nanomagnetism-2011-12-02.pdf

(6150 KB) Pobierz
Lecture notes on
Nanomagnetism
OlivierFruchart
Institut Neel (CNRS & UJF) { Grenoble
Version:December2,2011
Olivier.Fruchart-at-grenoble.cnrs.fr
http://perso.neel.cnrs.fr/olivier.fruchart/
902194355.001.png
Contents
Introduction
5
Content
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Notations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Formatting
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
I
Setting the ground for nanomagnetism
7
1
Magnetic elds and magnetic materials . . . . . . . . . . . . . . . . .
7
1.1
Magnetic elds
. . . . . . . . . . . . . . . . . . . . . . . . . .
7
1.2
Magnetic materials . . . . . . . . . . . . . . . . . . . . . . . .
9
1.3
Magnetic materials under eld { The hysteresis loop
. . . . .
11
1.4
Domains and domain walls . . . . . . . . . . . . . . . . . . . .
15
2
Units in Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3
The various types of magnetic energy . . . . . . . . . . . . . . . . . .
17
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
3.2
Zeeman energy
. . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.3
Magnetic anisotropy energy
. . . . . . . . . . . . . . . . . . .
18
3.4
Exchange energy
. . . . . . . . . . . . . . . . . . . . . . . . .
19
3.5
Magnetostatic energy . . . . . . . . . . . . . . . . . . . . . . .
20
3.6
Characteristic quantities . . . . . . . . . . . . . . . . . . . . .
20
4
Handling dipolar interactions
. . . . . . . . . . . . . . . . . . . . . .
21
4.1
Simple views on dipolar interactions
. . . . . . . . . . . . . .
21
4.2
Ways to handle dipolar elds
. . . . . . . . . . . . . . . . . .
22
4.3
Demagnetizing factors
. . . . . . . . . . . . . . . . . . . . . .
23
5
The Bloch domain wall . . . . . . . . . . . . . . . . . . . . . . . . . .
26
5.1
Simple variational model . . . . . . . . . . . . . . . . . . . . .
26
5.2
Exact model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
5.3
Dening the width of a domain wall . . . . . . . . . . . . . . .
28
6
Magnetometry and magnetic imaging . . . . . . . . . . . . . . . . . .
29
6.1
Extraction magnetometers . . . . . . . . . . . . . . . . . . . .
30
6.2
Faraday and Kerr eects . . . . . . . . . . . . . . . . . . . . .
30
6.3
X-ray Magnetic Dichroism techniques . . . . . . . . . . . . . .
30
6.4
Near-eld microscopies . . . . . . . . . . . . . . . . . . . . . .
30
6.5
Electron microscopies . . . . . . . . . . . . . . . . . . . . . . .
31
Problems for Chapter I
32
1. More about units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
1.1. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
1.2. Expressing dimensions . . . . . . . . . . . . . . . . . . . . . . . .
32
1.3. Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2
Contents
3
2. More about the Bloch domain wall . . . . . . . . . . . . . . . . . . . . .
33
2.1. Euler-Lagrange equation . . . . . . . . . . . . . . . . . . . . . . .
33
2.2. Micromagnetic Euler equation
. . . . . . . . . . . . . . . . . . .
34
2.3. The Bloch domain wall
. . . . . . . . . . . . . . . . . . . . . . .
34
3. Extraction and vibration magnetometer
. . . . . . . . . . . . . . . . . .
36
3.1. Preamble
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3.2. Flux in a single coil
. . . . . . . . . . . . . . . . . . . . . . . . .
36
3.3. Vibrating in a single coil . . . . . . . . . . . . . . . . . . . . . . .
36
3.4. Noise in the signal . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3.5. Winding in opposition . . . . . . . . . . . . . . . . . . . . . . . .
37
4. Magnetic force microscopy
. . . . . . . . . . . . . . . . . . . . . . . . .
37
4.1. The mechanical oscillator
. . . . . . . . . . . . . . . . . . . . . .
37
4.2. AFM in the static and dynamic modes . . . . . . . . . . . . . . .
38
4.3. Modeling forces . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
II Magnetism and magnetic domains in low dimensions
39
1
Magnetic ordering in low dimensions
. . . . . . . . . . . . . . . . . .
39
1.1
Ordering temperature
. . . . . . . . . . . . . . . . . . . . . .
39
1.2
Ground-state magnetic moment . . . . . . . . . . . . . . . . .
41
2
Magnetic anisotropy in low dimensions
. . . . . . . . . . . . . . . . .
42
2.1
Dipolar anisotropy
. . . . . . . . . . . . . . . . . . . . . . . .
42
2.2
Projection of magnetocrystalline anisotropy due to dipolar en-
ergy
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.3
Interface magnetic anisotropy
. . . . . . . . . . . . . . . . . .
44
2.4
Magnetoelastic anisotropy
. . . . . . . . . . . . . . . . . . . .
46
3
Domains and domain walls in thin lms . . . . . . . . . . . . . . . . .
48
3.1
Bloch versus Neel domain walls
. . . . . . . . . . . . . . . . .
48
3.2
Domain wall angle
. . . . . . . . . . . . . . . . . . . . . . . .
49
3.3
Composite domain walls
. . . . . . . . . . . . . . . . . . . . .
50
3.4
Vortices and antivortex . . . . . . . . . . . . . . . . . . . . . .
51
3.5
Films with an out-of-plane anisotropy . . . . . . . . . . . . . .
52
4
Domains and domain walls in nanostructures . . . . . . . . . . . . . .
54
4.1
Domains in nanostructures with in-plane magnetization . . . .
54
4.2
Domains in nanostructures with out-of-plane magnetization
.
55
4.3
The critical single-domain size . . . . . . . . . . . . . . . . . .
56
4.4
Near-single-domain . . . . . . . . . . . . . . . . . . . . . . . .
57
4.5
Domain walls in stripes and wires . . . . . . . . . . . . . . . .
58
5
An overview of characteristic quantities . . . . . . . . . . . . . . . . .
59
5.1
Energy scales
. . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5.2
Length scales
. . . . . . . . . . . . . . . . . . . . . . . . . . .
60
5.3
Dimensionless ratios
. . . . . . . . . . . . . . . . . . . . . . .
61
Problems for Chapter II
62
1. Short exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
2. Demagnetizing eld in a stripe
. . . . . . . . . . . . . . . . . . . . . . .
62
2.1. Deriving the eld . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
2.2. Numerical evaluation and plotting
. . . . . . . . . . . . . . . . .
63
III Magnetization reversal
64
4
Contents
1
Coherent rotation of magnetization
. . . . . . . . . . . . . . . . . . .
64
1.1
The Stoner-Wohlfarth model . . . . . . . . . . . . . . . . . . .
64
1.2
Dynamic coercivity and temperature eects
. . . . . . . . . .
65
2
Magnetization reversal in nanostructures . . . . . . . . . . . . . . . .
65
2.1
Multidomains under eld (soft materials) . . . . . . . . . . . .
65
2.2
Nearly single domains
. . . . . . . . . . . . . . . . . . . . . .
65
2.3
Domain walls and vortices . . . . . . . . . . . . . . . . . . . .
65
3
Magnetization reversal in extended systems . . . . . . . . . . . . . . .
65
3.1
Nucleation and propagation
. . . . . . . . . . . . . . . . . . .
65
3.2
Ensembles of grains . . . . . . . . . . . . . . . . . . . . . . . .
65
4
What do we learn from hysteresis loops?
. . . . . . . . . . . . . . . .
66
4.1
Magnetic anisotropy
. . . . . . . . . . . . . . . . . . . . . . .
66
4.2
Nucleation versus propagation . . . . . . . . . . . . . . . . . .
66
4.3
Distribution and interactions . . . . . . . . . . . . . . . . . . .
66
Problems for Chapter III
67
1. Short exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
2. A model of pinning - Kondorski's law for coercivity . . . . . . . . . . . .
67
IV Precessional dynamics of magnetization
69
1
Ferromagnetic resonance and Landau-Lifshitz-Gilbert equation . . . .
69
2
Precessional switching of macrospins driven by magnetic elds
. . . .
69
3
Precessional switching driven by spin transfer torques . . . . . . . . .
69
4
Precessional dynamics of domain walls and vortices { Field and current 69
Problems for Chapter IV
70
V Magnetic heterostructures: from specic properties to applications 71
1
Coupling eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
2
Magnetotransport . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3
Integration for applications . . . . . . . . . . . . . . . . . . . . . . . .
71
Problems for Chapter V
72
Appendices
73
Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Acronyms
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
Bibliography
75
Introduction
Content
This manuscript is based on series of lectures about Nanomagnetism. Parts have
been given at the European School on Magnetism , at the Ecole Doctorale de Physique
de Grenoble , or in Master lectures at the Cadi Ayyad University in Marrakech.
Nanomagnetism may be dened as the branch of magnetism dealing with low-
dimension systems and/or systems with small dimensions. Such systems may display
behaviors dierent from those in the bulk, pertaining to magnetic ordering, mag-
netic domains, magnetization reversal etc. These notes are mainly devoted to these
aspects, with an emphasis on magnetic domains and magnetization reversal.
Spintronics,i.e.the physics linking magnetism and electrical transport such as
magnetoresistance, is only partly and phenomenologically mentioned here. We will
consider those cases where spin-polarized currents inuence magnetism, however not
when magnetism inuences the electronic transport.
This manuscript is only an introduction to Nanomagnetism, and also sticking
to a classical and phenomenological descriptions of magnetism. It targets beginners
in the eld, who need to use basics of Nanomagnetism in their research. Thus the
explanations aim at remaining understandable by a large scope of physicists, while
staying close to the state-of-the art for the most advanced or recent topics.
Finally, these notes are never intended to be in a nal form, and are thus
by nature imperfect. The reader should not hesitate to report errors or
make suggestions about topics to improve or extend further. A consequence
is that it is probably unwise to print this document. Its use as an electronic le is
anyhow preferable to benet from the included links within the le. At present only
chapters I and II are more or less completed.
Notations
As a general rule, the following typographic rules will be applied to variables:
Characters
A microscopic extensive or intensive quantity appears as slanted uppercase or
Greek letter, such as H for the magnitude of magnetic eld, E for a density
of energy expressed in J=m 3 , for a density.
An extensive quantity integrated over an entire system appears as handwritten
uppercase. A density of energy E integrated over space will thus be written
E, and expressed in J.
5

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin