Spin-Polarized Positron Annihilation Spectroscopy

188 Pages·2017·5.53 MB·English

SPIN-POLARIZED POSITRON ANNIHILATION SPECTROSCOPY
josef andreas weber
Investigation of Complex Metallic Systems
Doktor der Naturwissenschaften (Dr. rer. nat.)
Physik Department
Technische Universität München

TECHNISCHE UNIVERSITA¨ T MU¨ NCHEN
lehrstuhl e21
SPIN-POLARIZED POSITRON ANNIHILATION SPECTROSCOPY
INVESTIGATION OF COMPLEX METALLIC SYSTEMS
josef andreas weber
Vollsta¨ndiger Abdruck der von der Fakulta¨t fu¨r Physik der Technischen Universita¨t
Mu¨nchen zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
genehmigten Dissertation.
Vorsitzender: Prof. Dr. Norbert Kaiser
Pru¨fer der Dissertation: 1. Priv.-Doz. Dr. Christoph P. Hugenschmidt
2. Prof. Dr. Rudolf Gross
3. Prof. Dr. Claudia Felser (nur schriftliche Beurteilung)
Die Dissertation wurde am 21.09.2016 bei der Technischen Universita¨t Mu¨nchen ein-
gereicht und durch die Fakulta¨t fu¨r Physik am 03.02.2017 angenommen.

ABSTRACT
This thesis focuses on the investigation of the electronic structure and the Fermi
surface (FS) of copper, iron, vanadium and Cu MnAl. To this end the data acqui-
2
sition for the new angular correlation of electron positron annihilation radiation
(ACAR) spectrometer at the Technische Universität München was designed and
newapproachesfordataevaluationweredevelopedincludinganovelalgorithmto
reconstruct 3D electron-positron momentum densities from projections. Using the
new toolkit the elemental systems copper, iron and vanadium were investigated
andcomparedtopreviouslyreportedexperimentalandtheoreticaldata.Addition-
ally, an extensive study on the Heusler compound Cu MnAl with spin-polarized
2
ACAR and magnetic Compton scattering (MCS) was conducted. Spin-polarized
ACAR in particular made it possible to measure for the first time the spin de-
pendent FS of this system and to determine the individual contribution of each
sheet to the total magnetization. Via the comparison with MCS measurements in
combination with suitable ab initio calculations it is now possible to attribute the
magnetic momentum density to specific electronic states. This information sub-
stantially contributes to the deeper understanding of the technical highly relevant
material class of Heusler alloys.
ZUSAMMENFASSUNG
Diese Arbeit widmet sich der Untersuchung der elektronischen Struktur und der
Fermi-FlächevonKupfer,Eisen,VanadiumundCu MnAl.ZudiesemZweckwur-
2
de für das neue Spektrometer zur Messung der Winkelkorrelation der Annihilati-
onsstrahlung von Elektronen-Positronen-Paaren (ACAR) an der Technische Uni-
versität München die Datenaufnahme entworfen und Methoden zur Datenverar-
beitung inklusive eines neuartigen Algorithmus zur Rekonstruktion von dreidi-
mensionalen Elektron-Positron-Impulsdichten aus ihren Projektionen entwickelt.
MittelsdieserTechnikenwurdendieelementarenSystemeKupfer,EisenundVana-
dium untersucht und in den Kontext bisheriger theoretischer und experimenteller
Ergebnisse aus der Literatur gestellt. Darüber hinaus wurde das Heusler-System
Cu MnAl mithilfe von spinpolarisiertem ACAR und magnetischer Comptonstreu-
2
ung (MCS) ausführlich erforscht. Insbesondere spinpolarisiertes ACAR erlaubte
erstmals spinaufgelöst die Fermifläche dieses Metalls zu bestimmen und daraus
den individuellen Beitrag jeder Subfläche zur Gesamtmagnetisierung zu extrahie-
ren.EinVergleichderSpektrenundderMCSMessungenmitgeeignetenAb-initio-
Rechnungen erlaubt es nun die magnetische Impulsdichte spezifischen elektroni-
schen Zuständen zuzuordnen. Diese Information trägt wesentlich zum grundle-
genden Verständnis der technisch hoch relevanten Heusler Legierungen bei.
v

CONTENTS
1 introduction 1
i solid state physics with positrons 3
2 positron sources 5
2.1 Radionuclides as Positron Sources 5
2.2 Positron Sources at Large-Scale Research Centers 8
3 positrons in vacuum and condensed matter 11
3.1 Positrons and Positronium in Vacuum 11
3.2 Positrons in Condensed Matter 13
3.3 Positron Lifetime Spectroscopy 18
3.4 Doppler Broadening Spectroscopy 19
4 investigation of the electronic structure with acar 23
4.1 History of ACAR Spectroscopy 23
4.2 Theory of the Electronic Structure of Solids 27
4.3 Theory of ACAR Spectroscopy 30
4.4 Complementary Methods 38
ii experimental setup and procedures 43
5 design details of the munich acar spectrometer 45
5.1 Source Sample Stage 45
5.2 Position Sensitive Detectors 47
6 data acquisition 49
6.1 Analog Data Processing 49
6.2 Problems of the Original Data Acquisition 52
6.3 Improved Data Acquisition 52
7 data treatment 57
7.1 Correcting Nonlinearities 57
7.2 The Momentum Sampling Function 57
7.3 Finding the Center of the Spectrum 59
7.4 The Radial Anisotropy 60
7.5 Determining the Gauge Between Pixels and Angle 61
8 comparison of γ detector technologies 65
8.1 General Considerations 65
8.2 Detector Technologies 67
8.3 Conclusion 71
iii reconstruction of 3d densities from projections 75
9 overview of reconstruction methods 77
9.1 The Radon Transform 77
9.2 Fourier Slice Theorem 79
9.3 Filtered Back-Projection 80
9.4 Cormack’s Method 81
vii
viii contents
9.5 The Algebraic Reconstruction Techniques 83
10 novel algorithm for the reconstruction of ρ2γ 85
10.1 Mathematical Principles 85
10.2 Numerical Implementation 87
10.3 Effect of Regularization 91
iv experimental results 97
11 investigation of elementary systems 99
11.1 Temperature Dependent Measurements on Copper 99
11.2 Spin-Polarized Positron Measurements on Iron 105
11.3 The Electronic Structure of Vanadium 116
12 spin-polarized studies on the heusler system cu2mnal 123
12.1 Sample Preparation 123
12.2 Sample Characterization 124
12.3 Theoretical Band Structure Calculations 130
12.4 Results and Discussion 131
13 conclusion and outlook 143
v appendix 147
a additional details 149
a.1 Fermi function 149
a.2 Line Driver Circuit 150
a.3 Resolution of an ACAR spectrometer 151
b acronyms 153
c list of publications 155
bibliography 157
acknowledgments 179
The Fermi surface is the stage on which the “drama of the life of
the electron” is played out. And in the same way in which the life
of mountain people is essentially different from people living in the
valleys, the propeties of electrons in lead, which has an exceedingly
complicated Fermi surface [...], do not resemble the properties of
sodium, whose Fermi surface is a sphere much smoother than a
billiard ball.
—Kaganov and Lifshits [1979]
1
INTRODUCTION
The figurative quote of Kaganov and Lifshits already gives an idea how important
the knowledge about the Fermi surface (FS) is to understand the properties of a
solid. Although theory has made great progress in modeling electronic systems,
therearestillmaterialswithpropertiesbeyondthepossibilitiesoftheoreticalmod-
eling like e.g., the spin density wave in chromium. Especially if one wants to
design new materials with desired features or functionalities, an in-depth under-
standing of electronic correlations is necessary. However, there is only a limited
number of techniques to probe the FS each exhibiting strengths and weaknesses.
The most commonly used techniques today comprise e.g., angle-resolved photoe-
mission spectroscopy (ARPES) and characterization via the de Haas-van Alphen
(dHvA) effect. Even though ARPES can not only measure the FS but the whole
band structure it is limited to the surface of a material while dHvA can probe the
bulk properties but requires cryogenic temperatures and high magnetic fields.
An alternative technique which is being used to investigate the electronic struc-
tureisthemeasurementoftheangularcorrelationofelectronpositronannihilation
radiation (ACAR). It enables the analysis of the electronic structure in the bulk or
the surface at any desired temperature and independent of a magnetic field. With
2D-ACAR a projection of the electron-positron momentum density ρ2γ is mea-
sured. Therearetwodifferentapproachestoprocesstheacquireddata: i)Datacan
be quantitatively compared to band structure calculations in order to find mean-
ingful input parameters for the theory. ii) The fully three-dimensional ρ2γ can be
reconstructed by measuring several projections and the FS can then be identified
via discontinuities in the reconstruction. Either way, ACAR can provide valuable
information about the electronic structure of a material.
In order to fully utilize the possibilities of ACAR spectroscopy, a careful data
treatment is essential. Since positron sources have a limited activity and detec-
tors with sufficient high angular resolution only detect a very small fraction of
the annihilating positrons (usually less than 10−6), it typically takes a long time -
up to a few weeks - to record a single 2D-ACAR projection. Hence, for the sub-
sequent analysis of the data it is crucial to not introduce artifacts by unnecessary
interpolation and to preserve the information about the statistical accuracy. This
1
2 introduction
requires both a specifically adapted data acquisition and carefully programmed
data processing algorithms.
In this thesis, a new 2D-ACAR spectrometer at the Technische Universität
München (TUM) was co-developed with the particular goal to improve the data
acquisitionandto establishnoveldataprocessingalgorithms. Tothisend, analgo-
rithm for the reconstruction of ρ2γ from projections was established. Using these
tools, an investigation on the elementary metals copper, iron and vanadium was
conducted. Furthermore, the electronic structure of the Heusler system Cu MnAl
2
was studied in detail.
The following chapter explains the basic principles of ACAR spectroscopy and
the theory of electrons in solids. In the second part of this work, the spectrometer
and thedata acquisitionis introduced. Subsequently, the reconstruction algorithm
is presented after introducing the principles of reconstructing densities from its
projections. Finally in the third part, the measurements and the results on the
aforementioned systems will be addressed and discussed.