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

1. Magnetism • 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

2. Introduction 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)

3. Introduction The Earth Strong Laboratory Magnets Levitating Frog www.youtube.com/watch?v=m-xw_fmB2KA

4. Introduction 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)

5. – no effect from B – 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

6. 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

7. Torque, then F2 i out of page n i i i into page F1 Magnetic moments define magnetic dipole moment: B Magnetic potential energy

8. Sources of the magnetic field moving charges produce a field permeability of free space currents produce a field Biot-Savart law - small current element

9. idl r B R Field from current loop Field produced by current loop field from current element: total field at centre of loop

10. Electronic moments 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

11. 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:

12. Principal 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

13. Atomic moments Eg. Iron [Ar] 4s2 3d6 Filled shells up to [Ar] don’t contribute. Filled 4s has zero ang. mom. 3d6 has

14. Moments in bulk materials 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

15. 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

16. Bapp 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

17. Types of magnetic material 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)

18. Types of magnetic material 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

19. 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

20. Hard Disks • 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?

21. 4 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)