Single crystals of (Mg₉₉.₇₅Mn₀.₂₅)₂P₂O₇ have been investigated by esr through the temperature range from room temperature to 200ºC. One phase transition was observed extended through the temperature range between 59.5ºC to 63ºC where the α-and β phase coexist. Accurate spectra were recorded at 74ºC, 84ºC and 94ºC at the three magnetic axis, and the spin-Hamiltonian parameters were obtained from these data. The phase transition mechanism and the significance of the spin-Hamiltonian parameters in the theory of S-state splitting are discussed in the light of current literature. / Thesis / Master of Science (MSc)

Experimental methods based on the magnetic resonance phenomenon belong to the most widely used experimental techniques for investigations of molecular and electronic structure. The difficulty with such experiments, usually a proper interpretation of data obtained from high-resolution spectra, opens new challenges for pure theoretical methods. One of these methods is density functional theory (DFT), that now has an advanced position among a whole variety of computational techniques. This thesis constitutes an effort in this respect, as it presents theory and discusses calculations of electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) parameters of paramagnetic molecules. It is known that the experimental determination of the magnetic resonance parameters of such molecules, especially in the case of NMR, is quite complicated and requires special techniques of spectral detection. On the other hand, paramagnetics play an important role in many areas, such as molecular magnets, active centers in biological systems, and defects in inorganic conductive materials. Therefore, they have spurred great interest among experimentalists, motivating us to facilitate the interpretation of spectral data through theoretical calculations. This thesis describes new methodologies for the determination of magnetic properties of paramagnetic molecules in the framework of DFT, which have been developed in our laboratory, and their applications in calculations of a wide range of molecular systems. The first two papers of this thesis deal with the theoretical determination of NMRparameters, such as nuclear shielding tensors and chemical shifts, in paramagnetic nitroxides that form core units in molecular magnets. The developed methodology is aimed to realize a high calculational accuracy for these systems. The effects of hydrogen bonding are also described in that context. Our theory for the evaluation of nuclear shielding tensors in paramagnetic molecules is consistent up to second order in the fine structure constant and considers orbital, fully anisotropic dipolar, and isotropic contact contributions to the shielding tensor. The next projects concern electron paramagnetic resonance. The well-known EPR parameters, such as the g-tensors and the hyperfine coupling constants are explored. Calculations of electronic g-tensors were carried out in the framework of a spin-restricted open-shell Kohn-Sham method combined with the linear response theory recently developed in our laboratory and allowing us to avoid by definition the spin-contamination problem. The inclusion of solvent effects, described by the polarizable continuum model, extends the possibility to treat molecular systems often investigated in solution. For calculations of the hyperfine coupling constants a so-called restricted-unrestricted approach to account for the spin polarization effect has been developed in the context of DFT. To examine the validity of the approximations implicit in this scheme, the neglect ii of singlet operators, a generalized RU methodology was implemented, which includes a fully unrestricted treatment with both singlet and triplet operators. The small magnitude of the changes in hyperfine coupling constants confirms the validity of the original scheme. / QC 20100923

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In this work, I present nuclear probe spectroscopy studies, in detail, µ+SR and 57Fe-Mössbauer spectroscopy on solid-state systems with localized magnetic moments of 3d transition-metal ions supported by density functional theory calculations. Local probes are able to extract local quantities, e.g. the spin dynamics of the 57Fe site or the local, mostly interstitial µ+ site to distinguish between di_erent magnetic phases. The density functional theory calculations help to identify the muon site position from which the local quantity depends. My µ+SR studies on frustrated 3d magnets with quenched disorder concern the physics of phase transitions, avoided order-by-disorder, quantum uctuations or the appearance of spin-liquid-by-disorder. µ+SR is able to identify quantum spinliquid-like ground states without symmetry breaking or static magnetic order by the magnetic field at the muon site. BaTi0.5Mn0.5O3 is a magnetically highly-frustrated double perovskite with quenched disorder.It shows no freezing temperature or no frequency dependence of x1as expected for a spin glass. Microscopically, it is proposed that local interactions between magnetic orphan spins, dimers, and magnetic trimers of Mn4+ play an important role. The µ+SR experiment on BaTi0.5Mn0.5O3 shows an increase of the dynamical muon spin relaxation rate below 3 K which saturates down to 0.019 K coexisting with residual short-range magnetic order (<20% of the signal). A clear difference is observed in comparison with the classical cluster-spin glass SrTi0.5Mn0.5O3 which shows a peak of the zero-field muon spin relaxation rate: a persistent low-energy spin dynamics is present in BaTi0.5Mn0.5O3 down to 20 K. My DFT calculations propose a positive muon site insight the Ba plane close to O atoms. Here, a slight preference of the muon site close to Mn4+ is possible which could put the muon close the orphan spins, dimers, and magnetic trimers, respectively, avoiding the nonmagnetic Ti4+ face-sharing octahedra. Theoretically, a specific ground state of BaTi0.5Mn0.5O3 is not proposed. A clear discrimination between a quantum spin liquid ground state and a mimicry state with the appearance of spin-liquid-by-disorder is not possible from the existing data. I present a µ+SR study on the bond-disordered magnetically highly frustrated pyrochlore fluoride NaCaCo2F7. Neutron spectroscopy studies on NaCaCo2F7 revealed static short-range order consistent with a continuous manifold of cluster-like states being a superposition of noncoplanar ψ2(m3z2-r2) and coplanar ψ3(mx2-y2) states with a correlation length of around 16Å. No evidence for static magnetic long-range order is found in NaCaCo2F7 probed by µ+SR confirming the absence of an order-by-disorder mechanism. The experimental results are not consistent with a classical local-planar XY cluster-spin glassiness. In these µSR experiments, two muon sites are observed. The relative occupancy of both muon sites is nearly temperature independent. Muon site I is a collinear diamagnetic F-µ+-F bound state pulling two F- close towards the muon revealed by the muon spin time evolution. To investigate the pure F-µ+-F bound state in a broad temperature range I have performed an additional µ+SR study on CaF2. This study solved open questions of muon diffusion around 290 K which was observed in NaCaCo2F7 as well. The F-µ+-F spin relaxation indicates the slowing down of the magnetic Co2+ spin fluctuations upon cooling towards the NMR spin freezing temperature Tf≈ 2.4 K. The relaxation rate saturates below 800 mK and remains constant down to 20 mK. The dominant part of the magnetic short-range relaxation signal is a dynamical relaxation as probed by longitudinal magnetic-field experiments. Muon site II exhibits a strong dynamical relaxation rate at 290 K and below and shows persistent µ+ spin dynamics down to 20 mK. Qualitatively, muon site II shows persistent µ+ spin dynamics with one order of magnitude higher dynamical relaxation rates compared to muon site I. DFT calculations of a comparison of the unperturbed unit cells of NaCaCo2F7 and NaCaNi2F7, which has shown just one muon site experimentally, are consistent with a decrease of the energy differences of energy minima and support the experimentally observed muon site ambivalence. In summary, the µ+SR studies propose NaCaCo2F7 as a quantum cluster-spin glass candidate. I present a systematic 57Fe-Mössbauer study on highly diluted Fe centers in Li2(Li1-xFex)N as a function of temperature and magnetic field applied transverse and longitudinal with respect to the single-ion anisotropy axis. Here, Fe is embedded in an α-Li3N matrix. The oxidation state of Fe and possible ferromagnetic nature are in controversial discussions in the literature. Below 30 K the Fe centers exhibit a giant magnetic hyperfine field of BA=70.25(2) T parallel to the axis of strongest electric field gradient Vzz=-154.0(1) V / Å 2. This observation is consistent with a Fe1+d7 charge state with unquenched orbital moment and J=7/2. Fluctuations of the magnetic hyperfine field are observed between 50 K and 300 K and described by the Blume two-level relaxation model consistent with single-atomic magnetism as proven by the invariance of Blume relaxation parameters for the concentration tuning x< 0.025 excluding a ferromagnetic nature. From the temperature dependence of the fluctuation rate an Orbach spin-lattice relaxation process is deduced. An Arrhenius analysis yields a single thermal-activation barrier of EA=570(6) K and an attempt frequency v0=309(10) GHz. Mössbauer spectroscopy studies with applied transverse magnetic fields up to 5 T reveal a large increase of the fluctuation rate by two orders of magnitude. In longitudinal magnetic fields a splitting of the fluctuation rate into two branches is observed. The experimental observations are qualitatively reproduced by a single-ion spin Hamiltonian analysis. It demonstrates that for dominant magnetic quantum tunneling relaxation processes a weak axial single-ion anisotropy D of the order of a few Kelvin can cause a two orders of magnitude larger energy barrier for longitudinal spin fluctuations.

The existence of bulk magnetism in matter can be attributed to the magnetic properties of the sub-atomic particles that constitute the former. The fact that the origin of these microscopic magnetic moments cannot be related to the existence of microscopic currents became apparent when this assumption predicted completely featureless bulk magnetic properties in contradiction to the observation of various bulk magnetic properties [1]. This microscopic magnetic moment, independent of other motions, hints at the existence of a hitherto unknown degree of freedom that a particle can possess. This property has come to be known as the "spin" of the particle. The atomic nucleus is comprised of the protons and the neutrons which possess a spin each. The composite object- the atomic nucleus is therefore a tiny magnet itself. In the presence of an external bias like a magnetic field, the nucleus therefore evolves like a magnetic moment and attains a characteristic frequency in its evolution called the Larmor frequency given by, (formula) where η is the magnetogyric ratio of the particle and B is the applied magnetic field. The existence of a natural frequency presents the possibility of a resonance behaviour in the response of the system when probed with a driving field. This is the basic principle of magnetic resonance, which in the context of the atomic nucleus, was discovered independently by Purcell [2] and Bloch [3]. From its conception, the technique and the associated understanding of the involved phenomena have come a long way. In its original form the technique involved the study of the steady-state response of the nuclear magnetic moment to a driving field. This continuous wave NMR had the basic limitation of exciting resonances in a given sample, serially. In due course of time, this technique was replaced by the Fourier transform NMR (FTNMR) [4]. This technique differed from the continuous wave NMR in its study of the transient response of the system in contrast to the steady-state response in the former. The advantage of this method is the parallel observation of all the resonances present in the system ( within the band-width of the excitation). In addition to the bias created by the external field, other internal molecular fields produce additional bias which in turn produce interesting signatures on the spectrum of the system, which are potential carriers of information about the molecular state. The fact that the spins are not isolated from the molecular environment, produces a striking effect on the ideal spectrum of the system. These effects contain in them, the signatures of the molecular local environment and are hence of immense interest to physicists, chemists and biologists.

Nesta tese discutimos sistematicamente os efeitos magnetocalórico e barocalórico em sistemas físicos com transição de fase magnética de primeira e de segunda ordem em sistemas físicos cujo magnetismo tem carater local. Para essa finalidade, utilizamos um modelo de momentos magnéticos locais interagentes, incluindo um termo de acoplamento magnetoelástico. Nossos cálculos mostram que a relação entre a interação de troca e o acoplamento magnetoelástico é responsável pela ordem da transição de fase e pelo aparecimento da histerese térmica e magnética. Os resultados mostram que as grandezas magnetocalóricas exibem grandes valores quando o sistema sofre uma transição de fase de primeira ordem. Além disso, quando existe uma histerese visível as grandezas magnetocalóricas dependem do processo de aquecimento e resfriamento do sistema. Ainda de acordo com nossos resultados, existe um efeito barocalórico normal (sistema aquece sob aumento de pressão) quando a pressão aplicada aumenta a temperatura de ordenamento magnético sem alterar a ordem da transição de fase magnética. O efeito barocalórico inverso (sistema resfria sob aumento de pressão) ocorre quando a pressão aplicada diminui a temperatura crítica sem mudar a ordem da transição de fase. Nossos cálculos mostram, ainda, que um efeito barocalórico anômalo (mudança de sinal nas grandezas barocalóricas) ocorre em casos especiais onde a pressão aplicada muda a natureza da transição de fase magnética do primeira para segunda ordem e vice-versa. / In this thesis we systematically discuss the magnetocaloric and barocaloric effects in physical systems, whose magnetism has a localized character and undergo both second and first order phase transitions. For this purpose, we use a model of interacting localized magnetic moments, including the magnetoelastic coupling. Our calculations show that the ratio between the exchange and magnetoelastic parameters is responsible for the appearance of the first order transition and consequently the thermal and magnetic hysteresis. Our calculations also show that the magnetocaloric quantities exhibit large values when the system undergoes a first order transition. Furthermore, when the hysteresis is not negligible, the magnetocaloric quantities depend on the heating and cooling processes. As far as the barocaloric effect is concerned, our calculations show that the normal barocaloric effect occurs (the system heat up with increasing applied pressure) when the applied pressure increases the magnetic ordering temperature without changing the order of the magnetic phase transition. On the other hand, the inverse barocaloric effect (the system cools down with increasing applied pressure) occurs when the applied pressure reduces the magnetic ordering temperature without changing the order of the magnetic phase transition. Finally, our calculations show that an anomalous barocaloric effect (i.e., change of sign in the barocaloric quantities) occurs in special cases when the applied pressure change the nature of the magnetic phase transition from first to second order and vice-versa.

Nesta tese discutimos sistematicamente os efeitos magnetocalórico e barocalórico em sistemas físicos com transição de fase magnética de primeira e de segunda ordem em sistemas físicos cujo magnetismo tem carater local. Para essa finalidade, utilizamos um modelo de momentos magnéticos locais interagentes, incluindo um termo de acoplamento magnetoelástico. Nossos cálculos mostram que a relação entre a interação de troca e o acoplamento magnetoelástico é responsável pela ordem da transição de fase e pelo aparecimento da histerese térmica e magnética. Os resultados mostram que as grandezas magnetocalóricas exibem grandes valores quando o sistema sofre uma transição de fase de primeira ordem. Além disso, quando existe uma histerese visível as grandezas magnetocalóricas dependem do processo de aquecimento e resfriamento do sistema. Ainda de acordo com nossos resultados, existe um efeito barocalórico normal (sistema aquece sob aumento de pressão) quando a pressão aplicada aumenta a temperatura de ordenamento magnético sem alterar a ordem da transição de fase magnética. O efeito barocalórico inverso (sistema resfria sob aumento de pressão) ocorre quando a pressão aplicada diminui a temperatura crítica sem mudar a ordem da transição de fase. Nossos cálculos mostram, ainda, que um efeito barocalórico anômalo (mudança de sinal nas grandezas barocalóricas) ocorre em casos especiais onde a pressão aplicada muda a natureza da transição de fase magnética do primeira para segunda ordem e vice-versa. / In this thesis we systematically discuss the magnetocaloric and barocaloric effects in physical systems, whose magnetism has a localized character and undergo both second and first order phase transitions. For this purpose, we use a model of interacting localized magnetic moments, including the magnetoelastic coupling. Our calculations show that the ratio between the exchange and magnetoelastic parameters is responsible for the appearance of the first order transition and consequently the thermal and magnetic hysteresis. Our calculations also show that the magnetocaloric quantities exhibit large values when the system undergoes a first order transition. Furthermore, when the hysteresis is not negligible, the magnetocaloric quantities depend on the heating and cooling processes. As far as the barocaloric effect is concerned, our calculations show that the normal barocaloric effect occurs (the system heat up with increasing applied pressure) when the applied pressure increases the magnetic ordering temperature without changing the order of the magnetic phase transition. On the other hand, the inverse barocaloric effect (the system cools down with increasing applied pressure) occurs when the applied pressure reduces the magnetic ordering temperature without changing the order of the magnetic phase transition. Finally, our calculations show that an anomalous barocaloric effect (i.e., change of sign in the barocaloric quantities) occurs in special cases when the applied pressure change the nature of the magnetic phase transition from first to second order and vice-versa.

Abstract In this thesis, the theory of static magnetic resonance spectral parameters of nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy is investigated in terms of the molecular Breit-Pauli Hamiltonian, which is obtained from the relativistic Dirac equation via the Foldy-Wouthuysen transformation. A leading-order perturbational relativistic theory of NMR nuclear shielding and spin-spin coupling tensors, and ESR electronic g-tensor, is presented. In addition, the possibility of external magnetic-field dependency of NMR parameters is discussed. Various first-principles methods of electronic structure theory and the role of one-electron basis sets and their performance in magnetic resonance properties in terms of their completeness profiles are discussed. The presented leading-order perturbational relativistic theories of NMR nuclear shielding tensors and ESR electronic g-tensors, as well as the theory of the magnetic-field dependent NMR shielding and quadrupole coupling are evaluated using first-principles wave function and density-functional theories.

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