Die Untersuchung stark korrelierter Elektronensysteme anhand des zweidimensionalen Hubbard-Modells bildet das zentrale Thema dieser Arbeit. Wir analysieren das Schicksal des Mott-Isolators bei Dotierung als auch bei Reduzierung der Wechselwirkungsstärke. Die numerische Auswertung erfolgt mit Hilfe von Quanten-Cluster-Approximationen, die eine thermodynamisch konsistente Beschreibung der Grundzustandseigenschaften garantieren. Der hier verwendete Rahmen der Selbstenergiefunktional-Theorie bietet eine große Flexibilität bei der Konstruktion von Cluster-Näherungen. Eine detaillierte Analyse gibt Aufschluss über die Qualität und das Konvergenzverhalten unterschiedlicher Cluster-Näherungen innerhalb der Selbstenergiefunktional-Theorie. Wir verwenden für diese Untersuchungen das eindimensionale Hubbard-Modell und vergleichen unsere Resultate mit der exakten Lösung. In zwei Dimensionen finden wir als Grundzustand des Teilchen-Loch-symmetrischen Modells bei Halbfüllung einen antiferromagnetischen Isolator unabhängig von der Wechselwirkungsstärke. Die Berücksichtigung kurzreichweitiger räumlicher Korrelationen durch unsere Cluster-Näherung führt, im Vergleich mit der dynamischen Mean-Field-Theorie, zu einer deutlichen Verbesserung des antiferromagnetischen Ordnungsparameters. Darüberhinaus beobachten wir in der paramagnetischen Phase einen Metall-Isolator-Übergang als Funktion der Wechselwirkungsstärke, der sich qualitativ vom reinen Mean-Field-Szenario unterscheidet. Ausgehend vom antiferromagnetischen Mott-Isolator zeigt sich ein füllungsgetriebener Metall-Isolator-Übergang in eine paramagnetische metallische Phase. Abhängig von der verwendeten Cluster-Approximation tritt dabei zunächst eine antiferromagnetische metallische Phase auf. Neben langreichweitiger antiferromagnetischer Ordnung haben wir in unseren Rechnungen auch Supraleitung berücksichtigt. Das Verhalten des supraleitenden Ordnungsparameters als Funktion der Dotierung ist dabei in guter Übereinstimmung sowohl mit anderen numerischen Verfahren als auch mit experimentellen Ergebnissen. / The central goal of this thesis is the examination of strongly correlated electron systems on the basis of the two-dimensional Hubbard model. We analyze how the properties of the Mott insulator change upon doping and with interaction strength. The numerical evaluation is done using quantum cluster approximations, which allow for a thermodynamically consistent description of the ground state properties. The framework of self-energy-functional theory offers great flexibility for the construction of cluster approximations. A detailed analysis sheds light on the quality and the convergence properties of different cluster approximations within the self-energy-functional theory. We use the one-dimensional Hubbard model for these examinations and compare our results with the exact solution. In two dimensions the ground state of the particle-hole symmetric model at half-filling is an antiferromagnetic insulator, independent of the interaction strength. The inclusion of short-range spatial correlations by our cluster approach leads to a considerable im\-prove\-ment of the antiferromagnetic order parameter as compared to dynamical mean-field theory. In the paramagnetic phase we furthermore observe a metal-insulator transition as a function of the interaction strength, which qualitatively differs from the pure mean-field scenario. Starting from the antiferromagnetic Mott insulator a filling-controlled metal-insulator transition in a paramagnetic metallic phase can be observed. Depending on the cluster approximation used an antiferromagnetic metallic phase may occur at first. In addition to long-range antiferromagnetic order, we also considered superconductivity in our calculations. The superconducting order parameter as a function of doping is in good agreement with other numerical methods, as well as with experimental results.

The work described in this thesis uses oxygen NMR to probe the electronic system of rare earth co-doped La_{2-x}Sr_xCuO_4, the prototypical high temperature superconducting cuprate (HTSC). Oxygen NMR turns out to be a powerful tool for this purpose. The nucleus is located directly inside the CuO_2 planes. It has a spin of 5/2 and a quadrupole moment and therefore can probe both, interactions with the magnetic hyperfine field as well as interactions through the electric field gradient of the crystal. Furthermore, the spin lattice relaxation time T_1 and the spin spin relaxation time T_2 contain information about the dynamics of these interactions. Such a link between the spin and charge structures in high temperature superconductors has been elusive until today. Instead, there are magnetic probes such as neutron scattering and muSR that provide evidence for a modulation of the spin structure and static magnetic moments, respectively, and charge probes like STM that reveal inhomogeneous doping distributions in the CuO_2 planes. In either case, inhomogeneities in the spin and charge system seem to be typical for HTSCs. Whereas the spin and charge modulations are believed to be dynamic in the superconducting compounds, they become static at low temperatures in Eu doped La_{2-x}Sr_xCuO_4, where superconductivity is suppressed. As could be demonstrated here, evidence for such a spin and charge separation, that often revealed stunning similarities to the spin ladder compounds, is apparent in almost all measured NMR parameters. / In dieser Arbeit werden Sauerstoff NMR Untersuchungen der elektronischen Struktur von Selten-Erd dotiertem La_{2-x}Sr_xCuO_4, dem prototypischen Hochtemperatursupraleiter (HTSL), vorgestellt. Sauerstoff NMR ist zu diesem Zweck besonders gut geeignet. Der Kern befindet sich innerhalb der Kupferoxid-Ebenen. Er hat einen Spin von 5/2 und ein Quadrupolmoment. Damit lassen sich Wechselwirkungen mit dem magnetischen Hyperfeinfeld der Cu-Atome sowie Wechselwirkungen mit dem elektrischen Feldgradienten des Kristalls untersuchen. Des Weiteren geben die Spin-Gitter-Relaxationszeit T_1 sowie die Spin-Spin-Relaxationszeit T_2 Aufschluss über die Dynamik dieser beiden Wechselwirkungen. Eine Verbindung zwischen der Spin- und Ladungsordnung gibt es in den HTSL bisher nicht. Statt dessen haben magnetische Messmethoden wie Neutronenstreuung oder muSR Aussagen über die magnetische Ordnung geliefert. Unabhängig davon liefern Messmethoden wie STM nur Informationen über eine Ladungsordnung oder inhomogene Ladungsverteilungen. Inhomogenitäten der Spins und Ladungen scheinen aber typisch für die HTSL zu sein. Man vermutet, dass diese Inhomogenitäten dynamisch in den supraleitenden Verbindungen sind, während sie in Eu dotiertem La_{2-x}Sr_xCuO_4 bei tiefen Temperaturen statisch werden und die Supraleitung unterdrücken. In dieser Arbeit wird gezeigt, dass sich diese Ladungs- und Spininhomogenitäten in vielen Parametern der NMR Spektren bemerkbar machen.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

In this thesis, the electronic properties in superconducting LiFeAs single crystal are investigated using low temperature scanning tunneling microscopy and spectroscopy (STM/S) at various temperatures. For this purpose, the differential conductance (dI/dV) measured by STS which is directly proportional to the local density of states (LDOS) of the sample to the sub-atomic precision, is used together with the topography information. The dI/dV spectra within the ±1 V energy range reveal a characteristic feature at around -350 mV to -400 mV in stoichiometric LiFeAs. This feature seems to be a universal property among all the Fe-based high temperature superconductors, because it is also found in Fe0.965Se1.035 and NaFe0.975Co0.025As single crystals at the energy of -210 mV and -200 mV, respectively. The temperature dependent spectroscopy data averaged over a spatially fixed clean area of 2 nm × 2 nm are successfully executed between 5 K and 20 K. The two distinct superconducting phases with critical temperatures Tc = 16 K and 18 K are observed. In addition, the distance between the dip position outside the superconducting gap and the superconducting coherence peak in the spectra remains temperature independent which confirms that it is not connected to an antiferromagnetic (AFM) spin resonance. The temperature dependent spectra have been measured between 5 K and 61 K within the energy range of ±100 mV as well. The hump structure at 42 mV tends to disappear around 60 K from unknown origin. The temperature dependent quasiparticle interference (QPI) has been studied within the temperature range between 6.7 K and 25 K and analyzed by the Fourier transformation of the measured spectroscopic maps. The dispersion plots in momentum space as a function of temperature show an enhancement of QPI intensity (±5.5 mV) within the superconducting gap at the Fermi level at 6.7 K near q ~ 0. This is interpreted on the basis of Andreev bound state. In both polarities outside of this, a depletion of QPI intensity is noticed between 5.5 mV and around 9 mV. At positive energies, the QPI intensity becomes very rich above 9 mV. The size of the enhanced QPI intensity near the Fermi level, and the edge of the rich QPI intensity beyond 9 mV are found to behave like superconducting order parameter with rising of temperature. Furthermore, an energy mode peaked at around 14 mV appears in the integrated QPI intensity below superconducting Tc (6.7 K). This is consistent with the observed peak at 1st derivative of the dI/dV spectra. In both of these cases, such 14 mV peak is suppressed at normal state (25 K). This mode is therefore directly related to superconductivity in LiFeAs. The off-stoichiometric LiFeAs single crystal with superconducting Tc of 6.5 K has a 10 mV rigid band shift of the Fermi level towards electron doping. The absence of the rich QPI intensity between 9 mV and 17 mV is found compared to the stoichiometric LiFeAs, and hence the 14 mV mode is absent here. This brings us to conclude once more time that such 14 mV energy mode is relevant for superconductivity in LiFeAs.

The thesis is dealing with the investigation of charge and orbital order and their behaviour under external pressure. Therefore, a new pressure cell has been developed which allows the observation of superlattice reflections corresponding to the order phenomena under pressure using scattering of high-energy synchrotron radiation. The maximum pressure that can be reached is 1.25 GPa. Until today there has been no possibility to conduct such studies of charge and orbital order superlattice reflections under pressure using x-ray scattering. The intensities of the reflections of the single crystalline samples are quite weak compared to fundamental peaks. Therefore the measurements are strongly affected by the absorption of the radiation in the pressure cell itself. Further difficulties result from the facts that low temperatures are needed and the sample has to be oriented in reciprocal space after being mounted into the cell. Therefore, the design of a compact clamp-type piston pressure cell was chosen here. The cell is made from a copper-beryllium alloy with the wall thickness reduced in the height of the sample volume. This allows the usage inside a closed-cycle cryostat mounted on a three-axis-diffractometer. Absorption effects are minimized due to the combination of reduced wall thickness and the usage of high energy synchrotron radiation (E = 100 keV at the beamline BW5 at HASYLAB/DESY). The new experimental technique was established and used for a study of two representatives of the transition metal oxide compounds, i.e. doped cuprates and manganites, which belong to the class of strongly correlated electron systems. The 1/8-doped cuprate La_{2-x}Ba_{x}CuO_{4} reveals an ordered state at low temperatures. Inside the CuO_{2} planes a combined order of charge stripes and antiferromagnetic spin stripes is observed. The ordering results from the interaction between charge, spin and lattice degrees of freedom. Here the lattice degrees of freedom play a major role. Particularly, a structural transition from an orthorhombic to a tetragonal symmetry is prerequisite for the observation of the ordered state. The cell constructed in this work allows a more exact analysis of the coupling between the crystal lattice and the formation of the charge and spin ordered phase. The manganite system Pr_{0.7}(Ca_{0.9}Sr_{0.1})_{0.3}MnO_{3} shows a strong magnetoresistive effect, called colossal magnetoresistance (CMR). In this system, several ordered phases can be found, which exhibit charge, spin and - since the orbital degree of freedom is also present in the manganites - additionally orbital ordering phenomena. In particular, an antiferromagnetically spin ordered insulating phase, which is connected to a charge- and orbital ordered state competes with a ferromagnetic metallic phase. This competition leads to a phase separation, which determines the properties of the sample. Both phases are strongly coupled to the lattice degrees of freedom, so that application of external pressure drastically affects the interplay between the different phases and allows a detailed study of the relation between the charge and orbital ordered phase and the crystal structure. / Die vorliegende Arbeit befaßt sich mit dem Studium der Ordnungszustände von Ladungen und Orbitalen und deren Beeinflußung durch externen Druck. Als experimentelle Neuentwicklung wurde dafür eine Druckzelle entworfen, mit deren Hilfe die Beobachtung der jeweiligen Ordnungsphänomene unter Druck mittels der Streuung hochenergetischer Synchtrotronstrahlung möglich ist. Die Zelle erlaubt die Messung der orbitalen und Ladungsüberstrukturreflexe, welche aus den geordneten Zuständen resultieren, in einem Druckbereich bis 1.25 GPa. Die experimentelle Herausforderung ergibt sich hierbei aus der Tatsache, dass die Überstrukturreflexe im Vergleich zu den fundamentalen Reflexen der einkristallinen Proben sehr schwach sind und zusätzlich durch die Absorption im Mantelmaterial der Druckzelle stark beeinträchtigt werden. Darüber hinaus soll die Zelle bei tiefen Temperaturen einsetzbar und die Probe auch innerhalb der Zelle im reziproken Raum orientierbar sein. Bei dem hier realisierten Ansatz wurde für das Design daher der Typ einer kompakten Klemmdruckzelle aus einer Kupfer-Beryllium-Legierung gewählt, deren Zellwände im Bereich des Probenvolumens reduziert wurden. Dadurch ist der Einsatz der Zelle im Inneren eines Closed-Cycle-Kryostaten auf einem Einkristall-Diffraktometer möglich. Aufgrund der geringen Wandstärke der Zelle und der Nutzung von hochenergetischer Röntgenstrahlung (E = 100 keV am Messplatz BW5 des HASYLAB/DESY) werden Absorptionseffekte minimiert. Die neue Messmethode wurde im Rahmen der Arbeit etabliert und zur Untersuchung zweier wichtiger Übergangsmetalloxidverbindungen (dotierte Kuprate, Manganate), die zur Klasse der stark korrelierten Elektronensysteme gehören, eingesetzt. Das 1/8-dotierte Kupratsystem La_{2-x}Ba_{x}CuO_{4}, weist bei tiefen Temperaturen einen statisch geordneten Zustand auf. Innerhalb der CuO_{2}-Schichten des Kristalls ergibt sich eine Ordnung, bei der sich Streifen lokalisierter Löcher und antiferromagnetische Bereiche abwechseln. Ursache dieses Zustands ist das Wechselspiel von Ladungen, Spins und strukturellen Freiheitsgraden. Dabei spielen letztere eine herausgehobene Rolle. So ist insbesondere ein struktureller Übergang von einer orthorhombischen zu einer tetragonalen Phase Voraussetzung für die Beobachtung der Ordnung. Die in dieser Arbeit aufgebaute Druckzelle erlaubt eine genauere Analyse des Zusammenhangs zwischen Struktur des Kristalls und der Ausbildung der ladungs- und spingeordneten Phase. Das Manganatsystem Pr_{0.7}(Ca_{0.9}Sr_{0.1})_{0.3}MnO_{3}, zeichnet sich durch einen sehr starken magnetoresistiven Effekt aus, der auch als kolossaler Magnetowiderstand (CMR) bezeichnet wird. Auch hier kann bei tiefen Temperaturen eine geordnete Phase beobachtet werden. Allerdings spielt in diesem System zusätzlich der orbitale Freiheitsgrad der Elektronen eine entscheidende Rolle, so dass sich eine kombinierte Ladungs- und Orbitalordnung ergibt. Diese Phase, die isolierend und zusätzlich antiferromagnetisch geordnet ist, steht im direkten Wettbewerb zu einer ferromagnetischen Phase. Aus dieser Konkurrenz ergibt sich eine Tendenz zur Phasenseparation, deren Effekte die Eigenschaften des Kristalls dominieren. Da beide Phasen stark an die strukturellen Freiheitsgrade gekoppelt sind, läßt sich das Gleichgewicht zwischen ihnen durch externen Druck beeinflussen und die Abhängigkeit der ladungs- und orbitalgeordneten Phase von den strukturellen Eigenschaften des Kristalls im Detail untersuchen.

The thesis is dealing with the investigation of charge and orbital order and their behaviour under external pressure. Therefore, a new pressure cell has been developed which allows the observation of superlattice reflections corresponding to the order phenomena under pressure using scattering of high-energy synchrotron radiation. The maximum pressure that can be reached is 1.25 GPa. Until today there has been no possibility to conduct such studies of charge and orbital order superlattice reflections under pressure using x-ray scattering. The intensities of the reflections of the single crystalline samples are quite weak compared to fundamental peaks. Therefore the measurements are strongly affected by the absorption of the radiation in the pressure cell itself. Further difficulties result from the facts that low temperatures are needed and the sample has to be oriented in reciprocal space after being mounted into the cell. Therefore, the design of a compact clamp-type piston pressure cell was chosen here. The cell is made from a copper-beryllium alloy with the wall thickness reduced in the height of the sample volume. This allows the usage inside a closed-cycle cryostat mounted on a three-axis-diffractometer. Absorption effects are minimized due to the combination of reduced wall thickness and the usage of high energy synchrotron radiation (E = 100 keV at the beamline BW5 at HASYLAB/DESY). The new experimental technique was established and used for a study of two representatives of the transition metal oxide compounds, i.e. doped cuprates and manganites, which belong to the class of strongly correlated electron systems. The 1/8-doped cuprate La_{2-x}Ba_{x}CuO_{4} reveals an ordered state at low temperatures. Inside the CuO_{2} planes a combined order of charge stripes and antiferromagnetic spin stripes is observed. The ordering results from the interaction between charge, spin and lattice degrees of freedom. Here the lattice degrees of freedom play a major role. Particularly, a structural transition from an orthorhombic to a tetragonal symmetry is prerequisite for the observation of the ordered state. The cell constructed in this work allows a more exact analysis of the coupling between the crystal lattice and the formation of the charge and spin ordered phase. The manganite system Pr_{0.7}(Ca_{0.9}Sr_{0.1})_{0.3}MnO_{3} shows a strong magnetoresistive effect, called colossal magnetoresistance (CMR). In this system, several ordered phases can be found, which exhibit charge, spin and - since the orbital degree of freedom is also present in the manganites - additionally orbital ordering phenomena. In particular, an antiferromagnetically spin ordered insulating phase, which is connected to a charge- and orbital ordered state competes with a ferromagnetic metallic phase. This competition leads to a phase separation, which determines the properties of the sample. Both phases are strongly coupled to the lattice degrees of freedom, so that application of external pressure drastically affects the interplay between the different phases and allows a detailed study of the relation between the charge and orbital ordered phase and the crystal structure. / Die vorliegende Arbeit befaßt sich mit dem Studium der Ordnungszustände von Ladungen und Orbitalen und deren Beeinflußung durch externen Druck. Als experimentelle Neuentwicklung wurde dafür eine Druckzelle entworfen, mit deren Hilfe die Beobachtung der jeweiligen Ordnungsphänomene unter Druck mittels der Streuung hochenergetischer Synchtrotronstrahlung möglich ist. Die Zelle erlaubt die Messung der orbitalen und Ladungsüberstrukturreflexe, welche aus den geordneten Zuständen resultieren, in einem Druckbereich bis 1.25 GPa. Die experimentelle Herausforderung ergibt sich hierbei aus der Tatsache, dass die Überstrukturreflexe im Vergleich zu den fundamentalen Reflexen der einkristallinen Proben sehr schwach sind und zusätzlich durch die Absorption im Mantelmaterial der Druckzelle stark beeinträchtigt werden. Darüber hinaus soll die Zelle bei tiefen Temperaturen einsetzbar und die Probe auch innerhalb der Zelle im reziproken Raum orientierbar sein. Bei dem hier realisierten Ansatz wurde für das Design daher der Typ einer kompakten Klemmdruckzelle aus einer Kupfer-Beryllium-Legierung gewählt, deren Zellwände im Bereich des Probenvolumens reduziert wurden. Dadurch ist der Einsatz der Zelle im Inneren eines Closed-Cycle-Kryostaten auf einem Einkristall-Diffraktometer möglich. Aufgrund der geringen Wandstärke der Zelle und der Nutzung von hochenergetischer Röntgenstrahlung (E = 100 keV am Messplatz BW5 des HASYLAB/DESY) werden Absorptionseffekte minimiert. Die neue Messmethode wurde im Rahmen der Arbeit etabliert und zur Untersuchung zweier wichtiger Übergangsmetalloxidverbindungen (dotierte Kuprate, Manganate), die zur Klasse der stark korrelierten Elektronensysteme gehören, eingesetzt. Das 1/8-dotierte Kupratsystem La_{2-x}Ba_{x}CuO_{4}, weist bei tiefen Temperaturen einen statisch geordneten Zustand auf. Innerhalb der CuO_{2}-Schichten des Kristalls ergibt sich eine Ordnung, bei der sich Streifen lokalisierter Löcher und antiferromagnetische Bereiche abwechseln. Ursache dieses Zustands ist das Wechselspiel von Ladungen, Spins und strukturellen Freiheitsgraden. Dabei spielen letztere eine herausgehobene Rolle. So ist insbesondere ein struktureller Übergang von einer orthorhombischen zu einer tetragonalen Phase Voraussetzung für die Beobachtung der Ordnung. Die in dieser Arbeit aufgebaute Druckzelle erlaubt eine genauere Analyse des Zusammenhangs zwischen Struktur des Kristalls und der Ausbildung der ladungs- und spingeordneten Phase. Das Manganatsystem Pr_{0.7}(Ca_{0.9}Sr_{0.1})_{0.3}MnO_{3}, zeichnet sich durch einen sehr starken magnetoresistiven Effekt aus, der auch als kolossaler Magnetowiderstand (CMR) bezeichnet wird. Auch hier kann bei tiefen Temperaturen eine geordnete Phase beobachtet werden. Allerdings spielt in diesem System zusätzlich der orbitale Freiheitsgrad der Elektronen eine entscheidende Rolle, so dass sich eine kombinierte Ladungs- und Orbitalordnung ergibt. Diese Phase, die isolierend und zusätzlich antiferromagnetisch geordnet ist, steht im direkten Wettbewerb zu einer ferromagnetischen Phase. Aus dieser Konkurrenz ergibt sich eine Tendenz zur Phasenseparation, deren Effekte die Eigenschaften des Kristalls dominieren. Da beide Phasen stark an die strukturellen Freiheitsgrade gekoppelt sind, läßt sich das Gleichgewicht zwischen ihnen durch externen Druck beeinflussen und die Abhängigkeit der ladungs- und orbitalgeordneten Phase von den strukturellen Eigenschaften des Kristalls im Detail untersuchen.

In this thesis the superconducting and magnetic phases of LiOH(Fe,Co)(Se,S), CuFeAs/CuFeSb, and LaFeP_1-xAs_xO - belonging to the 11, 111 and 1111 structural classes of iron-based arsenides and chalcogenides - are investigated by means of 57Fe Mössbauer spectroscopy and muon spin rotation/relaxation (μSR). Of major importance in this study is the application of high magnetic fields in Mössbauer spectroscopy to distinguish and characterize ferro- (FM) and antiferromagnetic (AFM) order. A user-friendly Mössbauer data analysis program was developed to provide suitable model functions not only for high field spectra, but relaxation spectra or parameter distributions in general. In LaFeP_1-xAs_xO the reconstruction of the Fermi surface is described by the vanishing of the Γ hole pocket with decreasing x. The continuous change of the orbital character and the covalency of the d-electrons is shown by Mössbauer spectroscopy. A novel antiferromagnetic phase with small magnetic moments of ~ 0.1 μ_B state is characterized. The superconducting order parameter is proven to continuously change from a nodal to a fully gapped s-wave like Fermi surface in the superconducting regime as a function of x, partially investigated on (O,F) substituted samples. LiOHFeSe is one of the novel intercalated FeSe compounds, showing strongly increased T_C = 43 K mainly due to increased interlayer spacing and resulting two-dimensionality of the Fermi surface. The primary interest of the samples of this thesis is the simultaneously observed ferromagnetism and superconductivity. The local probe techniques prove that superconducting sample volume gets replaced by ferromagnetic volume. Ferromagnetism arises from magnetic order with T_C = 10 K of secondary iron in the interlayer. The tendency of this system to show (Li,Fe) disorder is preserved upon (Se,S) substitution. However, superconductivity gets suppressed. The results of Mössbauer spectroscopy indicate that the systems tends to a secondary structural phase, where the local iron environment observed in pure FeS is absent. Moreover, two interlayer positions of the iron are identified. The absence of enhanced superconducting T_C in LiOHFeS thus is related to a structural instability. Also, in CuFeAs the role of secondary iron at the Cu position turns out to be decisive for the observed magnetic behaviour. As in LiOHFeSe, it orders ferromagnetically at T_C ~ 11 K and superimposes with the magnetic instability of the main iron site. It is shown that a small charge doping of 0.1e/Fe, which is expected from (Cu,Fe) disorder, is sufficient to switch the system between a paramagnetic and an AFM ground state. Both magnetic orders are indistinguishable, because the magnetic order parameters are strongly coupled. This coupling was observed in the structurally identical CuFeSb, where the magnetic order parameters of both iron sites scale perfectly. The magnetically unstable CuFeAs and the ferromagnetic CuFeSb can be classified according to the theory of As height driven magnetism, predicting a change from paramagnetism to AFM and finally FM with increasing As height.

Die vorliegende Arbeit befasst sich mit der elektronischen Struktur von Bi-Kupraten vom Normalzustand bis in den supraleitenden Zustand. Der Normalzustand von einschichtigen Bi-Kupraten wurde mittels polarisationsabhängiger XAS untersucht. Es konnte eine deutliche Polarisationsabhängigkeit der CuL3- und OK-Kante innerhalb der Kupferoxidebene beobachtet werden. Insbesondere in den Merkmalen, die den dotierten Löchern zugeordnet werden. Die Winkelabhängigkeit geht über die erwartete Hybridisierung von Cu3dx^2-y^2- und O2px,y-Orbitalen hinaus, und unterstützt somit Theorien, die auch Orbitale ausserhalb der Kupferoxidebene zur Beschreibung der elektronischen Struktur einbeziehen. Desweiteren wurde beobachtet, dass die Ladungs-Transfer-Lücke sich mit steigender Lochkonzentration vergrößert konform zu Theorien zum Zusammenbruch der Zhang-Rice-Singuletts im überdotierten Bereich. Mittels ARPES wurden die Anregungen nahe der Fermikante in antinodaler Richtung an zweischichtigen Bi-Kupraten untersucht. Die komplexe Linienform im zweischichtigen Bi-Kuprat, die aus Interlageneffekten resultiert, wurde durch die gezielte Ausnutzung von Matrixelementeffekten vereinfacht. Dadurch konnten, in Kombination mit der spezifischen Ausrichtung der Polarisation, vorherige, sich scheinbar widersprechende Beobachtungen am einschichtigen und zweischichtigen Bi-Kuprat in Einklang gebracht werden. Es konnte gezeigt werden, dass im zweischichtigen Bi-Kuprat eine Anregung zusätzlich zum bindenden und antibindenden Band existiert, welche mit dem antibindenden Band korreliert zu sein scheint. Außerdem zeigt es Gemeinsamkeiten mit dem scharfen Peak, der im einschichtigen Bi-Kuprat gefunden wurde. So besteht es über die supraleitende Sprungtemperatur Tc hinaus, und verschwindet vermutlich bei oder über der Pseudolücken-Temperatur T*. Die ARPES Messungen lassen sich am Besten innerhalb des Modells elektronischer Inhomogenitäten erklären, welches Hochtemperatursupraleitung aus Streifen ableitet. / The electronic structure of Bi cuprates from the normal state down to the superconducting state has been investigated. The normal state electronic structure is probed by polarization dependent XAS on single layer Bi cuprates. With the x-ray beam being incident normal to the CuO2 plane the azimuthal angle was varied to explore the polarization effects on orbitals within the plane. In the CuL3- as well as the OK-edge spectra, the spectral features related to the doped holes showed a distinct polarization dependence within the CuO2 plane. The revealed polarization dependence is more complex than expected from hybridization of Cu3dx^2-y^2 and O2px,y orbitals only. Thus, the results support the inclusion of out-of-plane orbitals into the description of the electronic structure as has been previously theoretically proposed. Furthermore, the charge transfer gap has been observed to rise with rising hole concentration supporting theories of the instability of Zhang-Rice-singlets in the overdoped regime. By ARPES the excitations close to the Fermi surface in the antinodal region of double layer Bi cuprates have been investigated. The complex lineshape in double layer Bi cuprates that results from interlayer effects has been disentangled by exploiting matrix element effects. In combination with distinct polarization settings this enabled to unify seemingly inconsistent observations made on single and double layer Bi cuprates. The existence of an excitation additional to antibonding and bonding band could be shown in the double layer Bi cuprate. This additional excitation is probably connected to the antibonding band. It furthermore shows similarities to the sharp peak observed in single layer Bi cuprates. It persists to temperatures above the superconducting temperature Tc, and presumably vanishes at or above the pseudogap temperature T*. The ARPES results could be best explained within the model of electronic inhomogeneity which derives superconductivity from stripes.

No description available.

In this thesis the superconducting and magnetic phases of LiOH(Fe,Co)(Se,S), CuFeAs/CuFeSb, and LaFeP_1-xAs_xO - belonging to the 11, 111 and 1111 structural classes of iron-based arsenides and chalcogenides - are investigated by means of 57Fe Mössbauer spectroscopy and muon spin rotation/relaxation (μSR). Of major importance in this study is the application of high magnetic fields in Mössbauer spectroscopy to distinguish and characterize ferro- (FM) and antiferromagnetic (AFM) order. A user-friendly Mössbauer data analysis program was developed to provide suitable model functions not only for high field spectra, but relaxation spectra or parameter distributions in general. In LaFeP_1-xAs_xO the reconstruction of the Fermi surface is described by the vanishing of the Γ hole pocket with decreasing x. The continuous change of the orbital character and the covalency of the d-electrons is shown by Mössbauer spectroscopy. A novel antiferromagnetic phase with small magnetic moments of ~ 0.1 μ_B state is characterized. The superconducting order parameter is proven to continuously change from a nodal to a fully gapped s-wave like Fermi surface in the superconducting regime as a function of x, partially investigated on (O,F) substituted samples. LiOHFeSe is one of the novel intercalated FeSe compounds, showing strongly increased T_C = 43 K mainly due to increased interlayer spacing and resulting two-dimensionality of the Fermi surface. The primary interest of the samples of this thesis is the simultaneously observed ferromagnetism and superconductivity. The local probe techniques prove that superconducting sample volume gets replaced by ferromagnetic volume. Ferromagnetism arises from magnetic order with T_C = 10 K of secondary iron in the interlayer. The tendency of this system to show (Li,Fe) disorder is preserved upon (Se,S) substitution. However, superconductivity gets suppressed. The results of Mössbauer spectroscopy indicate that the systems tends to a secondary structural phase, where the local iron environment observed in pure FeS is absent. Moreover, two interlayer positions of the iron are identified. The absence of enhanced superconducting T_C in LiOHFeS thus is related to a structural instability. Also, in CuFeAs the role of secondary iron at the Cu position turns out to be decisive for the observed magnetic behaviour. As in LiOHFeSe, it orders ferromagnetically at T_C ~ 11 K and superimposes with the magnetic instability of the main iron site. It is shown that a small charge doping of 0.1e/Fe, which is expected from (Cu,Fe) disorder, is sufficient to switch the system between a paramagnetic and an AFM ground state. Both magnetic orders are indistinguishable, because the magnetic order parameters are strongly coupled. This coupling was observed in the structurally identical CuFeSb, where the magnetic order parameters of both iron sites scale perfectly. The magnetically unstable CuFeAs and the ferromagnetic CuFeSb can be classified according to the theory of As height driven magnetism, predicting a change from paramagnetism to AFM and finally FM with increasing As height.:1 Acronyms and Symbols 2 Introduction 3 Iron-based arsenides and chalcogenides 3.1 Structural properties 3.2 Electronic properties 3.2.1 Magnetism 3.2.2 Superconductivity 3.2.3 Nematic phase 3.3 Investigated samples 4 Moessfit - a free Mössbauer fitting program 4.1 Aspects of program design 4.2 Errors 4.2.1 Uncorrelated 4.2.2 Hesse 4.2.3 MonteCarlo 4.2.4 Minos 4.3 Fitting algorithm 4.4 Maximum entropy method (MEM) 4.5 Kolmogorov-Smirnov confidence 5 Mössbauer spectroscopy 5.1 Mössbauer effect 5.2 Relativistic Doppler effect 5.3 Full static Hamiltonian 5.3.1 Quadrupole interaction 5.3.2 Isomer shift. 5.3.3 Zeeman splitting 5.3.4 Combined interaction 5.3.5 Transition probabilities 5.3.6 The magic angle 5.4 Transmission integral 5.4.1 Absorption area 5.4.2 Ideal thickness 5.4.3 Line width and line shape 5.4.4 Levelling 5.5 Applied field measurements of powder samples 5.5.1 Paramagnet, axial symmetric EFG in transverse field geometry 6 5.5.2 Uniaxial antiferromagnet, axial symmetric EFG in transverse field geometry 6 5.5.3 Paramagnet, axial symmetric EFG in longitudinal field geometry 6 5.5.4 Uniaxial ferromagnet, axial symmetric EFG in transverse field geometry 6 5.5.5 Polarised photons 5.5.6 Total absorption cross section 5.5.7 Polarised sources 5.6 Blume line shape model 6 μSR 6.1 Muon decay and detection 6.2 Magnetic order and dynamic relaxation 6.2.1 Magnetic order 6.2.2 Time dependent field distributions 6.2.3 Aspects of μSR in iron-based arsenides and chalcogenides 6.2.4 Weak transverse field (WTF) 6.3 Superconductivity - transverse field (TF) experiments 7 Intercalated FeSe 7.1 Bulk properties: XRD, susceptibility, resistivity 7.2 Structural characterization 7.3 LiOHFeSe - Mössbauer spectroscopy 7.3.1 Applied transverse field 7.4 LiOHFeSe - μSR 7.4.1 Zero field (ZF) 7.4.2 Pinning experiment 7.4.3 Transverse field (TF) 7.5 Mössbauer investigation of LiOHFe_1-yCo_ySe_1-xS_x. 7.6 Discussion 8 LaFeO(As,P) 8.1 Preliminary measurements and electronic structure calculations 8.2 Mössbauer spectroscopy 8.3 μSR 8.3.1 Magnetic characterization 8.3.2 Spin dynamics 8.3.3 Superconductivity 8.4 Discussion 9 CuFeAs and CuFeSb 9.1 Preliminary results of CuFeAs and CuFeSb 9.2 CuFeAs: Mössbauer spectroscopy 9.2.1 Zero field (ZF) 9.2.2 Longitudinal field (LF) 9.2.3 Transverse field (TF) 9.3 CuFeAs: μSR 9.3.1 Zero field (ZF) 9.3.2 Weak transverse field (WTF) 9.4 Further investigations on CuFeAs 9.4.1 Neutron scattering 9.4.2 Theoretical calculation 9.4.3 Local element analysis with EDX/WDX 9.5 CuFeSb: Mössbauer spectroscopy 9.5.1 Zero Field (ZF) 9.5.2 Transverse field (TF) 9.6 Discussion 10 Conclusion 11 Appendix 11.1 Derivation of the quadrupole interaction and isomer shift 11.2 Matrix form of the static nuclear Hamiltonian 11.3 Mössbauer line intensities 11.4 Blume line shape model 11.4.1 Special case: two states with diagonal Hamiltonians 11.5 Moessfit models 11.5.1 FeSe_1-xS_x(Li_1-zFe_zOH) ZF, standard 11.5.2 FeSe_1-xS_x(Li_1-zFe_zOH) ZF, 4 fractions 11.5.3 FeSe_1-xS_x(Li_1-zFe_zOH) Pinning 11.5.4 FeSe_1-xS_x(Li_1-zFe_zOH) TF 11.5.5 FeSe_1-xS_x(Li_1-zFe_zOH) CS-Vzz-MEM 11.5.6 LaFeP_1-xAs_x+ ferrocene, ZF 11.5.7 LaFeP_1-xAs_x+ ferrocene, LF 11.5.8 LaFeP_1-xAs_x+ iron foil, ZF 11.5.9 LaFeAsO ZF 11.5.10 LaFeAsO TF 11.5.11 CuFeAs + ferrocen, ZF 11.5.12 CuFeAs + ferrocen, ZF, high statistics 11.5.13 CuFeAs + ferrocen, LF 11.5.14 CuFeAs + ferrocen, TF 11.5.15 CuFeSb ZF 11.5.16 CuFeSb TF