STM study of the (001) and (110) surfaces of magnetite

LEABHARLANN CHOLAISTE NA TRIONOIDE, BAILE ATHA CLIATH TRINITY COLLEGE LIBRARY DUBLIN OUscoil Atha Cliath The University of Dublin

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ST M stu d y o f th e (001) and (110)

surfaces o f m a gn etite

A thesis subm itted to the University of Dublin, Trinity College,

in application for the degree of Doctor in Philosophy

by

Sergio F. C eb allos

Physics D epartm ent

Trinity College Dublin

I

D eclaration

This thesis is submitted by the undersigned for the degree of Doctor in

Philosophy at the University of Dubhn.

It has not been subm itted as an exercise for a degree at any other university.

Apart from the advice, assistance and joint effort mentioned in the

acknowledgements and in the text, this thesis is entirely my own work.

I agree th at the library may lend or copy this thesis freely on request.

n

A ck n ow led gem en ts

II

Firstly, I would like to thank my supervisor Prof. I.V. Shvets giving me

the opportunity to work in the Nanomag Group for the last four years. He

introduced me to the field of surface science, nanotechnology and Scanning

Tunneling Microscopy, always providing excellent guidance during my stud­

ies. W ithout his support, encouragement, enthusiasm and determination, this

work would not have been possible.

Ill

group who have moved on other directions such as Dr. Maina Karsanova for

the AGFM/VSM characterization of MnNi samples. Anselm Gademann who

could fix anything computer related and William Signac for his friendship and

dinner parties. I also have to mention other ’’extra-official” members such as

Gregory Cabailh who shared with me the amazing story of the ” funny” trick

and the unforgettable trip through the ’’Valley of silence” .

The group could not operated without the efforts and background sup­

port of other members of the Physics Department namely John Kelly, Mick

Reilly, Ken Concannon, Joe McCauley, P at Flanagan, James Kavanagh,

Kevin Thompson and all the secretarial staff, Michelle Duffy, Susan Priest

and Elaine O ’Malley.

Thanks to my friends in Santander, Luis, Jose, David and specially Rafa

for still being part of my life. Friends in Ireland, Marie for those lovely meals

and ” frustrating” clubbing nights we have shared together. Mr. McSweeney

for being a good friend and letting me stay in his house for a cheap rent in

’’Sarajevo” . M att for mutual support in tough moments. Thanks to Ana who

showed me Ireland 10 years ago. Special mention to Patrick Gaffney, for his

his excellent friendship, exceptional advice and the good times during the

thousand ’’nites” out in Dublin.

IV

A bstract

In this thesis the surface of single crystals and thin films of magnetite

(001) and (110) have been studied by scanning tunneling microscopy (STM),

scanning tunneling spectroscopy (STS), Auger electron spectroscopy (AES)

and low-energy electron diffraction (LEED). The use of STM tips made of

magnetic materials is highlighted in this work. A novel technique has been de­

veloped by the author in order to provide STM tips made of paramagnetic,

ferromagnetic and antiferromagnetic materials. Special emphasis has been

placed on the study and characterization of tips made of antiferromagnetic

MnNi alloy. Chemical and magnetic characterization has been performed

by AES, X-ray diffraction (XRD), alternating gradient force magnetometer

(AGEM) and transmission electron microscope (TEM). Scanning electron

microscope (SEM) has also been employed for characterization of the tips.

The potential of the MnNi tips for SP-STM measurements has been con­

firmed by STS/STM studies of Mn/Fe(001), a test sample whose magnetic

properties are well known. These tips are routinely used by the group for

SP-STM experiments on magnetite.

A detailed analysis of the nature and topography of contam inant free

and contaminated m agnetite (001) single crystals and thin films is given.

It has been dem onstrated how the surface topography of a contaminated

and clean surface of m agnetite (001) is intimately related to the preparation

conditions, with the 0 /E e ratio playing a crucial role in determining the

surface terminations of magnetite.

V

ions surrounded by oxygen ions. A ( \/ 2 x \/2 )/? 4 5 ° surface reconstruction has been observed on a clean m agnetite (001) surface. A high exposure of the surface to oxygen during preparation leads to an octahedral term inated surface. On the other hand, the light exposure of the surface to a hydrogen atmosphere leads to a co-existence of tetrahedral and octahedral term inated surfaces. A combined tetrahedral and octahedral term ination has been rarely observed in the past.

Continuous anneahng of the single crystals and m agnetite thin films leads to a contam inated (001) m agnetite surface. T he typical contam inants found were calcium and potassium . Self assembled patterns of rows and nan­ otrenches on the surface are observed and explained in terms of the formation of a C a i_ iF e2+ i0 4-like and Mgi_j;Fe2+ i0 4-like phases. A range of different surface reconstructions have been observed w ith increase of the annealing time, related to a variation of the local [0 /F e] stoichiom etry ratio at the surface and the concentration of contam inants, p ( l x l ) , p ( l x 2 ) , p ( l x 3 ) and p ( l x 4 ) superlattices have been found on the Fe3 0 4 (001) surface.

VI

P u b lication s

1. Journals

C. Daul, S. Fernandez-Ceballos, I. Ciofini, C. Rauzy and C. Sclilapfer.

” A novel D ensity Functional Study of th e G round S tate Properties of a

Localized Trinuclear Copper (II,II,III) Mixed-Valence System” .

Chem. Eur.

J., 4392-4401 8 19 (2002)

S. F. Ceballos, G. M ariotto, S. M urphy, I.V. Shvets. ’’Fabrication of magnetic

STM probes and their application to studies of the Fe

(001) surface” .

Surf. Sci., 131-140 523 (2003)

G. M ariotto, S. F. Ceballos, S. M urphy, and I. Shvets. ’’Scanning Tunneling

microscopy studies of the Fe

(001) surface using antiferrom agnetic

probes” .

J. Appl. Phys., 93 10 (2003)

S.F. Ceballos., G. M ariotto, K. Jo rd an , S. M urphy and I. Shvets. ” An atomic

scale study of the Fe

(001) surface” .

Surf. Sci., 548 106-116 (2004)

G. M ariotto, S. F. Ceballos, S. M urphy and I. Shvets. ’’Alkaline and

alkaline-earth m etals self-assembled n an o -p attern s on th e Fe

(001)

surface” .

Phys. Rev. B

70, 035417 (2004)

VI]

K. Jordan, G. M ariotto, S. F. Ceballos, S. M urphy and I. Shvets. ’’Spin

Polarised scanning tunnehng microscopy of Fe

(001) charged ordered

surface” .

Submitted: Surf. Sci.,

Aug (2004)

K. Jordan, G. M ariotto, S. F. Ceballos, S. M urphy and I. Shvets. ’’Atomic

scale SPSTM imaging of the Fc

(001) surface using antiferrom agnetic

tips” .

Accepted: J. Mag. Mag. M at.,

Sep (2004)

S. Murphy, S. F. Ceballos, G. M ariotto, N. Berdunov, K. Jordan, and

I. Shvets. ’’Atomic scale spin-dependent scanning tunneling microscopy

using antiferrom agnetic STM tip s” .

In press: J. Microsc. R. Tech.,

Sep (2004)

S.F. Ceballos, K. Jordan, G. M ariotto, N. Berdunov, S. M urphy and I.V.

Shvets. ” Surface studies of m agnetite (110)” .

In preparation

2. C o n fe r en ce P r o c e d in g s

S. F. Ceballos, K. Jordan, S. M urphy, C. Seoighe, and I. V. Shvets. "C on­

tam inan ts Induced Onset of N anostripes and N anotrenches on th e Fe

(001) Surface” .

A IP Conf. Proc.,

696, 879 (2003)

G. M ariotto, K. Jordan, S. F. Ceballos, S. M urphy, C. Seoighe, and I. V.

Shvets. ” C harge O rdering on th e (\/2 x -\/2)i?45° R econstructed Fea

(001)

Surface” .

A IP Conf. Proc.,

696, 873 (2003)

v;ii

V. Shvets. ’’Polaronic Superlattice Form ed on Oxidised M agnetite (111)

Surface” .

A I P Conf. Proc.,

696, 865 (2003)

S. F. Ceballos, G. M ariotto, N. Berdunov, S. Murphy, K. Jordan, and I. V.

Shvets. ’’Fabrication of M agnetic Probes for Spin-Polarized STM Studies of

th e Fe3 0 4

(001) and (111) Surfaces”

A I P Conf. Proc.,

696, 298 (2003)

IX

List o f a b b rev ia tio n s

ID - one dimensional

2D - two dimensional

3D - three dimensional

AES - Auger electron spectroscopy

AGFM - Alternating gradient force magnetometer

CMA - cylindrical mirror analyser

DLA - diffusion limited aggregation

DOS - density of states

e-beam - electron beam

EGG - electrostatic centre of gravity

HT - liigh-temperature

L - Langmuir

LBL - layer-by-layer

LDOS - local density of states

LEED - low energy electron diffraction

LT - low-temperature

LTSTM - low-temperature scanning tunneling microscopy

MBE - molecular beam epitaxy

ML - monolayer

RT - room tem perature

K

SPM - scanning probe microscopy

SPSTM - spin polarised scanning tunneling microscopy

STM - scanning tunneling microscopy

STS - scanning tunneling spectroscopy

TEM - transmmission electron microscope

TMR - tunneling magneto resistance

TPD - tem perature programmed desorption

TSP - titanium sublimation pump

UHV - ultra high vacuum

List o f Figures

2.1

Schematic diagram of the process of Auger emission in a sohd

5

2.2 Schematic representation of a STM tunnehng junction . . . .

8

2.3

The m ultidisciphnary n atu re of iron oxide research

... 15

2.4

Phase diagram for the Fe — O system ... 17

2.5

Unit cell of Fe

... 18

2.6

The (001) B -term inated surface of Fe

... 20

2.7

The (001) A -term inated surface of Fe

... 21

2.8

Fe

(110)

A

and

B

term inated s u r f a c e ... 22

2.9

Representation of the charge neutrality of m agnetite (001) . .

25

3.1

Top view of the UHV system

... 32

3.2

Schematic of the resistive h e a t e r ... 35

3.3

Schematic illustration of th e e-beam h e a t e r ...36

3.4

Schematic illustration of a STM h e a d ... 40

3.5

Schematic of four-grid optics in LEED m o d e ...42

3.6

Schematic of LEED screen geom etry ...43

4.1

electrochemical set up ... 47

4.2

etching p r o c e s s ... 48

4.3

MnNi structure and m agnetic o r d e r ... 51

4.4

X-ray diffraction s p e c t r u m ... 52

L IS T OF FIGURES

XII

4.5

MnNi SEM i m a g e s ... 54

4.6 G eneral m agnetic behaviour for magnetic m a t e r i a l s ... 56

4.7 m agnetisation versus external magnetic field for a MnNi sam-

p le(etch ed /n o t e t c h e d ) ... 57

4.8 X-ray diffraction spectra c o m p a r i s o n ... 59

4.9 AES analysis of a MnNi

sample 1 ... 62

4.10 AES analysis of a MnNi

sample 2 ...63

4.11 M agnetic contrast w ith a MnNi p r o b e ... 67

4.12 m agnetisation orientation schematic for F e /W and MnNi tips . 68

4.13 SEM image of a C r t i p ... 71

4.14 SEM image of a Ni t i p ... 72

4.15 SEM image of a Fe3 0 4

(001) surface taken w ith a MnNi tip . . 73

5.1

AES and LEED of a clean Fe3 0 4

(001) s u r f a c e ... 79

5.2 STM image, B -term ination surface ... 80

5.3 STM image, B -term ination surface, Z o o m - in ...81

5.4 STM image. A- B- coexisting t e r m in a t io n s ... 84

5.5 STM image. Zoom-in on A - te r m in a tio n s ...85

6.1

Surface reconstructions on m agnetite (001) s u rfa c e ...92

6.2 AES spectrum of low level of contam inants Fc304

(001) surface 93

6.3

O nset of form ation of tr e n c h e s ... 94

6.4

O nset of form ation of trenches. Z o o m - i n ... 96

6.5 T he onset of form ation of p (1 x 3) superlattice by contam inants 97

6.6 A E S /L E E D for a contam inated m agnetite (001) surface . . . . 99

6.7 Different surface rearrangem ents on the surface

... 100

6.8

p ( l

2) surface reconstruction...102

L I S T OF F IG U R E S

X III

6.10 AES and LEED for a p (l x 3) surface re c o n s tr u c tio n ... 106

6.11 p (l

3) STM surface reconstruction...107

6.12 p (l

3) STM surface reconstruction. Z o o m -in ... 108

6.13 p (l

3) schematic m o d e l ...109

6.14 LEED p a tte rn for a p (l x 4) surface re c o n s tru c tio n ... I l l

6.15 STM image, p (l x 4) surface r e c o n s tr u c tio n ...113

6.16 Models proposed for a p (l x 4) surface re c o n stru c tio n ... 115

6.17 STM image of Fe

th in film annealed at low tem p eratu re. . 118

6.18 AES d a ta for a 70 nm contam inated m agnetite th in film . . .1 1 9

6.19 STM image for rounded terrace f o r m a t i o n ... 120

6.20 I/V curves for a contam inated m agnetite 70 nm th in film . . . 121

6.21 STM image of a p ( l x 1) r e c o n s tr u c ti o n ... 122

7.1

LEED p a tte rn for m agnetite (1 1 0 )... 127

7.2

LEED p a tte rn of a m agnetite (110) surface w ith fractional

order s p o ts ...129

7.3

STM image of a m agnetite (110) terraced s u r f a c e ...130

7.4

STM image of a m agnetite (110) nanostructed s u rfa c e ... 131

7.5

STM image of a m agnetite th in film ( 1 1 0 ) ... 133

7.6

Ball model for m agnetite (110) n a n o s tr u c tu r e s ... 135

7.7

I/V curves for m agnetite (110) s u r f a c e ...137

A .l

AES spectrum for a p ( l x 3) surface re c o n s tru c tio n ... 145

B .l Lattice param eters calculation of a p ( l x 3) LEED p a tte rn . . 149

C .l Classification of surfaces according to T a s k e r ...151

List o f Tables

2.1

Properties of iron oxides

C ontents

1

In trod u ction

1

2

B ackground

4

2.1

Introduction to experim ental techniques ...

4

2.1.1 Auger Electron Spectroscopy (A E S )...

4

2.1.2 Scanning Tunneling Microscopy ( S T M ) ...

6

2.1.3 Scanning tunneling spectroscopy ( S T S ) ... 10

2.1.4 Low Energy Electron Diffraction (L E E D )... 12

2.2

M agnetite: Fe

... 14

2.2.1 I n tr o d u c tio n ... 14

2.2.2 The surface of Fe

( 0 0 1 ) ... 19

2.2.3 The surface of m agnetite (110)

... 19

2.2.4 A utocom pensated s u r f a c e s ... 23

2.2.5 L iteratu re r e v i e w ...26

3

E xp erim en tal d eta ils

31

3.1

The ultrahigh vacuum set u p ... 31

3.2 The preparation c h a m b e r... 33

3.2.1 The resistive h e a t e r ... 34

3.2.2 The e-beam h e a t e r ... 36

CONTENTS

XVI

3.2.3

The ion g u n ... 37

3.2.4

Sample Characterization: Auger Electron Spectroscopy

38

3.3

The room -tem perature S T M ... 39

3.3.1 Four-grid L E E D ... 41

4 ST M tip s

44

4.1

In tro d u c tio n ... 44

4.2

Tip fabrication procedure ... 46

4.3

MnNi t i p s ... 50

4.3.1 MnNi alloy ... 50

4.3.2 Tip p re p a ra tio n ... 50

4.3.3 MnNi tips ch aracteriza tio n ... 53

4.3.4 Magnetic contrast: Scanning tunneling spectroscopy

(STS) ... 64

4.4

Cr t i p s ... 69

4.5

Other t i p s ... 70

4.6

STM results on magnetite (001) taken with a MnNi tip . . . . 70

4.7

C o n clu sio n s... 74

5 T he Clean Fe3 0 4

(001) surface

76

5.1

In tro d u c tio n ... 76

5.2

Sample p re p a ra tio n ... 77

5.3

Surface p re p a ra tio n ... 77

5.4

STM results and discussion ... 78

5.4.1 B- temination su rfa c e ... 78

5.4.2 Co-existing A- and B- te rm in a tio n s ... 82

CONTENTS

XVII

6 T h e C on tam in ated Fe3 0 4

(0 0 1

) surface

88

6.1

In tr o d u c tio n ... 88

6.2

Sample p r e p a r a t io n ... 89

6.3

C ontam inated Fe

(

) s u r f a c e ... 90

6.3.1 Breaking of long range (-\/2 x \/2)i?45° order by the

presence of c o n ta m in a n ts ... 93

6.3.2 p (l

2) reconstruction

... 98

6.3.3 p ( l

3) reconstruction

... 104

6.3.4 p (l

4) surface r e c o n s tr u c tio n ...110

6.4

p ( l X 1 ) ... 122

6.5

C o n c lu s io n s ...123

7 Surface stu d ies o f Fe3 0 4

(110)

125

7.1

In tr o d u c tio n ...125

7.2

Sample p r e p a r a t io n ... 126

7.3

Results and d i s c u s s i o n ... 126

7.3.1

Form ation of n a n o s tr u c tu r e s ... 126

7.3.2 D is c u s sio n ... 132

7.4

C o n c lu s io n s ...138

8 Sum m ary

139

8.1

C o n c lu s io n s ...139

8.2

Further work ... 141

8.2.1

Further characterisation of MnNi p r o b e s ... 141

8.2.2

Further characterisation of Fc

... 142

A A E S calcu lation s

144

C O NT EN T S

XVIII

C hapter 1

In trod u ction

M etal-oxide surfaces have recently draw n increasing atten tio n due to their

im p o rtan t technological applications,

i.e. corrosion, catalysis and microelec­

tronics. Iron oxides have also a ttra c te d much interest, in particular Fe

,

commonly known as m agnetite, as it is predicted to be half a m etallic ferro-

m agnet [1].

Fes

(001) and (110) artificial and n atu ral single crystal and th in film

surfaces are th e focus of the study presented here. M agnetite is one of the

few oxides w ith very high, almost m etallic conductivity, which is due to

Fe ions of different valence states being located at identical crystallographic

positions. At room tem perature, the electrical conductivity of Fe

is about

200

cni“ ^ [2]. M agnetite is also predicted to be a half-metallic ferrim agnet

[1,3], m eaning th a t in th e spin-up sub-band it is a m etal and in the spin-

down sub-band it is an insulator. At a tem p eratu re of 120 K bulk m agnetite

exhibits a m etal-insulator transition, known as th e Verwey tran sitio n [2,4],

a t which its conductivity decreases by two orders of m agnitude [5,6]. The

change of conductivity is accompanied by a change in its crystallographic

structure, whose sym m etry is lowered from cubic to monoclinic. The surfaces

C H APTER 1. INTRO D U CTIO N

of m agnetite show a highly complex behavior which is due to m any factors

such as, the stoichiometry; i.e. the ratio of th e Fe to O ions on th e to p most

layer [7-9].

A detailed investigation of probes m ade of magnetic m aterials for Scan­

ning Tunneling Microscope (STM) and Spin polarised STM (SP-STM ) ap­

plication is perform ed in this study. A spects such as fabrication, geom etry

and com position are studied. A reproducible technique for th e fabrication of

STM tips from a range of magnetic m aterials has been developed. The tips

are formed by electrochemical etching in an aqueous solution (NaOH, HCl),

using polym er tubing to physically restrict the active etching region. Tips,

w ith apexes in the 50-100 nm range, have been produced from polycrystalline

MnNi, Cr, Fe and Ni. Atomic resolution STM images have been achieved on

the Fe

(001) surface, using MnNi tips.

CH APTE R 1. INTRO D U CTIO N

Ca and K. A detailed investigation of the self-assembly of impurities onto

the surface is given at a nano- and atomic- scale on both surfaces.

C hapter 2

Background

2.1

In tro d u ctio n to ex p erim en ta l tech n iq u es

2.1.1

A u ger E lectron S p e ctro sco p y (A E S )

Auger Electron Spectroscopy (AES) represents one of the most im portant

chemical surface analysis tool for conducting samples. The method is based

on the excitation of so-called ’’Auger electrons” . AES is based on the use

of primary electrons with typical energies between 3 and 30 keV and the

possibility to focus and scan the primary electron beam in the nanometer

and micrometer range analyzing the top-most atomic layers of m atter. Figure

2.1 shows the sequence of events following ionisation of a core level. For

this example the K level is shown as being ionised by an incident electron,

whose energy Ep must obviously be greater than the binding energy

of

an electron in K. Following the creation of a hole in the level K, the atom

relaxes by filling the hole via a transition from an outer level, in this example

shown as Li. As a result of th at transition the energy difference (E/c — E/,i)

becomes available as excess energy, and this excess energy can be used by

CHAPTER 2. B AC K G R O U N D

5

u

1 EF I M, etc

L2 .3

Ji

•

---Initial state

Vac 0

EF M, etc L * 2 .3

E

K

K

-Excitation and

emission

Final state

Vac

1 EF z M, etc

L * 2 .3

- Li

Figure 2.1: The ground sta te is shown on the left. In the center an incident

electron of energy Ep has created a hole in the core level K by ionisation.

The hole in the K shell is filled by an electron from Li, releasing an am ount

of energy

wich can appear as a photon or can be given up

to another electron. The double ionised final state is shown on the right.

Reproduced from [10].

the atom in either of two ways.

CH APTER 2. BACKGROUND

6

obtained under electron bombardment with a characteristic energy allowing

one to identify the emitting elements. Auger electrons render information

2.1.2

Scanning Tunneling M icroscopy (ST M )

Comprehensive reviews of the theory and operating principles of scanning

tunneling microscopy (STM) and spectroscopy (STS) are given in dedicated

texts by Chen and Wiesendanger [12,13]. The fundamental theory of STM is

modelled on the quantum-mechanical description of an electron with energy

E travelling in a ID potential U(z) of the form shown in figure 2.2(a). This

electron is described by a wavefunction

ip{z),

which satisfies the Schrodinger

equation:

where m is the electron mass and

h = h/2iT

(where h is Planck’s constant).

In the classically allowed region where E > U(z), this equation has solutions

of the form:

__________

where the electron can move in either the positive or negative direction.

In the classically forbidden 6am'er region where E < U(z), the Schrodinger

equation has the solution:

The

K,

term describes the decay of the electron wavefunction within the bar­

rier region. For a finite potential U(z), there is a non-zero probability

P

of

finding the electron at a position z inside the barrier region, which is given

essentially on the elemental composition of the first 2-10 atomic layers [11].

^

+ U{z)^(z) = Eii{z)

(2.2)

CH APTER 2. BACKGROUND

7

Consequently, if the width of the tunnel barrier is sufficiently narrow, there

is a finite probability th at the electron can tunnel through the barrier region.

In the tip-vacuum-sample configuration of an STM junction (figure

2.2(b)), the height of the tunnel barrier is determined by the

work func­

tion 4>

of the tip and sample (assumed to be identical for convenience), which

is the minimum energy required to remove an electron from the metal to vac­

uum. An electron at the tip or sample surface, with Fermi energy

E p = —(f)

eV, will have the greatest opportunity to tunnel through the barrier, since

by definition the

Fermi level denotes the upper limit of electron occupancy

in the metal. In the absence of an externally applied bias, the electron can

tunnel through the barrier in either direction so th at there is no net tunnel

current. By applying an external voltage V, electrons in the sample within

the energy range

Ep — eV < E < Ep have an opportunity to tunnel through

the barrier. If

eV

0, then only electron states very near to the Fermi

level are })robed. The probability for an electron in the nth states to tunnel

through a barrier of width W is given by:

P

a |

-ipniO) p

K, =

(2.5)

Taking all the possible states in the energy range

Ep — eV < E < Ep into

account, the tunnel current is:

h<x

^

I ^(0) p

(2.6)

E = E p —eV

If V is small enough th at the density of electronic states does not vary sig­

nificantly within it, the latter sum can be conveniently w ritten in terms of

the

local density o f states (LDOS). At the Fermi level, at a location z and

energy E, the LDOS Ps(z,E) of the sample is defined as:

CH APT ER 2. BACKGROUND

8

U(z)

0

(a)

vacuum level

sample

eV

0

z

CHA PTER 2. BACKGROUND

9

for a sufficiently small

e. The LDOS is the number of electrons per unit

volume per unit energy , at a given point in space and at a given energy. The

tunneling current can be conveniently written in terms of the LDOS of the

sample at z=0 and E = E^p:

I t < x V p s { 0 , E F ) e - ^ ' ^ ^ (2.8)

It is clear from this equation that: (1) the tunnel current is directly pro­

portional to the bias applied across the junction, (2) it decays exponentially

as the distance between the tip apex and the sample surface is increased.

The significance of the probe-tip LDOS contribution is realised through a

time-dependent perturbation model of metal-insulator-metal tunneling pro­

posed by Bardeen [14], Here, a

Transfer Hamiltonian H r

is used to describe

the transfer of a tunneling electron from a sample state

ip to a. tip state

x-

The tunnel current can be taken as a convolution of the sample LDOS

and the tip LDOS

pt-A -rrp /*eV

h = - -

P.{Ef - e V + E)pt{EF - E) \ M

d E

(2.9)

a Jo

It also includes a tunneling m atrix element M, describing the am phtude of

electron transfer across the tunnel barrier (through the overlap of the 'ip

and

X

states). The integral describing M is evaluated over any surface lying within

the barrier region and rate of electron transfer is determined by the Fermi

golden rule [15].

Bardeen and Giaever [14] assumed th at the magnitude of the tunneling

m atrix element | M | does not change appreciably in the interval of interest.

Then, the tunneling current is determined by the convolution of the DOS of

two electrodes:

A qrp r e V

CHA PTER 2. BACKGROUND

2.1.3

S can n in g tu n n e lin g sp e c tro sco p y (S T S )

Equation 2.11 shows th a t the tunnehng current can be expressed as a

convolution of the sample LDOS

Ps

and tip LDOS

pt

(see equation 2.9). In

the semiclassical WKB approximation the tunneling current density between

two planar electrodes can be expressed by:

27TP / \

=

T ( s , V , E ) [ f { E ~ e V ) - f ( E ) Y ! > . ( E ) p ^ ( E - e V ) d E

where s is the tip-sample distance, V is the sample bias voltage, T(s,V,E)

is the tunneling transmission probability,

and

are LDOS of the

surface and the tip respectively. f(E) is the Fermi-Dirac distribution function.

In scanning tunneling spectroscopy formalism, the first derivative of the

tunneling current is usually analysed:

“

A\eT{s,

\/, B )p .(B )p ,(£ -

e V ) \ ^ „ y +

f

T (s, K

E)i>,(E) ■

J e V

aV

f ~

^

P

‘ (E)P.(E - eV)dE\

(2,12)

J e V

dV

C H A P T E R 2. BACKGROUND

measurement is known a priori. Otherwise, the sample DOS does not have a

definitive relation to the tunneling spectrum. In equation 2.12, if the second

and third terms are neglected, a constant tip LDOS and a weak voltage

dependence of the tunneling probability are assumed, d l/d V is proportional

to the sample LDOS

This simple proportionality forms the basis of

the STS and mostly d l/d V measurements are directly compared to calculated

sample densities of states. In order to obtain reproducible tunneling spectra,

the STM tip must have reproducible DOS, preferably flat DOS, th at is,

with a free-electron-metal behavior. Tip DOS are usually highly structured.

Feenstra

et al.

[16] developed an in-situ tip preparation procedure which

causes local melting and recrystallisation of the tip apex. This procedure

results in flattening of the tip DOS allowing one to obtain reproducible STS

d ata with W tips.

From the present discussion it is already clear th at the relation between

d l/d V and the sample LDOS is highly complicated. In the case of a tip with

a more complicated DOS, such as Fe or MnNi tips, this approximation has

to be taken with caution and it might not be so accurate as for the case of

W tips. Nevertheless, reproducible STS results have been obtained with W

coated with Fe tips on the surface of Mn/Fe(110) [17].

CH APTE R 2. BACKGROUND

probability function, T, is given by:

12

T = ts

exp

- 2 s ( ^ ( 4 > + V / 2 ) y '^

+ (,e x p

The first (second) term of T describes tunnehng from the sample(tip)

Fermi level to unoccupied tip(sample) states, t [nA/V] is a proportional­

ity coefficient which is related to the tip-surface effective contact area and is

proportional to the sample (for t^) or the tip (for t*) densities of states at the

Fermi level. 0 [eV] is given by the local work function (which is the avarage

of the tip and sample work functions in a first approximation). S [nm] is the

tip-sample distance and m the electron mass. To extract these parameters

from the experimental data, d l/d V should be fitted to T [17,22,23].

2.1 .4

Low E n erg y E lectron D iffraction (L E E D )

A plane wave incident on an atom or atoms within a unit cell will be scattered

in all directions, but interference between waves scattered from neighboring

unit cells will restrict the net flux to those directions in which the scattered

waves from all vmit cells are in phase. This requires th a t the scattered waves

from neighboring cells differ only by an integral number of wavelengths A.

In the simple case of a one-dimensional lattice, the in-phase condition is met

for all integers n which satisfy the condition:

a{sin4>n — sin4>o) = nX

(2-14)

C H APTE R 2. BACKGROUND

13

the lattice plane. This is known as the Laue condition. If the incident and

emergent beams are described by unit vectors

and s„ then this can be

w ritten in vector form as:

a ■

{sn —

So) = nX

(2-15)

or

a ■

Asn

=

nX

(2-16)

where

As„ =

- So

(2.17)

The diffracted beams are determined by A s„ and, in the one-dimensional

case, they are given by integral multiples of the basic unit (A / a). This

involves the reciprocal of the real space lattice vector a. We can define a

reciprocal lattice vector a*= (1/a).

For surface diffraction in a 2D system, the electron beam must conserve

both its energy and the component of its momentum parallel to the surface.

k\\^ +

+ k'j_^ ,

k^^ = k\\+ghi

(2.18)

where

k\\ and

kj_ are the parallel and perpendicular momentum compo­

nents of the incident beam, while

k'^^

and k'^ are those of the diffracted beam.

The

reciprocal lattice vector Qhi

is related to the beam energy

Eev, electron

mass

rrie

and diffraction angle

a by;

C H A P T E R 2. B A C K G R O U N D

14

where

a* and

b*

are the reciprocal lattice vectors. These are related to

the real space vectors a and

b by [26]:

d.a* = b.b* = 2

a.b* = b.a* = 0

(2.20)

This shows th e direct correspondance between th e observed diffraction

p a tte rn and th e reciprocal lattice of th e surface. The reciprocal lattice vec­

to r

Qhi lies in a direction th a t is orthogonal to th e plane of th e real space

lattice th a t is denoted by th e Miller indices h and 1. The Miller indices of

the diffracting planes are used to index the diffraction spots of th e LEED

p attern .

2.2

M a g n e tite : Fe3 0 4

2 .2.1

I n tr o d u c t io n

CHAPTER 2. BACKGROUND

Iron Oxides

M edicine - Iron O verload - Polynuclear organic com plexes Biology Biomlnerals Ferritin Navigation Chemistry - sorbents

Oxidants

ndustrial Chemistry

Pigments - Tapes - Catalysts

eochem istr^ Crystal chemistry Redox buffering

- Aggregation Plant nutrient Pedogenesi

ineral Properties Sorbents _{- Formcmo}

iron Oxides

Figure 2.3; The m u ltid is c ip lia n ry nature o f iro n oxide researcli

M a gne tite is p a rt o f the iro n oxide fam ily. These compounds are in fact ei­ ther oxides, hydroxides and oxide hydroxides [36]. The F e -0 system is form ed by w iis tite Fei_j:0 , m agnetite Fe3 0 4, hem atite a-Fe2 0 3 and m aghem ite 7- Fe2 0 3. Some physical properties are described for the different iro n oxides

on table 2.1.

Iro n oxides are essential for other fundam ental sciences as well as for a wide range o f applications. M edicine, biology, environm ental chemistry,

geology and soil science are examples o f the m ultidiscip lin es using of iro n oxides (see figure 2.3) [36].

In th is thesis the surfaces o f m agnetite (001) and (110) are studied.

Preparing the surface o f m agnetite is not tr iv ia l and undesirable iro n oxide- phases tra n s itio n need to be avoided. Figure 2.4 shows the e q u ilib riu m phase

diagram o f the iron-oxygen system and the s ta b ility dom ains fo r w iis tite

CH APTER 2. BACKGROUND

16

M a g n etite

H a em a tite

M agh em ite

W ixstite

Formula

Fe3 0 4

a-Fe2 0 3

FeO

Structural

type

Inverse

spinel

Corundum

Defect

spinel

Defect

NaCl

Crystal system

Cubic

Hexagonal

Cubic/

Tetragonal

Cubic

Space group

0^-Fd3m

D16-R3C

0^-F d3m /

P432i2

0^,Fm 3m

Cell

dimensions

(nm)

a; 0.84

a: 0.50

c: 1.38

a; 0.84/

a: 0.83

c: 2.50

a: 0.43

Colour

Black

Red

Brown

Black

Magnetic order

Ferri-

Weakly

ferro-Ferri-

Antiferro-Curie/Neel

temperature (K)

850

Tv-.

119

956

820-986^1)

203-211

R T Saturation

magnetisation

(J 'T ^K g -^)

92-100

0.3

60-80

Density (gcm^)

5.18

5.26

4.87

5.9

Formula units

per unit cell

8

6

8

4

CHAPTER 2. BACKG ROU N D

17

L IQ U ID [RON

1600

5 - IRON 1400

>200

i - I RON

UJ 5 IDOO

y eoo

600

H E M A T I T E

200

-60 -50 -40

LOG P o j (ATM.)

-30 -!0

Figure 2.4: Phase diagram for the Fe — O system. Reproduced from [36]

function of the tem p eratu re and oxygen content.

Bulk Fe

has a cubic inverse-spinel structure, where th e 32 0 ^ “ anions

form an face centered cubic (f.c.c.) lattice, half of th e Fe^"*" cations occupy 1/8

of th e available tetrah ed ral sites (64 available A-sites) and th e other half of

the Fe^"*" cations are located in 1/4 of the available octahedral interstices (32

available B-sites). 1/4 sites of the octahedral interstices is occupied by Fe^"^

cations. The unit cell edge constant is a = 0.83963 nm [37]. For stoichiometric

C H A P T E R 2. B A C K G R O U N D

18

a

w

a

0 16 octahcdral interstices arc occupied by Fe' and

I'c ions in equal pri)porlions

# S tetrah ed ral in terstices arc o ccu p ied hy Fe

32 ox y g en an io n s form an r.c.c. latticc

Figure 2.5: Unit cell of Fe

M agnetite is also predicted to be a half-metallic ferrim agnet [1,19], m ean­

ing th a t in th e spin-up sub-band it is a m etal and in the spin-down sub-band

it is an insulator. There is a gap in the m ajority spin band a t th e Fermi

level bu t there is not in the m inority spin band. Filled bands of the m ajority

spin are mainly composed of

3d

levels of Fe in the B site. For th e A site

3d

orbitals of Fe are filled by th e m inority spin electron. Moreover, th e orbitals

ju st below th e Fermi level are composed of 3d levels of Fe in th e B sites [1,38].

Alvarado et al.

have also dem onstrated [38] th a t the electrons from the O 2p

states lie well below th e Fermi energy.

C H AP T E R 2. BACKGROUND

19

has not been fully resolved [41,42]. The transition has been viewed as an

order-disorder transition in relation to the arrangement of cations on the

octahedral sites of the inverse spinel structure whose formal chemical formula

can be w ritten as Fe4

^"*"[Fe^“*'Fe^’'']B0 4

^“ [43-47].

2.2.2

T h e surface o f Fe

3 0 4

(001)

The (001) plane of magnetite can be viewed as a stacking sequence of two

alternating layers. The A-layer contains tetrahedrally coordinated Fe^'*' ions,

while the B-layer is composed of rows of octahedrally coordinated Fe^"^ and

Fe^"'' ions surrounded by oxygen ions. The separation between neighbouring

planes (i.e. the A-B interplanar separation) is 1.05 A, while the separation

between successive like planes (i.e. the A-A or B-B interplanar separation)

is 2.10 A. In each octahedral plane, the nearest-neighbor 5-site cations form

rows th at run along the [110] and [lIO] directions.

The rows in successive octahedral planes are rotated by 90° with respect to

one another, giving these planes a two-fold rotational symmetry. In contrast,

the arrangement of cations in the A-layers give them a four-fold rotational

symmetry. A ball model of Fe3 0 4

(001) is shown in figures 2.6 and 2.7 where

a full

B

and >l-terminated surface are depicted respectively.

2.2.3

T h e surface o f m a g n e tite (110)

The bulk of Fe3 0 4 can be thought to consist of two different planes perpen­

dicular to [110] with arrangement of the Fe and O ions as given in figure

2.8.

C H APTER 2. BACKGROUND

20

OoO O

O O

o

c

o o o o

g

Q

OoO OoO

Q

O

'

o o o o

(V2 X V2)R45°

unit cell

0 0 0 Oo

O O

Oo

o

O O

0 0 0 1 Oo

O

...

(1x1)

unit cell

O

"ITop p la n e : O ctahedral

O

Iron

O

Iron

Tetrahedral p la n e below

CH APTER 2. BACKGROUND

(V2

unit cell

O 0.0 ox 0^0

ooo o

‘ vO 0 .0

. o

_c

o o

OoO O

0<1©^©4)Q O

o

C)--Q.(|,,|

unit cell

U Iron

Top plane: Tetrahedral

O Oxygen \ o c ta h e d ra l p la n e below

O Iron

^

OoO O

Figure 2.7: The (001) A-terminated surface of Fe

. The large circles rep­

resent oxygen atoms forming an f.c.c. lattice on the layer below. The small

circles depict iron atoms located at the

A

and

B

sites. The p (l x 1) primi­

tive unit cell is marked with an black square. The (-\/2 x \/2)/?45° unit cell

CHAPTER 2. BACKGROUND

6 A

A t e r m i n a t i o n

( -1 1 0)

O

t

1.1 A

o

c

'

--►

o

c

o

c

o

c

o

€)

•

C)

€)

€)

O

C

Octahedral Fe

Tetrahedral Fe

o o o o

o

o

o

o

o

o

Q

o

o

o

o

o

o

o

o

c

o

Figure 2.8: The atom ic arrangem ent in th e two types of (110) layers A and

C H A P T E R 2. B A C K G R O U N D

23

positions. The type-B contains b o th octahedrally and tetrah ed rally coordi­

n ated Fe ions which have antiparallel m agnetic m oments (see figure 2.8).

M agnetite (110) is a non-polar surface. This means th a t the surface of Fe

(

) has no dipole moment perpendicular to the surface, therefore it has a

finite surface energy m eaning th a t the surface may retain the stru ctu re of

th e bulk term ination w ith minor relaxations [48] (see appendix C).

2.2.4

A u tocom p en sa ted surfaces

The concept of autocom pensation, originally developed for surfaces of

com pound semiconductors, such as GaAs and ZnSe [49], is very sucessful

for predicting reconstructions of m etal oxide surfaces [50]. The m ost stable

surfaces are predicted to be those which are autocom pensated, which

means th a t excess charge from cation-derived dangling bonds com pensates

anion-derived dangling bonds. The surface is th en ’’self-com pensated” , th a t

is th e cation-(anion) derived dangling bonds are completely em pty (full) on

stable surfaces. This model allows for the partially covalent character found

in m any m etal oxides, including oxides of iron. This simple electron-counting

approach is somewhat more com plicated in Fe

because of the mixed

valency and coordination of iron ions in th e inverse spinel structure.

For m agnetite, one te tra h ed ral Fe^"^ ion contributes three electrons to a

to ta l of four bonds to neighboring oxygen atom s in bulk Fe

. Therefore,

each bond contains

e“ th a t are donated from the tetrah ed ral iron ions.

Above th e Verwey transition, electrons hop freely between octahedral Fe^"^

and Fe^"^, giving rise to an average formal oxidation state for iron of 2.5.

Each octahedral iron ion contributes 2.5 e“ to a to ta l of six bonds to oxygen

C H A P T E R 2. B A C K G R O U N D

24

ions. Assuming two electrons per bond, each oxygen contributes 2 — | e“

= I e“ to each F e (te t)-0 bond, and 2 — ^ e“ = y| e“ , to each Fe(oct)-

0 bond. These num bers can be used to determ ine danghng bond charges

when different surfaces structures are created. This is known as th e

electron-counting model.

This is formally equivalent to conditions for creating a non-polar surfaces

of ionic (or p artially ionic) crystals introduced by Tasker [51]. T he

electro­

static model

proposed by Tasker classifies the surfaces of any ionic or partially

ionic m aterials into three types. Type 1 consists of neutral planes w ith b o th

anions and cations (i.e. (001) and (110) surfaces of rocksalt m etal oxides, such

as MgO and NiO). Type 2 consists of charged planes arranged sym m etrically

so th a t there is no dipole m oment perpendicular to the im it cell (i.e. ( I l l )

surface of the fluorite stru ctu re term inated w ith an anion plane). N either of

these surfaces affect ions in the bulk of th e crystal and they should therefore

have modest surface energies (also called

non-polar),

which diverges when

a net dipole is presence on the surface. The type 3 surface is charged and

there is a perpendicular dipole moment. These surfaces have infinite surface

energies (i.e. ( I l l ) surfaces in the rocksalt structure). These surfaces are also

called

polar

(see appendix C).

For

A

or B -bulk term inated Fe

(001) surface electrostatic argum ents

lead to uncom pensated charge at th e surface. In figure 2.9 a schem atic rep­

resentation of a polar crystal is shown. The ionic charge of ± 6 per layer

unit cell is autocom pensated throughout the bulk of th e crystal in m agnetite

(001). However, an ex tra charge of ± 3 (depending on

an A or B

surface

term ination) is not com pensated when th e surface is created. For energetic

reasons charge neutrality is required. Charge n eutrality a t th e polar (001)

C H A PTE R 2. BACKGROUND

25

S u r f a c e

B

A

B

A

B

-3

-3

+3

+3

-3

-3

+3

+3

-3

-3

Figure 2.9: Schematic representation of the charge neutrality of magnetite

(001). A 5-term inated surface is depicted with a total charge of —3 on the

surface.

the composition of the surface layer. Magnetite (001) surface undergoes ma­

jor transformations(reconstructions) on the surface to minimise the surface

energy in agreement with our STM and LEED results ^

The stable surfaces (types 1 and 2) may occur with only small relax­

ations from the bulk structure whereas the type 3 surfaces can only occur

with substantial reconstructions [51]. The surface of magnetite (001) is a

CH APTER 2. BACKGROUND

26

polar surfaces, therefore intrinsically unstable. It belongs to type 3 surfaces

according to Tasker’s model. The surface of magnetite (110) is a non-polar

surface [48].

2.2.5

L iteratu re review

T h e clean Fe,30 4 (0 0 1 ) surface

As explained in section 2.2.2, the (001) plane of magnetite can be viewed as

a stacking sequence of two alternating layers,

A

and

B,

containing iron ions

on the tetrahedral and octahedral sites respectively .

Both A- [52-54] and B- [47, 55, 56] term inated surfaces have been re­

ported in the literature, with no satisfactory explanation as to why the (001)

magnetite surface should be term inated at either plane. However it is clear

th at the preparation conditions play a crucial role in determining the surface

termination.

A

{\/2

v^)/?45° reconstruction has been observed by several groups

on the clean magnetite (001) surface of both natural and synthetic single

crystals, and on thin films grown by Molecular Beam Epitaxy (MBE)^.

STM studies carried out by Tarrach

et al.

[52] have suggested th at the

top-most surface layer consists of a full monolayer of tetrahedral Fe ions.

Chambers

et al.

[54] used x-ray photoelectron spectroscopy (XPS), X-ray

^Two different notations to define the same surface reconstruction are used in the

literature leading to confusion. Some authors [52,53,57] reference the reconstructed surface

to the bulk unit cell and call it p (l x 1). O thers [56,58-60] reference the simplest primitive

unit mesh to the unreconstructed surface, and consequently this reconstruction is called

{\/2 X y/2)Ri5°. In surface crystallography it is common to denote any unreconstructed

surface w ith the smallest prim itive ( 1 x 1 ) unit cell and the latter notation is adopted in

C H A P T E R 2. B A C K G R O U N D

27

photoelectron diffraction (XPD) and STM to sup p o rt the conclusion th a t

th e Fe

(001) surface is constituted by half filled layer of te tra h ed ral Fe

ions. The la tte r surface term ination is charge com pensated. W iesendanger

et al.

[34] imaged two distinct stru ctu res on different areas of a n atu ral

crystal of m agnetite; the two structures were a ttrib u te d to bulk term inated

te tra h ed ral and octahedral term inations of th e surface. In contrast, Voogt

et

al.

[55] and more recently Stanka

et al.

[56] have proposed a B -terniinated

layer on a single crystal and a Fe

/M g

(

) film, respectively. In b o th

cases, they have proposed th a t charge com pensation is achieved by an array

of oxygen vacancies accom panied by a change in th e valence state of the Fe.

M ariotto

et al.

[47] observed a (\/2 x \/2)i?45° reconstruction on a clean

m agnetite (001) single crystal surface in terp retated as a B-layer surface

term ination. M ariotto

et al.

further proposed th a t the reconstruction is due

to charge ordering of th e Fe cations in octahedral positions, and not to an

ordered array of vacancies as proposed by previous studies. Such a surface

is not charge com pensated.

T h e c o n ta m in a te d Fe

(

) su rfa ce

Surface reconstructions induced by alkaline and alkaline-earth m etals have

been observed on a range of different systems, such as th in films of Fe

grown on MgO(OOl) substrates [60,61], th in films of Fe

grown on P t ( l l l )

substrates [62] and T i02 single crystals [63,64]. A p ( lx 4 ) reconstruction was

observed by Anderson

et al.

[60] on a 1 /xm thick film of m agnetite grown

on a MgO (001) substrate. A similar effect was observed by Voogt

et al.

[55]

who reported th e onset of a p ( lx 3 ) reconstruction on a m agnetite th in film

C H A P T E R 2. B A C K G R O U N D

28

to th e segregation of magnesium from th e substrate, leading to th e form ation

of a MgFe

phase. Kim

et al.

[59] in a study of m agnetite th in films grown

on MgO (001) suggested th a t th e Mg ions diffuse through th e iron oxide via

vacancies in the octahedral cation sublattice. Once they reach the surface,

they decorate the rows of octahedral

B -site

cations. Norenberg

et al.

[64]

have investigated Ca-induced surface reconstructions on Ti02- They have

observed a variety of surface reconstructions, including p ( lx 3 ) and p ( lx 4 ) .

They a ttrib u te d th e p ( lx 3 ) reconstruction to Ca^'*' cations replacing the Ti

cations a t th e surface of the crystal. A p ( l x 4 ) reconstruction, caused by an

ordered array of trenches, was found to succeed th e p ( l x 3 ) reconstruction

and it was a ttrib u te d to oxygen loss from th e surface.

M agnetite is a particularly well suited m aterial for these studies. The po­

lar surface of m agnetite m ust reconstruct or undergo a charge redistribution

to minimize the surface energy. As explained and dem onstrated in chap­

ter 5, a clean surface of m agnetite term inated a t the (001) plane exhibits a

(\/2x-\/2)i?45° reconstruction. The contam inant free m agnetite surface had

revealed interesting d a ta of its fundam ental properties. These fundainental

properties are modified by the presence of contam inants on the surface.