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The Moon displays weak magnetic fields resulting from areas of the lunar crust that are remanently magnetised. The origins of the magnetic fields that produced this remanent magnetisation are still under discussion, and theories include among several, an ancient lunar dynamo, or processes occurring on the Moon as a result of impacts. Lunar crustal fields have been mapped globally by the Magnetometer (MAG) and Electron Reflectometer (ER) on the satellite Lunar Prospector, providing vector magnetic field measurements at an average altitude of 30 km, and estimates of the total surface field. This thesis presents global and regional models of the magnitude and direction of lunar magnetisation within a layer, produced from both the MAG and ER data independently and jointly using several inversion methods. The inverse modelling techniques are based on those developed for terrestrial and Martian data sets, employing equivalent source dipoles as basis functions, and Green’s functions relating a magnetic field observation to a spatially continuous magnetisation distribution. A unique magnetisation solution is selected having the smallest rootmean- square (RMS) magnetisation for a given fit to the data, controlled by a damping parameter. The non-uniqueness in magnetisation distributions and the determination of source parameters is discussed with the use of forward models to assist the interpretation of the crustal magnetisation models. Suites of magnetisation models for layers with thicknesses between 10 and 50 km, and with different dipole depths, are able to reproduce both the ER and MAG data well. Inverse models utilising the scalar ER data have been developed successfully, resulting in a joint inversion of the ER and MAG data for one of the strongest magnetic anomalies on the Moon, Reiner Gamma. The largest concentrations of strongly magnetised crust are, like the crustal fields themselves, located antipodal to the youngest large impact basins, and in some isolated areas associated with the strongest crustal fields. The magnetisation distributions show robust magnitudes with different data sets and modelling techniques showing the extent of magnetised sources, but can not be used to infer the direction of the magnetising fields. Average magnetisation values in magnetised regions of 30-40 mA/m are similar to the measured magnetisations of the Apollo samples and significantly weaker than crustal magnetisations for Mars and the Earth. A global preference for a 30 km thick magnetised layer suggests that a dynamo field may be more consistent with these magnetisation models. The magnetisation models in this thesis are the first global magnetisation models for the Moon, and the first to combine the vector MAG and the scalar ER data. These magnetisation models can be used to predict the crustal contribution to the lunar magnetic field environment at a particular location, and in the absence of reliable sample returns, provide valuable information on the magnitude of lunar crustal magnetisation.

In this thesis the results of several different experimental techniques are presented. Time-resolved scanning Kerr microscopy and time-resolved optically pumped scanning optical microscopy measurements were made in Exeter on bi-component anti-dot lattices and permalloy films respectively. Magnetic transmission x-ray microscopy measurements were performed on cobalt nanostructures at the Advanced Light Source at the Lawrence Berkeley National Laboratory in Berkeley, California, USA. Time-resolved Kerr microscopy was used to study bi-component 400nm anti-dot lattices with a 1μm lattice constant. At 200 Oe the mode frequencies were obtained using time-resolved measurements. The mode frequencies of the cobalt filled anti-dots (binary sample) are 3 and 4.4 GHz. The 4.4 GHz mode has propagating character; the 3 GHz mode has non-propagating character. The mode frequencies of the air –filled anti-dot arrays (anti-dot reference sample) are 3.84 and 4.72 GHz. The 3.84 GHz mode has propagating character; the 4.72 GHz mode has non-propagating character. The alteration of the internal field by the air-filled anti-dots lowers the propagating mode frequency compared to the binary sample. Scanning Kerr microscopy was used to study the spatial character of the anti-dot modes. By fitting the spatial character the effective damping parameter(s) were determined. The effective damping parameter for the binary sample was 0.023 and 0.044 for the 4.4 and 3.04 GHz modes respectively. The 3.04GHz mode exists through the cobalt filled anti-dots leading to a high effective damping. The effective damping parameters for the anti-dot reference sample 0.026 and 0.028 for the 3.84 and 4.72 GHz modes respectively. Time-resolved optically pumped measurements have been performed on a continuous 20nm permalloy film. This is a new experimental technique developed during my PhD. Early data acquired on the optical microscope is compared with data measured later and attempts are made to explain the discrepancies. With a 500 Oe out-of-plane field initial time resolved signals show an oscillation at 17 GHz, the origin of the oscillation is unknown and is thought to originate from a magnon or phonon contribution. The experiment overlapping sub-micron pump and probe spots makes acquiring consistent time-resolved signals a difficult challenge. Images revealing circular lobe shapes are observed, the origin of these images is not fully understood. Later measurements are compared to the early measurements. In the recent measurements, images of spin waves with a wavelength and frequency of 2.5 μm and 4 GHz respectively are observed. These values are not reconcilable with the wavelengths and frequencies of 1μm and 17GHz seen in the images and time-resolved signals respectively. Recent measurements also revealed a strong dependence on the pump focus position on the measured images. Lastly, magnetic transmission x-ray microscopy measurements are presented on 700nm cobalt anti-dot structures overlaid on continuous permalloy films of thicknesses ranging from 20 to 60nm. The magnetic ground states of the nanostructures are investigated using L3 edge x-ray absorption and x-ray magnetic circular dichroism as a magnetic contrast mechanism. The reversal fields are determined and consistent with hysteresis loops measurements in Exeter. The dipolar fields from the complex shape of the cobalt anti-dots are expected to modulate the magnetic ground state of the permalloy. Reversal of the permalloy occurs suddenly over a consistent field window, starting and finishing between 13 ~ 17 Oe respectively. The reversal process in the cobalt occurs gradually and full saturation is not observed until fields of up to 350Oe.

The first eight chapters of this thesis describe a study of the magnetic effects of drilling on bore cores of sedimentary rocks. Extensive rock and palaeo- magnetic methods were used to investigate such effects in three collections of bore cores from the North Sea and Sellafield, U.K., and Prudhoe Bay, Alaska. It is evident that a drilling imposed remanent magnetisation (DIRM) resides in the North Sea and Prudhoe Bay bore cores which is characterised by symmetries in its intensity and direction relative to the core axis. Such DIRM correlated well with the theoretically modelled magnetic field at one end of a steel drill barrel. The DIRM intensity distribution also appeared to be correlated with variation in the radial remanence susceptibility (i.e. the capacity of remanence acquisition) in the North Sea and Prudhoe Bay cores and magnetic susceptibility in the North Sea cores. Simulation experiments of shock impact conducted on bore core materials suggests that shock/vibration of the drill barrel is the major process that is responsible for the radial variation in core magnetic properties. Titanomagnetite (including magnetite) and pyrrhotite are the major carriers of DIRM but there is no DIRM identified in bore cores in which hematite is the only ferromagnetic mineral. Chapter 9 describes a novel attempt in using fractal geometry to statistically depict the geomagnetic field reversal sequence. A fractal distribution is shown to occur for longer geomagnetic polarity intervals (> 0.28 Ma) in terms of a power law relationship between interval length and cumulative number for the last 158 Ma. A simulation study indicates that the deviation from the power law at shorter intervals (< 0.28 Ma) is caused by missing of short intervals due to the limit of resolving power. This is strongly supported by a fractal model (i.e. a Cantor set) introduced for relating the shortest polarity interval, the transition time and the fractal dimension. Normal and reversed polarity intervals have similar fractal dimensions, suggesting that there is no, statistically, fundamental difference between the two magnetic polarity states.

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Magnetism of the rare earth intermetallics present some of the most important challenges for understanding correlated electron systems . In this thesis I distil this immense challenge, to understanding the unusual magnetic properties of the rare earth intermetallic PrPtAl. At first glance, PrPtAl appears to be a typical local f moment system, where the electronic states of Pr3+ are composed of nine singlet states, split by the crystal electric field for the J = 4 spin-orbit state in low crystal symmetry (orthorhombic, Pnma). The absence of a magnetic ground state would naively lead us to expect PrPtAl to be a simple paramagnet, but the results from this thesis show that the material is more complex, ordering magnetically at 5.7 K in spite of its singlet ground state. This thesis investigates the emergence of magnetic order in PrPtAl. For this purpose, the properties of PrPtAl were measured using high quality single crystals grown using the Czochralski technique. These crystals were used to measure: bulk properties at the Centre for Science at Extreme Conditions (CSEC, University of Edinburgh) and to perform neutron and x-ray magnetic scattering experiments at central facilities within Europe (ISIS, ESRF) and North America (NCNR). The results of this thesis conclusively show that PrPtAl does not directly realise ferromagnetism, but initially orders into two modulated magnetic states between 5.7-5.2 K and 5.2-4.7 K. These states cannot be explained using a simple local moment picture, but appear to be driven by a complex interaction between local moments and conduction electrons, in a possible quantum order-by-disorder type mechanism.

This thesis presents a study of two-dimensional electron systems in GaAs-(Al,Ga)As heterojunctions and quasi-two-dimensional electron and hole systems in graphite within the quantum Hall effect regime of low temperature and high magnetic field. This thesis covers three main sets of experimental work as well as details of the experimental methods (chapter 2) used and the background theory behind the observed results (chapter 1). The first experimental results presented in this thesis in chapter 3 focus on contactless measurement of the equilibrium magnetisation of sample A2268, a ten layer multiple quantum well sample. Fitting the shape of dHvA oscillations at various temperatures to different models for the density of states, various properties of the system can be estimated, such as the shape of the disorder-broadened density of states and the presence of a background density of states between the Landau levels. Chapter 4 focuses on measurements of the decay of induced circulating currents in the quasi-dissipationless quantum Hall regime in two samples, V0049 and T73. The induced current is measured via contactless measurement of the associated magnetic moment. The magnitude of the induced current is found to be affected by the sweep rate of the magnetic field and also the distance of approach. The decay of the induced currents is observed at several temperatures and for different magnetic field sweep rates and distances of approach. Decays are observed for up to several days at time, far longer than previously possible. Information about the rate of decay can be used to build a picture of the decay mechanisms present in the quantum Hall regime. The presence of a power-law decay regime indicates many decay mechanisms contribute to the decay of a circulating current in the quasi-dissipationless quantum Hall regime. Chapter 5 focuses on both contactless magnetometry and transport experiments carried out on a graphite sample. The experiments aim to confirm or dispute recent claims of Dirac fermions in graphite. Experiments are carried out at temperatures in the range 30 mK to ~4 K and at two different angles to the applied magnetic field. Phase analysis of both Shubnikov de Haas and de Haas van Alphen oscillations is used to distinguish between normal and Dirac fermions. Observation of quantum Hall effect displays the presence of a half-integer quantum Hall staircase similar to that observed in graphene.

The debate over the origin of the ultrafast demagnetization has been intensively active for the past 16 years. Several microscopic mechanisms have been proposed but none has managed so far to provide direct and incontrovertible evidences of their validity. In this context I have proposed an approach based on spin dependent electron superdiffusion as the driver of the ultrafast demagnetization. Excited electrons and holes in the ferromagnetic metal start diffusing after the absorption of the laser photons. Being the material ferromagnetic, the majority and minority spin channels occupy very different bands. It is then not surprising that transport properties are strongly spin dependent. In most of the ferromagnetic metals, majority spin excited electrons have better transport properties than minority ones. The effect is that majority carriers are more efficient in leaving the area irradiated by the laser, triggering a net spin transport. Recent experimental findings are revolutionising the field by being incompatible with previously proposed models and showing uncontrovertibly the sign of spin superdiffusion. We have shown that spin diffusing away from a layer undergoing ultrafast demagnetization can be used to create an ultrafast increase of magnetization in a neighboring magnetic layer. We have also shown that optical excitation is not a prerequisite for the ultrafast demagnetization and that excited electrons superdiffusing from a non-magnetic substrate can trigger the demagnetization. Finally we have shown that it is possible to control the time shape of the spin currents created and developed a technique to detect directly spin currents in a contact-less way.  The impact of these new discoveries goes beyond the solution of the mystery of ultrafast demagnetization. It shows how spin information can be, not only manipulated, as shown 16 years ago, but most importantly transferred at unprecedented speeds. This new discovery lays the basis for a full femtosecond spintronics.

We studied the edge states and their roles in conductivity and magnetism of graphene nanoribbions and flakes. we studied the Aharonov-Bohm effect in graphene nanodisks and rings. We described the quantum oscillations of the magnetization of graphene flakes. we have examined the snake-like states of transport electrons in the configurations of graphene ribbons with a domain wall in the centre.

Ce travail de thèse décrit (i) la synthèse de complexes hétérométalliques d’ions 3d et 4f à partir de précuseurs de Mn, Fe et Co, de sels de lanthanides et de ligands organiques et (ii) l'étude de leurs structures et propriétés. 41 complexes polynucléaires ont été synthétisés dans le cadre de ce travail. Les structures moléculaires de tous les composés ont été déterminées par diffraction des rayons X. Les propriétés magnétiques de 22 complexes ont été étudiées, dont quatre montrent une relaxation lente de leur aimantation considérée comme la signature d’un comportement de molécule-aimant. L'activité catalytique du complexe {Mn4Dy6Li2} calciné a aussi été étudiée et s'est avérée efficace pour l'oxydation du monoxyde de carbone. L'étude systématique de complexes isostructuraux de lanthanides a montré que l'incorporation d’ions 4f peut introduire de l’anisotropie magnétique et que l’ion DyIII est généralement le meilleur candidat pour le ciblage de molécules-aimants hétérométalliques 3d- 4f. / This dissertation describes the syntheses of 3d-4f-metal complexes starting from preformed compounds of Mn, Fe and Co, lanthanide salts and organic ligands and also the investigation of their structures and properties. 41 new polynuclear heterometallic metal complexes were synthesised in the course of this work with different interesting properties. The structures of all obtained compounds have been confirmed using X-ray diffraction. The magnetic properties of 22 complexes were studied, of which four show frequency dependent out-of-phase signals as expected for SMMs. The catalytic activity of calcinated {Mn4Dy6Li2} was investigated and proved effective for the oxidation of CO. It was established, that the use of precursors leads to new families of compounds. Moreover the study of isostructural compounds across the lanthanide series showed 1) that the incorporation of 4f ions introduces magnetic anisotropy and 2) DyIII is usually the best candidate for targeting 3d-4f-SMMs.