Chapter 10 Experimental Methods

10.1Materials preparation 10.2 Magnetic ﬁelds 10.3 Atomic-scale magnetism 10.4 Domain-scale measurements 10.5 Bulk magnetization measurement 10.6 Excitations 10.7 Numerical methods

TCD April 2007 1 10.1 Materials Preparation

10.1.1 Bulk material

Metals: Melt in an arc furnaces or a rf induction furnace. Heat treat in a resistance furnace (controlled temperature or atmosphere.

Arc A meltermorphous me Gloveboxtals are produceX-rayd b Diffractometery rapid solidiﬁcaSQUIDtion magnetometer - melt spinning

Insulators: Mill components e.g. CoO + Fe2O3 ! CoFe2O4 . Grind and ﬁre nx Mix ions in solutions. Precipitate gel as a precusror.

Crystals: seed temperature

seed Bridgeman method Czochralski method

TCD April 2007 2 10.1.2 Thin ﬁlms

Physical vapour deposition

Substrate 400 - 1000 C

source

Evaporation: Thermal e-beam e.g. 10 kV, 1A

Mean-free path " = 6/P "in mm, P in Pa.

TCD April 2007 3 cap ﬁlm substrate

TCD April 2007 4 Pulsed-laser deposition (PLD) ns pulses of UV light ! 1 J cm2 on the target, ! 10 Hz. directed plume cos11#

Growth rate ! 1 nm s-1

TCD April 2007 5 Molecular-beam epitaxy (MBE)

Carried out in UHV 10-7 - 10-9 Pa Needed to avoid conamination of a slowly-growing ﬁlm by residual gas.

Time for a monolayer 1/2 2 $t = (12MkBT/M) /Pa

e..g Oxygen a ! 0.2 nm, P = 10-5 Pa, $t ! 6 0s Growth rate < 0.2 nm s-1

• Franck-van der Merwe • Volmer-Weber • Strannsky-Krastanov

TCD April 2007 6 10.1.3 Small particles

TCD April 2007 7 TCD April 2007 8 Sputtering

Use Ar gas, Ar+ ions are accelerated towards the cathode (target). A glow- discharge is formed.

Target-substrate distance ! 100 mm

DC sputtering for metals. P ! 0.05 - 1 Pa

RF sputtering for insulators. 13.56 MHz P ! 0.02 Pa

To enhance the ionization of Ar, a magnetic ﬁeld is applied with a ‘magnetron’’

Growth rate ! 10 nm s-1

TCD April 2007 9 Multiple-target sputtering tool

6 targets

2x3-clusters 2 tfts

MgO ! ! Chamber B !Chamber A Base pressure < 3 x 10-8 Torr Base pressure < 3 x 10-7 Torr 2 Target Facing Target guns (MgO) 6 Series-III S Guns (DC& RF)

TCD April 2007 10 DMTJ stack

Cu10 50 Top Contacts Ta 5 IrMn10 AAFM CoFe2 Ru0.85 CoFeB5 Tunnel Barrier MgO2.5 Middle Free layer CoFeB3.5

MgO2.5 Tunnel Barrier CoFeB5 Ru0.85 AFFM CoFe2 IrMn10 NiFe5 Seed Layer Ta5 Ru50 Bottom Contacts

Ta5

TCD April 2007 11 Chemical methods

Electrodeposition.

Good for thick ﬁlms of alloys of metals which are not too electronegative. e.g. Ni78Fe22 1 microamp mm-2 deposits a monolayer in 5s. 1 milliamp mm-2 deposits 40 nm s-2.

Chemical vapour deposition (CVD). Use organometallic precursors, decompose by heated substrates or laser light.

TCD April 2007 12 10.2 Magnetic fields

10.2.1 Generation Steady ﬁelds

Helmholtz coils 0.01 T Bitter magnet 33 T

Electromagnet 1 T Polyhelix Hybrid magnet 42 T record Superconducting magnet 10 T

TCD April 2007 13 50 MJ capacitor bank

54 T 75 ms pulsed magnet, Nijmegen 100 T pulsed magnet laboratory, Dresden

TCD April 2007 14 TCD April 2007 15 10.2.2 Field Measurement

E = -Nd %/dt

a) Search coil b) Rotating coil b) Hall generator d) 77Rb vapour magnetometer

TCD April 2007 16 10.2.3 Shielding

Static: Soft magnetic shields. Permalloy µ > 10,000 Superconducting shields, exclude ﬂux penetration

High-frequency: Faraday cage.

TCD April 2007 17 10.3 Atomic-scale magnetism

10.3.1 Diffraction

K’ - K = &; '’ - ' = (

Elastic scattering; 2d sin # = n" & = ghkl

Differential scattering cross section 2 )diff = d )(&,(,T)/d&d(

Ineastic scattering; & = ghkl + q K = 2*/" ghkl = 2*/dhkl

TCD April 2007 18 Intensities of Bragg reﬂection are proportional to the square of the structure factor

Fhkl = +I ﬁ exp (i &.ri) = +I ﬁ exp (hxi + kli + mzi)

The sum is over the i atoms in the unit cell at (x i, yi, zi)

Cu Kedge 8.98 keV 1016 photons s-1 X-ray tube

2 ! 4 2 Synchrotron 5 GeV ,mc 10 mc 2 "c = 0.00714/B , m 1017 photons s-1 in 0.1% bandwidth

TCD April 2007 19 SmCo5. Sintered magnet c || & Powder

Magnetic scattering of X-rays is 106 times weaker than X-ray scattering. The effect can reach 1% near an absorption edge. A good method for Sm, Gd. (huge neutron scattering cross section)

TCD April 2007 20 Magnetic neutron scattering

P = 1.91reS fS or if both spin and orbital moments are present 1.91re(S fS + (1/2) L fL ) fL,S = [J(J+1) ± S(S+!) - L(L+1)]/[2(J+1)]

Magnetic interaction vector µ = m - &(&.m)/&2

TCD April 2007 21 TCD April 2007 22 Inelastic neutron scattering

The triple-axis spectrometer allows scan so be made at constant E or constant q. The dispersion relation for any excitation can be mapped out.

2*/a q Antiferromagnetic magnon

TCD April 2007 23 The triple-axis spectrometer

TCD April 2007 24 TCD April 2007 25 TCD April 2007 26 TCD April 2007 27 10.3.2 Spectroscopy

Absorption and photoemissio nprocesses for a single photon

X-ray photoemission spectroscopy (XPS) X-ray absorption spectroscopy (XAS); X-ray absorption ﬁne structure (EXAFS). Measure structure near the X-ray absorpftion edge - element speciﬁc local structure X-ray magnetic circular dichroism (XMCD). Measure difference of absorption for left and right circular polarised light. Deduce ~~and for the element~~

~~TCD April 2007 28 Mossbauer spectroscopy of FeFe lines powder k || , k -, 1,6 (±3/2 !±1/2 ) 3(1+cos2#) 3 3 3 2,4 (±1/2 !±1/2 ) 4 sin 2# 2 0 4 3,4 (±1/2 !-/+1/2 ) (1+cos2#) 1 1 1~~

~~TCD April 2007 29 TCD April 2007 30 Mossbauer spectra of BaFe12O19 There are ﬁve different sites. The ferrimagnetic sublattices are separated by an applied ﬁeld.~~

~~TCD April 2007 31 10.3.3 Electronic structure~~

Dispersion relations for spin- polarized electrons E(k)are a complete description of the electronic structure of a solid. UV Photoemission spectroscopy gives some information on the dispersion rlations and the density of states N(E) Computation Is now the main source of informations, especially density functional theory (DFT) calculations in the local spin density Spin-polarized densities of states for SmCo5 approximation (LSDA)

~~TCD April 2007 32 10.4 Domain-scale measurements~~

~~10.4.1 Strayy ﬁeld methods~~

~~Stray-ﬁeld methods for observing domain structure, a) Bitter method (magnetic colloid) b) Magnetic force microscopy and c) scanning electron microscopy~~

TCD April 2007 33 10.4.1 Radiation methods Hysteresis Loops Pt(2nm)/Co(t)/Pt(2nm) 0.5nm 30 3.6eV 25 0.6nm 20 3.6eV 15 0.6nm 10 (4eV) 5 0 RAS units -5 -10 -15 -20 -25 Faraday effect and Kerr effect -30 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Current Electromagnet [A]

~~MOKE spectra Pt(2nm)/Co(t)/Pt(2nm) 35 0.5nm 30 0.6nm 0.8nm 25~~

~~RAS units 15~~

~~0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 photon energy~~

~~TCD April 2007 34 Faraday effect spectrum of BaFe12O19~~

~~Kerr image of a polisher surface of Nd2Fe14B~~

~~TCD April 2007 35 Imaging schemes in transmission electron microscopy. Fresnel and Foucoult~~

~~Samples are Nd2Fe14B~~

TCD April 2007 36 A TEM image of a thin foil of melt-spun Nd2Fe14B showing domain walls oinned at grain boundaries. Left Fresnel image, right Foucallt image. Top is a lattice image showing the planes in the structure.

~~TCD April 2007 37 10.5 Magnetization~~

~~10.5.1 Open circuit~~

~~Force methods; a) Faraday balance, b)Torque magnetometer c)Alternating gradient force magnetometer~~

~~TCD April 2007 38 Flux methods: a) Extraction b) Vibrating sample magnetometer (VSM) c) Superconducting quantum interference device (SQUID)~~

~~TCD April 2007 39 Measurement of anisotropy ﬁeld, Ha = 2K1/Ms H is the internal ﬁeld.~~

~~TCD April 2007 40 10.5.2 Closed circuit~~

Schematic illustration of a hysteresigraph for measuring B (or M) as a function of the internal ﬁeld H in a cylindrical sample. On the right are the compensated coils needed to measure M and the potential coil used to measure H.

~~The compensated coil has n1A1 = n2A2. The emf is then proportional to (N1 - N2) Amµ0M~~

~~TCD April 2007 41 The potential coil~~

~~Use of a potential coil to measure potential difference between two points of a magnetic circuit~~

~~a -1 a The long coil has cross section and n turns m . .% = µ0n (/x - /y). Measure .% with an integrating voltmeter. E = -Nd%/dt.~~

~~TCD April 2007 42 10.6 Excitations~~

~~10.6.1 Thermal analysis The methods of thermal analysis involve heating a small sample at a uniform rate (e.g. 10 K min -1), and recording some parameter.~~

~~Differential thermal analysis; differential scanning calorimetry thermogravimetry thermopiezic analysis~~

~~TCD April 2007 43 10.6.2 Spin waves Inelastic neutron scattering.~~

~~TCD April 2007 44 10.7 Numerical methods~~

~~A grid used to obtain numerical solutions of differential equations using the ﬁnite difference method in two dimensions~~

~~TCD April 2007 45 A triangular mesh used fro two-dimensional ﬁnite element calculations~~

~~TCD April 2007 46~~