching of chirality by using a magnetic field of appropriate strength and direction will be discussed

Chapter 6 discusses the magnetostatic interaction of the hexagons arranged in ring network with an adjacent nanowire Field-induced switching of the composite ferromagnetic structures will be discussed Moreover, current driven domain wall motion in the above-mentioned structures will be investigated

Chapter 7 concludes this thesis with a summary of the results obtained and provides several recommendations for future work

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in bulk magnetic materials As one of the dimensions is reduced and the bulk material becomes a thin film, Neél walls will be more favoured than the Bloch walls due to the strong demagnetising field perpendicular to the film plane With a further size reduction

in the lateral direction, various types of domain structures can be formed depending on the shape, size and material of the micro- or nanostructures Although various types of domain structures have been observed, in general they can be divided into three main categories, i.e., multi-domain, vortex and single domain states In multi-domain states, the magnetostatic energy term dominates, favouring FC states As the size of the magnetic elements is reduced, the exchange energy becomes dominant which favours the formation of a SD state below a critical dimension The vortex state occurs at an intermediate state where the interplay between the magnetostatic and the exchange energy favours an in-plane flux closure structure in the outer region, and an out-of-

plane magnetisation at the centre of the element A sound understanding of the formation mechanism of the different domain structures is crucial for the interpretation

of the magnetic domains observed, and allows the design of domain structures for targeted applications To this end, in this chapter, we will first give an overview on micromagnetic simulation based on the Landau-Lifshitz-Gilbert (LLG) equation by focusing on patterned ferromagnetic elements which complements the experimental observations Subsequently, different magnetic domain imaging techniques will be briefly discussed

2.2 Domain Walls in Ferromagnetic Material

A uniformly magnetised material is energetically unstable because of its large magnetostatic energy induced by the stray field Therefore, in most ferromagnetic materials, small magnetic domains are formed to lower the magnetostatic energy The region between neighbouring domains is called a domain wall inside which the magnetisations are distributed non-uniformly The shape and size of the domain walls are strongly affected by not only the intrinsic properties of the material but also its shape and dimension; therefore, the study of domain wall formation mechanism and exploration of its applications attach special importance to nanomagnetism and spintronics In this section, we will give an overview of different types of domain walls which are formed in different types of magnetic structures

2.2.1 Bloch wall

A Bloch wall occurs as a planar 180° domain wall which separates two domains of opposite magnetisation in an infinite uniaxial medium [1 ], [4] The magnetisation distribution of a typical Bloch wall is depicted in Fig 2.1 The magnetisations in adjacent domains are anti-parallel to each other Inside the wall, the magnetisation

rotates parallel to the wall plane (in an out-of plane manner) [Fig 2.1(a)], so there will

be no magnetic charges The magnetisations do not change their direction abruptly to

avoid drastic increase in exchange energy The wall thickness of such a Bloch wall is

given by:

u wall

K

A d

dz

πθ

πδ

π θ

(2.1)

where A is the exchange stiffness constant and K u is the anisotropy constant

Figure 2.1 (a) Schematic of a ferromagnetic material containing a 180° Bloch wall and (b) its spin

orientations in a uniaxial material

2.2.2 Neél wall

As the sample thickness is reduced, the magnetostatic energy of the wall that extends

through the thickness of the sample increases due to the free poles at the top and bottom

of the wall To reduce the magnetostatic energy, the spins inside the wall may be rotated

180° in the plane of the surface This lowers magnetostatic energy at the internal face of

the wall by removing the larger magnetostatic energy at the surface of the sample Such

a wall is called a Neél wall and is illustrated in Fig 2.2 Unlike the Bloch wall, the Neél

wall has its magnetisation rotated by 180°, but stays in the surface plane In addition, Neél walls are observed to be stable in many types of magnetic films for thicknesses up

to about 50 nm as Neél walls have high energy with thick films because of high anisotropy

Figure 2.2 (a) Schematic of a ferromagnetic material containing a Neél wall (b) Magnified sketch of

the spin orientations of a Neél wall in a uniaxial material

2.2.3 Domain walls in ferromagnetic nanowires

Macroscopic magnetic structures will generally form flux-closure magnetic domain structures, which lower their energy In sufficiently narrow wires made from soft ferromagnetic materials, such as sub-micrometer wide permalloy wire, flux-closed domain structures are no longer energetically favoured Due to its shape anisotropy, the magnetic domains are aligned along the length of the nanowire, with magnetisation pointing towards (or away) from each other These domains are separated by head-to-head (or tail-to-tail) domain walls

Figure 2.3 Schematic of spin orientation of a (a) transverse and (b) vortex head-to-head domain wall in

a soft ferromagnetic nanowire

The structure of head-to-head domain walls was first studied using micromagnetic

simulations by McMichael and Donahue [2] The two distinct domain wall structures

are: the transverse wall [Fig 2.3(a)] and the vortex wall [Fig 2.3(b)] For both vortex

and transverse walls, the domain wall width parameter Δ was found (by energy

minimisation) to depend on the wire width w, according to the approximate relations: