Introduction Force exerted by a magnetic field Current loops, torque, and magnetic moment
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Transcript of Introduction Force exerted by a magnetic field Current loops, torque, and magnetic moment
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Magnetism
PA2003: Nanoscale Frontiers
• Introduction• Force exerted by a magnetic field• Current loops, torque, and magnetic moment• Sources of the magnetic field• Atomic moments• Magnetism in materials• Types of magnetic material• Hard disks
Tipler Chapters 28,29,37
Magnetism
Dr Mervyn Roy, S6
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Magnetism
PA2003: Nanoscale Frontiers
Introduction
800 BC Documentation of attractive power of lodestone1088 First clear account of suspended magnetic compass
(Shen Kua, China)1200’s Compass revolutionises exploration by sea1600’s William Gilbert discovers the Earth is a natural magnet1800’s Connection between electricity and magnetism (Faraday, Maxwell)
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Magnetism
PA2003: Nanoscale Frontiers
Introduction
The Earth
Strong Laboratory Magnets
Levitating Frogwww.youtube.com/watch?v=m-xw_fmB2KA
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Magnetism
PA2003: Nanoscale Frontiers
Introduction
The Earth
Strong Laboratory Magnets
Levitating Frogwww.youtube.com/watch?v=m-xw_fmB2KA
~0.3 Gauss = 3£10-5 T ( 1 T = 1 N / (A m) )
0.5 to 1 T
~15 T (Leicester magnetometer 10T)
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Magnetism
PA2003: Nanoscale Frontiers
B fields exert forces on moving charges
force acts at right angles to both v and B+ve chargeB into page(right hand rule)
v
F
– particle spirals around field lines
– no effect from B
– B induces circular motion
cyclotron frequency
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Magnetism
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• Net force zero • B exerts a torque on the current loop • align n of current loop with B• Torque, ( = angle between n and B )
B fields exert forces on current carrying wires
current, i - moving charges.i
A
n charges per unit volume
l
B field exerts a force on a current carrying wire
i
i n
B
F1
F2
i into page
i out of page
B
F
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Magnetism
PA2003: Nanoscale Frontiers
Magnetic moments
i
i n
F1
F2
i into page
i out of page
Magnetic potential energy
B
Torque,
then
define magnetic dipole moment:
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Magnetism
PA2003: Nanoscale Frontiers
Sources of the magnetic field
moving charges produce a field
currents produce a field
Biot-Savart law - small current element
permeability of free space
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Magnetism
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Field from current loop
Field produced by current loop
i dl
Br
R
field from current element:
total field at centre of loop
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Magnetism
PA2003: Nanoscale Frontiers
Electronic moments
Semi-classical pictureElectron orbiting the nucleus = current loopatomic ‘current’
Orbital moment
In terms of ang. mom.
Electron also has intrinsic angular momentum, ‘spin’Spin moment
Total moment: Moments are quantised
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Magnetism
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Atomic moments
Lots of electrons!need total orbital and spin angular momenta
Use ‘LS’ coupling scheme (J = L-S , L+S)
Full electron shells have zero net orbital and spin angular momentum
For partially filled shells:
Total moment:
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Magnetism
PA2003: Nanoscale Frontiers
Atomic moments
Use Hunds rules:1. make as large as possible2. make as large as possible
SpinQuantum Number
s = +½ , -½
PrincipalQuantum Number
n=1, 2, 3, …
Angular MomentumQuantum Numberl = 0, 1, 2, …, n-1
MagneticQuantum Number
ml = -l, (-l-1), …0…, (l-1), l
n=1 l=0 1s
s = +½s = -½
n=2
n=3
n=4
n=5
l=0l=1
l=1l=0
l=2 ml=2ml=1ml=0ml=-1ml=-2
2s2p
3d3p3s
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Magnetism
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Atomic moments
ml =Element n-2 -1 0 1 2
|S| |L| |J| State
Sc 1 1/2 2 3/2 2D3/2
Ti 2 1 3 2 3F2
V 3 3/2 3 3/2 4F3/2
4 2 2 0 5D0
Cr, Mn 5 5/2 0 5/2 6S5/2
Fe 6 2 2 4 5D4
Co 7 3/2 3 9/2 4F9/2
Ni 8 1 3 4 3F4
9 1/2 2 5/2 2D5/2
Cu 10 0 0 0 1S0
Table 2.1
Ground state electron configurations of the 3d transition metals according toHunds rules.
Eg. Iron [Ar] 4s2 3d6
Filled shells up to [Ar] don’t contribute. Filled 4s has zero ang. mom.3d6 has
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Moments in bulk materialsTypically in bulk materials the orbital moment is quenched (QM result).The spin moment can give us a rough idea of ‘how magnetic’ a material is.
When considering the magnetic properties of a material we can think of the material as being made from a large number of current loops – atomic moments.
The question is: how are each of these moments oriented? - It depends on the magnetic exchange interaction!
4 classes of materialDiamagnetic moments are zeroParamagnetic moments are randomly orientedFerromagnetic moments alignAntiferromagnetic moments align in opposite directions
distance
exchange
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Magnetism
PA2003: Nanoscale Frontiers
Magnetisation
Describe materials by magnetisation, M or by magnetic susceptibility,
magnetisation = net magnetic moment per unit volume
Material with a magnetisation M has an associated field
Applied fields tend to magnetise a material (align moments). Then, total field:
In para/diamagnetic materials, M proportional to
typically small ~ 10-5 but - as large as ~103 to105 in ferromagnets (not constant)
If all moments in material have aligned – material is saturated
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Magnetism
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Types of magnetic material
Diamagnetsatoms have zero angular momentum – ie. no permanent momentWhen field applied, M is small and in opposite direction to Bapp
small and negative (superconductor = perfect diamagnet )B oM
Bapp
Paramagnetsatoms have angular momentum and permanent momentsWhen field applied small fraction of moments align, small and >0Moments would ‘like’ to align but get randomised by thermal motion B
oMBapp
M
Bapp
MsMagnetisation depends on applied field and temperature
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Magnetism
PA2003: Nanoscale Frontiers
Types of magnetic material
FerromagnetsAtoms have large permanent momentsMoments align in small fields. Alignment can persist when field is removed.
large, positive and field dependent,
Region over which moments are aligned is called a
Magnetic Domain
Black = , White =
Domain structure in Ni thin film imaged with MFM(www.aps.org/units/dmp/gallery/domains.cfm)
Domain structure in Fe thin film imaged with PEEM at
DIAMOND
100
nm
40 n
m
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Magnetism
PA2003: Nanoscale Frontiers
Types of magnetic material
Hysteresis curves
Bapp
B saturation reached
remnant field, Br
In magnetically hard materials Br is large
energy lost during magnetisation cycle = area enclosed by hysteresis curve
In magnetically soft materials Br is smallnot much energy is dissipated during a cycle
Bapp
B
Use hard or soft ferromagnetic material depending on the application
Br
Bc
Bc
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Hard Disks
• magnetic data storage• platters:
• rigid substrate• thin film coating
• Co based alloy• data on concentric rings • In-plane magnetisation • read/write head analogous to electromagnetic coil• head flying height < 20 nm!
• “1” stored as field reversal
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• Use higher coercivity media – but then:• need higher fields in write head
- nanostructured films?
Hard Disks
IBM GMR Demo
• Goal - increase bit density - but bits must not interact.
• Use weaker magnetic signals - but then:• need a more sensitive read head - GMR• Reduce flying height of head
- need smoother platter surfaces (nm) – glass?
• Limit is set by exchange interaction / domain size. Manipulate this?• Use ordered array of individual nanoparticles – but then need to overcome super-paramagnetic limit
- stabilise iron nanocluster moment with Cr shell?
STM of Fe nanoclusters
Fe / Co nanostructured film
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Magnetism
PA2003: Nanoscale Frontiers
Fe volume fraction
Mag
netic
mom
ent
per
atom
(µ
B)
data points for nanostructured film0
1
2
3
4
0 0.2 0.4 0.6 0.8 1
conventional FeCo film
Fe volume fraction
Mag
netic
mom
ent
per
atom
(µ
B)
data points for nanostructured film
LUMPS
2006: 400 Gb / in2
< 5
nm
>10 Tb / in2
(required by 2012)
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Magnetism
PA2003: Nanoscale Frontiers
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Magnetism
PA2003: Nanoscale Frontiers