Magnetization dynamics of confined ferromagnetic systems [Elektronische Ressource] / vorgelegt von Ingo Neudecker

Ingo Neudecker

Sujets

• Physik

Informations

• Publié par: universitat_regensburg
• Publié le: 01 janvier 2006
• Nombre de lectures: 18
• Langue: English
• Poids de l'ouvrage: 12 Mo

Extrait

Magnetization Dynamics of
Confined
Ferromagnetic Systems
Dissertation
zur Erlangung des Doktorgrades
der Naturwissenschaften (Dr. rer. nat.)
der Fakulta¨t Physik
der Universita¨t Regensburg
vorgelegt von
Ingo Neudecker
aus Trostberg
2006Promotionsgesuch eingereicht am: 22.03.2006
Tag der mundlichen Prufung: 17.05.2006¨ ¨
Die Arbeit wurde angeleitet von: Prof. Dr. C. H. Back
Pruf¨ ungsausschuss:
Vorsitzender: Prof. Dr. J. Schliemann
1. Gutachter: Prof. Dr. C. H. Back
2. Gutachter: Prof. Dr. D. Weiss
Prufer: Prof. Dr. S. Ganichev¨
iiContents
Glossary vii
1 Introduction 1
2 Theory 3
2.1 Introduction to Magnetism and Magnetostatics . . . . . . . . . . . . . 3
2.1.1 Magnetic Interactions. . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 The Energy Functional of a Magnet . . . . . . . . . . . . . . . . 5
2.2 Dynamic Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 The Dynamic Susceptibility . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Spin Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Experimental Techniques and Introduction to Micromagnetics 19
3.1 Inductive Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 Conventional Ferromagnetic Resonance . . . . . . . . . . . . . . 19
3.1.2 Vector Network Analyzer Ferromagnetic Resonance . . . . . . . 20
3.1.3 Pulsed Inductive Microwave Magnetometry. . . . . . . . . . . . 20
3.2 Optical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.1 The Magneto-Optical Kerr Effect . . . . . . . . . . . . . . . . . 23
3.2.2 Time Resolved Scanning Kerr Microscopy . . . . . . . . . . . . 24
3.2.3 Ferromagnetic Resonance Scanning Kerr Microscopy . . . . . . 26
3.3 Introduction to Micromagnetics . . . . . . . . . . . . . . . . . . . . . . 29
4 Ultrathin Fe Film on GaAs 31
4.1 Static Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Dynamic Susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3 Inductive VNA-FMR Investigations . . . . . . . . . . . . . . . . . . . . 35
4.3.1 The Excitation Field Amplitude . . . . . . . . . . . . . . . . . . 35
4.3.2 Precessional Frequency and Effective Damping . . . . . . . . . . 36
4.3.3 Effect of Waveguide Excitation . . . . . . . . . . . . . . . . . . 39
4.4 Comparison to Other Techniques . . . . . . . . . . . . . . . . . . . . . 40
4.4.1 Precessional Frequency and Effective Damping . . . . . . . . . . 41
4.4.2 Signal to Noise Ratio . . . . . . . . . . . . . . . . . . . . . . . . 44
iv5 Confined Magnetic Structures I – Cylindrical Disks 45
5.1 Permalloy Disks with 200 nm Diameter . . . . . . . . . . . . . . . . . . 45
5.1.1 TheFlux-ClosureVortexConfigurationanditsBiasFieldBehavior 46
5.1.2 Dynamic Measurements and Numerical Calculations. . . . . . . 47
5.1.3 The Dispersion of the Observed Modes . . . . . . . . . . . . . . 50
5.2 Permalloy Disks with 4 μm Diameter . . . . . . . . . . . . . . . . . . . 51
5.2.1 Static Characterization . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.2 Energetics and Micromagnetics . . . . . . . . . . . . . . . . . . 52
5.2.3 Normal Mode Structure at Zero Bias Field . . . . . . . . . . . . 53
5.2.4 Modal Spectrum as a Function of an External Bias Field . . . . 58
6 Confined Magnetic Structures II – Cylindrical Rings 69
6.1 Static Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 Dynamic Characterization of the Double Switching Process . . . . . . . 71
6.3 Modal Spectrum at 80 mT Bias Field . . . . . . . . . . . . . . . . . . . 74
6.4 Dynamic Inter-Ring Coupling . . . . . . . . . . . . . . . . . . . . . . . 77
7 Summary and Outlook 80
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
A Appendix 83
A.1 Vector Network Analyzer Operation Mode . . . . . . . . . . . . . . . . 83
A.2 Waveguide Characterization . . . . . . . . . . . . . . . . . . . . . . . . 86
A.3 From Scattering Parameters to Magnetic Susceptibility . . . . . . . . . 90
A.3.1 The Concept of Scattering Parameters . . . . . . . . . . . . . . 90
A.3.2 Conversion to Susceptibility . . . . . . . . . . . . . . . . . . . . 91
A.4 Sample Dimensions and Preparation . . . . . . . . . . . . . . . . . . . 93
Publications 95
Bibliography 105
Acknowledgements 107
vviGlossary
Acronyms:
BLS Brillouin Light Scattering
cw continuous wave
DUT Device Under Test
FMR FerroMagnetic Resonance
FT Fourier Transform
HWHM Half Width at Half Maximum
hf high frequency
LL Landau-Lifshitz
LLG Landau-Lifshitz-Gilbert
ML Mono Layer
MOKE Magneto-Optical Kerr Effect
MSBVW MagnetoStatic Backward Volume Wave
MSSW MagnetoStatic Surface Wave
OOMMF Object Oriented MicroMagnetic Framework
PIMM Pulsed Inductive Microwave Magnetometry
Py permalloy (Ni Fe )81 19
RHEED Reflection High Energy Electron Diffraction
SKEM Scanning KErr Microscopy
SNR Signal to Noise Ratio
SQUID Superconducting Quantum Interference Device
TR Time Resolved
VNA Vector Network Analyzer
Physical constants:
dB = 10 log (P /P ) decibel10 out in
ε electric permittivity of free space0
g g-factor
γ =gμ /h =g×13.996 GHz/T gyromagnetic ratioB
~ =h/2π Planck’s constant divided by 2π
2−24μ =|e|~/(2m ) = 9.274×10 Am Bohr magnetonB e
m electron masse
−7μ = 4π×10 Vs/Am Permeability0
viiSymbols:
2A = 2JS p/a exchange constant
a nearest neighbor distance
α damping constant
α , α , α , directional cosinesx y z
B vector of magnetic induction
χ susceptibility
d diameter
D effective demagnetizing factorM
E energy
ε =E/V energy density
f precessional frequency
F area
Φ magnetic flux
H magnetic field vector
h high frequency exciting field vector
IF intermediate frequency
J exchange integral
K anisotropy constant
k wave vector
L angular momentum vector
l exchange lengthex
M magnetization vector
m, n number of azimuthal and radial nodes
m = M/M reduced magnetization vectorS
m orbital angular momentum quantum numberl
M saturation magnetizationS
m spin momentum quantum numbers
N , N , N demagnetizing factorsx y z
ω = 2πf angular frequency
p number of sites in the unit cell
P power
S spin operator
S scattering parameterij
s separation
t thickness
V volume
w signal line width of a coplanar waveguide
All equations and constants in the present work are expressed in SI units [1].
viii1 Introduction
In recent years an enormous technological progress has been made in the field of
fabricating high quality thin films as well as laterally confined elements. By means
of lithographical processes, the miniaturization has been pushed down well into the
nanometer regime. For applications, this progress amounts to formidable challenges
for magneto-electrical devices. Most applications are geared towards novel magnetic
recording media as well as sensors [2–4]. Due to its promises concerning speed, storage
density, and non-volatility, advanced magnetic recording technology is thought to have
the potential to become the long-awaited universal memory. In order to achieve high
storagedensitythememorycellscallforsmallmagneticelementswhichideallyarefree
of magnetic stray field and hence avoid crosstalk with neighboring cells. This in turn
requires to reduce the dimensions of the single storage cell down into the micrometer
orevennanometersizeregime. Moreover, sinceswitchingtimesneedtobepushedinto
the gyromagnetic regime, a detailed comprehension of the response of small magnetic
elements to high frequency magnetic fields is a central question. For this reason the
identification of the excitation spectrum of ferromagnetic elements in the micro- and
even nanometer lateral length scale [5–24] as well as the investigation of their switch-
ing behavior in the precessional regime [25–27] has attracted much attention in recent
years. While these problems can be addressed in the frequency domain using Brillouin
Light Scattering (BLS) or Ferromagnetic Resonance (FMR) techniques [7, 28, 29], a
direct imaging of the magnetic excitations on the picosecond time scale is presently
only possible by Time Resolved Scanning Kerr Microscopy (TR-SKEM) [8, 16, 30] or
micro-focus BLS [24, 31] experiments.
The aim of this thesis is to illustrate the effects of reducing the dimensions of a fer-
romagnetic system on the dynamic response to microwave magnetic fields. As exper-
imental access to the magnetization dynamics, inductive as well as spatially resolved
optical techniques are employed. The microwave response is studied either in the time
domain by applying a short magnetic field pulse or in the frequency domain by apply-
ing a sinusoidal magnetic excitation. Unless the magnetic excitations are eigenmodes
of the system, the dynamic response obtained from the two complementary techniques
should be transformable into each other via Fourier transformation.
The thesis is organized as follows:
Chapter 2 gives a brief introduction to the physics of magnetism and the relevant
concepts of magnetization dynamics