The effects of surface plasmon for InGaN/GaN multi-quantum wells and ZnO nanoparticles optical linear and nonlinear emission efficiency had been experimentally studied. Due to the critical design for InGaN MQWs with inverted hexagonal pits based on GaN, both contribution of surface plasmon effect and image charge effect at resonant and off resonant frequencies were experimentally and theoretically investigated. With off- resonant condition, the InGaN MQWs emission significantly enhanced by metal nanoparticles. This enhancement was caused by the image charge effect, due to the accumulation of carriers to NPs region. When InGaN emission resonated with metal particles SP modes, surface Plasmon effect dominated the emission process. We also studied the surface plasmon effect for ZnO nanoparticles nonlinear optical processes, SHG and TPE. Defect level emission had more contribution at high incident intensity. Emissions are different for pumping deep into the bulk and near surface. A new assumption to increase the TPE efficiency was studied. We thought by using Au nanorods localized surface plasmon mode to couple the ZnO virtual state, the virtual state’s life time would be longer and experimentally lead the emission enhancement. We studied the TPE phenomena at high and near band gap energy. Both emission intensity and decay time results support our assumption. Theoretically, the carriers dynamic mechanism need further studies.

Ce manuscrit porte sur l’étude de cuprates de basse dimensionnalité, les systèmes à chaînes de spins SrCuO₂ et Sr₂CuO₃. Un des intérêts de ces deux composés est qu’ils présentent des conductions thermiques fortement anisotropes. Celles-ci comportent une contribution magnétique due au transport de la chaleur via les excitations de spinons qui se manifeste uniquement dans la direction des chaînes de spins. Notre étude a pour objectif la mise en évidence des mécanismes qui gouvernent ces propriétés de transport, notamment à travers l’étude des interactions entre les spinons, les phonons et les défauts. Les interactions spinons (phonons)-défauts ont été sondées par l’introduction intentionnelle de dopants (1-2%) non-magnétiques sur le site du cuivre : Mg²⁺, Zn²⁺, Pd²⁺ ou Ni²⁺, ou encore par l’introduction d’éléments possédant des degrés d’oxydation différents sur le site du strontium : La³⁺ ou K⁺. Les composés ont été synthétisés sous leur forme monocristalline par la méthode de fusion de la zone solvante. Des caractérisations structurales, magnétiques et thermiques des composés purs et dopés ont été réalisées. Les spectres d’excitations magnétiques de ces cuprates ont été déterminés par diffusion inélastique de neutrons, spectroscopie RMN et spectroscopie de photoémission résolue en angle afin de révéler l’impact de la substitution. L’étude des spectres de phonons a également été réalisée par diffusion inélastique de neutrons. Les résultats de ces mesures sont corrélés aux propriétés de conduction thermique des composés purs et dopés.. / This manuscript deals with the study of low dimensional cuprates, namely, the spin chains systems SrCuO₂ and Sr₂CuO₃. These two compounds exhibit highly anisotropic thermal conduction properties along the spin-chains direction, where magnetic thermal conduction contributes to the heat transport process via spinon excitations. Our study aims to highlight the mechanisms that govern the heat transport properties, particularly through the study of the scattering channels involving spinon, phonon and defects. The spinon (phonon)–defect scattering was probed by the intentional introduction of nonmagnetic dopants (1-2%) on the copper site, by: Mg²⁺, Zn²⁺, Pd²⁺ or Ni²⁺, or by the introduction of elements carrying different oxidation level on the strontium site, by: La³⁺ or K⁺. Single crystals of the pure and doped materials have been grown by the travelling solvent floating zone method. The structural, magnetic and thermal characterizations of the pure and doped compounds were performed. The magnetic excitation spectra of the compounds were determined by inelastic neutron scattering, NMR spectroscopy, and angle resolved photoemission spectroscopy to reveal the impact of the substitution on the spin dynamics of the doped compounds. The study of phonon spectra has also been performed by inelastic neutron scattering. Results from inelastic neutron scattering have been correlated to the heat transport properties of the pristine and substituted materials.

Semilocal density functionals up to the generalized gradient approximation (GGA) level cannot accurately describe band gaps of bulk solids. Meta-GGA density functionals with a dependence on the kinetic energy density ingredient (τ) can potentially give wider band gaps compared with GGAs. The recently developed TASK meta-GGA functional yields excellent band gaps of bulk solids. The accuracy of the TASK functional for band gaps of bulk solids cannot be straightforwardly transferred to low-dimensional materials due to reduced screening in low-dimensional materials. We have developed mTASK from TASK by changing (a) the tight upper-bound for one or two-electron systems (h0X) from 1.174 to 1.29 and (b) the limit of the interpolation function fX(α → ∞) of the TASK functional that interpolates the exchange enhancement factor FX(s,α) from α = 0 to 1, so that mTASK has the screening appropriate for low-dimensional materials. These two conditions guarantee the increased nonlocality within the generalized Kohn-Sham scheme in the mTASK functional and yield a better description of band gaps of low-dimensional materials. We computed the band gaps of bulk solids from mTASK having a wide range of gaps such as Ge, CdO, ZnS, MgO, NiF, Ar. The improvement in the band gaps from mTASK is more consistent than TASK for the large-gaps crystals. We have studied the band structures in two forms of transition metal dichalcogenide (TMD) monolayers, i.e., monolayer hexagonal (1H) and monolayer trigonal (1T) and their nanoribbons. The mTASK functional systematically improves the band gaps and is in close agreement with the experiments or the hybrid level HSE06 density functional for 2D single-layer and nanoribbon systems. In the second part of this assessment, we explore the large tunability of band gaps and optical absorption of phosphorene nanoribbons under mechanical bending from first-principles. Bending can induce an unoccupied edge state in armchair phosphorene nanoribbons. The electronic and optical properties of nanoribbons drastically change because of this edge state. GW-Bethe–Salpeter equation calculations for armchair phosphorene nanoribbons at different bending curvatures show that the absorption peaks generally shift toward the high energy direction with increasing curvature. Our study suggests that bright excitons can also be formed from the transition from the valence bands to the edge state when the edge state completely separates out from the continuum conduction bands. We systematically study the role of the edge state to form bound excitons at large curvatures. Our analysis suggests that the optical absorption peaks of zigzag phosphorene nanoribbons shift toward the low-energy region, and the height of the absorption peaks increases while increasingthe bending curvature. In the third part of this assessment, we extend our study of phosphorene nanoribbons to MoS2 nanoribbons under bending from GW and Bethe-Salpeter equation approaches. We find three critical bending curvatures for armchair MoS2 nanoribbons, and the edge and non-edge band gaps show a non-monotonic trend with bending. The edge band gap shows an oscillating feature with ribbon width n, with a period of ∆n=3. The binding energy and the lowest exciton energy decrease with the curvature. The large tunability of optical properties of bent MoS2 nanoribbon is applicable in tunable optoelectronic nanodevices. / Physics

Across scientific and engineering disciplines, the algorithmic pipeline forprocessing and understanding data increasingly revolves around deep learning, a data-driven approach to learning features for tasks that uses high-capacity compositionally-structured models, large datasets, and scalable gradient-based optimization. At the same time, modern deep learning models are resource-inefficient, require up to trillions of trainable parameters to succeed on tasks, and their predictions are notoriously susceptible to perceptually-indistinguishable changes to the input, limiting their use in applications where reliability and safety are critical. Fortunately, data in scientific and engineering applications are not generic, but structured---they possess low-dimensional nonlinear structure that enables statistical learning in spite of their inherent high-dimensionality---and studying the interactions between deep learning models, training algorithms, and structured data represents a promising approach to understand practical issues such as resource efficiency, robustness and invariance in deep learning. To begin to realize this program, it is necessary to have mathematical model problems that capture the nonlinear structures of data in deep learning applications and features of practical deep learning pipelines, and there is a question of how to translate mathematical insights into practical progress on the aforementioned issues, as well. We address these considerations in this thesis. First, we pose and study the multiple manifold problem, a binary classification task modeled on applications in computer vision, in which a deep fully-connected neural network is trained to separate two low-dimensional submanifolds of the unit sphere. We provide an analysis of the one-dimensional case, proving for a rather general family of configurations that when the network depth is large relative to certain geometric and statistical properties of the data, the network width grows as a sufficiently large polynomial in the depth, and the number of samples from the manifolds is polynomial in the depth, randomly-initialized gradient descent rapidly learns to classify the two manifolds perfectly with high probability. Our analysis demonstrates concrete benefits of depth and width in the context of a practically-motivated model problem: the depth acts as a fitting resource, with larger depths corresponding to smoother networks that can more readily separate the class manifolds, and the width acts as a statistical resource, enabling concentration of the randomly-initialized network and its gradients. Next, we turn our attention to the design of specific network architectures for achieving invariance to nuisance transformations in vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of transformations, making them unable to cope with natural variabilities in visual data such as changes in pose and perspective. We identify a common limitation of these approaches---they rely on sampling to traverse the high-dimensional space of transformations---and propose a new computational primitive for building invariant networks based instead on optimization, which in many scenarios provides a provably more efficient method for high-dimensional exploration than sampling. We provide empirical and theoretical corroboration of the efficiency gains and soundness of our proposed method, and demonstrate its utility in constructing an efficient invariant network for a simple hierarchical object detection task when combined with unrolled optimization. Together, the results in this thesis establish the first end-to-end theoretical guarantees for training deep neural networks with data with nonlinear low-dimensional structure, and provide a methodology to translate these insights into the design of practical neural network architectures with efficiency and invariance benefits.

<p>In this thesis, we present the results for the finite frequency response of a variety of materials. These materials all share the common theme that their low energy excitations are Dirac-like. This coincidence was not by design, and highlights the now-ubiquitous nature of Dirac-quasiparticles in condensed matter physics. We present results for graphene, the high temperature superconducting cuprates, and Weyl semi metals. For graphene, our calculations revolve around a new experimental technique: Near field infrared spectroscopy. Conventionally it is ok to use the $\vec{q}\rightarrow 0$ limit when calculating the low energy optical response. This new technique is able to directly probe the finite $\vec{q}$ response by using an atomic force microscope tip as an antenna. We computed the optical conductivity of graphene at finite wavevector and studied how the quasiparticle peak is altered by disorder and the electron-phonon interaction. The calculations on the high $T_c$ cuprates use a model of the pseudogap phase known as the Yang, Rice and Zhang (YRZ) model. We employed the model to study the resistivity in the pseudogap regime, both in-plane and along the c-axis. We used a coherent tunneling matrix element to describe transport along the c-axis. We found that the model was able to reproduce the metaliclike behavior in the plane while being resistive out of plane. We then extended the model to the finite frequency response, as well as the superconducting phase. We found a pseduogap feature at finite frequency that was previously explained through an interlayer collective mode. We also found that microwave spectroscopy puts strong limits on the form of the scattering rate. Finally, we computed the optical response of Weyl semimetals subjected to an applied magnetic field. Weyl semimetals are a topological phase of matter that have yet to be observed. The form of the conductivity contains a series of asymmetric peaks, whose spacing is a signature of the underlying relativistic dispersion. These peaks remain robust, even with moderate disorder.</p> / Doctor of Philosophy (PhD)

This thesis presents the investigation of magnetism in a selection of low-dimensional systems and its relation to other physical properties, such as superconductivity. The techniques employed are muon spin rotation and pulsed magnetic field magnetisation. The ability of muons to directly probe the local field is used to study SrFeAsF, which is a parent compound of the high-temperature superconducting pnictides. This revealed that the magnetic and structural transitions are separated in this system. I then demon- strate the coexistence of magnetism and superconductivity in NaFeAs for the first time. This discovery is of great interest since the interplay between magnetism and supercon- ductivity is thought to play an important role for high-temperature superconductivity. I further investigate the effect of partially replacing Fe with Co in NaFeAs. I study the ordering and spin reorientation in the Mott insulator Sr₂IrO₄, which has been suggested as a possible high-temperature superconductor. The complex magnetism observed in this system is contrasted to that in related iridates Ca₄IrO₆, Ca₅Ir₃O₁₂ and Sr₃Ir₂O₇. By combining pulsed-field magnetization and low magnetic field experiments with μSR on a series of coordination polymers. I am able to determine the size and direction of the magnetic exchange interaction. I demonstrate how it is possible to adjust the in- teractions by altering the molecular architecture of these Cu-based spin- 1 2 compounds. This is a significant contribution since it will lead to the targeted design of magnetic systems that can be utilized to experimentally test fundamental theories of magnetism.

Neste trabalho utilizamos o método k.p na aproximação de função envelope, que é uma ferramenta muito útil para a solução de problemas relacionados a heteroestruturas em geral. Apresentamos a análise de heteroestruturas semicondutoras com confinamento espacial nas três direções de crescimentos {Quantum Dots}, utilizando o Hamiltoniano de Kane (8x8) em sua forma generalizada para descrever os estados do elétrons na banda de condução e na banda valência. Fazendo uso dessa ferramenta foram realizadas simulações de estruturas de banda em sistemas quase zero-dimensionais de InAs em matrizes de GaAs, em vários formatos e dimensões e sob diferentes estados de tensionamento. Um estudo sistemático de como as propriedades geométricas e as dimensões de um dado sistema podem influenciar os estados eletrônicos do mesmo foi também realizado, onde puderam ser confirmadas a presença de estados localizados e a sensibilidade do comportamento dos estados eletrônicos a estas propriedades. Pudemos observar um deslocamento para o vermelho no espectro de fotoluminescência com o aumento das dimensões do sistemas estudados. Foram ainda realizados cálculos de {Quantum Dots} de InN em matriz de GaN, que permitem explorar outras regiões do espectro eletromagnético e observamos o comportamento dos mesmos sob estados de tensionamentos diferentes. Com base nos autoestados do sistema foram calculados espectros de fotoluminescência para as heteroestruturas aqui estudadas, permitindo uma comparação direta com resultados experimentais. Como pode-se verificar o strain exerce importância primordial na determinação dos estados eletrônicos dos sistemas estudados e na presença do hidrostático pode-se verificar mudanças apreciáveis na resposta óptica do material, onde pode ser observado um deslocamento para o azul quando levado em consideração a presença de um hidrostático. / In this work, we use the k.p method in the approximation of the envelope function, that is a very useful tool, to the solution of heterostructure related problems. We present a semiconductor heterostructure analysis with confinement on the three directions (Quantum Dots), using the Kane Hamiltonian (8x8) on its generalized form to describe electron eigenstates on the conduction and valence bands. Using this tool, we have made band structure simulations in quasi zero-dimensional systems of InAs in GaAs matrices, in diverse shapes and dimensions and on different tension states. A systematic study of how the geometrical properties and dimensions of a given system could influence the electronic states was also done. There can be confirmed the presence of localized states and the sensitivity of the electronic states to these properties.We could observe a deviation to the red on the photoluminescence spectrum with the increase of the system dimensions. There were also made calculations on InN dots in a GaN matrix, which allow to explore other electromagnetic spectral regions and we have studied their behavior under different tension states. From the system eigenvalues, we calculated the photoluminescence spectra from the heterostructures studied here, allowing a direct comparison with experimental results. It can be verified that the strain is is extremely important on the determination of the electronic states of the studied systems in the presence of an hydrostatic strain. We could observe important modifications on the optical responseof the material, where there is a deviation to the blue when it is considered the presence of the hydrostatic strain.

Orientador: Guillermo Gerardo Cabrera Oyarzun / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Abstract: Quantum spin systems are caracterized by huge spaces of states, whose dimensions grow exponentially with the particles number. If following the preparation of the initial state, the system is kept isolated from external variables, it will develop a unitary time evolution according to Schrödinger equation or to Liouville equation. The system is driven exclusively by quantum uctuations, whose origin is the Uncertainty Principle. The evolution of a quantum state or a physical observable or mathematical nonobservable operator mean values may involve all states of the whole space of states, or big or small fractions of the total number of states. The analysis of the relaxation of a spin system from an arbitrary initial state to the equilibrium has to cope in general with the difficulty of requiring an extraordinarily great number of eigenstates and eigenvalues. In this work the main interest is centered on the evolution of magnetization¿s Fourier components in low dimensional systems of spins 1/2, whose interactions be given by the exchange modeled by Heisenberg Hamiltonians with axial anisotopy, XXZ. Exact solutions, analitic or numeric, are obtained. This is the continuation of work done in our research group which dealt with XY Hamiltonian families. In the analysis of the systems with the Hamiltonian XXZ, it was specially analysed the subspace defined by null total magnetization and the subspace defined by one spin wave, where chains up to 14 and 1200 were treated, respectively. There are emergence of fast and slow relaxation processes, which depend on the interations and on the initial state, and which result from destructive or constructive quantum interferences. Connections between the presence of those processes and the energy spectrum structure is discussed. Finally, the time evolution of some measures of global entanglement from initial states in the subspace of one spin wave are analised: the considered dynamics creates global entanglement until each entanglement measure reaches a saturation / Made available in DSpace on 2018-09-24T18:24:44Z (GMT). No. of bitstreams: 1 Carvalho_JulioGarcia_D.pdf: 5851086 bytes, checksum: fe9467d4e143df319d98e75ddb334401 (MD5) Previous issue date: 2006 / Resumo: Os sistemas quânticos de spin são caracterizados por espaços de estados muito grandes, cujas dimensões crescem exponencialmente com o número de partículas. Se após a preparação do estado inicial, o sistema for mantido isolado de variáveis externas, desenvolve-se uma evolução temporal unitária prescrita pela equação de Schrödinger ou pela equação de Liouville. O sistema é movido exclusivamente por flutuações quânticas, as quais têm sua origem no Princípio da Incerteza. A evolução de um estado quântico ou de valores médios de observáveis físicos ou de operadores matemáticos não observáveis pode envolver todos os estados do espaço de estados, ou frações grandes ou pequenas do número total de estados. A análise da relaxação de um sistema de spins desde um estado inicial arbitrário até o equilíbrio apresenta a dificuldade de requerer em geral um número extraordinariamente grande de auto-estados e autovalores. Neste trabalho o maior interesse está na evolução das componentes de Fourier da magnetização em sistemas de baixa dimensão espacial, com spins 1/2 e cujas interações sejam dadas pela troca modelada por Hamiltonianos de Heisenberg com anisotropia axial, XXZ. Serão obtidas soluções exatas: numéricas ou analíticas. A motivação proveio de trabalhos anteriores realizados no grupo de pesquisa referentes a famílias do Hamiltoniano XY. Ao se considerar o Hamiltoniano XXZ, analisou-se especialmente o subespaço definido por magnetização total nula e o subespa¸ co de uma onda de spin, onde trataram-se cadeias com até 14 e 1200 sítios, respectivamente. Há emergência de processos rápidos e lentos de relaxação, os quais dependem das interações e do estado inicial, e resultam de interferência quântica destrutiva ou construtiva. Serão discutidas conexões entre a presença desses processos e a estrutura do espectro de energia. Finalmente serão analisadas as evoluções temporais de algumas medidas de emaranhamento global, a partir de estados contidos no subespaço de uma onda de spin: a dinâmica considerada cria emaranhamento global até cada medida atingir uma saturação / Doutorado / Física da Matéria Condensada / Doutor em Ciências

Ce travail de thèse porte sur l'étude par la résonance paramagnétique électronique (RPE) des sels à transfert de charge quasi-unidimensionnels (TMTTF)$ {2}$X (X=AsF$ {6}$, PF$ {6}$, SbF$ {6}$), matériaux modèles de chaînes de spins quantiques. Tout d'abord, nous avons examiné en onde continue et sur une large gamme de température et de fréquence, la phase d'ordre de charge déjà observée dans ces matériaux en dessous de la température T$ {CO}$. Nous avons mis en évidence deux nouveaux phénomènes à T < T$ {CO}$: la rotation des axes principaux du facteur g et une modification structurale liée à un dédoublement de la maille cristallographique. Un calcul de chimie quantique a été réalisé à l'aide de la méthode DFT confirmant nos résultats expérimentaux. Dans la seconde partie de ces travaux de thèse, nous avons présenté les résultats obtenus par RPE en onde continue et en onde pulsée sur l'étude des défauts corrélés dans les systèmes à chaînes de spins. En onde continue, nous avons détecté pour la première fois une raie RPE fine à basse température, suggérant la présence de défauts corrélés ayant les caractéristiques de solitons. Les mesures par RPE pulsée nous ont permis d'observer les premières oscillations de Rabi de solitons piégés et de déterminer leur caractère robuste. Ces derniers résultats offrent une approche alternative aux qubits à base de spins pour le traitement de l’information quantique. / This thesis focuses on the study by Electron Paramagnetic Resonance (EPR) of the quasi-one-dimensional charge transfer salts (TMTTF)$ {2}$X (X=AsF$ {6}$, PF$ {6}$, SbF$ {6}$), model materials of quantum spin chains. First, we have examined in continuous wave and on a wide range of temperature and frequency, the charge-ordered phase already observed in these materials below the temperature T$ {CO}$. We have identified two new phenomena at T <T$ {CO}$: the rotation of the principal axes of the g factor and a structural change related to a doubling of the unit cell parameter. A quantum chemical calculation was carried out using DFT confirming our experimental results. In the second part of the thesis, we have presented the results obtained by EPR in continuous wave and pulsed wave on the correlated defects study in spin chain systems. In continuous wave, we have detected for the first time a narrow EPR line at low temperature, suggesting the presence of correlated defects having the characteristics of solitons. The pulsed EPR measurements allowed us to observe the first Rabi oscillations of trapped solitons and to determine their robust character. These latter results offer an alternative approach for spin qubits in quantum information processing.

In this dissertation we reported our experimental investigation of the magnetic properties of nine low-dimensional vanadium compounds. Two of these materials are completely new (Pb2V5O12 and Pb2VO(PO4)2) and were found during our search for new low-dimensional vanadium oxides. Among the other seven vanadium compounds studied, three were physically investigated for the first time (Sr2VO(PO4)2, BaZnVO(PO4)2 and SrZnVO(PO4)2). Two had hitherto only preliminary, and wrongly interpreted, susceptibility measurements reported in the literature (Sr2V3O9 and Ba2V3O9) while the remaining two (Li2VOSiO4 and Li2VOGeO4) were previously investigated in some detail but the interpretation of the data was controversial. We investigated the magnetic properties of these materials by means of magnetic susceptibility and specific heat (Cp(T)) measurements (as well as single crystal ESR measurements in the case of Sr2V3O9). We synthesized the samples necessary for our physical studies. That required a search of the optimal synthesis conditions for obtaining pure, high quality, polycrystalline samples. Single crystals of Sr2V3O9 and Pb2VO(PO4)2 were also successfully grown. Pb2VO(PO4)2, BaZnVO(PO4)2, SrZnVO(PO4)2, Li2VOSiO4 and Li2VOGeO4 were found to be experimental examples of frustrated square-lattice systems which are described by the J1-J2 model. We found that Li2VOSiO4 and Li2VOGeO4 posses a weakly frustrated antiferromagnetic square lattice while Pb2VO(PO4)2, BaZnVO(PO4)2 and SrZnVO(PO4)2 form a more strongly frustrated ferromagnetic square lattice. Pb2V5O12 is structurally and compositionally related to the two dimensional A2+V4+nO2n+1 vanadates. Its structure consists of layers formed by edge- and corner-shared square VO5 pyramids. The basic structural units are plaquettes consisting of six corner-shared pyramids pointing in the same direction, which form a spin lattice of novel geometry. / In dieser Dissertation berichteten wir über unsere experimentelle Untersuchung der magnetischen Eigenschaften von neun Niedrigdimensionalen vanadiumverbindungen. Zwei dieser Materialien sind vollständig neu (Pb2VO12 und Pb2VO(PO4)2) und wurden während unserer Suche nach neuen Niedrigdimensionalen Vanadiumoxiden gefunden. Unter den anderen sieben studierten Vanadiumverbindungen, wurden drei physikalisch zum ersten Mal nachgeforscht (Sr2VO(PO4)2, BaZnVO(PO4)2 und SrZnVO(PO4)2). Zwei hatten bisher nur einleitendes, und falsch gedeutet, magnetische Susceptibilitaet Messungen, die in der Literatur berichtet wurden (Sr2V3O9 und Ba2V3O9) während die restlichen zwei (Li2VOSiO4 und Li2VOGeO4) vorher in irgendeinem Detail aber in der Deutung der Daten waren umstritten nachgeforscht wurden. Wir forschten die magnetischen Eigenschaften dieser Materialien mittels der magnetischen Susceptibilitaet und der spezifischen Waerme (Cp(T)) nach (sowie ESR-Messungen des einzelnen Kristalles im Fall von Sr2V3O9). Wir synthetisierten die Proben, die für unsere körperlichen Studien notwendig sind. Das erforderte eine Suche der optimalen Synthesezustände für das Erreichen der reinen, hohen Qualität, polykristalline Proben. Einzelne Kristalle von Sr2V3O9 und von Pb2VO(PO4)2 wurden auch erfolgreich gewachsen. Pb2VO(PO4)2, BaZnVO(PO4)2, SrZnVO(PO4)2, Li2VOSiO4 und Li2VOGeO4 werden gefunden, um experimentelle Beispiele der frustrierten Quadrat-Gittersysteme zu sein, die durch das J1-j2 model. Wir fanden daß posses Li2VOSiO4 und Li2VOGeO4 ein schwach frustriertes antiferromagnetische quadratisches Gitter, während Pb2VO(PO4)2, BaZnVO(PO4)2 und SrZnVO(PO4)2 ein stärker frustriertes ferromagnetisches quadratisches Gitter bilden. Pb2V5O12 strukturell und zusammenhängt kreativ mit den zweidimensionalen vanadates A2+V4+nO2n+1 beschrieben werden. Seine Struktur besteht aus den Schichten, die durch Rand und Ecke-geteilte quadratische Pyramiden VO5 gebildet werden. Die grundlegenden strukturellen Maßeinheiten sind die plaquettes, die aus sechs Ecke-geteilten Pyramiden bestehen, die in die gleiche Richtung zeigen, die ein Drehbeschleunigunggitter von Romangeometrie bilden.