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Introduction Force exerted by a magnetic field Current loops, torque, and magnetic moment

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- 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

Dr Mervyn Roy, S6

800 BC Documentation of attractive power of lodestone

1088 First clear account of suspended magnetic compass

(Shen Kua, China)

1200’s Compass revolutionises exploration by sea

1600’s William Gilbert discovers the Earth is a natural magnet

1800’s Connection between electricity and magnetism (Faraday, Maxwell)

The Earth

~0.3 Gauss = 3£10-5 T ( 1 T = 1 N / (A m) )

Strong Laboratory Magnets

0.5 to 1 T

Levitating Frog

www.youtube.com/watch?v=m-xw_fmB2KA

~15 T (Leicester magnetometer 10T)

– B induces circular motion

cyclotron frequency

– particle spirals around field lines

B fields exert forces on moving charges

force acts at right angles to both v and B

F

+ve charge

B into page

(right hand rule)

v

B fields exert forces on current carrying wires

B

l

n charges per unit volume

current, i - moving charges.

i

F

A

B field exerts a force on a current carrying wire

F2

- Net force zero
- B exerts a torque on the current loop
- align nof current loop withB
- Torque,
- ( = angle between n and B)

i out of page

n

i

B

i

i into page

F1

then

F2

i out of page

n

i

i

i into page

F1

Magnetic moments

define magnetic dipole moment:

B

Magnetic potential energy

moving charges produce a field

permeability of free space

currents produce a field

Biot-Savart law - small current element

r

B

R

Field from current loop

Field produced by current loop

field from current element:

total field at centre of loop

Semi-classical picture

Electron orbiting the nucleus = current loop

atomic ‘current’

Orbital moment

In terms of ang. mom.

Electron also has intrinsic angular momentum, ‘spin’

Spin moment

Total moment:

Moments are quantised

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:

Quantum Number

n=1, 2, 3, …

Angular Momentum

Quantum Number

l = 0, 1, 2, …, n-1

Magnetic

Quantum Number

ml = -l, (-l-1), …0…, (l-1), l

Spin

Quantum Number

s = +½ , -½

n=5

n=4

3s

l=0

n=3

3p

l=1

ml=2

l=2

3d

ml=1

ml=0

ml=-1

l=0

2s

n=2

s = +½

ml=-2

2p

l=1

s = -½

n=1

l=0

1s

Atomic moments

Use Hunds rules:

1. make as large as possible

2. make as large as possible

Eg. Iron [Ar] 4s2 3d6

Filled shells up to [Ar] don’t contribute. Filled 4s has zero ang. mom.

3d6 has

Typically 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.

exchange

The question is: how are each of these moments oriented?

- It depends on the magnetic exchange interaction!

distance

4 classes of material

Diamagnetic moments are zero

Paramagnetic moments are randomly oriented

Ferromagnetic moments align

Antiferromagnetic moments align in opposite directions

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

oM

B

oM

Bapp

B

M

Ms

Bapp

Types of magnetic material

Diamagnets

atoms have zero angular momentum – ie. no permanent moment

When field applied, M is small and in opposite direction to Bapp

small and negative (superconductor = perfect diamagnet )

Paramagnets

atoms have angular momentum and permanent moments

When field applied small fraction of moments align, small and >0

Moments would ‘like’ to align but get randomised by thermal motion

Magnetisation depends on applied field and temperature

Ferromagnets

Atoms have large permanent moments

Moments 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

100 nm

40 nm

Black = , White =

Domain structure in Ni thin film imaged with MFM

Domain structure in Fe thin film imaged with PEEM at DIAMOND

(www.aps.org/units/dmp/gallery/domains.cfm)

Hysteresis curves

B

saturation reached

remnant field, Br

In magnetically hard materials Br is large

Bc

Bapp

energy lost during magnetisation cycle = area enclosed by hysteresis curve

B

Br

In magnetically soft materials Br is small

not much energy is dissipated during a cycle

Bc

Bapp

Use hard or soft ferromagnetic material depending on the application

- 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

- Goal - increase bit density - but bits must not interact.

IBM GMR Demo

- Use weaker magnetic signals - but then:
- need a more sensitive read head - GMR
- Reduce flying height of head
- - need smoother platter surfaces (nm) – glass?

- Use higher coercivity media – but then:
- need higher fields in write head
- - nanostructured films?

Fe / Co nanostructured film

STM of Fe nanoclusters

- 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?

conventional FeCo film

3

Magnetic moment per atom(µB)

2

1

data points for nanostructured film

0

0

0.2

0.4

0.6

0.8

1

Fe volume fraction

LUMPS

Magnetic moment per atom(µB)

data points for nanostructured film

Fe volume fraction

2006: 400 Gb / in2

< 5 nm

>10 Tb / in2

(required by 2012)

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