Neutron scattering investigations of zero- and one-dimensional quantum magnets [Elektronische Ressource] / vorgelegt von Oliver Pieper

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Neutron Scattering Investigations of Zero- andOne-dimensional Quantum Magnetsvorgelegt vonDiplom-Physiker Oliver Piepergeb. am 17. April 1979 in RodewischVon der Fakultät II - Mathematik und Naturwissenschaftender Technischen Universität Berlinzur Erlangung des akademischen GradesDoktor der NaturwissensschaftenDr. rer. nat.genehmigte DissertationPromotionsausschuss:Vorsitzender: Prof. Dr. M. DähneBerichter/Gutachter: Prof. Dr. B. Lake Prof. Dr. D. A. Tennant Prof. Dr. J. SchnackTag der wissenschaftlichen Aussprache: 09. Juni 2010Berlin 2010D83iiAbstractThis thesis deals with the investigation of two different types of low-dimensionalquantum magnets using the technique of neutron scattering.In the first part, the magnetic properties of three Mn -based single molecule mag-6nets are explored by means of inelastic neutron scattering. The experimental datareveal that small structural distortions of the molecular geometry produce a signifi-cant effect on the energy level diagram and therefore on the magnetic properties ofthe molecule. It will be shown that the giant spin model completely fails to describethe spin level structure of the ground spin multiplets. The data enabled the deter-mination of the parameters of the microscopic spin Hamiltonian and based on thisit is shown that the excited S-multiplets play a key role in determining the effectiveenergy barrier for the magnetization reversal.

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Neutron Scattering Investigations of Zero- and
One-dimensional Quantum Magnets
vorgelegt von
Diplom-Physiker Oliver Pieper
geb. am 17. April 1979 in Rodewisch
Von der Fakultät II - Mathematik und Naturwissenschaften
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissensschaften
Dr. rer. nat.
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. M. Dähne
Berichter/Gutachter: Prof. Dr. B. Lake Prof. Dr. D. A. Tennant Prof. Dr. J. Schnack
Tag der wissenschaftlichen Aussprache: 09. Juni 2010
Berlin 2010
D83ii
Abstract
This thesis deals with the investigation of two different types of low-dimensional
quantum magnets using the technique of neutron scattering.
In the first part, the magnetic properties of three Mn -based single molecule mag-
6
nets are explored by means of inelastic neutron scattering. The experimental data
reveal that small structural distortions of the molecular geometry produce a signifi-
cant effect on the energy level diagram and therefore on the magnetic properties of
the molecule. It will be shown that the giant spin model completely fails to describe
the spin level structure of the ground spin multiplets. The data enabled the deter-
mination of the parameters of the microscopic spin Hamiltonian and based on this
it is shown that the excited S-multiplets play a key role in determining the effective
energy barrier for the magnetization reversal.
The second part of this thesis presents an in-depth study of the nuclear and mag-
netic properties of the quasi-one-dimensional Heisenberg antiferromagnet CaV O .
2 4
3+The magnetism in this system arises from the partially filled t -levels of the V -
2g
ions, which in addition give an orbital degree of freedom to the system. The crystal
structure consists of weakly coupled double-chains of edge-sharing VO -octahedra,
6
where the particular octahedral staggering creates a zigzag-like arrangement of the
vanadium ions. This in return gives rise to strong magnetic direct exchange interac-
tions between nearest and next nearest neighbour vanadium ions and to geometrical
frustration. However, the strength of the exchange interactions is strongly influ-
enced by the particular occupation of the t -orbitals.
2g
Single crystal and powder neutron diffraction as well as neutron spectroscopy are
used to determine the nuclear and magnetic structure as well as the complex excita-
tion spectrum of CaV O . The results are analysed theoretically and from this the
2 4
leading exchange paths are deduced and discussed in terms of orbital ordering.Zusammenfassung
Die vorliegende Arbeit beschäftigt sich mit der Untersuchung von zwei unter-
schiedlichen Arten von niedrigdimensionalen Quantenmagneten unter Verwendung
der Methode der Neutronenstreuung.
Im ersten Teil der Arbeit werden die magnetischen Eigenschaften von drei Mn -
6
basierenden Einzelmolekülmagneten mit Hilfe der inelastischen Neutronenstreuung
erforscht. Die experimentellen Daten verdeutlichen, dass geringe strukturelle Ver-
formungen der Molekülgeometrie einen erheblichen Einfluss auf das Energieleveldia-
gramm und demzufolge auf die magnetischen Eigenschaften der Moleküle haben. Es
wird gezeigt, dass das Giant-Spin Modell nicht in der Lage ist, die Spinlevelstruktur
des Grundmultipletts zu beschreiben. Die gewonnen Daten erlauben die Bestim-
mung der relevanten Parameter des mikroskopischen Spin-Hamiltonoperators und
basierend auf diesen Erkenntnissen wird gezeigt, dass die angeregten S-Multipletts
eine Schlüsselrolle bei der Bestimmung der effektiven Energiebarriere für die Um-
kehrung der Magnetisierung spielen.
Der zweite Teil dieser Arbeit präsentiert eine detaillierte Untersuchung der nu-
klearen und magnetischen Eigenschaften des quasi-eindimensionalen Heisenberg-
Antiferromagneten CaV O . Der Magnetismus dieses Systems resultiert von den
2 4
3+teilweise gefüllten t -Orbitalen der V -Ionen, welche dem System noch einen zu-
2g
sätzlichen orbitalen Freiheitsgrad zu Verfügung stellen. Die Kristallstruktur besteht
aus schwach gekoppelten Doppelketten von eckteilenden VO -Oktaedern, wobei die
6
spezielle Staffelung der Oktaeder zu einer zigzagartigen Anordnung der Vanadiumio-
nen führt. Dies gibt wiederum Anlass zu starken magnetischen Wechselwirkungen
zwischen nächsten und übernächsten Vanadiumnachbarn und impliziert geometri-
sche Frustration. Allerdings wird die Stärke der Wechselwirkungen stark von der
speziellen Besetzung der t -Orbitale beeinflusst.
2g
Zur Bestimmung der nuklearen und magnetischen Struktur, sowie des komplexen
Anregungsspektrums wurde sowohl die Methode die Einzelkristall- und Pulverdif-
fraktion, als auch die der Neutronenspektroskopie verwendet. Die experimentellen
Resultate werden theoretisch analisiert und auf Grundlage dessen werden die domi-
nanten Austauschpfade bestimmt und bezüglich orbitaler Ordnung diskutiert.Acknowledgements
I would like to use the following lines to thank all those people who helped me with
both the preparation of this thesis and also with the work that is described in it. First
and foremost, I would like to thank my supervisor Bella Lake for all her great support
and encouragement, for the many inspiring conversations and for her tireless availability.
Without her this thesis would have never been possible. Thank you Bella!
Further, I am especially grateful to my ‘quasi-supervisor’ Tatiana Guidi, who not only
introduced me to the fascinating world of molecular magnetism, but has always been an
incredibly helpful, encouraging and very special friend to me. Thank you Tati!
I would like the thank all members of the MN-1 group, who always provided a very
pleasant working atmosphere. Whenever I got stuck with things like programming,
sample preparation or any other physical or non-physical issues, you were the ones who
always helped me out. Furthermore, I very much enjoyed the culinary delicacies that you
brought from all over the world to share them. Those always were my ‘gleam of hope’
after I had one of those interesting canteen dishes. Thank you Elisa, Diana, Nazmul and
Sándor!
The most essential need for an experimentalist are the samples to measure and a special
thanks goes to all the people who supplied me with their crystals and powders during
the last years. In particular, I thank Jiaqiang Yan who did an amazing job in growing
large quantities of high quality CaV O single crystals. Further, I thank Constantinos2 4
Milios, who prepared most of the Mn samples measured for this thesis. Additionally, I6
also thank David C. Johnston, Azad Niazi, Euan Brechin, Jan Tejeda and Anna Julia
and Joris van Slageren for their great help.
The neutron experiments have been performed at various institutions and it was the
excellent expertise and support of all the instrument scientists that made a great contri-
bution to the success of the experiments. In particular, I would like to thank: Manfred
Reehuis, Mechthild Enderle, Toby Perring, Aziz Daoud-Aladine, Hannu Mutka, Marek
Koza, Klaus Habicht, Klaus Kiefer, Bastian Klemke, Kirrily Rule, Margarita Russina,
Karel Prokeˇs, Konrad Siemensmeyer, Andreas Schnegg, Oksana Zaharko, Phil Pattison,
Herman Emerich and Andreas Kreyssig. Aziz deserves a special thanks for all his pa-
tience while teaching me the secrets of FULLPROF.
I had the great opportunity to collaborate with various theoreticians, with whom I had
very fruitful discussions and who helped me a lot to understand the experimental data.
In particular, I thank Stefano Carretta, Paolo Santini and Giuseppe Amoretti for their
invaluable help with the single molecule magnets. Further, my thanks go to Andreas
Honecker, Natalia Perkins and Volker Eyert who provided me important insights into
the physics of CaV O .2 4
I would also like to express gratitude to Alan Tennant and Jürgen Schnack for agreeingvi
to examine this thesis.
A big thanks goes to John, Marko and Simon for proof-reading the manuscript.
I am extremely grateful to my family. I thank my parents for all their support, not only
during the time of this thesis. In particular, I would like to thank my mother, who is
always there for me.
Finally, I would like to thank Antje for all her love, patience and belief in me.Contents
1. Introduction 1
2. Low-dimensional quantum magnetism 5
2.1.Spins,orbitalsandexchangeinteractions................... 5
2.1.1.Orbitalphysics..................... 6
2.1.2.Orbitalorderandmagneticexchange................. 9
2.2.Molecularmagnetism......................1
2.2.1.Slowrelaxationofmagnetization...................12
2.2.2. Quantum tunnelling of the magnetization . . ....15
2.2.3.SpinHamiltonian............................17
2.2.4.Spinstates ...............2
2.2.5.Strongexchangelimit-GiantSpinApproximation.........24
2.2.6. Beyond the Giant Spin Approximation - S-mixing.....25
2.2.7.CriterionfortheanisotropybarierinSMM.............26
2.3.One-dimensionalmagnetism..................27
2.3.1.Magneticordering.......................27
2.3.2.Excitations.......................30
2.3.3.Effectsofanisotropy......................34
2.3.4.Effectsof3Dcoupling.................34
2.3.5.Frustration...........................35
3. Experimental techniques 37
3.1.Neutronscatering...............................37
3.1.1.Neutronscateringcrossection ...........38
3.1.2.NeutronDiffraction ..........................4
3.1.3.Neutronspectroscopy .............58
3.2.Othertechniques................................63
3.2.1.X-raydiffraction............63
3.2.2. Magnetic susceptibility . . . . .....................6
4. The hexanuclear single molecule magnets Mn 716
4.1.Introduction...................................71
4.2.Experimentalmethod .............73
4.3.Theoreticalmodelingandexperimentalresults ...............74
4.3.1. Mn (1)(S=4)U ≈28K..............756 eff
4.3.2. Mn (2) U ≈ 53 K vs. Mn (3) U ≈ 86.4K;(S=12)......836 eff 6 eff
4.4.Discusion................................94viii Contents
4.5.Conclusions...................................98
5. Nuclear and magnetic structure of CaV O 992 4
5.1.Nuclearstructure................................9
5.1.1.Introduction ..............9
5.1.2.Experimentaldetails..........................101
5.1.3.Experimentalresultsandanalysis...........103
5.1.4.Discusion................................17
5.1.5.Conclusions...............126
5.2. Magnetic susceptibility . ............................128
5.2.1.Introduction ..............128
5.2.2.Experimentaldetails..........................128
5.2.3.Experimentalresults..............129
5.2.4.Dataanalysisanddiscusion .....................131
5.3.Magneticstructure...................14
5.3.1.Introduction ..........................14
5.3.2.Theproblemoftwinning ...........145
5.3.3.Theoreticalanalysis-representationtheory.............146
5.3.4.Experimentaldetails..................150
5.3.5.Experimentalresults......................153
5.3.6.Discusion........................167
5.3.7.Conclusions.......................175
6. Magnetic excitations in CaV O 1772 4
6.1.Introduction...................................17
6.2.Experimentaldetails..............178
6.2.1.MAPSexperiment...........................178
6.2.2.IN20set-up...................179
6.2.3.V2experiment.........................180
6.3.Theoreticalmodel,spinwavecalculations..........181
6.4.Experimentalresultsanddataanalysis....................187
6.4.1.Lowenergyexcitations.................195
6.4.2.Spinwaveanalysis.......................198
6.4.3.Resolutioneffects....................21
6.5.Discussion............................215
6.6.Conclusions...........................21
7. Conclusions and perspectives 223
A. Exact diagonalization 227
B. Additional details about the nuclear structure of CaV O 2312 4
B.1. T = 160K synchrotrondata..........................231
B.2.Hightemperaturesinglecrystaldiffractiondata.......23Contents ix
C. Linear spin wave theory for the CaV O lattice 2352 4
C.1.Thefoursublaticecase............................235
C.2.The32sublaticecase.............246
D. Neutron scattering instruments 253
D.1.IN5........................................253
D.2.IN6....................253
D.3.NEAT,V3....................................25
D.4.MAPS......................256