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Heterogeneous ferromagnetic-superconducting systems such as a regular array of ferromagnetic nano dots deposited on the top of a superconducting thin film have attracted many research teams both experimental and theoretical. The interest in these systems does not only stem from being good candidates for technological applications, but also because they represent a new class of physical systems where two competing order parameters can coexist. This work focuses on the theoretica laspects of these systems by studying the static and dynamics of few model systems. In the first part, the static properties of a superconducting thin film interacting with a ferromagnetic texture are considered within the London approximation. In particular, the ferromagnetic textures considered here are a circular dot of submicrometer size with in-plane magnetization, an elliptical dot magnetized in the direction perpendicular to the superconductor, and a ferromagnetic dot magnetized in the direction normal to the superconducting film and containing non magnetic cavities. I also consider the interaction of vortices in the superconductor with a ferromagnetic columnar defect which penetrates the supercondcting film. In each case the vector potential and magnetic field of the ferromagnet in the presence of the superconductor are calculated. Afterward the presence of vortices in the superconductor is assumed and the energy of vortex-texture system is found. The pinning potential and force supplied by the texture are then derived from the energy of interaction between the ferromagnet and superconductor. I show that if the magnetization of the ferromagnet exceeds a critical value then vortices are spontaneously created in the ground state of the system. Such spontaneous creation of vortices is possible mostly in a close vicinity of the superconducting transition temperature Ts. For every case, the threshold value of the magnetization at which vortices start to be spontaneously created in the SC is calculated as a function of the parameters of the texture geometry. The phase diagrams for transitions from vortexless regime to regimes with one or more vortices are determined for all cases. In the second problem, the transport properties of a ferromagnetic superconducting bilayer with alternating magnetization and vortex density are studied within a phenomenological model. I show that pinning forces do not appear for continuous distribution of vortices, so a discrete model for the bilayer system is constructed. Afterward, I calculate the pinning forces acting on vortices and antivortices resulting from highly inhomogeneous distribution of flux lines and prove that this system has strong transport anisotropy. In the absence of random pinning, the system displays a finite resistance for the current in the direction perpendicular to the domains while its resistance vanishes for the parallel current. The transport anisotropy strongly depends on temperature. I study this dependence and show that the ratio of parallel to perpendicular critical current is largest close to the superconducting transition temperature Ts and the vortex disappearance temperature Tv while it has a minimum in between them.

Iron oxyhydroxides are ubiquitous in surface environments, playing a key role in many biogeochemical processes. Their characterization is made challenging by their nanophase nature. Magnetometry serves as a sensitive non-destructive characterization technique that can elucidate intrinsic physical properties, taking advantage of the superparamagnetic behaviour that nanoparticles may exhibit. In this work, synthetic analogues of common iron oxyhydroxide minerals (ferrihydrite, goethite, lepidocrocite, schwertmannite and akaganéite) are characterized using DC and AC magnetometry (cryogenic, room temperature), along with complementary analyses from Mössbauer spectroscopy (cryogenic, room temperature), powder X-ray diffraction and scanning electron microscopy. It was found that all of the iron oxyhydroxide mineral nanoparticles, including lepidocrocite, schwertmannite and akaganéite were superparamagnetic and therefore magnetically ordered at room temperature. Previous estimates of Néel temperatures for these three minerals are relatively low and are understood as misinterpreted magnetic blocking temperatures. This has important implications in environmental geoscience due to this mineral group’s potential as magnetic remanence carriers. Analysis of the data enabled the extraction of the intrinsic physical parameters of the nanoparticles, including magnetic sizes. The study also showed the possible effect on these parameters of crystal-chemical variations, due to elemental structural incorporation, providing a nanoscale mineralogical characterization of these iron oxyhydroxides. The analysis of the intrinsic parameters showed that all of the iron oxyhydroxide mineral nanoparticles considered here have a common magnetic moment formation mechanism associated with a random spatial distribution of iv uncompensated magnetic spins, and with different degrees of structural disorder and compositional stoichiometry variability, which give rise to relatively large intrinsic magnetization values. The elucidation of the magnetic nanostructure also contributes to the study of the surface region of the nanoparticles, which affects the particles’ reactivity in the environment.

Iron oxyhydroxides are ubiquitous in surface environments, playing a key role in many biogeochemical processes. Their characterization is made challenging by their nanophase nature. Magnetometry serves as a sensitive non-destructive characterization technique that can elucidate intrinsic physical properties, taking advantage of the superparamagnetic behaviour that nanoparticles may exhibit. In this work, synthetic analogues of common iron oxyhydroxide minerals (ferrihydrite, goethite, lepidocrocite, schwertmannite and akaganéite) are characterized using DC and AC magnetometry (cryogenic, room temperature), along with complementary analyses from Mössbauer spectroscopy (cryogenic, room temperature), powder X-ray diffraction and scanning electron microscopy. It was found that all of the iron oxyhydroxide mineral nanoparticles, including lepidocrocite, schwertmannite and akaganéite were superparamagnetic and therefore magnetically ordered at room temperature. Previous estimates of Néel temperatures for these three minerals are relatively low and are understood as misinterpreted magnetic blocking temperatures. This has important implications in environmental geoscience due to this mineral group’s potential as magnetic remanence carriers. Analysis of the data enabled the extraction of the intrinsic physical parameters of the nanoparticles, including magnetic sizes. The study also showed the possible effect on these parameters of crystal-chemical variations, due to elemental structural incorporation, providing a nanoscale mineralogical characterization of these iron oxyhydroxides. The analysis of the intrinsic parameters showed that all of the iron oxyhydroxide mineral nanoparticles considered here have a common magnetic moment formation mechanism associated with a random spatial distribution of iv uncompensated magnetic spins, and with different degrees of structural disorder and compositional stoichiometry variability, which give rise to relatively large intrinsic magnetization values. The elucidation of the magnetic nanostructure also contributes to the study of the surface region of the nanoparticles, which affects the particles’ reactivity in the environment.

La progresiva miniaturización de los materiales a la escala nanométrica ha abierto en la última década nuevas expectativas en el campo de la Ciencia de Materiales. Dichos materiales nanométricos presentan propiedades únicas, difiriendo a menudo de las propiedades del propio material a la macroescala, las cuales abren un amplio abanico de nuevas fenomenologías, y en consecuencia, de aplicaciones tecnológicas. De especial interés han sido los nanomateriales magnéticos, incluyendo las nanopartículas magnéticas o sistemas moleculares, dado que emergen como sistemas clave en el desarrollo de nuevas tecnologías de interés tales como sistemas de almacenamiento de memoria, computación cuántica o dispositivos de espintrónica. El desarrollo de aplicaciones reales en base al uso de dichos nanomateriales requiere primero la búsqueda de nuevas estrategias de estructuración que permitan organizar dichos sistemas magnéticos en superficies, a la vez que estudiar cómo es su comportamiento en la transición de la macroescala a la micro- o nanoescala. En este sentido es de interés estudiar cómo sus propiedades magnéticas pueden verse afectadas por efectos de la estructuración o de la propia superficie. En este contexto, de cara a estudiar las propiedades magnéticas de estos sistemas, una de las aproximaciones que está atrayendo mayor interés es el uso de dispositivos superconductores de interferencia cuántica (SQUIDs) y sensores Hall. Estos sensores han experimentado una gran revolución al ser miniaturizados, lo que ha permitido aumentar notablemente su sensibilidad hasta la detección de la magnetización de una sola nanopartícula o molécula. En este continuo avance, una de las principales limitaciones es la necesidad de desarrollar nuevas estrategias de integración que permitan depositar los sistemas magnéticos de un modo controlado en las zonas de máxima sensibilidad de estos sensores miniaturizados. En este contexto, la presente Tesis doctoral ha sido dedicada al desarrollo de nuevas estrategias de integración de cara a mejorar el control en la integración de sistemas magnéticos. Las estrategias propuestas han permitido por primera vez realizar este proceso sin la necesidad de modificar previamente ni el material magnético ni la superficie del sensor, consiguiendo depositar en zonas definidas del sensor con control (sub)micrométrico. En concreto, se ha demostrado la viabilidad y la universalidad de la técnica de deposición directa por litografía de AFM (conocida como Dip-pen Nanolithography, DPN) para la integración de nanomateriales magnéticos, abarcando un amplio rango de materiales desde nanopartículas hasta sistemas moleculares con comportamiento de imán unimolecular, en una gran variedad de sensores con diferentes dimensiones y requisitos. / The reduction of magnetic materials to the nanometric scale has opened in the last decades new perspectives in Material Science. Nanosized materials exhibit unique properties, which can considerably differ from the properties of the corresponding bulk materials, opening a wide range of new phenomenologies and therefore of technological applications. Two of the most prospective nanomaterials over the last years have been magnetic nanoparticles and molecular materials. Such nanostructured materials have attracted much interest not only from a fundamental point of view but also because their potential use in high-density information storage devices, quantum computing applications and in spintronics. However, before these applications become a reality, there is a fundamental issue that needs to be addressed, namely, the development of strategies to evolve from bulk materials to single entities suitable to be grafted on surfaces, sensors or other systems able to act as a device. The challenge is the definition of experimental strategies to properly assemble and integrate these molecular materials into functional devices without compromising their properties. In this context, there is an interest in understanding how the structuration procedure or even the surface can modify the behavior of such nanomaterials once deposited. Nevertheless, to answer these questions one of the approximations that is attracting more attention and probably more results is that of typical magnetic characterization techniques for bulk crystalline samples such as superconducting quantum interference devices (SQUID) or Hall magnetometer sensors. These systems have been miniaturized to increase their sensitivity down to a single magnetic or NP moment, involving the need for the development of specific deposition and structuration techniques to integrate the magnetic materials into the sensors with the required control on positioning and quantity of material. In this context, the present Thesis has been devoted to the development of novel structuration strategies to improve the control on the integration of magnetic nanosystems. The proposed strategies have allowed for first time to perform this process without the need of pre-modifying either the magnetic nanomaterial or the surface of the sensor, while depositing on specific areas of the sensor with (sub)micrometric precision. In particular, we have demonstrated the viability and generality of direct-write atomic force microscopy (AFM) lithography (also known as Dip-pen Nanolithography, DPN) to overcome most of the challenges that implies such integration. For this, different experimental approaches have been explored for the integration of magnetic nanomaterials intended to be as much representative as possible, ranging from magnetic nanoparticles to molecular systems exhibiting single molecule magnet (SMM) behavior, on a wide variety of sensors displaying different dimensions and requirements.

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).

Magnetite, Fe3O4, is a strongly electronically correlated system and thus exhibits remarkable electrical and magnetic properties, including the Verwey transition at TV 122 K, which has attracted much attention since its 1939 discovery. Fe3O 4 has recently revealed a new effect. By performing experiments at the nanoscale, we have discovered a novel electric-field driven transition (EFD) in magnetite below TV, from high- to low-resistance states driven by application of high bias. The EFD transition is detected both in Fe3O4 nanoparticles and thin films, is hysteretic in voltage under continuous biasing, and is not caused by self-heating. In this thesis we report on a thorough investigation of this new EFD transition. First, we unveil the origin of hysteresis observed in I-V curves. By applying voltage in a pulsed manner with controlled parameters, we unambiguously demonstrate that while the transition is field-driven, hysteresis results from Joule heating in the low-resistance state. A simple relaxation-time thermal model captures the essentials of the hysteresis mechanism. Second, by doing multilead (four-terminal) electrical measurements, we quantitatively separate the contributions of the Fe3O4 channel and each metal/electrode interface, and explore the contact effects upon testing devices incorporating various contact metals We demonstrate that on the onset of the transition, contact resistances at both source and drain electrodes and the resistance of Fe3O4 channel decrease abruptly. Finally, we measured the distribution of switching voltages, V sw, its evolution with temperature, and its dependence on out-of-plane magnetic field. Based on the experimental facts collected in this work we suggest the possible mechanism of EFD transition in Fe 3O4 as a charge gap closure by electric field. This is one of the first experimental observation of a theoretically predicted EFD transition in correlated insulators. These studies demonstrate that nanoscale, nonequilibrium probes can reveal much about the underlying physics of strongly correlated materials.

Metal-dielectric nanostructures capable of supporting electromagnetic resonances at optical frequencies are the vital component of the emerging technology called plasmonics. Plasmon is the electromagnetic wave confined at the metal-dielectric interface, which may effectively couple to the external electromagnetic excitation with the wavelength much larger than the geometric size of the supporting structure. Plasmonics can improve virtually any electromagnetic technology by providing subwavelength waveguides, field enhancing and concentrating structures, and nanometer size wavelength-selective components. The focus of this work is the fabrication, characterization and modeling for novel plasmonic nanostructures. Effects of the symmetry in plasmonic structures are studied. Symmetric metal nanoparticle clusters have been investigated and show highly tunable plasmon resonances with high sensitivity to the dielectric environment. Efficient, highly-scalable methods for nanoparticle self-assembly and controlled partial submicron metal sphere coatings are developed. These partially Au coated dielectric spheres have shown striking properties such as high tunability, as well as the control on resonant electromagnetic field enhancement and scattering direction. Studied effects are of vital importance for plasmonics applications, which may improve virtually any existing electromagnetic technology. Optical resonances in metal-dielectric nanostructures were correlated with LC circuit resonances elaborating on the resonance tunability, dielectric environment, symmetry breaking and mode coupling (Fano resonance) effects.

Wavelet-based algorithms are developed for solution of quantum and electromagnetic differential equations. Wavelets offer orthonormal localized bases with built-in multiscale properties for the representation of functions, differential operators, and multiplicative operators. The work described here is part of a series of tools for use in the ultimate goal of general, efficient, accurate and automated wavelet-based algorithms for solution of differential equations. The most recent work, and the focus here, is the elimination of operator matrices in wavelet bases. For molecular quantum eigenvalue and dynamics calculations in multiple dimensions, it is the coupled potential energy matrices that generally dominate storage requirements. A Coefficient Product Approximation (CPA) for the potential operator and wave function wavelet expansions dispenses with the matrix, reducing storage and coding complexity. New developments are required, however. It is determined that the CPA is most accurate for specific choices of wavelet families, and these are given here. They have relatively low approximation order (number of vanishing wavelet function moments), which would ordinarily be thought to compromise both wavelet reconstruction and differentiation accuracy. Higher-order convolutional coefficient filters are determined that overcome both apparent problems. The result is a practical wavelet method where the effect of applying the Hamiltonian matrix to a coefficient vector can be calculated accurately without constructing the matrix. The long-familiar Lanczos propagation algorithm, wherein one constructs and diagonalizes a symmetric tridiagonal matrix, uses both eigenvalues and eigenvectors. We show here that time-reversal-invariance for Hermitian Hamiltonians allows a new algorithm that avoids the usual need to keep a number Lanczos vectors around. The resulting Conjugate Symmetric Lanczos (CSL) method, which will apply for wavelets or other choices of basis or grid discretization, is simultaneously low-operation-count and low-storage. A modified CSL algorithm is used for solution of Maxwell's time-domain equations in Hamiltonian form for non-lossy media. The matrix-free algorithm is expected to complement previous work and to decrease both storage and computational overhead. It is expected- that near-field electromagnetic solutions around nanoparticles will benefit from these wavelet-based tools. Such systems are of importance in plasmon-enhanced spectroscopies.