INTRODUCTION

TO
NANOMAGNETISM
Alberto P. Guimarães
Centro Brasileiro de Pesquisas Físicas

22/03/2006
 Outline

Introduction

Why nanomagnetism is important?

Why nanomagnetism is different from bulk

magnetism?

Types of low-dimensional solids?

New effects in nanomagnetic systems

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A.P. Guimarães CBPF
 The nano scale

Phenomena in objects
with 1-100 nanometers

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 Nanomagnetism-
mesomagnetism

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A.P. Guimarães CBPF Wernsdorfer 1996
 Nanoscopic systems

• Grains or particles (free-standing or

embedded in a matrix) (0D)

• Wires (free-standing or in a matrix) (1D)

• Films or multilayers (2D)

• Rings, etc

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 Relevance of nanomagnetism

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A.P. Guimarães CBPF
 Areas of influence of
nanomagnetism

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A.P. Guimarães CBPF Bader 2005
 Nanomagnetism as a research
topic ?

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A.P. Guimarães CBPF Web of Science (ISI)
 Evolution of magnetic
recording

Three generations of
magnetic hard disks

Areal density evolution 9

A.P. Guimarães CBPF IBM
 The importance of magnetic
recording

Magnetic 92%
About 10 exabytes=1019 bytes

Film 7.5%

Paper and optical 0.03%

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Proportion of data stored under different forms in 2003 (UCBerkeley 2004)
A.P. Guimarães CBPF
 Spin diffusion lengths:
examples

Co Ni80Fe20 Cu

lds 5,5 nm 4,6 nm 22,6 nm

l*ds 0,6 nm 0,6 nm 22,6 nm

lds : majority spin lengths,

l*ds minority
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A.P. Guimarães CBPF Dennis 2002
 Magnetic Particles

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A.P. Guimarães CBPF Galatea, Salvador Dali 1952
 Magnetic behavior of magnetic
particles

Three regimes:

a) Superparamagnetic

b) Monodomain FM

c) Multidomain

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A.P. Guimarães CBPF Cullity 1972
 Example: coercivity and grain
size in nanocrystalline Fe alloys

Coercivity and permeability

versus grain size in
nanocrystalline
Fe alloys

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A.P. Guimarães CBPF Herzer 2005
 Superparamagnetism

Monodomain particle: anisotropy energy KV cos2q

Transition over barrier of height KV is thermally

activated

The magnetization of an ensemble of magnetized

particles, when field H is set to zero, varies as

 KV 
dM 1 −  M
= Me  kT 
=
dt τ 0 τ
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A.P. Guimarães CBPF Cullity 1972
 Superparamagnetism:
relaxation time t

Diameter t
(nm) (s)
Relaxation time:
6,8 10-1

 KV 
  9,0 3,2X109=
τ =τ0e  kT 
100 years

(Values at room temperature)

(t depends exponentially on V and T)

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A.P. Guimarães CBPF Cullity 1972
 Macroscopic quantum tunneling
(MQT)

At very low temperatures the

particles may invert their
magnetization by tunneling, i.e.,
without thermal assistance.

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 Particle size and anisotropy

A grain of Co of 1.6 nm has 60% of the atoms on the surface! 18

A.P. Guimarães CBPF Pujada 2003
 S-W Model: hysteresis

Hysteresis curves for ellipsoidal domains in the Stoner-Wohlfarth model

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for different directions of H
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Cullity 1972
 Nanomagnets in bacteria

Nanocrystals of magnetic materials

were found in many living beings

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 Nanowires, rings, etc

d
L

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 Nanowires I

Al2O3 porous
MFM image of a 35 nm diameter
membrane used for
Co wire with H a) parallel and b)
deposition of
perpendicular
nanowires.
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A.P. Guimarães CBPF Dennis 2004
 Nanowires II

Scanning electron microscope image of

an ordered lattice of nanopores
Sellmyer 2001

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A.P. Guimarães CBPF Caffarena 2005
 Co rings

a) b)

c)

Hysteresis of sub-micron Co rings showing a) two ‘onion’ states; b)

same states and a vortex, and c) computed local magnetizations
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A.P. Guimarães CBPF Klaui 2004
 Thin Films

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 TC of ultra-fine films

Ratio TC of ultra-fine films to TC of

the corresponding bulk materials,
as a function of thickness (in
atomic layers).
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A.P. Guimarães CBPF Gradmann 1993
 Magnetic moment of ultra-fine
films

Computed magnetic moment of Ni atoms in 8 multilayers of

metal deposited on Cu 27
A.P. Guimarães CBPF Tersoff and Falicov 1982
 Direction of magnetization as
a function of thickness

Phase diagram of a film in the graph of surface anisotropy versus thickness

(in units of exchange length ξ)
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A.P. Guimarães CBPF O’Handley 2000
 Properties of the surfaces I

Changes in the neighborhood of the atom:

Symmetry

Coordination Consequences

Distances

Change in electronic structure

Change in TC

Change in magnetic moment

Change in anisotropy, etc. 29

A.P. Guimarães CBPF
 Properties of the surfaces II

Spin density at Fe
monolayer

Spin density at Fe surface

(Blue indicates negative
spin density)
(Freeman)
Computed charge density at Fe(001)
surface (Ornishi et al. 1983) 30
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 Differences in coordination
(2D)

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 Proportion of surface atoms

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 Proportion of surface atoms

A grain of Co of 1.6 nm has 60% of the atoms on the surface. 33

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 Density of states and
dimensionality

a. Dispersion relation E(k)

b. Density of electronic states (DOS)

as a function of energy N(E) in 1, 2,
and 3 dimensions

Relevance of DOS: Pauli susceptibility,

electronic specific heat, etc.
a. b.
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A.P. Guimarães CBPF Borisenko and Ossicini 2004
 New phenomena

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 Spin dependent resistance and
giant magnetoresistance (GMR)
The electrical resistance
depends on the relative
orientation of electron
spin and magnetization
of the layer

Applying a field to
change from antiparallel
to parallel
magnetization changes
the resistance

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 Applications of GMR

Magnetic random access

memory (MRAM) using a tunnel
junction (Wolf 2001)
Reading head using GMR
(Prinz 1998) 37
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 Application of GMR: Pseudo
Spin Valve
Resistance vs.
magnetic field

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A.P. Guimarães CBPF Scheme of a Pseudo Spin Valve Katti 2005
 Tunnel magnetoresistance
(TMR)

Magnetoresistance of a tunnel junction

(FM-insulator-FM) 39
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 Spin injection

Spin injection from a

ferromagnetic metal (FM)
into a nonmagnetic metal
(N).

a) Geometry of the device

b) Distribution of
magnetization

c) Conduction band scheme

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A.P. Guimarães CBPF Zutic (2004)
 Spin torque I

Spin polarized current turns the magnetization of a layer; above

a certain critical current (or duration) the magnetization is
inverted
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A.P. Guimarães CBPF Krivorotov in Sciencemag 14/01/2005
 Spin torque II

Transverse magnetization Mx
versus pulse duration, showing
the magnetization reversal.

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 In conclusion…

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 Origin of nanomagnetic
behavior
Dimensions comparable to characteristic lengths

Break in translation symmetry

Reduced coordination number

Higher proportion of surface atoms

Change in electronic density of states

Anisotropy energy ~ kT
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 Some consequences

Increase in overall anisotropy

In metals, narrower band

Lower TC

Higher magnetic moment

Other (higher reactivity, etc)

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 New phenomena

Giant magnetoresistance

Tunnel magnetoresistance

Spin injection

Spin torque

Exchange bias, Spin Hall effect, etc

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Obrigado!
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 Exchange bias

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