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This thesis describes a series of experiments probing the millimetre-wave response of the low-dimensional organic superconductors β"-(BEDT-TTF)₄[(H₃O)-M(C₂O₄)₃]S, κ-(BEDT-TTF)₂Cu(NCS)₂ and (TMTSF)₂ PF₆ in applied magnetic fields. Chapter 1 introduces the physics of charge carriers in the presence of a mag- netic field and field-induced resonant phenomena in the conductivity of metals. The basic concept of Fermi liquid theory, that of the existence of quasiparticles with effective mass, is presented, as well as the principles of electron spin resonance. Chapter 2 outlines the experimental technique of millimetre-wave spectroscopy, the principle of guided radiation and the use of metallic resonators and for perturbative measurements. Some results on novel dielectric whispering-gallery resonators and hybrid "tunnel-gap" resonators for potential use in pulsed and destructive field experiments are also presented. Chapter 3 is a detailed angle-, temperature- and frequency- dependent investigation of electron spin resonance in the family of quasi-two-dimensional charge transfer salts β"-(BEDT-TTF)₄[(H₃O)M(C₂O₄)₃]S, where M = Cr³⁺ and Fe³⁺. The effective spin Hamiltonians for the Cr³⁺ and Fe³⁺ ions are identified, and the presence of weak antiferromagnetic correlations established; insight is gained into the relaxation mechanism and the effect of the superconducting state on the localised spins. Chapter 4 reports the angle-dependent magneto-optical response of isotopically substituted β"-(BEDT-TTF)₂Cu(NCS)₂. Both normal and superconducting states are investigated, and Josephson plasma resonances and Fermi-surface traversal resonances are identified. Chapter 5 presents some preliminary results from the investigation of the quasi- one-dimensional Bechgaard salt (TMTSF)₂PF₆ under hydrostatic pressure and in applied magnetic field. The millimetre-wave response is investigated as a function of frequency as the field-induced spin-density-wave cascade is crossed. Possible evidence for resonant absorptions due to collective spin excitations is reported.

The results from EPR studies of CVD diamond which was intentionally silicon doped with isotopes in natural abundance or isotopically enriched are reported. The observation of hyperfine satellites arising due to the presence of 29Si has provided definitive evidence for the involvement of silicon in two EPR centres in diamond which were previously suspected to involve silicon: KUL1 and KUL3. KUL1 is unambiguously identified as the neutral silicon split vacancy defect (V-Si-V)0, whilst KUL3 is shown to be (V-Si-V)0 decorated with a hydrogen atom. Data have also revealed that (V-Si-V)0 is preferentially oriented in samples grown on {110} substrates. The negative nitrogen-vacancy centre (NV‑) has been investigated. Published parameters for the nitrogen hyperfine interaction produce an unsatisfactory fit to the experimental spectra and hence these parameters are redetermined. Optically-excited EPR has been used to estimate the degree of spin polarisation of the NV-ground state and the increase in signal intensity with illumination has permitted the interaction between the unpaired electron and neighbouring 13C atoms to be studied. Two sets of 13C hyperfine satellites have been identified, which account for ~100% of the unpaired electron probability density. Despite the predictions that the neutral charge state of NV should have an S = ½ ground state, this charge state has not previously been detected by EPR. Optically excited EPR measurements reveal a trigonal nitrogen containing defect in diamond with an excited state populated via optical excitation. Analysis of the spin-Hamiltonian parameters and the wavelength dependence of the optical excitation leads to assignment of this state to the 4A2 excited state of NV0.

La résonance paramagnétique électronique est une technologie permettant de localiser et de caractériser les radicaux libres, fondée sur la propriété de résonance des électrons libres lorsqu’ils sont placés dans un champ magnétique spécifique. Afin d’augmenter la qualité des reconstructions obtenues par des dispositifs d’imagerie de résonance paramagnétique électronique, ce travail propose l’utilisation de méthodes variationnelles pour inverser le modèle de formation des images, qui combine une convolution avec une transformée de Radon. La fonctionnelle proposée repose sur la norme L2 pour le terme d’attache aux données, et sur la variation totale et une seminorme de Besov pour le terme de régularisation. La seminorme de Besov est implémentée grâce à la transformée en curvelets et à la norme L1 qui permet d’appliquer un critère de parcimonie. Les propriétés de ces termes de régularisation permettent de reconstruire des images à la fois pertinentes dans les zones où l’acquisition des données est insuffisante, notamment sur les bords, et suffisamment détaillées dans les zones où l’échantillon est texturé. L’augmentation de la qualité des images reconstruites permet d’envisager des acquisitions sur des durées réduites, ouvrant la voie à des expériences in vivo ou cliniques actuellement limitées par des durées d’acquisition de l’ordre de plusieurs dizaines de minutes. Les algorithmes de minimisation primal-dual de Chambolle-Pock et FISTA sont utilisés pour résoudre les problèmes d’optimisation que pose l’utilisation de méthodes variationnelles. L’étude détaillée du modèle direct permet de mettre en évidence une structure de Toeplitz, dont les propriétés sont utilisées pour résoudre le problème inverse en évitant le recours à la rétroprojection filtrée ou aux transformées de Fourier non-uniformes. Des simulations numériques sont menées sur le fantôme de Shepp-Logan, et valident le modèle proposé qui surpasse à la fois visuellement et quantitativement les techniques de reconstruction couramment utilisées, combinant déconvolution et rétroprojection filtrée. Des reconstructions menées sur des acquisitions réelles, consistant en un échantillon papier d’une encre paramagnétique et en une phalange distale irradiée, valident par l’expérience le choix des fonctionnelles utilisées pour inverser le modèle direct. La grande souplesse de la méthode variationnelle proposée permet d’adapter la fonctionnelle au problème de la séparation de sources qui se pose lorsque deux molécules paramagnétiques différentes sont présentes au sein d’un même échantillon. La fonctionnelle proposée permet de séparer les deux molécules dans le cadre d’une acquisition classique d’imagerie de résonance paramagnétique électronique, ce qui n’était possible jusqu’alors que sur des acquisitions dites hyperspectrales beaucoup plus gourmandes en temps. / Spatial electron paramagnetic resonance imaging (EPRI) is a recent method to localize and characterize free radicals in vivo or in vitro, leading to applications in material and biomedical sciences. To improve the quality of the reconstruction obtained by EPRI, a variational method is proposed to inverse the image formation model. It is based on a least-square data-fidelity term and the total variation and Besov seminorm for the regularization term. To fully comprehend the Besov seminorm, an implementation using the curvelet transform and the L1 norm enforcing the sparsity is proposed. It allows our model to reconstruct both image where acquisition information are missing and image with details in textured areas, thus opening possibilities to reduce acquisition times. To implement the minimization problem using the algorithm developed by Chambolle and Pock, a thorough analysis of the direct model is undertaken and the latter is inverted while avoiding the use of filtered backprojection (FBP) and of non-uniform Fourier transform. Numerical experiments are carried out on simulated data, where the proposed model outperforms both visually and quantitatively the classical model using deconvolution and FBP. Improved reconstructions on real data, acquired on an irradiated distal phalanx, were successfully obtained. Due to its great versatility, the variational approach is easily extended to the source separation problem which happens when two different paramagnetic species are present in the sample. The objective function is consequently modified, and a classic EPRI acquisition yields two images, one for each species. Until now, source separation could only be applied to hyperspectral EPRI data, much more costly in acquisition time.