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 PA2003: Nanoscale Frontiers Introduction 800 BCDocumentation of attractive power of lodestone 1088First 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)

Magnetism PA2003: Nanoscale Frontiers Introduction The Earth Strong Laboratory Magnets Levitating Frog

Magnetism PA2003: Nanoscale Frontiers Introduction The Earth Strong Laboratory Magnets Levitating Frog ~0.3 Gauss = 3 £ T ( 1 T = 1 N / (A m) ) 0.5 to 1 T ~15 T (Leicester magnetometer 10T)

Magnetism PA2003: Nanoscale Frontiers B fields exert forces on moving charges force acts at right angles to both v and B +ve charge B into page (right hand rule) v F – particle spirals around field lines – no effect from B – B induces circular motion cyclotron frequency

Magnetism PA2003: Nanoscale Frontiers 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 F1F1 F2F2 i into page i out of page B F

Magnetism PA2003: Nanoscale Frontiers Magnetic moments i i n F1F1 F2F2 i into page i out of page Magnetic potential energy B Torque, then define magnetic dipole moment:

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

Magnetism PA2003: Nanoscale Frontiers Field from current loop Field produced by current loop i dli dl B r R field from current element: total field at centre of loop

Magnetism PA2003: Nanoscale Frontiers 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

Magnetism PA2003: Nanoscale Frontiers 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 PA2003: Nanoscale Frontiers Atomic moments Use Hunds rules: 1. make as large as possible 2. make as large as possible Spin Quantum Number s = +½, -½ Principal Quantum Number n=1, 2, 3, … Angular Momentum Quantum Number l = 0, 1, 2, …, n-1 Magnetic Quantum Number m l = -l, (-l-1), …0…, (l-1), l n=1l=01s s = + ½ s = - ½ n=2 n=3 n=4 n=5 l=0 l=1 l=0 l=2 m l =2 m l =1 m l =0 m l =-1 m l =-2 2s 2p 3d 3p 3s

Magnetism PA2003: Nanoscale Frontiers Atomic moments Eg. Iron [Ar] 4s 2 3d 6 Filled shells up to [Ar] don’t contribute. Filled 4s has zero ang. mom. 3d 6 has

Magnetism PA2003: Nanoscale Frontiers 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. The question is: how are each of these moments oriented? - It depends on the magnetic exchange interaction! 4 classes of material Diamagnetic moments are zero Paramagneticmoments are randomly oriented Ferromagneticmoments align Antiferromagneticmoments align in opposite directions distance exchange

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 ~ but - as large as ~10 3 to10 5 in ferromagnets (not constant) If all moments in material have aligned – material is saturated

Magnetism PA2003: Nanoscale Frontiers 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 B app small and negative (superconductor = perfect diamagnet ) B oMoM B app 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 B oMoM B app M MsMs Magnetisation depends on applied field and temperature

Magnetism PA2003: Nanoscale Frontiers 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 Black =, White = Domain structure in Ni thin film imaged with MFM ( Domain structure in Fe thin film imaged with PEEM at DIAMOND 100 nm 40 nm

Magnetism PA2003: Nanoscale Frontiers Types of magnetic material Hysteresis curves B app Bsaturation reached remnant field, B r In magnetically hard materials B r is large energy lost during magnetisation cycle = area enclosed by hysteresis curve In magnetically soft materials B r is small not much energy is dissipated during a cycle B app B Use hard or soft ferromagnetic material depending on the application BrBr BcBc BcBc

Magnetism PA2003: Nanoscale Frontiers 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 PA2003: Nanoscale Frontiers 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 PA2003: Nanoscale Frontiers Fe volume fraction Magnetic moment per atom (µ B ) data points for nanostructured film LUMPS 2006: 400 Gb / in 2 < 5 nm >10 Tb / in 2 (required by 2012)

Magnetism PA2003: Nanoscale Frontiers

Magnetism PA2003: Nanoscale Frontiers