Chapter 8 Nanoscale

8.1 Characteristic length scales 8.2 Thin films 8.3 Thin film heterostructures 8.4 Wires and needles 8.5 8.6 Bulk nanostructures

TCD March 2007 1 One nanoscale dimension: Thin films

Two nanoscale dimensions: Nanowires and acicular particles

Three nanoscale dimensions: Nanoparticles

TCD March 2007 2 Fig 8.1 in iron thin films

TCD March 2007 3 8.1 Characteristic length scales

Exchange length Hardness parameter

Spin diffusion length !sd >> ! mean free path

TCD March 2007 4 8.2 Thin films

surface Intrinsic magnetic properties Ms, TC, K1, !s can be significantly different in thin films and in the bulk. interface

substrate

Epitaxial films Oriented films

Lattice parameters are influenced by the substrate, when the difference is < 4%

Seed and cap layers.

TCD March 2007 5 2.1 and Curie Point

Some metals become ferromagnetic in thin film form (V, Rh) although they are not magnetically ordered in the bulk; Others become ferromagnetic when deposited on a ferromagnetic substrate (Pd on Ni) Magnetism of iron is especially sensitive to structure and lattice parameters.

Fe has moment of 4 µB as an isolated atom;

3.3 µB in a chain,

3.0 µB as a plane

2.2 µB in the bulk bcc iron has a surface layer wth a moment 20% greater than the bulk.. Moment enhancement is due to band narrowing related to reduction in the number of nearest-neighbours

TCD March 2007 6 Number of planes

Curie temperature of thin films of 3d transition metals on various substrates

TC is weakened in ultra-thin films by the reduction in the number of exchange bonds, Also by surface spin waves, structural relaxation.

TCD March 2007 7 A uniformly-magnetized thin film produces no stray field.

B" = µ0 (H"+ M")= 0. B" is continuous Hence H" = 0 outside

-N M"; N =1

H|| = -NM|| .; N= 0. H|| is continuous. Hence H|| = 0 outside

TCD March 2007 8 2.2 Anisotropy and domain structure

Extra ‘3s’ contributions to the anisotropy of a thin film: – shape; surface; strain.’

– Shape The demagnetizing factor for a uniformly magnetized film is N = (0, 0, 1)

The anisotropic contribution to the self energy in the demagnetizing field is -(1/2)µ0MHd

2 2 E = -Ku sin # where Kshape = -(1/2) µ0Ms

# Fe -1.85 MJ m-3 Co -1.27 Ni -0.15

This has to be overcome by some other form of anisotropy if we want to make a true permanent .

TCD March 2007 9 – Surface

Surface anisotropy often leads to perpendicular anisotropy in films about one nm thick.

8.4 Surface anisotropy per unit area cobalt thickness for CoPd multilayers ! -2 Intercept gives Esurface 1 mJ m

-3, Monolayer thickness is about 0.25 nm; This surface anisotropy corresponds to 4 MJ m as in L10 compounds

TCD March 2007 10 – Strain

Fig 8.5 Strain anisotropy induced by epitaxy. The strain in Ni layers on Cu is relaxed beyond 4.5 nm

0 5 10

TCD March 2007 11 Magnetic structure of thin films

K (mJ m-2+ ) Fig 8.6 Twist of magnetization due to surface anisotropy s

Euler equation

2 Out of plane with a twist when Kv > (1/2)µ0Ms

TCD March 2007 12 Maze domains

Bubble domains

Fig 8.7 Magnetization and domain structure in a film with perpendicular anisotropy

TCD March 2007 13 2 Magnetization of thin films. Q = -Ku/Kd where Kd = (1/2)µ0Ms

Perpendicular anisotropy for Q > 1; Maze domains

In plane when Q < 1 and t < 2$w

Fig 8.8 Magnetic structure of a thin film as a function of Q and thickness t

TCD March 2007 14 Fig 8.9. Magnetization curves and surface domain structure for a 200 nm film of Ni. Magnetization curves show the magnetization is largely in-plane. The MFM image of stray

field at the surface picks up the small perpendicular component.

TCD March 2007 15 8.3 Thin film heterostructures

A magnetic multilayer is a stack of alternating magnetic and nonmagnetic layers. A bilayer is a pair of layers of different magnetic materials A superlattice is an epitaxial multilayer

3.1 Direct exchange coupling;

FM2 FM

FM1 F1

FM2

YCo2 AF GdCo2

Field-controllable

TCD March 2007 16 Exchange Bias. Discovered by Mieklejohn and Bean; 1956 ‘A new type of has been discovered, which is best described as exchange anisotropy. This anisotropy is a result of an interaction between an antiferromagnetic material and a ferromagnetic material’

Co

CoO

Fig 8.11 Rotational hysteresis of the same particles

Fig 8.10 Shifted hysteresis loop of Co particles measured on field cooling in 1 T to 77 K

TCD March 2007 17 Exchange bias of thin films. AFM Néel 1964 FM

Fig 8.13

TCD March 2007 18 ! ! It is as if an effective field Heff = H + Hex is acting on the film; Hex 4 kA/m; µ0Hex 50 mT

H z % y M H = K /µ M2 ex ex 0 x

The energies are better written per unit area of film as exchange bias scales with the area.

Kex = &/tp The energy per unit area is:

The corresponding field is EA/µ0Mptp

Minimize EA

Switching occurs when %='/2; H = Hex = -&/Mptp Perpendicular anisotropy field Ha = (&+2Kutp )/µ0Mptp

TCD March 2007 19 Dependence on layer thickness

! There is a threshold taf necessary for exchange bias to become effective; tcritKas &; -3 ! -2 tcrot = 10 nm, Kaf = 20 kJ m & 0.2 mJ m

! Hex 1/t p

Fig 8.14

TCD March 2007 20 Table 8.2. Antiferromagnetic Materials for Exchange Bias

Exchange bias only becomes effective below a blocking temperature Tb which is considerably lower than TN

TCD March 2007 21 Models for exchange bias

*Atomically flat antiferomagnetic surface. A) could be spin compensated; & = 0; B) could present one ferromagnetic plane; & = A/d ! 200 mJ m-2

*Only about 1/1000 of the spins seem to participate in the exchange coupling.

Surface is inevitably rough. Regions of dimension L contain (L/a)2 atoms. Uncompensated moment is that of ((L/a)2 atoms. Hence L ≈ 1000a ! 200 nm. OK But these regions will themselves add randomly. * Exchange bias may arise from defects of grain boundaries where there are frustrated spins

TCD March 2007 22 Models for exchange bias

Fig 8.16

* Interfacial coupling leads to perpendicular fm and afm axes. Coupling energy will be similar to that in a 90 ! -2 degree domain wall; (1/2)((KAaf) 0.4 mJ m

TCD March 2007 23 Fig. 8. 17

Fig. 8. 18

TCD March 2007 24 3.2 Indirect exchange coupling

Fig 8.21 Oscillations of the exchange coupling between ferromagnetic layers as a function of the ruthenium spacer thickness

Fig. 8. 17

TCD March 2007 25 Best for af coupling is 0.8 nm Ru

FM Ru FM

Artificial Antiferromagnet

FM Ru Fig 8.20 The aliasing effect FM

Artificial Ferrimagnet

TCD March 2007 26 TCD March 2007 27 3.3 Dipolar coupling

A perfectly smooth film creates no stray field. Correlated roughness leads to orange-peel coupling

-2 With tn,the spacer thickness - 5nm, roughness $ = 1 nm, period l = 20 nm, the coupling is 0.03 mJ m

TCD March 2007 28 3.4 Giant magnetoresistance

The GMR effect was discovered by Fert et al in 1988 Magnetoresistance in an Fe/Cr multilayer was as high as 80 % at low temperature and in high fields Much greater than AMR - hence the name.

First understanding in terms of the Mott two-current model. The ) and * channels conduct in parallel, with no spin-flip scattering. +)and +* are the resistivities of the two Fig 8.23 GMR of an Fe/Cr multilayer channels. , = +)/+*

Fig 8.22 Derivation of GMR in the two-current model

TCD March 2007 29 Fig 8.24

TCD March 2007 30 3.5 Spin valves

FM Cu FM

(pseudo) Spin valve

TCD March 2007 31

TCD March 2007 32

TCD March 2007 33 3.6 Magnetic tunnel junctions

I

FM

AlO x FM

V Magnetic tunnel junction 3 I = GV + -V E •Nonlinear I:V ! • Current decreases exponentially with thickness w V • Little temperature dependence

w

TCD March 2007 34 Juliere formula for TMR

I Parallel ))

magnetic tunnel junction

Julière formula: Antiparallel )* MR = 2P1P2/(1 - P1P2)

If P1 = P2 MR = 2P2/(1 - P2)

Taking P = 45%, MR = 51%

TCD March 2007 35 500 % TMR

Fig 8.25

TCD March 2007 36 Exchange-biased MgO magnetic tunnel junction Calculation of tunelling through a an Fe/MgO/Fe crystalline tunnel barrier R/R% . 100 200 200 100

µ0H (mT) •Majority channel tunneling is dominated by the transmission through a !1 (sp) state •! 1 state decays rapidly in anti-parallel configuration

TCD March 2007 37 Spin filter

A thin layer of ferromagnetic can act as a spin filter, producing a spin- polarized tunnel current. An N/F/N structure. F = EuO, NiFe2O4, CoFe2O4…

I Evac

* The spin-split barrier

) .ex favours)electron tunneling. w1 w2 %

EF

t

TCD March 2007 38 Metal/Insulator/Superconductor junctions

Tederov-Meservey experiment

Fig 8.27

TCD March 2007 39

TCD March 2007 40 8.4 Wires and needles

Acicular particles 30x30x300 nm are used in magnetic recording. N < 0.1 Shape anisotropy 2 Kshapa = [(1-3N)/4]µ0Ms 2 For a long wire Kshapa = (1/4]µ0Ms

Maximum anisotropy field 2Kshape/µ0Ms = Ms/2

The coercivity cannot exceed Ms/2 – not enough for a permanent magnet.

TCD March 2007 41 Alnico

Sophisticated nanostructures with spinodal nanostructure NiAl of oriented acicular Fe-Co in a nonmagnetic Al-Ni matrix, developed mainly in the 1930s.

2 2 2 Shape anisotropy: Ea = (1/4)µ0(1- 3N)Ms sin # = "1 sin # FeCo Anisotropy field : Ha = 2K1/µ0Ms = (1/2)(1- 3N)MS

HC < -H A

Coercivity due to shape anisotropy < Ms/2 Insufficient for a permanent magnet!

TCD March 2007 42 8.5 Superparamagnetism

! 1//0 1 GHz

Energy landscape of a superparamagnetic particle

TCD March 2007 43 T

0 blocked Tb superparamagnetic TC paramagnetic

Blocking is not a phase transition, but an exponential variation of fluctuation tims

Superparamagnetic behaviour of cobalt nanoparticles

TCD March 2007 44 When an ensemble of superparamagnetic particles is cooled through Tb in a magnetic field, it acquires a thermoremanent magnetization.

Igneous rocks (basalts) contain superparamagnetic magnetite particles. They acquire a TRM as they cool in the Earth’s magnetic field.

TCD March 2007 45 5.1 Magnetic viscosity

The entire hysteresis loop reflects metastable states. The magnetization at any point evolves with time

spontaneous magnetization

remanence

coercivity virgin curve initial susceptibility

major loop

M

M(t) = M(0) - S ln t Ln t Viscosity coefficient TCD March 2007 46 8.6 Bulk nanostructures

Fig 8 .29

TCD March 2007 47 6.1 Single-phase nanostructures

In single-phase nanostructures the bulk anisotropy can be greatly reduced by exchange coupling of nanocrystallites with different anisotropy axes. Exchange-averaging occurs when 1. Crystallites are single-domain with D << $w and 2. There is exchange coupling across grain boundaries.

TCD March 2007 48

Fig 8.30 Coercivity vs. grain size for a range of soft magnetic materials.

TCD March 2007 49 Remanence enhancement:

TCD March 2007 50 6.2 Two-phase nanostructures

Two-phase nanostructures can be produced by partial recrystallization of an amorphous material

If vc is the volume fraction of the crystalline phase, which has anisotropy K1, and the amorphous phase has no anisotropy.

TCD March 2007 51 Recrystallization of amorphous Fe-Cu-Nb- Si-B to obtain a two-phase crystalline/ amorphous soft nanocomposite

Finemet is a near-ideal soft magnetic material

with high polarization ! 1.6 T zero magnetostriction Minimal anisotropy

TCD March 2007 52

TCD March 2007 53 Hard/soft nanocomposite;

Nd2Fe14B/Fe

SmCo5/Co35Fe65

$w is too short to average away anisotropy, ! When the size of the soft region is < 2$w the soft and hard phases are exchange coupled. and behave in an averaged way, In this way it is possible to obtain a hard material with a magnetization greater than any single-phase hard magnet.

Fig 8.33

TCD March 2007 54 Fig. 8.33

TCD March 2007 55 Fig 8.35

TCD March 2007 56