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X-ray studies of magnetism and electronic order in Fe-based materials [Elektronische Ressource] / von Jorge Enrique Hamann Borrero

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151 pages
X-ray Studies of Magnetism and ElectronicOrder in Fe-based MaterialsDissertationzur Erlangung des akademischen GradesDoctor rerum naturalium (Dr. rer. nat.)vorgelegtder Fakult¨at Mathematik und Naturwissenschaftender Technischen Universita¨t DresdenvonJorge Enrique Hamann Borrerogeboren am 28 September 1981 in Medell´ın (Colombia)Dresden 2010ii1. Reviewer: Prof. Dr. Bernd Bu¨chner2. Reviewer: Prof. Dr. Ru¨diger KlingelerthDay of the defense: 17 of December, 2010To my familyiiContents1 Introduction 1I Theory and Experimental Techniques 52 X-ray Scattering by Solids 72.1 Kinematical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 X-ray Magnetic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.1 The Non-Resonant X-ray Magnetic Scattering Cross Section . . . . . . . . 112.2.1.1 X-ray Magnetic Scattering at High Photon Energies . . . . . . . 132.2.2 Resonant X-ray Magnetic Scattering . . . . . . . . . . . . . . . . . . . . . 142.3 Magnetic Superlattice Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 X-ray Diffraction by Powder Samples . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.1 The Rietveld Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.1.1 The R Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Phase Transitions 233.1 Some Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.
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X-ray Studies of Magnetism and Electronic
Order in Fe-based Materials
Dissertation
zur Erlangung des akademischen Grades
Doctor rerum naturalium (Dr. rer. nat.)
vorgelegt
der Fakult¨at Mathematik und Naturwissenschaften
der Technischen Universita¨t Dresden
von
Jorge Enrique Hamann Borrero
geboren am 28 September 1981 in Medell´ın (Colombia)
Dresden 2010ii
1. Reviewer: Prof. Dr. Bernd Bu¨chner
2. Reviewer: Prof. Dr. Ru¨diger Klingeler
thDay of the defense: 17 of December, 2010To my familyiiContents
1 Introduction 1
I Theory and Experimental Techniques 5
2 X-ray Scattering by Solids 7
2.1 Kinematical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 X-ray Magnetic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 The Non-Resonant X-ray Magnetic Scattering Cross Section . . . . . . . . 11
2.2.1.1 X-ray Magnetic Scattering at High Photon Energies . . . . . . . 13
2.2.2 Resonant X-ray Magnetic Scattering . . . . . . . . . . . . . . . . . . . . . 14
2.3 Magnetic Superlattice Reflections . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 X-ray Diffraction by Powder Samples . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.1 The Rietveld Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.1.1 The R Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Phase Transitions 23
3.1 Some Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Landau Theory of Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 The Correlation Length ξ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Experimental Techniques 31
4.1 High Energy X-Ray Scattering: Beamline BW5 . . . . . . . . . . . . . . . . . . . 31
4.1.1 The Triple Axis Diffractometer . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Resonant Magnetic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.1 Magnetic Scattering Beamline ID20 . . . . . . . . . . . . . . . . . . . . . 34
4.2.1.1 Azimuthal Dependence and Polarization Analysis . . . . . . . . 35
4.2.1.2 Incoming Light Polarization . . . . . . . . . . . . . . . . . . . . 36
4.2.2 MAGS Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37iv CONTENTS
4.3.1 Integrated Intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.3 Powder X-ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
II Structure and Magnetism of (La,Sm,Ce)FeAsO F Superconductors 431−x x
5 High Temperature Superconductivity in Iron Pnictides 45
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Crystal Structure of the Iron Based Superconductors . . . . . . . . . . . . . . . . 46
5.2.1 Effect of F Doping on the Layered Structure . . . . . . . . . . . . . . . . 47
5.2.2 Temperature Dependent Structure . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.4 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.4.1 Superconducting Pairing Mechanism . . . . . . . . . . . . . . . . . . . . . 55
5.5 The 1111 Electronic Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.6 Structural Transition and Magnetic Ordering in Sm-1111 and Ce-1111 . . . . . . 59
5.6.1 Room Temperature Structure . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.6.1.1 Effect of F Doping on the Layered Structure . . . . . . . . . . . 59
5.6.2 The Tetragonal to Orthorhombic Phase Transition . . . . . . . . . . . . . 62
5.6.2.1 Determination of T . . . . . . . . . . . . . . . . . . . . . . . . . 62s
5.6.3 μSR Magnetic Order Parameter . . . . . . . . . . . . . . . . . . . . . . . 68
5.6.4 Electrical Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.6.5 Discussion and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.6.5.1 The Electronic Ce-1111 and Sm-1111 Phase Diagram . . . . . . 72
5.6.5.2 Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
III X-ray Magnetic Scattering on RFe (BO ) 793 3 4
6 Non-Resonant X-ray Magnetic Scattering on RFe (BO ) 813 3 4
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.3.1 Structural Transition at T . . . . . . . . . . . . . . . . . . . . . . . . . . 84S
6.3.2 Superlattice Reflections in the Antiferromagnetic Phase . . . . . . . . . . 87
6.3.3 Field Dependence of the (0,0,1.5) Reflection . . . . . . . . . . . . . . . . . 88
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92CONTENTS v
6.4.1 q and Azimuth Dependence of the Magnetic Reflection . . . . . . . . . . . 93
6.4.2 Correlation Length ξ of the Magnetic Domains . . . . . . . . . . . . . . . 95
6.4.3 MagneticOrderingandCriticalExponentsinNdFe (BO ) andYFe (BO ) 953 3 4 3 3 4
6.4.4 The Magnetic Structure Factor and the Spin-moment S in GdFe (BO ) 963 3 4
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7 Resonant Magnetic Scattering on NdFe (BO ) 993 3 4
7.1 Multiferroics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.1.1 Multiferroic Spiral Magnets . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.2 Resonant Enhancement of the Magnetic Reflections . . . . . . . . . . . . . . . . . 103
7.2.1 Temperature Dependence of the Resonant Intensities . . . . . . . . . . . . 105
7.2.2 Effect of Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
7.2.2.1 Polarization analysis of the (0,0,15/2) reflection . . . . . . . . . 113
7.2.3 Effect of an Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.2.4 Effect of E and B on the Sample’s Magnetic History . . . . . . . . . . . . 118
7.2.5 Chirality of the Spin Spiral . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8 Summary 125
References 129vi CONTENTSChapter 1
Introduction
Among all the physical phenomena present in nature, light and magnetism have intrigued
mankind for centuries. From Thales of Miletus to the actual times we have seen, maybe
unexpectedly, that the use of light has served as a mean to understand many properties of solids,
including magnetism. The first applications of light to the study of magnetism started in the
19th century with Faraday and Kerr who demonstrated the influence of magnetization on the
polarization of incoming and reflected light. But it is only after the discovery of x-rays by W.
C. Ro¨ntgen in 1895 that light has become an invaluable tool for probing the structure of matter
and its properties.
Since then, the interaction of x-rays with solids has been widely used not only for the
determination of their crystalline structure, but also as a spectroscopic tool for probing their
electronicproperties. Nottoforget, x-raysareelectromagnetic waves, i.e. theyinteractalsowith
the magnetic moments of magnetic materials and therefore they can also be used to unveil their
magnetic properties. Even though, this “photon/sample’s magnetism” interaction is present, it
is so weak that to measure it is an experimental odyssey. However, the development of high
brilliance and high energy synchrotron radiation facilities has become a breakthrough in order
to overcome this experimental difficulties.
Many fields within solid state physics have profited from the advent of synchrotron sources,
but is perhaps the physics of strongly correlated electron systems where more light has been
shed. Not tobesurprisedsincemanyorderingphenomena(e.g. magnetic, chargeand
orbitalordering)arepresentinthesesystems, whoseenergyandlength scales arecomparabletothat ofof
x-rays, and which are responsible for some of the most interesting and marvelous phenomena of
modern physics such as superconductivity and multiferroicity. Therefore, the study of ordering
phenomena in these systems is an important key for their understanding. For example,
superconductivity in most cuprates and in the newly discovered iron pnictides, emerges only when
magnetic ordering and structural distortions are suppressed after doping the structure whether2 1. Introduction
withelectrons orholes. Thisbehaviorrisessomequestionssuchas: whichisthedrivingforcefor
the onset of superconductivity or the destruction of magnetism?, are there competing orders?,
what is the role of fluctuations?
Another example are multiferroics where, although magnetic order and electric
polarization tend to exclude each other, at least two “ferroic” orders (e.g. ferro/antiferromagnetism,
ferro/antiferroelectricity and ferroelasticity) are present simultaneously. So far several
mechanism have been proposed to explain multiferroicity, one is due to magneto elastic dimerization,
where magnetic ions form dimers with alternating spin directions (e.g. ⇈). This dimerization
inducesalattice distortionwhichisresponsiblefortheelectric polarization. Anothermechanism
is that induced by spiral magnets since, as any other magnetic order, the magnetic spiral
spontaneously breaks time reversal symmetry and in addition it breaks inversion symmetry, which
are fundamental conditions for the development of these orders respectively. Thus the proper
determination of the magnetic and crystallographic structure is of preponderant importance to
fully understand multiferroicity. Then, due to the nature of the challenge that these systems
bring, anaturalinstrumentto make frontat itare high energyphotons. Where long rangeorder
properties can be addressed by x-ray diffraction while usingx-rays as spectroscopic probewould
bring information about the electronic states.
In the present work high energy photons are exploited in several ways in order to study
the magnetic and structural properties of two types of strongly correlated systems. On the
one hand, powder x-ray diffraction is used to follow and properly determine structural phase
transitions and lattice instability of iron pnictide superconductors as a function of temperature
and dopant content. On the other hand, resonant and non-resonant magnetic scattering are
used to study the magnetic structure of several compounds of the iron borates family. The
measurements were done at extreme conditions (i.e. by applying external electric and magnetic
fields at different temperatures) and using all the available tools such as full control of incident
photonpolarization,polarizationanalysisofthescatteredintensitiesaswellastuningthephoton
energy to match electronic transitions of the ions in the system, in order to extract the most
amount of information regarding magnetism on these compounds.
The work is divided in three main parts. The first part concerns the theoretical and
experimental details needed to follow the results and discussions presented in the course of the thesis.
Inchapter 2, derivation ofrelevant formulasrelated to scattering ofx-rays bysolidsispresented,
special consideration is given to the interaction between the photon electric field with the
sample’s magnetism and the subsequentpolarization dependencesemerging as a consequence of this
interaction. In this chapter, there is also a section dedicated to the x-ray diffraction of powder
samples, where details on the Rietveld refinement method are discussed. Chapter 3
contemplates definitions and theories of phase transitions such as the Landau theory. Fluctuations and

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