In this PhD thesis, the physics of vacancies in two-dimensional ordered Heisenberg antiferromagnets is investigated. We use semi-classical methods to study the influence of a single vacancy in long-range ordered states, with a focus on non-collinear order. Here, on a classical level, a magnetic distortion is created as the spins readjust in response to the vacancy. We use the non-collinear $120^\\circ$ state on the frustrated triangular lattice as an example, where we determine the impurity contributions to the magnetization and susceptibility. An important discovery is the vacancy moment not being quantized due to non-universal partial screening. The resulting effective moment $m_0 \\ll S$ can be observed as a fractional prefactor to an impurity-induced Curie response $m_0^2/(3k_BT)$ at finite temperature. This is in sharp contrast to collinearly ordered states. Here the moment is always quantized to the bulk spin value, $m_0=S$. Furthermore, we present a detailed analysis of the vacancy-induced distortion cloud. Due to Goldstone modes, it decays algebraically as $r^{-3}$ with distance $r$ to the vacancy. Using leading-order $1/S$-expansion, we determine the quantum corrections to both size and direction of the distorted magnetic moments. Secondly, we study the same problem in the presence of an external magnetic field $h$, both for the square and triangular lattice. For the triangular lattice we use a biquadratic exchange term $K$ to stabilize a unique ground state from a degenerate manifold. The finite-field vacancy moment $m(h)$ is generated by field-dependent screening clouds, as different non-collinear bulk states evolve with increasing field. These distortion clouds decay exponentially on a magnetic length scale $l_h\\propto 1/h$. Most importantly, we find that the magnetic-field linear-response limit $h \\rightarrow 0^+$ is generically singular for $SU(2)$ ordered local-moment antiferromagnets, as the vacancy moment in zero field differs fundamentally from even an infinitesimal but finite field, $m(h \\rightarrow 0^+)\\neq m_0$. Moreover, a part of the screening cloud itself becomes universally singular. Particularly for spin-flop states, this leads to a semi-classical version of perfect screening. We present general arguments to support these claims, as well as microscopic calculations. Another remarkable result is an impurity-induced quantum phase transition for overcompensated vacancies in the $M=1/3$ plateau phase on the triangular lattice with $K<0$. We close our analysis with a discussion about important limits for finite vacancy concentrations, as well as a possible experimental verification of our predictions.

In this PhD thesis, the physics of vacancies in two-dimensional ordered Heisenberg antiferromagnets is investigated. We use semi-classical methods to study the influence of a single vacancy in long-range ordered states, with a focus on non-collinear order. Here, on a classical level, a magnetic distortion is created as the spins readjust in response to the vacancy. We use the non-collinear $120^\\circ$ state on the frustrated triangular lattice as an example, where we determine the impurity contributions to the magnetization and susceptibility. An important discovery is the vacancy moment not being quantized due to non-universal partial screening. The resulting effective moment $m_0 \\ll S$ can be observed as a fractional prefactor to an impurity-induced Curie response $m_0^2/(3k_BT)$ at finite temperature. This is in sharp contrast to collinearly ordered states. Here the moment is always quantized to the bulk spin value, $m_0=S$. Furthermore, we present a detailed analysis of the vacancy-induced distortion cloud. Due to Goldstone modes, it decays algebraically as $r^{-3}$ with distance $r$ to the vacancy. Using leading-order $1/S$-expansion, we determine the quantum corrections to both size and direction of the distorted magnetic moments. Secondly, we study the same problem in the presence of an external magnetic field $h$, both for the square and triangular lattice. For the triangular lattice we use a biquadratic exchange term $K$ to stabilize a unique ground state from a degenerate manifold. The finite-field vacancy moment $m(h)$ is generated by field-dependent screening clouds, as different non-collinear bulk states evolve with increasing field. These distortion clouds decay exponentially on a magnetic length scale $l_h\\propto 1/h$. Most importantly, we find that the magnetic-field linear-response limit $h \\rightarrow 0^+$ is generically singular for $SU(2)$ ordered local-moment antiferromagnets, as the vacancy moment in zero field differs fundamentally from even an infinitesimal but finite field, $m(h \\rightarrow 0^+)\\neq m_0$. Moreover, a part of the screening cloud itself becomes universally singular. Particularly for spin-flop states, this leads to a semi-classical version of perfect screening. We present general arguments to support these claims, as well as microscopic calculations. Another remarkable result is an impurity-induced quantum phase transition for overcompensated vacancies in the $M=1/3$ plateau phase on the triangular lattice with $K<0$. We close our analysis with a discussion about important limits for finite vacancy concentrations, as well as a possible experimental verification of our predictions.

Die hier vorgelegte Dissertation beschäftigt sich mit Untersuchungen an nanoskopischen Emittern und den Möglichkeiten, deren Fluoreszenzverhalten durch kontrollierte Ankopplung an photonische und plasmonische Strukturen zu beeinflussen. Zum einen werden mit Ytterbium- und Erbium-Ionen kodotierte NaYF4 -Nanokristalle untersucht, die hervorragende Eigenschaften bei der Umwandlung von niederenergetischen Photonen in solche höherer Energie besitzen. Das so entstehende Fluoreszenzlicht einer Ansammlung von Nanokristallen wird auf seine Abhängigkeit von der Anregungsintensität untersucht. Mit der Hilfe eines Rasterkraftmikroskops (AFM) wird eine Abhängigkeit der spektralen Zusammensetzung des Fluoreszenzlichts einzelner Nanokristalle von deren Größe im Bereich von wenigen bis 50 nm aufgezeigt. Durch gezielte Manipulation mit dem AFM werden ebenfalls einzelne Nanokristalle an Goldnanokügelchen gekoppelt und die Mechanismen der beobachteten plasmonischen Verstärkung der Emission durch zeitaufgelöste Messungen analysiert. Einzelne Stickstoff-Fehlstellen-Zentren in Nanodiamanten werden in einem zweiten Themenkomplex als Einzelphotonenquellen eigesetzt. Diese werden durch den Einsatz einer Nahfeld-Sonde auf Mikrokugel-Resonatoren aufgebracht, wodurch die Emission aufgrund der Ankopplung an die Flüstergalerie-Moden der Kugeln die typischen, scharfen Überhöhungen im Spektrum aufweist. Diese Methode lässt sich nicht nur verwenden, um zwei oder mehr Emitter an die selben Resonanzen einer Kugel zu koppeln. Es ist auch möglich, die Kugeln in einem Vorbereitungsschritt zu charakterisieren, und so kann insbesondere eine spektrale Übereinstimmung zwischen einer der Resonanzen und dem Emitter erreicht werden. Desweiterne wird demonstriert, wie durch die Kopplung an eine plasmonische Antenne aus Goldnanokugeln mittels AFM auch die Effizienz der Einzelphotonenquelle gesteigert werden kann. / The topic of the dissertation presented here is the investigation of nanoscopic emitters and the possibilities to influence their fluorescence behavior by controlled coupling to photonic and plasmonic structures. NaYF4 nanocrystals codoped with ytterbium and erbium are investigated since they provide excellent properties in upconverting of low-energetic photons to photons with higher energy. The fluorescence light that is generated in this process of a small cluster of nanocrystals is investigated on its dependence on the excitation intensity. With the help of an atomic force microscope (AFM) a dependence of the spectral composition of the fluorescence light from single nanocrystals on their size ranging between a few to 50 nm is demonstrated. By selective manipulation with the AFM, individual nanocrystals are coupled to gold nanospheres and the mechanisms of the observed plasmonic amplification of the emission is analyzed with time-resolved measurements. Single nitrogen–vacancy centers in nanodiamonds are employed as single-photon sources in a second subject area. A near-field probe is employed to attach these single quantum systems to microspherical resonators, by which their emission features the typical peaks in the spectrum due to the coupling to the whispering gallery modes of the spheres. This method can not only be applied to couple two or more single-photon emitters to the very same modes of a microsphere, but the resonators themselves can be pre-characterized to match one of the modes with the emitter. Furthermore, it will be demonstrated how the efficiency of a single-photon source can be enhanced by coupling the nitrogen-vacancy center to a plasmonic antenna made of gold nanospheres.

Gegenstand der vorliegenden Dissertation ist die Untersuchung von einzelnen nano- und mikrometergroßen Partikeln, zum Verständnis und zur Entwicklung von neuartigen nanooptischen Elementen, wie Lichtquellen und Sensoren, sowie Strukturen zum Aufsammeln und Leiten von Licht. Neben der Charakterisierung stehen dabei verschiedene Methoden zur elektromagnetischen Manipulation im Vordergrund, die auf eine Kontrolle der Position oder der Geometrie der Partikel ausgerichtet sind. Die gezielten Manipulationen werden verwendet, um vorausgewählte Partikel zu isolieren, modifizieren und transferieren. Dadurch können Partikel zu komplexeren photonischen Systemen kombiniert werden, welche die Funktionalität der einzelnen Bestandteile übertreffen. Der Hauptteil der Arbeit behandelt Experimente mit freischwebenden Partikeln in linearen Paul-Fallen. Durch die räumliche Isolation im elektrodynamischen Quadrupolfeld können Partikel mit reduzierter Wechselwirkung untersucht werden. Neben der spektroskopischen Charakterisierung von optisch aktiven Partikeln (farbstoffdotierte Polystyrol-Nanokügelchen, Cluster aus Nanodiamanten mit Stickstoff-Fehlstellen-Zentren, Cluster aus kolloidalen Quantenpunkten) sowie optischen Resonatoren (plasmonische Silber-Nanodrähte, sphärische Siliziumdioxid-Mikroresonatoren) werden neu entwickelte Methoden zur Manipulation vorgestellt, mit denen sich individuelle Partikel freischwebend kombinieren und elektromagnetisch koppeln sowie aus der Falle auf optischen Fasern zur weiteren Untersuchung bzw. zur Funktionalisierung photonischer Strukturen ablegen lassen. In einem weiteren Teil der Arbeit wird eine Methode zur Manipulation der Geometrie von plasmonischen Nanopartikeln vorgestellt. Dabei werden einzelne Goldkugeln auf einem Deckglas mit einem fokussierten Laserstrahl zum Schmelzen gebracht und verformt. Durch die kontrollierte und reversible Veränderung der Symmetrie lassen sich die lokalisierten Oberflächenplasmonen des Partikels gezielt beeinflußen. / The topic of the present thesis is the investigation of single nano- and microsized particles for the understanding and design of novel nanooptical elements as light sources and sensors, as well as light collecting and guiding structures. In addition to particle characterization, the focus is on different methods for electromagnetic particle manipulation aimed at controlling the particle’s position or geometry. The specific manipulations are used for isolation, modification and transfer of preselected particles, enabling combination of particles into more complex photonic systems, which exceed the functionalities of the individual constituents. The main part of this work deals with experiments on levitated particles in linear Paul traps. Due to the spatial isolation in the electrodynamic quadrupole field, particles can be investigated with reduced environmental interaction. In addition to spectroscopic characterization of optically active particles (dye-doped polystyrene nanobeads, clusters of nanodiamonds with nitrogen vacancy defect centers, clusters of colloidal quantum dots) and particles with optical resonances (plasmonic silver nanowires, spherical silica microresonators) new manipulation methods are presented that enable assembly and electromagnetic coupling of individual, levitated particles as well as deposition of particles from the trap on optical fibers for further characterization or functionalization of photonic structures. In a further part of this work a method to manipulate the geometry of plasmonic nanoparticles is presented. Single gold nanospheres on a coverslip are melted and shaped with a focused laser beam. The localized surface plasmons can be influenced specifically by controlled and reversible changes of the particle symmetry.