In this thesis we investigate the frustrated spin liquid Tb$_2$Ti$_2$O$_7$ theoretically. The low-energy effective Hamiltonian of this compound is derived by integrating out the excited crystal field states. It is shown that the pairwise interaction in the effective Hamiltonian is renormalized by all the other Tb$_2$Ti$_2$O$_7$ ions in the system and dynamically generate frustration. The phase diagram of Tb$_2$Ti$_2$O$_7$ in the single tetrahedron approximation is calculated. It is shown that Tb$_2$Ti$_2$O$_7$ is in a singlet state which is a linear combination of all frustrated two-in/two-out states. Motivated by experimental results, the diffuse neutron scattering of Tb$_2$Ti$_2$O$_7$ is obtained within the single tetrahedron approximation. This diffuse neutron scattering captures semi-quantitatively most of the experimental neutron scattering features. The magnetization of Tb$_2$Ti$_2$O$_7$ in the single tetrahedron approximation is calculated. Two experiments based on diffuse neutron scattering and magnetization in high symmetry directions are proposed to verify the spin ice like ground state of Tb$_2$Ti$_2$O$_7$.

The synthetic routes to the salts of the 3H-naphtho[1,2-d][1,2,3]dithiazolylium cation and its three selenium containing variants are described. The most efficient approach involves the condensation of bis-acetylated aminoselenolates and aminothiolates with sulfur and selenium halides. Cyclic voltammetry experiments illustrate that the four cations can be reduced to their neutral radical state and are stable in solution. The EPR spectra of all four radicals have been recorded and the spin distributions have been compared with those obtained from DFT calculations. It has been found that the selenium containing radicals are thermally unstable at room temperature, but the all sulfur species has been isolated and characterized by X-ray crystallography. In the solid state, the radicals associate into cofacial dimers and short interdimer S---Sʹ, S---Nʹ and C---Hʹ contacts are observed. The all-selenium species has been characterized in its oxidized state by X-ray crystallography. A series of four challenging crystallographic projects are presented. (1) 8-Phenyl-4-methyl-4H-bis[1,2,3]thiaselenazolo[4,5-b:5ʹ,4ʹ-e]pyridinyl has been prepared and its solid-state structure determined by powder X-ray diffraction methods. The radical crystallizes in the space group P3121 and is isostructural with its ethylated derivative and its all-sulfur containing analogue. Variable-temperature magnetic measurements confirm that the radical is an undimerized S = ½ system with weak intermolecular antiferromagnetic coupling. Pressed pellet variable-temperature electrical conductivity measurements provide a room-temperature conductivity (σRT) of 3.3 ×10-5 S cm-1 and an activation energy (Eact) of 0.29 eV. The results of Extended Hückel Theory (EHT) band structure calculations are presented. (2) Single-crystal and powder X-ray diffraction methods on a family of selenium-containing radicals based the 4-methyl-3H,4H-bis[1,2,3]dithiazolo[4,5-b:5ʹ,4ʹ-e]pyridin-3-yl radical are presented. All three radicals (SSN, SSeN and SeSeN) are isostructural, crystallizing in the space group P212121, and form slipped π-stacks of undimerized radicals with close E---Eʹ contacts. Pressed pellet variable-temperature electrical conductivity measurements of the systems provide σRT = 3 × 10-4 and 1 × 10-3 S cm-1 and Eact of 0.24 eV and 0.17 eV for the SSeN and SeSeN radicals respectively. (3) The crystal structures of 4-methyl-4H-bis[1,2,3]dithiazolo[4,5-b:5ʹ,4ʹ-e]pyrazin-3-yl at 298 K, 123 K and 88 K are presented. At 298 K the radicals remain undimerized, crystallizing in the space group Cmca and forming evenly-spaced π stacks. Upon cooling to 123 K the space group symmetry is lowered by loss of C-centering to Pccn such that the radicals are not evenly spaced within the π-stack. At 88 K a further lowering of space group symmetry to P21/c is observed. (4) [1,3,2]Dithiazolo[4,5-b]pyridin-2-yl is polymorphic, crystallizing in P21 and P21/n. A non-merohedral twin law is required to model the P21 system. The structures of both crystals are comprised of layers of head-to-head π dimers and the two structures differ in the orientation of the π dimers along the stacks. Variable-temperature magnetic data reveal that both phases are essentially diamagnetic at low temperatures and form weak π dimers at higher temperatures. Synthetic methods have been developed to generate the complete series of resonance stabilized heterocyclic thia/selenazyl radicals based on 8-chloro-4-ethyl-4H-bis[1,2,3]dithiazolo[4,5-b:5ʹ,4ʹ-e]pyridin-3-yl. X-ray crystallographic studies confirm that all four radicals are isostructural, belonging to the tetragonal space group P21m. The crystal structures consist of slipped π-stack arrays of undimerized radicals. Variable temperature conductivity measurements reveal an increase in conductivity with increasing selenium content, with σRT reaching a maximum of 3.0 × 10-4 S cm-1 with an Eact of 0.19 eV for the all-selenium containing variant. Variable temperature magnetic susceptibility measurements indicate that all four radicals exhibit S = ½ Curie-Weiss behaviour over the temperature range 20 - 300 K. At lower temperatures, the three selenium-based radicals display magnetic ordering. The first radical with selenium positioned at the E1 site, undergoes a phase transition at 14 K to a weakly spin-canted (φ = 0.010̊) antiferromagnetic state. By contrast, the radical containing the apical selenium and the all-selenium variant, which both possess selenium in the E2 position, order ferromagnetically, with Curie temperatures (Tc) = 12.8 K and 17.0 K respectively and coercive fields Hc at 2 K of 250 Oe and 1370 Oe respectively. The transport properties of the entire series of radicals are discussed in the light of EHT band-structure calculations. A series of bis-thiaselenazolyl radicals (R2BPTSR1) based on the bis-[1,2,3]-thiaselenazolo[4,5-b:5',4'-e]pyridin-3-yl (R1 = Et, Pr and CF3CH2, R2 = Cl; R1 = Et, R2 = Me and Br) have been prepared and characterized by X-ray crystallography. The radicals are formally isostructural, all belonging to the tetragonal space group P21m. The crystal structures consist of slipped π-stack arrays of undimerized radicals packed about centers. Variations in R1 (Et, Pr, CF3CH2) with R2 = Cl lead to significant changes in the degree of slippage of the π-stacks and hence the proximity of the Se---Seʹ contacts. By contrast, variations in R2 (Cl, Br, Me) with R1 = Et induce very little change in either the slippage angle or the Se---Seʹ contacts. Variable temperature conductivity measurements show relatively constant values for σRT (10-5 - 10-4 S cm-1) and Eact (0.27 - 0.31 eV) across the entire series. Variable temperature magnetic susceptibility measurements indicate major differences in the magnetic behaviour. Radicals with R1 = Pr, CH2CF3, R2 = Cl behave as weakly antiferromagnetically coupled Curie-Weiss paramagnets, but radicals with R1 = Et; R2 = Cl, Me, Br demonstrate ferromagnetic ordering, with Tc values of 12.8 K (R2 = Cl), 13.6 K (R2 = Me), and 14.1 K (R2 = Br).

<p>Complex artificial materials (metamaterials) strongly interact with light and can be used to fabricate structures which mimic a material response that has no natural equivalent. Classical tools for the design of optical or radio frequency devices are often ill-suited to utilize such media or have shortcomings in their ability to capture important physics in the device behavior. Recently it has been demonstrated that the structure of Maxwell's equations can be used to exploit this newly available freedom. By leveraging the `form-invariance' of Maxwell's equations under coordinate transforms, it is possible to develop material distributions in which light will behave as though flowing through warped coordinates. This design process is termed `transformation optics' and has inspired the creation of many novel electromagnetic structures such as the invisibility cloak.</p><p>In this dissertation the tools used in the field of transformation optics will be explored and expanded. Several new designs are discussed, each of which expands upon the ideas that have previously been employed in the field. To begin, I show that the explicit use of a transformation which extends throughout all space may be used to reduce the overall size of an optical device without changing its optical properties. A lens is chosen as a canonical device to demonstrate this behavior. For this work I provided the original idea for a compressing transformation as well as its dielectric-only implementation. I then mentored Dan Roberts as he confirmed the device properties through simulation. I further demonstrate that currents may be succesfully employed within the framework of transformation optics-resulting in novel antenna designs. For this work I suggested handling the sheet currents as the limit of a volumetric current density. I also demonstrated how an intermediate coordinate system could be used to easily handle the types of transformatios which were being explored.</p><p>For a particular functionality the choice of transformation is, in general, not unique. It is natural, then, to seek optimized transformations which reduce the complexity of the final structure. It was recently demonstrated that for some transformations a numerical scheme could be employed to find quasi-conformal transformations for which the requisite complex material distribution could be well approximated by an isotropic, inhomogeneous media. This process was previously used to demonstrate a carpet cloak-a device which masks a bump in a mirror surface. Unlike the more common transformation optical media, which exhibit strong losses at high frequencies, isotropic designs can be readily made to function at infrared or even optical frequencies.</p><p>The prospect of leveraging transformation optics in devices which operate at high frequencies, into the infrared and visible, motivates the use of quasi-conformal transformations in lens design. I demonstrate how transformation optics can be used to take a classical lens design based on spherical symmetry, such as a Luneburg lens, and warp it to suit the requirements of a planar imaging array. I report on the experimental demonstration of this lens at microwave frequencies. In the final design a lens is demonstrated in a two-dimensional field mapping waveguide to have a field of view of ~140 degrees and a bandwidth exceeding a full decade. In this work I proposed the idea of using the inverse of the quasi-conformal transform to arrive at the lens index profile. I performed all necessary simulations and wrote ray tracing code to confirm the properties of the lens. I proposed the metamaterial realization of the lens and performed the necessary retrievals for material design. I wrote code which would create the layout for an arbitrary gradient index structure in a standard computer aided drafting format. I fabricated three lenses-two of which are described in this thesis-and took all of the data shown in the thesis.</p><p>The most well known example of a transformation optical device is the invisibility cloak. Despite the great deal of attention paid to the cloak in the literature, the most natural way in which to quantify the efficacy of the cloak-its cross-section-has never been experimentally determined. This measurement is of practical interest because the cloak provides a useful canonical example of a medium which relies on the unique properties of metamaterials-strong anisotropy, inhomogeneity and both magnetic and electric response. Thus, a cloaking cross-section measurement provides a useful way to quantify advancements in the effective medium theories which form the basis for metamaterials. I report on the first such measurements, performed on the original microwave cloaking design. The experiments were carried out in a two-dimensional TE waveguide. Explicit field maps are used to determine the Bessel decomposition of the scattered wave. It is found that the cloak indeed reduces the scattering cross-section of a concealed metal cylinder in a frequency band from 9.91 to 10.14 GHz. The maximum cross-section reduction was determined to be 24%. The total cross-section and the Bessel decomposition of the scattered wave are compared to an analytical model for the cloaking design which assumes a discrete number of loss-less, homogenized cylinders. While the qualitative features of the cloak-a reduced cross-section at the cloaking frequency-are realized, there is significant deviation from the homogenized calculation. These deviations are associated with loss and inaccuracies of the effective-medium-model for metamaterials. In this work I proposed of direct integration of the fields to perform cross-section measurements. I worked out the necessary formulas to determine the coefficients in the Bessel expansion and the resulting scattering cross-section. I mentored an undergraduate student, Dan Gaultney, who scripted the application of the cross-section analysis and took the necessary data. All of the data in this thesis, however, is based on my own implementation of the data analysis.</p> / Dissertation

This dissertation concerns the use of bicyclic guanidinate ligands to prepare new dimetal paddlewheel compounds. Specifically, Ru_2^6+, Re_2^6+, Re_2^7+, and Os_2^7+ compounds will be examined to observe any changes brought about by using bicyclic guanidinate ligands with varying ring sizes. In the Ru_2^6+ compounds, different ligand ring sizes cause a change in the electronic configuration and magnetic properties. Bicyclic guanidinate ligands allow the preparation of Re_2^7+ compounds from Re_2^6+ compounds, both of which are examined structurally and electrochemically. [Os2(hpp)4]^+ is examined to improve upon earlier studies, yielding a model of the g-tensor components with respect to the compound structure. An additional project included in the dissertation involves the study of an asymmetric trinickel extended metal atom chain. The structural effects of the asymmetry are examined to help elucidate the magnetic behavior that differs significantly from symmetric trinickel extended metal atom chains.

Results of spin density functional theory (SDFT) calculations were used to construct and check features of a generally applicable semi-quantitative approach to understanding magnetic coupling in gadolinium-containing molecules, clusters, and solids. Using fragments based on structures of metal-rich lanthanide compounds, we have investigated molecular and low-dimensional extended structures, and have shown that open-d-shell clusters facilitate strong ferromagnetic coupling whereas closed-d-shell systems prefer antiferromagnetic coupling. The qualitative features can be interpreted using a perturbative molecular orbital (PMO) model that focuses the influence of the 4f 7- d exchange interaction on the d-based molecular orbitals. The f-d exchange interaction, mediated by spin polarization of both filled and partially-filled metal-metal bonding orbitals, is described for the model system Gd3I6(OPH3)12 n+ using basic perturbation methods. This approach is successful for predicting the magnetic ground state for Gd2Cl3, a semiconducting system for which calculations predict antiferromagnetic ordering of the 4f 7 moments in a pattern consistent with published neutron diffraction data. An attempt to account for the calculated magnetic energies of spin patterns using an Ising model was unsuccessful, indicating that the Ising model is inappropriate. Instead, the d-electron mediated f-f exchange interaction was interpreted using our basic perturbation theory approach. Computed density of states and spin polarization information was used to support the perturbation-theoretic analysis. This method has also been successful evaluating the ground state for Gd[Gd6FeI12]. Using the model [Gd6CoI12](OPH3)6, which has three unpaired electrons in the HOMO, the 4f moments prefer spin alignment with the unpaired electrons in the system and the ferromagnetic 4f 7 spin arrangement is the ground state. We have extended our analysis of R6X12 clusters to include nonmetal interstitial atoms, the bioctahedral cluster compounds Gd10Cl17C4 and Gd10I16C4, and Gd5(O)(OPri)5. Finally, we have shown that we can successfully predict the ground state magnetic structures of several metallic and semiconducting Gd-containing compounds, Gd2Cl3, GdB2C2,alpha-Gd2S3, Gd5Si4, and Gd5Ge4, using semi-empirical calculations which closely simulates the exchange effects exerted by the 4f electrons. In a more speculative vein, ideas concerning the incorporation of anisotropic rare-earth metal atoms to the cluster framework are touched upon.

Ferric ferrocyanide (Prussian blue) and its analogues are renowned for the variety of properties and applications associated with them. At the same time, however, they suffer from issues related to their variable composition and poor crystallinity. As a result, we are preparing discrete cyanide-bridged clusters both to mimic these materials and to search for properties unique to the molecule, such as single molecule magnetism. The work in this dissertation has focused on the expansion of series of trigonal bipyramidal (TBP) cyanide-bridged clusters, [M(tmphen)2]3[M′(CN)6]2, that exhibit a variety of properties including spin crossover, charge-transfer-induced spin transition, and photomagnetism. One goal of the work was focused on the preparation of new paramagnetic TBP clusters incorporating various 3d metal ion combinations. Nine new clusters were prepared and characterized, including several “model compounds” with only one type of paramagnetic metal ion. The magnetic properties of these model compounds were combined to better explain the coupling through the cyanide ligands in clusters with two paramagnetic metal centers. An additional two clusters were also prepared that were found to exhibit a thermally induced LS Fe^II -> HS Fe^II transition. The spin crossover event was confirmed by magnetic susceptibility and Mössbauer spectroscopy, and variable temperature X-ray crystallography revealed the transitions to be distinct for each FeII center and dependant on the interstitial solvent. Another major goal of the work was to investigate the TBP clusters for their potential to be used as building-blocks to prepare 1-D extended structures of linked clusters, such as a {[Co(tmphen)2]3[Fe(CN)6]2[Mn(MeOH)4]}∞(ClO4)3 chain. A final research goal was a search for photomagnetic behavior, the change in magnetic properties with irradiation, related to spin transitions in several key TBP clusters. The Fe3Fe2 and Fe3Co2 TBP clusters were found to exhibit a light-induced excited spin state trapping (the LIESST effect) similar to that observed in mononuclear FeII compounds, and the photo-induced charge transfer that has been observed in Co-Fe Prussian blue materials is mimicked by the Co3Fe2 TBP molecular analogue.

This dissertation investigates three topics in the field of multiple-bonded metal chemistry. The first topic concerns the synthetic and theoretical considerations of ditungsten formamidinates and guanidinates compounds. This work presents an enhanced synthetic path to the W2(hpp)4 molecule (Hhpp = 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine). The reflux of W(CO)6 with Hhpp in o-dichlorobenzene at 200 oC produces W2(hpp)4Cl2 in a one-pot reaction in 92% yield. This compound is stable and easily stored for further use, and it can be efficiently reduced in a one-step reaction to the most easily ionized compound W2(hpp)4. This work also examines the electronic structure and geometry of the intermediates W2(µ-CO)2(µ- hpp)2(η2-hpp)2 and W2(hpp)4Cl2. The second topic concerns the theoretical investigation by DFT of the electronic structure of [Mo2] units bridged by oxamidate ligands or bridging hydride ions ([Mo2] = (Mo2(DArF)3, where DArF is the anion of a diarylformamidine). It is shown that the effect of the gauche conformation of the α oxamidate isomers is due to steric interactions, and that the planar β oxamidate isomers have an electronic structure similar to that of naphthalene when it is doubly oxidized. The [Mo2](µ-H)2[Mo2] compound shows interdimetal unit interactions between the δ orbitals of the two [Mo2] units. These interactions are theoretically predicted and experimentally observed by a decrease in the [Mo2]---[Mo2] distance with a one-electron oxidation of [Mo2](µ- H)2[Mo2]. The final topic concerns the magnetic and structural properties of two Ru2(DArF)4Cl compounds. The compounds with Ar = p-anisyl (para) and m-anisyl (meta) both show different temperature dependence of their molar magnetic susceptibility, χ. For the para compound, there is a Boltzmann distribution between a π*3 ground state and a δ*2π* upper state, and this is confirmed by a temperature dependence of the Ru-Ru bond length: 2.4471(5) àat 23 K and 2.3968(5) àat 300 K. For the meta compound, a δ*2π*configuration persists over the range of 23-300 K as shown by an invariant Ru-Ru bond length and its molar magnetic susceptibility.

Thèse : Mathématiques : Paris, Faculté des sciences : 1888. / Titre provenant de l'écran-titre. Notes bibliogr.

The potential of terahertz time domain spectroscopy has until recently been neglected in the field of the ultrafast magnetism. At the same time this technique can serve as a useful complementary tool with respect with conventional methods to investigate ultrafast magnetization dynamics. This thesis aims to implement time domain terahertz spectroscopy to observe high frequency spin waves excited optically in different magnetic systems. This work covers several distinct phenomena related to the study of spin waves (magnonics) at terahertz frequencies. The generation of transient broadband nonlinear magnetization via inverse Faraday effect in terbium gallium garnet is described in chapter 4. We demonstrate a remarkable discrepancy of at least two orders of magnitude between the strengths of the direct and inverse Faraday effects, thereby challenging the commonly accepted understanding of their relationship. Additionally, a striking nonlocality of the optical response is found. In chapter 5 the results of THz absorption spectroscopy of the terbium gallium garnet are reported. The garnet exhibits an intricate paramagnetic state with several magnetic sub-lattices at cryogenic temperatures under the application of strong magnetic fields. Some precessional modes of these sub-lattices were measured. The components of the g-tensor of terbium ions were extracted from the data. In chapter 6 the ultrafast magnetization dynamics of thulium orthoferrite, studied my means of terahertz spectroscopy, is described. It is demonstrated that terahertz response of the orthoferrite provides crucial additional information with respect to the optical pump-probe signal. A novel exchange driven mechanism of optical manipulation of the magnetic state is demonstrated. Finally, chapter 7 is a theoretical discussion of so called planar magnonic metamaterials. It is shown that the arrays of ferromagnetic films may exhibit negative refraction index at sub-terahertz frequencies, provided the mechanism of spin wave quantization is introduced. The thesis ends with a brief conclusions chapter where a short summary of the results is given. Some possible future extensions of the conducted research are drawn as well.

Process generated particle contamination on unpatterned silicon wafers etched in an SF6/argon plasma using a Tegal MCR-1 etcher in the plasma triode-1 mode was characterized using response surface methodology. Particle deposition was observed to be a predictable function of plasma parameter space, which can be determined by relatively few statistically designed experiments. A model of particle deposition as a function of 13.56 MHz chamber electrode rf power, chamber pressure, gas flow rate, etch time and 100 kHz wafer electrode power was constructed. It is found that particle deposition depends linearly on etch time and both 13.56 MHz and 100 kHz power. In addition, particle deposition increased with gas flow rate at low flow rate, reaches a maximum, then decreased as flow rate increased further. Moreover, there was no observable effect on particle deposition due to pressure variation in the pressure range explored. Auger chemical analysis showed that the particles contained elemental sulfur, fluorine, silicon, aluminum, carbon and oxygen. Most particles were typically less than 2 μm in diameter.