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

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

Magnetism


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)

Magnetism


Introduction

The Earth

Strong Laboratory Magnets

Levitating Frogwww.youtube.com/watch?v=m-xw_fmB2KA

Magnetism


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)

Magnetism


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

Magnetism


• 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

Magnetism


Magnetic moments

i

i n

F1

F2

i into page

i out of page

Magnetic potential energy

B

Torque,

then

define magnetic dipole moment:

Magnetism


Sources of the magnetic field

moving charges produce a field

currents produce a field

Biot-Savart law - small current element

permeability of free space

Magnetism


Field from current loop

Field produced by current loop

i dl

Br

R

field from current element:

total field at centre of loop

Magnetism


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

Magnetism


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:

Magnetism


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

Magnetism


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

Magnetism


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

Magnetism


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

Magnetism


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

Magnetism



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

Magnetism



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

Magnetism


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

Magnetism


• 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

Magnetism


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)

Magnetism


Magnetism


Documents

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