@phdthesis{Winnerlein2020,
  author    = {Winnerlein, Martin},
  title     = {Molecular Beam Epitaxy and Characterization of the Magnetic Topological Insulator (V,Bi,Sb)\(_2\)Te\(_3\)},
  doi       = {10.25972/OPUS-21166},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-211666},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2020},
  abstract  = {The subject of this thesis is the fabrication and characterization of magnetic topological insulator layers of (V,Bi,Sb)\(_2\)Te\(_3\) exhibiting the quantum anomalous Hall effect. A major task was the experimental realization of the quantum anomalous Hall effect, which is only observed in layers with very specific structural, electronic and magnetic properties. These properties and their influence on the quantum anomalous Hall effect are analyzed in detail. First, the optimal conditions for the growth of pure Bi\(_2\)Te\(_3\) and Sb\(_2\)Te\(_3\) crystal layers and the resulting structural quality are studied. The crystalline quality of Bi\(_2\)Te\(_3\) improves significantly at higher growth temperatures resulting in a small mosaicity-tilt and reduced twinning defects. The optimal growth temperature is determined as 260\(^{\circ}\)C, low enough to avoid desorption while maintaining a high crystalline quality. The crystalline quality of Sb\(_2\)Te\(_3\) is less dependent on the growth temperature. Temperatures below 230\(^{\circ}\)C are necessary to avoid significant material desorption, though. Especially for the nucleation on Si(111)-H, a low sticking coefficient is observed preventing the coalescence of islands into a homogeneous layer. The influence of the substrate type, miscut and annealing sequence on the growth of Bi\(_2\)Te\(_3\) layers is investigated. The alignment of the layer changes depending on the miscut angle and annealing sequence: Typically, layer planes align parallel to the Si(111) planes. This can enhance the twin suppression due to transfer of the stacking order from the substrate to the layer at step edges, but results in a step bunched layer morphology. For specific substrate preparations, however, the layer planes are observed to align parallel to the surface plane. This alignment avoids displacement at the step edges, which would cause anti-phase domains. This results in narrow Bragg peaks in XRD rocking curve scans due to long-range order in the absence of anti-phase domains. Furthermore, the use of rough Fe:InP(111):B substrates leads to a strong reduction of twinning defects and a significantly reduced mosaicity-twist due to the smaller lattice mismatch. Next, the magnetically doped mixed compound V\(_z\)(Bi\(_{1-x}\)Sb\(_x\))\(_{2-z}\)Te\(_3\) is studied in order to realize the quantum anomalous Hall effect. The addition of V and Bi to Sb\(_2\)Te\(_3\) leads to efficient nucleation on the Si(111)-H surface and a closed, homogeneous layer. Magneto-transport measurements of layers reveal a finite anomalous Hall resistivity significantly below the von Klitzing constant. The observation of the quantum anomalous Hall effect requires the complete suppression of parasitic bulklike conduction due to defect induced carriers. This can be achieved by optimizing the thickness, composition and growth conditions of the layers. The growth temperature is observed to strongly influence the structural quality. Elevated temperatures result in bigger islands, improved crystallographic orientation and reduced twinning. On the other hand, desorption of primarily Sb is observed, affecting the thickness, composition and reproducibility of the layers. At 190\(^{\circ}\)C, desorption is avoided enabling precise control of layer thickness and composition of the quaternary compound while maintaining a high structural quality. It is especially important to optimize the Bi/Sb ratio in the (V,Bi,Sb)\(_2\)Te\(_3\) layers, since by alloying n-type Bi\(_2\)Te\(_3\) and p-type Sb\(_2\)Te\(_3\) charge neutrality is achieved at a specific mixing ratio. This is necessary to shift the Fermi level into the magnetic exchange gap and fully suppress the bulk conduction. The Sb content x furthermore influences the in-plane lattice constant a significantly. This is utilized to accurately determine x even for thin films below 10 nm thickness required for the quantum anomalous Hall effect. Furthermore, x strongly influences the surface morphology: with increasing x the island size decreases and the RMS roughness increases by up to a factor of 4 between x = 0 and x = 1. A series of samples with x varied between 0.56-0.95 is grown, while carefully maintaining a constant thickness of 9 nm and a doping concentration of 2 at.\% V. Magneto-transport measurements reveal the charge neutral point around x = 0.86 at 4.2 K. The maximum of the anomalous Hall resistivity of 0.44 h/e\(^2\) is observed at x = 0.77 close to charge neutrality. Reducing the measurement temperature to 50 mK significantly increases the anomalous Hall resistivity. Several samples in a narrow range of x between 0.76-0.79 show the quantum anomalous Hall effect with the Hall resistivity reaching the von Klitzing constant and a vanishing longitudinal resistivity. Having realized the quantum anomalous Hall effect as the first group in Europe, this breakthrough enabled us to study the electronic and magnetic properties of the samples in close collaborations with other groups. In collaboration with the Physikalisch-Technische Bundesanstalt high-precision measurements were conducted with detailed error analysis yielding a relative de- viation from the von Klitzing constant of (0.17 \(\pm\) 0.25) * 10\(^{-6}\). This is published as the smallest, most precise value at that time, proving the high quality of the provided samples. This result paves the way for the application of magnetic topological insulators as zero-field resistance standards. Non-local magneto-transport measurements were conducted at 15 mK in close collaboration with the transport group in EP3. The results prove that transport happens through chiral edge channels. The detailed analysis of small anomalies in transport measurements reveals instabilities in the magnetic phase even at 15 mK. Their time dependent nature indicates the presence of superparamagnetic contributions in the nominally ferromagnetic phase. Next, the influence of the capping layer and the substrate type on structural properties and the impact on the quantum anomalous Hall effect is investigated. To this end, a layer was grown on a semi-insulating Fe:InP(111)B substrate using the previously optimized growth conditions. The crystalline quality is improved significantly with the mosaicity twist reduced from 5.4\(^{\circ}\) to 1.0\(^{\circ}\). Furthermore, a layer without protective capping layer was grown on Si and studied after providing sufficient time for degradation. The uncapped layer on Si shows perfect quantization, while the layer on InP deviates by about 5\%. This may be caused by the higher crystalline quality, but variations in e.g. Sb content cannot be ruled out as the cause. Overall, the quantum anomalous Hall effect seems robust against changes in substrate and capping layer with only little deviations. Furthermore, the dependence of the quantum anomalous Hall effect on the thickness of the layers is investigated. Between 5-8 nm thickness the material typically transitions from a 2D topological insulator with hybridized top and bottom surface states to a 3D topological insulator. A set of samples with 6 nm, 8 nm, and 9 nm thickness exhibits the quantum anomalous Hall effect, while 5 nm and 15 nm thick layers show significant bulk contributions. The analysis of the longitudinal and Hall conductivity during the reversal of magnetization reveals distinct differences between different thicknesses. The 6 nm thick layer shows scaling consistent with the integer quantum Hall effect, while the 9 nm thick layer shows scaling expected for the topological surface states of a 3D topological insulator. The unique scaling of the 9 nm thick layer is of particular interest as it may be a result of axion electrodynamics in a 3D topological insulator. Subsequently, the influence of V doping on the structural and magnetic properties of the host material is studied systematically. Similarly to Bi alloying, increased V doping seems to flatten the layer surface significantly. With increasing V content, Te bonding partners are observed to increase simultaneously in a 2:3 ratio as expected for V incorporation on group-V sites. The linear contraction of the in-plane and out-of-plane lattice constants with increasing V doping is quantitatively consistent with the incorporation of V\(^{3+}\) ions, possibly mixed with V\(^{4+}\) ions, at the group-V sites. This is consistent with SQUID measurements showing a magnetization of 1.3 \(\mu_B\) per V ion. Finally, magnetically doped topological insulator heterostructures are fabricated and studied in magneto-transport. Trilayer heterostructures with a non-magnetic (Bi,Sb)\(_2\)Te\(_3\) layer sandwiched between two magnetically doped layers are predicted to host the axion insulator state if the two magnetic layers are decoupled and in antiparallel configuration. Magneto-transport measurements of such a trilayer heterostructure with 7 nm undoped (Bi,Sb)\(_2\)Te\(_3\) between 2 nm thick layers doped with 1.5 at.\% V exhibit a zero Hall plateau representing an insulating state. Similar results in the literature were interpreted as axion insulator state, but in the absence of a measurement showing the antiparallel magnetic orientation other explanations for the insulating state cannot be ruled out. Furthermore, heterostructures including a 2 nm thin, highly V doped layer region show an anomalous Hall effect of opposite sign compared to previous samples. A dependency on the thickness and position of the doped layer region is observed, which indicates that scattering at the interfaces causes contributions to the anomalous Hall effect of opposite sign compared to bulk scattering effects. Many interesting phenomena in quantum anomalous Hall insulators as well as axion insulators are still not unambiguously observed. This includes Majorana bound states in quantum anomalous Hall insulator/superconductor hybrid systems and the topological magneto-electric effect in axion insulators. The limited observation temperature of the quantum anomalous Hall effect of below 1 K could be increased in 3D topological insulator/magnetic insulator heterostructures which utilize the magnetic proximity effect. The main achievement of this thesis is the reproducible growth and characterization of (V,Bi,Sb)2Te3 layers exhibiting the quantum anomalous Hall effect. The detailed study of the structural requirements of the quantum anomalous Hall effect and the observation of the unique axionic scaling behavior in 3D magnetic topological insulator layers leads to a better understanding of the nature of this new quantum state. The high-precision measurements of the quantum anomalous Hall effect reporting the smallest deviation from the von Klitzing constant are an important step towards the realization of a zero-field quantum resistance standard.},
  subject      = {Bismutverbindungen},
  language  = {en}
}
@phdthesis{Schreyeck2016,
  author    = {Schreyeck, Steffen},
  title     = {Molecular Beam Epitaxy and Characterization of Bi-Based V\(_2\)VI\(_3\) Topological Insulators},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-145812},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2016},
  abstract  = {The present thesis is addressed to the growth and characterization of Bi-based V2VI3 topological insulators (TIs). The TIs were grown by molecular beam epitaxy (MBE) on differently passivated Si(111) substrates, as well as InP(111) substrates. This allows the study of the influence of the substrate on the structural and electrical properties of the TIs. The Bi2Se3 layers show a change of mosaicity-tilt and -twist for growth on the differently prepared Si(111) substrates, as well as a significant increase of crystalline quality for growth on the lateral nearly lattice matched InP(111). The rocking curve FWHMs observed for thick layers grown on InP are comparable to these of common zincblende layers, which are close to the resolution limit of standard high resolution X-ray diffraction (HRXRD) setups. The unexpected high structural crystalline quality achieved in this material system is remarkable due to the presence of weak van der Waals bonds between every block of five atomic layers, i.e. a quintuple layer (QL), in growth direction. In addition to the mosaicity also twin domains, present in films of the V2VI3 material system, are studied. The twin defects are observed in Bi2Se3 layers grown on Si(111) and lattice matched InP(111) suggesting that the two dimensional surface lattice of the substrates can not determine the stacking order ABCABC... or ACBACB... in locally separated growth seeds. Therefore the growth on misoriented and rough InP(111) is analyzed. The rough InP(111) with its facets within a hollow exceeding the height of a QL is able to provide its stacking information to the five atomic layers within a QL. By varying the roughness of the InP substrate surface, due to thermal annealing, the influence on the twinning within the layer is confirmed resulting in a complete suppression of twin domains on rough InP(111). Focusing on the electrical properties of the Bi2Se3 films, the increased structural quality for films grown on lattice matched flat InP(111)B results in a marginal reduction of carrier density by about 10\% compared to the layers grown on H-passivated Si(111), whereas the suppression of twin domains for growth on rough InP(111)B resulted in a reduction of carrier density by an order of magnitude. This implies, that the twin domains are a main crystal defect responsible for the high carrier density in the presented Bi2Se3 thin films. Besides the binary Bi2Se3 also alloys with Sb and Te are fabricated to examine the influence of the compound specific point defects on the carrier density. Therefore growth series of the ternary materials Bi2Te(3-y)Se(y), Bi(2-x)Sb(x)Se3, and Bi(2-x)Sb(x)Te3, as well as the quaternary Bi(2-x)Sb(x)Te(3-y)Se(y) are studied. To further reduce the carrier density of twin free Bi2Se3 layers grown on InP(111)B:Fe a series of Bi(2-x)Sb(x)Se3 alloys were grown under comparable growth conditions. This results in a reduction of the carrier density with a minimum in the composition range of about x=0.9-1.0. The Bi(2-x)Sb(x)Te3 alloys exhibit a pn-transition, due to the dominating n-type and p-type point defects in its binary compounds, which is determined to reduce the bulk carrier density enabling the study the TI surface states. This pn-transition plays a significant role in realizing predicted applications and exotic effects, such as the quantum anomalous Hall effect. The magnetic doping of topological insulators with transition metals is studied by incorporating Cr and V in the alloy Bi(2-x)Sb(x)Te3 by codeposition. The preferential incorporation of Cr on group-V sites is confirmed by EDX and XRD, whereas the incorporation of Cr reduces the crystalline quality of the layer. Magnetotransport measurements of the Cr-doped TIs display an anomalous Hall effect confirming the realization of a magnetic TI thin film. The quantum anomalous Hall effect is observed in V-doped Bi(2-x)Sb(x)Te3, where the V-doping results in higher Curie temperatures, as well as higher coercive fields compared to the Cr-doping of the TIs. Moreover the present thesis contributes to the understanding of the role of the substrate concerning the crystalline quality of van der Waals bonded layers, such as the V2VI3 TIs, MoS2 and WoTe2. Furthermore, the fabrication of the thin film TIs Bi(2-x)Sb(x)Te(3-y)Se(y) in high crystalline quality serves as basis to explore the physics of topological insulators.},
  subject      = {Bismutverbindungen},
  language  = {en}
}
@phdthesis{Klaas2019,
  author    = {Klaas, Martin},
  title     = {Spektroskopische Untersuchungen an elektrisch und optisch erzeugten Exziton-Polariton-Kondensaten},
  doi       = {10.25972/OPUS-17689},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-176897},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {Eine technologisch besonders vielversprechende Art von Mikrokavit{\"a}ten besteht aus einem optisch aktiven Material zwischen zwei Spiegeln, wobei das Licht auf Gr{\"o}ße seiner Wellenl{\"a}nge eingesperrt wird. Mit diesem einfachen Konzept Licht auf Chipgr{\"o}ße einzufangen entstand die M{\"o}glichkeit neue Ph{\"a}nomene der Licht-Materie Wechselwirkung zu studieren. Der Oberfl{\"a}chenemitter (VCSEL), welcher sich das ver{\"a}nderte Strahlungsverhalten aufgrund der schwachen Kopplung und stimulierten Emission zu Nutze macht, ist bereits l{\"a}nger kommerziell sehr erfolgreich. Er umfasst ein erwartetes Marktvolumen von ca. 5.000 Millionen Euro bis 2024, welches sich auf verschiedenste Anwendungen im Bereich von Sensorik und Kommunikationstechnologie bezieht. Dauerhaft hohe Wachstumsraten von 15-20\% pro Jahr lassen auf weiteres langfristiges Potential von Mikrokavit{\"a}ten in der technologischen Gesellschaft der n{\"a}chsten Generation hoffen. Mit fortschreitender Entwicklung der Epitaxie-Verfahren gelang es Kavit{\"a}ten solcher Qualit{\"a}t herzustellen, dass zum ersten Mal das Regime der starken Kopplung erreicht wurde. Starke Kopplung bedeutet in diesem Fall die Bildung eines neuen Quasiteilchens zwischen Photon und Exziton, dem Exziton-Polariton (Polariton). Dieses Quasiteilchen zeigt eine Reihe interessanter Eigenschaften, welche sowohl aus der Perspektive der Technologie, als auch aus der Sicht von Grundlagenforschung interessant sind. Bei systemabh{\"a}ngigen Teilchendichten erlaubt das Polariton ebenfalls die Erzeugung von koh{\"a}rentem Licht {\"u}ber den Exziton-Polariton-Kondensatszustand (Kondensat), den Polariton-Laser. Die Eigenschaften des emittierten Lichtes {\"a}hneln denen eines VCSELs, allerdings bei einigen Gr{\"o}ßenordnungen geringerem Energieverbrauch, bzw. niedrigerer Laserschwelle, bei Wahl geeigneter Verstimmung von Exziton und Photon. Diese innovative Entwicklung kann daher unter anderem neue M{\"o}glichkeiten f{\"u}r besonders energiesparende Anwendungen in der Photonik er{\"o}ffnen. Die vorliegende Doktorarbeit soll zur Erweiterung des Forschungsstandes in diesem Gebiet zwischen Photonik und Festk{\"o}rperphysik beitragen und untersucht zum einen den anwendungsorientierten Teil des Feldes mit Studien zur elektrischen Injektion, beleuchtet aber auch den interessanten Phasen{\"u}bergang des Systems {\"u}ber seine Koh{\"a}renz- und Spineigenschaften. Es folgt eine knappe {\"u}berblicksartige Darstellung der Ergebnisse, die in dieser Arbeit genauer ausgearbeitet werden. Rauschanalyse und die optische Manipulation eines bistabilen elektrischen Polariton-Bauelements Aufbauend auf der Realisierung eines elektrischen Polariton-Lasers wurde in dieser Arbeit ein optisches Potential in das elektrisch betriebene Kondensat mit einem externen Laser induziert. Dieses optische Potential erm{\"o}glicht die Manipulation der makroskopischen Besetzung der Grundzustandswellenfunktion, welches sich als ver{\"a}ndertes Emissionsbild im Realraum darstellt. Der polaritonische Effekt wird {\"u}ber Verschiebung der Emissionslinie zu h{\"o}heren Energien durch Wechselwirkung des Exzitonanteils nachgewiesen. Diese experimentellen Beobachtungen konnten mit Hilfe eines Gross-Pitaevskii-Differentialgleichungsansatzes erl{\"a}utert und theoretisch nachgebildet werden. Weiterhin zeigt der elektrische Polariton-Laser eine Bistabilit{\"a}t in seiner Emissionskennlinie an der polaritonischen Kondensationsschwelle. Die Hysterese hat ihren physikalischen Ursprung in der Lebenszeitabh{\"a}ngigkeit der Ladungstr{\"a}ger von der Dichte des Ladungstr{\"a}gerreservoirs durch die progressive Abschirmung des inneren elektrischen Feldes. In dieser Arbeit wird zum tieferen Verst{\"a}ndnis der Hysterese ein elektrisches Rauschen {\"u}ber den Anregungsstrom gelegt. Dieses elektrische Rauschen befindet sich auf der Mikrosekunden-Zeitskala und beeinflusst die Emissionscharakteristik, welche durch die Lebensdauer der Polaritonen im ps-Bereich bestimmt wird. Mit steigendem Rauschen wird ein Zusammenfall der Hysterese beobachtet, bis die Emissionscharakteristik monostabil erscheint. Diese experimentellen Befunde werden mit einem gekoppelten Ratengleichungssystem sowie mit Hilfe einer Gauss-verteilten Zufallsvariable in der Anregung modelliert und erkl{\"a}rt. Die Hysterese erm{\"o}glicht außerdem den Nachweis eines optischen Schalteffekts {\"u}ber eine zus{\"a}tzliche Ladungstr{\"a}gerinjektion mit einem Laser weit {\"u}ber der Bandkante des Systems, um den positiven R{\"u}ckkopplungseffekt zu erzeugen. Im Bereich der Hysterese wird das System auf den unteren Zustand elektrisch angeregt und dann mit Hilfe eines nicht-resonanten Laserpulses in den Kondensatszustand gehoben. Polaritonfluss geleitet durch Kontrolle der lithographisch definierten Energielandschaft Polaritonen k{\"o}nnen durch den photonischen Anteil weiterhin in Wellenleiterstrukturen eingesperrt werden, worin sie bei der Kondensation gerichtet entlang des Kanals mit nahe Lichtgeschwindigkeit fließen. Dies geschieht mit der Besonderheit {\"u}ber ihren Exzitonanteil stark wechselwirken zu k{\"o}nnen. Die M{\"o}glichkeit durch Lithographie solche eindimensionalen Kan{\"a}le zu definieren, wurde bereits in verschiedenen Prototypen f{\"u}r Polaritonen benutzt und untersucht. In dieser Arbeit werden zwei verschiedene, neue Ans{\"a}tze zur Lenkung von gerichtetem Polaritonfluss vorgestellt: zum einen {\"u}ber die sogenannte Josephson-Kopplung zwischen zwei Wellenleitern, realisiert {\"u}ber halbge{\"a}tzte Spiegel und zum anderen {\"u}ber eine Mikroscheibe gekoppelt an zwei Wellenleiter. Der Begriff der Josephson-Kopplung ist hier angelehnt an den bekannten Effekt in Supraleitern, welcher ph{\"a}nomenologische {\"A}hnlichkeiten aufweist. Die Verwendung in der Polaritonik ist historisch gewachsen. Die Josephson-Kopplung erm{\"o}glicht die Beobachung von Oszillationen des Polariton-Kondensats zwischen den Wellenleitern, in Abh{\"a}ngigkeit der verbleibenden Anzahl Spiegelpaare zwischen den Strukturen, wodurch eine definierte Selektion des Auskopplungsarms erm{\"o}glicht wird. Die Mikroscheibe funktioniert {\"a}hnlich einer Resonanztunneldiode. Sie erm{\"o}glicht eine Energieselektion der transmittierten Moden durch die Diskretisierung der Zust{\"a}nde in den niederdimensionalen Strukturen. Es ergibt sich die Bedingung, dass nur energetisch gleiche Niveaus zwischen Struktur{\"u}berg{\"a}ngen koppeln k{\"o}nnen. Gleichzeitig erlaubt die Mikroscheibenanordnung eine Umkehrung der Flussrichtung. Koh{\"a}renzeigenschaften und die Photonenstatistik von Polariton-Kondensaten unter photonischen Einschlusspotentialen Die Koh{\"a}renzeigenschaften der Emission von Polariton-Kondensaten ist seit l{\"a}ngerem ein aktives Forschungsfeld. Die noch ausstehenden Fragen betreffen die Beobachtung hoher Abweichungen von traditionellen, auf Inversion basierenden Lasersystemen (z.B. VCSELs). Diese haben selbst bei schwellenlosen Lasern einen Wert der Autokorrelationsfunktion zweiter Ordnung von Eins. Polariton-Kondensate jedoch zeigen erh{\"o}hte Werte in der Autokorrelationsfunktion, welches auf einen Mischzustand zwischen koh{\"a}rentem und thermischem Licht hinweist. In dieser Arbeit wurde ein systematischer Weg untersucht, die Koh{\"a}renzeigenschaften des Polariton-Kondensats denen eines traditionellen Lasers anzun{\"a}hern. Dies geschieht {\"u}ber den lateralen photonischen Einschluss der Kondensate mittels lithographisch definierter Mikrot{\"u}rmchen mit verschiedenen Durchmessern. In Koh{\"a}renzmessungen wird der Einfluss dieser Ver{\"a}nderung der Energielandschaft der Polariton-Kondensate auf die Autokorrelationseigenschaften zweiter Ordnung untersucht. Es wird ein direkter Zusammenhang zwischen großem Einschlusspotential und guten Korrelationseigenschaften nachgewiesen. Der Effekt wird theoretisch {\"u}ber den ver{\"a}nderten Einfluss der Phononen auf das Polariton-Relaxationsverhalten erkl{\"a}rt. Durch die st{\"a}rkere Lokalisierung der Polaritonwellenfunktion in kleineren Mikrot{\"u}rmchen wird die Streuwahrscheinlichkeit erh{\"o}ht, was eine effizientere Relaxation in den Grundzustand erm{\"o}glicht. Dies verhindert zu starke Besetzungsfluktuationen der Grundmode in der Polariton-Lebenszeit, was bisher als Grund f{\"u}r die erh{\"o}hte Autokorrelation postuliert wurde. Weiterhin wird eine direkte Messung der Photonenstatistik eines Polaritonkondensats entlang steigender Polaritondichte im Schwellbereich vorgestellt. Die Photonenstatistik eines thermischen Emitters zeigt einen exponentiellen Verlauf, w{\"a}hrend ein reiner Laser Poisson-verteilt emittiert. Der Zwischenbereich, der f{\"u}r einen Laser am {\"U}bergang zwischen thermischer und koh{\"a}renter Lichtquelle vorhergesagt wird, kann durch eine {\"U}berlagerung der beiden Zust{\"a}nde beschrieben werden. {\"U}ber eine Anpassungsfunktion der gemessenen Verteilungsfunktionen kann der Phasen{\"u}bergang des Kondensats mit Hilfe dem Anteil der koh{\"a}renten Partikel im System verfolgt werden. Dadurch, dass der gemessene {\"U}bergang dem Paradigma der thermisch-koh{\"a}renten Zust{\"a}nde folgt, wurde nachgewiesen, dass bei r{\"o}tlicher Verstimmung die Interaktionen keinen signifikanten Anteil an der Ausbildung von Koh{\"a}renz im Polaritonsystem spielen. Polarisationskontrolle von Polariton-Kondensaten Die Polarisationseigenschaften des durch Polaritonenzerfall emittierten Lichts korrespondieren zum Spinzustand der Quasiteilchen. Unterhalb der Kondensationsschwelle ist diese Emission durch Spin-Relaxation der Ladungstr{\"a}ger unpolarisiert und oberhalb der Schwelle bildet sich unter bestimmten Voraussetzungen lineare Polarisation als Ordnungsparameter des Phasen{\"u}bergangs aus. Der Prozess der stimulierten Streuung kann die (zirkulare) Polarisation des Lasers auch bei Anregung auf h{\"o}heren Energien auf dem unteren Polaritonast erhalten. Dies resultiert aus sehr schneller Einnahme des Grundzustands, welche eine Spin-Relaxation verhindert. Bisher wurde, nach unserem Kenntnisstand, nur teilweise Erhaltung zirkularer Polarisation unter nicht-resonanter Anregung beobachtet. In dieser Arbeit wird vollst{\"a}ndige zirkulare Polarisationserhaltung, energetisch 130 meV vom Kondensatszustand entfernt angeregt, nachgewiesen. Diese Polarisationserhaltung setzt an der Kondensationsschwelle ein, was auf den Erhalt durch stimulierte Streuung hinweist. Unter dieser Voraussetzung der Spinerhaltung erzeugt die linear polarisierte Anregung (als {\"U}berlagerung zirkularem Lichts beider Orientierungen) elliptisch polarisiertes Licht. Dies geschieht, weil eine linear polarisierte Anregung durch Fokussierung eines Objektivs leicht elliptisch wird. Der Grad der Elliptizit{\"a}t wird sowohl durch die Verstimmung zwischen Photon und Exziton Mode beeinflusst, als auch durch die Dichte im System. Dies kann erkl{\"a}rt werden {\"u}ber das spezielle Verhalten der Relaxationsprozesse auf dem unteren Polaritonast, welche von der transversal-elektrischen und transversal-magnetischen (TE-TM) energetischen Aufspaltung abh{\"a}ngen. Weiterhin werden elliptische Mikrot{\"u}rmchen untersucht, um den Einfluss dieses asymmetrischen photonischen Einschlusses auf die Kondensatseigenschaften herauszuarbeiten. Die Ellipse zwingt das Kondensat zu einer linearen Polarisation, welche sich entlang der langen Achse des T{\"u}rmchens ausrichtet. In asymmetrischen Mikrot{\"u}rmchen ist die Grundmode aufgespalten in zwei linear polarisierte Moden entlang der beiden orthogonal zueinander liegenden Hauptachsen, wobei die l{\"a}ngere Achse das linear polarisierte Energieminimum des Systems bildet. Der Grad der linearen Polarisation nimmt mit geringerem Mikrot{\"u}rmchendurchmesser und gr{\"o}ßerer Ellipzit{\"a}t zu. Dies geschieht durch erh{\"o}hten energetischen Abstand der beiden Moden. Bei Ellipsen mit einem langen Hauptachsendurchmesser von 2 Mikrometer und einem Achsenverh{\"a}ltnis von 3:2 kann ein nahezu vollst{\"a}ndig linear polarisierter Zustand eines Polariton-Kondensats nachgewiesen werden. Damit wurde erforscht, dass auch unter nicht-resonanter Anregung Exziton-Polariton-Kondensate experimentell und theoretisch jeglichen Spinzustand unter entsprechenden Anregungsbedingungen annehmen k{\"o}nnen.},
  subject      = {Exziton-Polariton},
  language  = {de}
}
@phdthesis{Trabel2019,
  author    = {Trabel, Mirko},
  title     = {Growth and Characterization of Epitaxial Manganese Silicide Thin Films},
  doi       = {10.25972/OPUS-18472},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-184720},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {This thesis describes the growth and characterization of epitaxial MnSi thin films on Si substrates. The interest in this material system stems from the rich magnetic phase diagram resulting from the noncentrosymmetric B20 crystal structure. Here neighboring spins prefer a tilted relative arrangement in contrast to ferro- and antiferromagnets, which leads to a helical ground state where crystal and spin helix chirality are linked [IEM+85]. This link makes the characterization and control of the crystal chirality the main goal of this thesis. After a brief description of the material properties and applied methods, the thesis itself is divided into four main parts. In the first part the advancement of the MBE growth process of MnSi on Si\((111)\) substrate as well as the fundamental structural characterization are described. Here the improvement of the substrate interface by an adjusted substrate preparation process is demonstrated, which is the basis for well ordered flat MnSi layers. On this foundation the influence of Mn/Si flux ratio and substrate temperature on the MnSi layer growth is investigated via XRD and clear boundaries to identify the optimal growth conditions are determined. The nonstoichiometric phases outside of this optimal growth window are identified as HMS and Mn\(_5\)Si\(_3\). Additionally, a regime at high substrate temperatures and low Mn flux is discovered, where MnSi islands are growing incorporated in a Si layer, which could be interesting for further investigations as a size confinement can change the magnetic phase diagram [DBS+18]. XRD measurements demonstrate the homogeneity of the grown MnSi layers over most of the 3 inch wafer diameter and a small \(\omega\)-FWHM of about 0.02° demonstrates the high quality of the layers. XRD and TEM measurements also show that relaxation of the layers happens via misfit dislocations at the interface to the substrate. The second part of the thesis is concerned with the crystal chirality. Here azimuthal \(\phi\)-scans of asymmetric XRD reflections reveal twin domains with a \(\pm\)30° rotation to the substrate. These twin domains seem to consist of left and right-handed MnSi, which are connected by a mirror operation at the \((\bar{1}10)\) plane. For some of the asymmetric XRD reflections this results in different intensities for the different twin domains, which reveals that one of the domains is rotated +30° and the other is rotated -30°. From XRD and TEM measurements an equal volume fraction of both domains is deduced. Different mechanisms to suppress these twin domains are investigated and successfully achieved with the growth on chiral Si surfaces, namely Si\((321)\) and Si\((531)\). Azimuthal \(\phi\)-scans of asymmetric XRD reflections demonstrate a suppression of up to 92\%. The successful twin suppression is an important step in the use of MnSi for the proposed spintronics applications with skyrmions as information carriers, as discussed in the introduction. Because of this achievement, the third part of the thesis on the magnetic properties of the MnSi thin films is not only concerned with the principal behavior, but also with the difference between twinned and twin suppressed layers. Magnetometry measurements are used to demonstrate, that the MnSi layers behave principally as expected from the literature. The analysis of saturation and residual magnetization hints to the twin suppression on Si\((321)\) and Si\((531)\) substrates and further investigations with more samples can complete this picture. For comparable layers on Si\((111)\), Si\((321)\) and Si\((531)\) the Curie-Weiss temperature is identical within 1 K and the critical field within 0.1 T. Temperature dependent magnetoresistivity measurements also demonstrate the expected \(T^2\) behavior not only on Si\((111)\) but also on Si\((321)\) substrates. This demonstrates the successful growth of MnSi on Si\((321)\) and Si\((531)\) substrates. The latter measurements also reveal a residual resistivity of less then half for MnSi on Si\((321)\) in comparison to Si\((111)\). This can be explained with the reduced number of domain boundaries demonstrating the successful suppression of one of the twin domains. The homogeneity of the residual resistivity as well as the charge carrier density over a wide area of the Si\((111)\) wafer is also demonstrated with these measurements as well as Hall effect measurements. The fourth part shows the AMR and PHE of MnSi depending on the angle between in plane current and magnetic field direction with respect to the crystal direction. This was proposed as a tool to identify skyrmions [YKT+15]. The influence of the higher C\(_{3\mathrm{v}}\) symmetry of the twinned system instead of the C\(_3\) symmetry of a B20 single crystal is demonstrated. The difference could serve as a useful additional tool to prove the twin suppression on the chiral substrates. But this is only possible for rotations with specific symmetry surfaces and not for the studied unsymmetrical Si\((321)\) surface. Measurements for MnSi layers on Si\((111)\) above the critical magnetic field demonstrate the attenuation of AMR and PHE parameters for increasing resistivity, as expected from literature [WC67]. Even if a direct comparison to the parameters on Si\((321)\) is not possible, the higher values of the parameters on Si\((321)\) can be explained considering the reduced charge carrier scattering from domain boundaries. Below the critical magnetic field, which would be the region where a skyrmion lattice could be expected, magnetic hysteresis complicates the analysis. Only one phase transition at the critical magnetic field can be clearly observed, which leaves the existence of a skyrmion lattice in thin epitaxial MnSi layers open. The best method to solve this question seems to be a more direct approach in the form of Lorentz-TEM, which was also successfully used to visualize the skyrmion lattice for thin plates of bulk MnSi [TYY+12]. For the detection of in plane skyrmions, lamellas would have to be prepared for a side view, which seems in principle possible. The demonstrated successful twin suppression for MnSi on Si\((321)\) and Si\((531)\) substrates may also be applied to other material systems. Suppressing the twinning in FeGe on Si\((111)\) would lead to a single chirality skyrmion lattice near room temperature [HC12]. This could bring the application of skyrmions as information carriers in spintronics within reach. Glossary: MBE Molecular Beam Epitaxy XRD X-Ray Diffraction HMS Higher Manganese Silicide FWHM Full Width Half Maximum TEM Tunneling Electron Microscopy AMR Anisotropic MagnetoResistance PHE Planar Hall Effect Bibliography: [IEM+85] M. Ishida, Y. Endoh, S. Mitsuda, Y. Ishikawa, and M. Tanaka. Crystal Chirality and Helicity of the Helical Spin Density Wave in MnSi. II. Polarized Neutron Diffraction. Journal of the Physical Society of Japan, 54(8):2975, 1985. [DBS+18] B. Das, B. Balasubramanian, R. Skomski, P. Mukherjee, S. R. Valloppilly, G. C. Hadjipanayis, and D. J. Sellmyer. Effect of size confinement on skyrmionic properties of MnSi nanomagnets. Nanoscale, 10(20):9504, 2018. [YKT+15] T. Yokouchi, N. Kanazawa, A. Tsukazaki, Y. Kozuka, A. Kikkawa, Y. Taguchi, M. Kawasaki, M. Ichikawa, F. Kagawa, and Y. Tokura. Formation of In-plane Skyrmions in Epitaxial MnSi Thin Films as Revealed by Planar Hall Effect. Journal of the Physical Society of Japan, 84(10):104708, 2015. [WC67] R. H. Walden and R. F. Cotellessa. Magnetoresistance of Nickel-Copper Single-Crystal Thin Films. Journal of Applied Physics, 38(3):1335, 1967. [TYY+12] A. Tonomura, X. Yu, K. Yanagisawa, T. Matsuda, Y. Onose, N. Kanazawa, H. S. Park, and Y. Tokura. Real-Space Observation of Skyrmion Lattice in Helimagnet MnSi Thin Samples. Nano Letters, 12(3):1673, 2012. [HC12] S. X. Huang and C. L. Chien. Extended Skyrmion Phase in Epitaxial FeGe(111) Thin Films. Physical Review Letters, 108(26):267201, 2012.},
  subject      = {Molekularstrahlepitaxie},
  language  = {en}
}