This dissertation discusses the Landau-Zener (LZ) theory and its application in noisy environments and in many-body systems. The first project considers the effect of fast quantum noise on LZ transitions. There are two important time intervals separated by the characteristic LZ time. For each interval we derive and solve the evolution equation, and match the solutions at the boundaries to get a complete solution. Outside the LZ time interval, we derive the master equation, which differs from the classical equation by a quantum commutation term. Inside the LZ time interval, the mixed longitudinal-transverse noise correlation renormalizes the LZ gap and the system evolves according to the renormalized LZ gap. In the extreme quantum regime at zero temperature our theory gives a beautiful result which coincides with that of other authors. Our initial attempts to solve two experimental puzzles - an isotope effect and the quantized hysteresis curve of a single molecular magnet - are also discussed. The second project considers an ultracold dilute Fermi gas in a magnetic field sweeping across the broad Feshbach resonance. The broad resonance condition allows us to use the single mode approximation and to neglect the energy dispersion of the fermions. We then propose the Global Spin Model Hamiltonian, whose ground state we solve exactly, which yields the static limit properties of the BEC-BCS crossover. We also study the dynamics of the Global Spin Model by converting it to a LZ problem. The resulting molecular production from the initial fermions is described by a LZ-like formula with a strongly renormalized LZ gap that is independent of the initial fermion density. We predict that molecular production during a field-sweep strongly depends on the initial value of magnetic field. We predict that in the inverse process of molecular dissociation, immediately after the sweeping stops there appear Cooper pairs with parallel electronic spins and opposite momenta.

Magnetism of carbon-based materials is a challenging area for both fundamental research and possible applications. We present studies of low-dimensional carbon-based magnetic systems (fullerene-diluted molecular magnets, carbon nanotubes, graphite fluoride, and nanoporous carbon) by means of SQUID magnetometer, X-ray diffraction and vibrational spectroscopy, the latter techniques used as complementary instruments to find a correlation between the magnetic behaviour and the structure of the samples.In the first part of the thesis, characteristic features of the magnetization process in aligned films of carbon nanotubes with low concentration of iron are discussed. It is shown that the magnetism of such structures is influenced by quantum effects, and the anisotropy behaviour is opposite to what is observed in heavily doped nanotubes.In the second part, Mn12-based single molecular magnets with various carboxylic ligands and their 1:1 fullerene-diluted complexes are studied. We prove that magnetic properties of such systems strongly depend on the environment, and, in principle, it is possible to design a magnet with desirable properties. One of the studied compounds demonstrated a record blocking temperature for a single molecular magnet. Both fullerene-diluted complexes demonstrated “magnetization training” effect in alternating magnetic fields and the ability to preserve magnetic moment.The third and the fourth parts of the thesis are dedicated to the analysis of various contributions to the magnetic susceptibility of metal-free carbon-based systems – intercalated compounds of graphite fluorides and nanoporous oxygen-eroded graphite. The magnetic properties of these systems are strongly dependent on structure, and can be delicately tuned by altering the π-electron system of graphite, i. e. by degree of fluorination of intercalated compounds and by introduction of boron impurity to the host matrix of nanoporous graphite. / Magnetism av kolbaserade material är ett utmanande område för både grundforskning och möjliga tillämpningar. Vi presenterar studier med låg-dimensionella kolbaserade magnetiska system (fulleren-utspädda molekylära magneter, kolnanorör, grafit fluorid och nanoporösa kol) med hjälp av SQUID magnetometer, röntgendiffraktion och vibrerande spektroskopi, de senare tekniker som används som komplement instrument för att finna sambandet mellan den magnetiska uppträdande och strukturen hos proven. I den första delen av avhandlingen är egenheter från magnetisering processen i linje filmer av kolnanorör med låg koncentration av järn diskuteras. Det visas att magnetism av sådana strukturer påverkas av kvantmekaniska effekter och anisotropin beteende är motsatsen till vad som observerats i kraftigt dopade nanorör. I den tvåa delen är Mn12-baserade enda-molekyl magneter med olika karboxylsyror ligander och deras 1:1 fulleren-utspädda komplex studeras. Vi visar att magnetiska egenskaperna hos sådana system beror i hög grad på miljön, och i princip är det möjligt att utforma en magnet med önskvärda egenskaper. En av de studerade föreningarna visade en post blockeringstemperaturen för en enda molekylär magnet. Både fulleren-utspädda komplex visade "magnetisering utbildning" effekt i alternerande magnetfält och möjligheten att bevara magnetiskt moment. Den tredje och fjärde delarna av avhandlingen är avsedda för inneboende magnetism av analys av olika bidrag till magnetisk susceptibilitet av metall-fritt kol-baserade system -inskjutna föreningar grafit fluorider och nanoporösa O2-eroderade grafit. Magnetiska egenskaperna hos dessa system är starkt beroende av strukturen, och kan fint avstämmas genom att man ändrar π-elektronsystem av grafit, i. e. med graden av fluorering av inskjutna föreningar och genom införandet av bor föroreningar till värd matris av nanoporösa grafit.

In this thesis, large organic molecules (DM15N, DM18N, Cu(dbm)2) were deposited. These molecules are cannot be deposited by thermal sublimation due the fact that they decompose at lower temperature than they sublime. The employed molecules to single molecular magnets, which can be potentially used as quantum bites (qubit). The new method of deposition atomic layer injection made by Bihur Crystal company was introduced and tested. The method uses liquid solution with molecules which is driven by argon gas through pulse valve to the sample placed in ultra-high vacuum chamber. During the deposition, droplets of solution are formed on the sample surface. The solvent can be removed by light annealing or by keeping the sample in the vacuum for couple of days. The molecules were investigated by x-ray photoelectron spectroscopy and by scanning electron microscopy to determine fragmentation of the molecules, to study topography of the resultant surface and homogeneity of the deposited layer. We found conditions at which the intact molecules are deposited on the sample surfaces and form molecular nano- and micro- crystals.