University of Groningen Spin Accumulation in Ferromagnetic/Normal and Ferromagnetic

133 Pages·2006·6.42 MB·English

University of Groningen

Spin Accumulation in Ferromagnetic/Normal and Ferromagnetic/Superconducting Systems
Zaffalon, Michele
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Spin Accumulation in
Ferromagnetic/Normal and
Ferromagnetic/Superconducting
Systems
MSC PhD thesis series 2006-02
ISSN 1570-1530
This work was carried out in the group ‘Physics of Nanodevices’ (part of the
Material Science Centre) at the Solid State Laboratory of the University of
Groningen,theNetherlands. TheprojectwasfinanciallysupportedbyMSCplus.
Printed by: Print Partners Ipskamp, Eschede
Cover: AsInOchilEgGe
RIJKSUNIVERSITEIT GRONINGEN
Spin Accumulation in
Ferromagnetic/Normal and
Ferromagnetic/Superconducting
Systems
Proefschrift
ter verkrijging van het doctoraat in de
Wiskunde en Natuurwetenschappen
aan de Rijksuniversiteit Groningen
op gezag van de
Rector Magnificus, dr. F. Zwarts,
in het openbaar te verdedigen op
vrijdag 10 februari 2006
om 16.15 uur
door
Michele Zaffalon
geboren op 27 juli 1973
te Venezia Itali¨e
Promotor: Prof. dr. ir. B.J. van Wees
Beoordelingscommissie: Prof. dr. Arne Brataas
Prof. dr. Bert Koopmans
Prof. dr. Dan Ralph
ISBN 90-367-2482-1
Contents
1 Introduction 1
1.1 Historical overview of spin transport in metallic systems . . . . . 3
1.1.1 Spin polarised tunnelling in superconductors/ferromagnets 3
1.1.2 Magnetic tunnel junctions and the tunnelling magnetore-
sistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 The giant magnetoresistance . . . . . . . . . . . . . . . . 5
1.1.4 Spin injection and detection in non-magnetic metals . . . 7
1.1.5 Spin is angular momentum: current induced magnetisa-
tion reversal and spin pumping . . . . . . . . . . . . . . . 8
1.1.6 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 Work in this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Basic concepts of spin transport 13
2.1 Band ferromagnetism. . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Magnetisation reversal . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Anisotropic magnetoresistance . . . . . . . . . . . . . . . 16
2.2 Basics of spin transport . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Why spin is not forever: spin relaxation processes. . . . . . . . . 18
2.4 The transport equations of charge and spin . . . . . . . . . . . . 20
2.5 The ferromagnet/(insulator/)normalmetal interface . . . . . . . 22
2.5.1 The clean case . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.2 The tunnel barrier case . . . . . . . . . . . . . . . . . . . 23
2.6 The physical origin of the interface polarisation . . . . . . . . . . 24
2.7 The resistor model . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.8 Non-collinear spin transport and spin precession . . . . . . . . . 27
2.8.1 The FM/(I/)N interface for non-collinear magnetisation . 28
2.9 The spin precession in 0, 1 and 2 dimensions . . . . . . . . . . . 29
2.10 Spin injection and accumulation in a 1-d system . . . . . . . . . 32
3 Spin injection in 0D systems: experimental results 35
3.1 Idea of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Device preparation . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Device characterisation . . . . . . . . . . . . . . . . . . . 38
3.3 Spin transport in the island . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Spin accumulation and spurious effects . . . . . . . . . . . 43
3.4 The measuring setup . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 The spin valve measurements . . . . . . . . . . . . . . . . . . . . 44
3.5.1 The side configuration . . . . . . . . . . . . . . . . . . . . 46
i
ii CONTENTS
3.5.2 The diagonal and opposite configurations . . . . . . . . . 47
3.5.3 The memory effect . . . . . . . . . . . . . . . . . . . . . . 47
3.6 The precession measurement, or Hanle measurement . . . . . . . 48
3.7 The reciprocity theorem for the spin accumulation . . . . . . . . 53
3.8 Comparison with other devices . . . . . . . . . . . . . . . . . . . 54
3.8.1 Spin valve measurements at 4.2 K . . . . . . . . . . . . . 54
3.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Spin transport in hybrid systems 61
4.1 The interface revisited . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 The interface parameters in magnetodynamics. . . . . . . . . . . 65
4.2.1 The finite element theory . . . . . . . . . . . . . . . . . . 66
4.3 Measuring the mixing conductance in the 0D island . . . . . . . 66
5 Spin injection in superconductors 71
5.1 Basics of BCS superconductivity . . . . . . . . . . . . . . . . . . 71
5.2 Non-equilibrium properties: charge and spin imbalance . . . . . . 74
5.2.1 Charge and spin accumulation: injection and detection. . 75
5.2.2 Charge and spin relaxation in SC . . . . . . . . . . . . . . 79
5.3 Transport properties in superconductors . . . . . . . . . . . . . . 80
5.4 Previous experiments . . . . . . . . . . . . . . . . . . . . . . . . . 81
6 Experimental results of spin injection in superconductor 83
6.1 Idea of the experiment . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Sample fabrication and experimental setup . . . . . . . . . . . . 85
6.3 The characterisationof the test tunnel barrier . . . . . . . . . . . 87
6.4 Characterisation of the island . . . . . . . . . . . . . . . . . . . . 90
6.5 Spin valve experiments . . . . . . . . . . . . . . . . . . . . . . . . 93
6.5.1 Spin valve: bias dependence . . . . . . . . . . . . . . . . . 95
6.5.2 Spin valve: dependence on AC modulation amplitude . . 96
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Summary 107
Samenvatting 111
Acknowledgements 115
List of publications 117
Chapter 1
Introduction
The most direct evidence for the electron spin and its magnetic moment first
came from the experiment of Stern and Gerlach in 1922, in which a beam of
silveratomswaspassedthroughanon-homogeneousmagneticfield. Theobser-
vations showed two distinct traces, giving clear proof of the discrete quantum
nature of the electron magnetic moment (the correct interpretation was given
by Goudsmit and Uhlenbeck in 1926). The electron magnetic moment µ was
B
found to be very close to the Bohr’s magneton, 57 µeV/T, which is classically
producedbyachargee=1.6 10 19 Crotatingwithorbitalangularmomentum
−
~/2,~=6.6 10 16 eVs being· Plank’sconstant. The Bohr’smagnetonsets the
−
· ·
spin characteristic energy scale.
As a quantum mechanical two state system, the electron spin is usually
represented by a two component vector, called spinor,
α
(1.1)
β
(cid:18) (cid:19)
where the top and bottom components, both complex numbers, represent the
amplitude probability to be in the “up” or “down” states, with reference to a
predefined direction in space.
Any spatial spin direction may be represented by appropriately choosing α
and β (with αα +ββ = 1). For instance, once the x and y axes are fixed,
∗ ∗
spins in the positive x, y and z directionare written in the basis spin up/down
in the z direction as
1 1 1 1 1
+xˆ , +yˆ , +ˆz (1.2)
→ √2 1 → √2 i → 0
(cid:18) (cid:19) (cid:18) (cid:19) (cid:18) (cid:19)
The spin itself interacts directly only with a magnetic field, the effect of
which being a rotation with constant angular velocity (if the field is constant
and uniform) of the spin directionin space aroundthe magnetic field direction:
in a 1 T field, the spin precesses with a frequency of 28 GHz.
Inanon-magnetic metal,onewouldexpectthatallspindirectionsareequiv-
alent and consequently, the two spin eigenstates are energy degenerate. How-
ever, there is a subtle interaction arising from the relativistic correction to the
electron’s motion in the host lattice, coupling the spin degree of freedom to
the orbital motion, in much the same way as the spin-orbit interaction does in
1
2 CHAPTER 1. INTRODUCTION
atomicphysics(there,onealsohastoaddarelativisticcorrectiontothe kinetic
operator). This implies that it is not possible to find a single spin quantisa-
tion axis for all k directions: an electron with crystal momentum k in a spin
eigenstatewillbe inalinearsuperpositionofspineigenstatesifscatteredtothe
k direction. In the presence of (elastic) momentum scattering, this leads to
′
randomisation of the spin direction, even from non-magnetic impurities. The
spin randomisation time, or spin relaxation time τ for Al is in the order of
sf
hundreds of picoseconds to tens of nanoseconds at 4 K, and tens of ps at room
temperature, where phonon scattering is the predominant source of spin relax-
ation.
In combination with the Pauli’s exclusion principle, the electron spin gives
rise to a wealth of phenomena. The oldest and most investigated is probably
the magnetism: long range ordering of the electron spins in each atom of the
magnetic solid and their orbital motion (protons’ and neutrons’ magnetic mo-
ment is about 2000 times smaller than the electron Bohr’s magnetic moment
µ , owing to the proton’s or neutron’s larger mass). In magnetic metals, also
B
thenetmagneticmomentoftheelectronsattheFermienergyi.e. thoserelevant
for the transport, differs from zero.
Controlling the spin is a different matter. By this, we mean a) creating
a spin accumulation, a non-equilibrium situation in which the local chemical
potential for the spin up population differs from the spin down population;
b) manipulating the spin accumulation by applying a magnetic field; and c)
measuring the final state of the spins. This is the subject of this thesis.
The first challenge is to create a spin current. Two main routes have been
attempted, optical injection (not discussed in this thesis) and electrical injec-
tion. The latter method relies on the fact that in a ferromagnet the transport
properties are dictated by the spin orientation and the magnetisation and a
current of electrons carries an excess of one of the two spin species. The most
straightforward way of creating a spin polarised current is simply to connect
a ferromagnet to a non-magnetic metal and drive a current through the two:
majority and minority electrons (electrons with spin antiparallel or parallel to
the local magnetisation) in the ferromagnet are injected at a different rate, de-
pending on the ferromagnet, on the non-magnetic metal and on the properties
of the ferromagnet/non-magnetic metal interface.
As previously noted, the spin dependent scattering to which the electrons
are subjected, both in the ferromagnet and at the interface, determines the
conductances for the majority and minority electrons. The conductances of
the two spin species are usually indicated by σ+ and σ for the majority and
−
minority spins in the bulk and by g+ and g for the interface. The transport
−
propertiesaredeterminedbythecomponent,whetherbulkorinterface,withthe
lowestconductance. Forexample,inthegiantmagnetoresistanceeffect(shortly
reviewedbelow),both the interfaceandthe bulk propertiesarerelevant. Inthe
opposite limit, in tunnelling magnetoresistance experiments, the interface has
very low conductance and totally determines the electron and spin transport.
The relevant parameter is the polarisation of an interface, defined as
g+ g
−
P − (1.3)
≡ g++g
−
Injecting excess spins in the non-magnetic metal creates an imbalance in
the spin populations. However, the polarisation of the spin is not forever: in
1.0. HISTORICAL OVERVIEW OF SPIN TRANSPORT IN... 3
Figure 1.1: Measurement of spin polarised tunnelling using Ni in 0 and 2 T
magnetic field. ∆ 300µeVis the gapofAlenhancedabovethe bulk value by
≈
theadditionof2%Cu,toincreasethesuperconductingtransitiontemperature,ξ
andbaccountsforthespin-orbitscatteringandorbitaldepairing. AfterMonsma
and Parkin (2000).
fact, the interactions between the electron spin and the host conductor leads
to a finite lifetime of the polarised electrons, and drives the imbalance towards
equilibrium (Sect. 2.3). The spin relaxation time τ , the averagetime the spin
sf
direction is randomised, can be as long as few hundreds of ns in Al and in
n-GaAs. During this time interval, the electrons diffuse a typical distance of
500 nm to 100µm, and so does the spin imbalance, fromthe point of injection:
this is the spin relaxation length λ . Thus, a device relying on the creation–
sf
manipulation–detection of a spin accumulation for its principle of functioning
has to have dimensions smaller than or comparable to λ .
sf
1.1 Historical overview of spin transport in metal-
lic systems
The understanding of the nature of the conductance in the bulk materials or
that of the interfaces between two different conductors has received a boost
with the prospect of commercially useable devices. Meanwhile, the utilisation
of such spin current to create a spin imbalance is being actively investigated
for fundamental reasons. Below is an overview of metallic systems and a brief
comparison with recent work in semiconductors. A somewhat more extended
introduction for semiconductors is given in Wolf et al. (2001).
1.1.1 Spin polarised tunnelling in superconductors/ferro-
magnets
The early experiments involving spin related effects did not require the cre-
ation of a spin accumulation, but only a spin current. The first study of spin
polarised tunnelling is the work of Tedrow and Meservey (1971, 1973) on alu-
minium/aluminium oxide/ferromagnet junctions. The idea is based on the ob-