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Concept# J-coupling

Summary

In nuclear chemistry and nuclear physics, J-couplings (also called spin-spin coupling or indirect dipole–dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins that arises from hyperfine interactions between the nuclei and local electrons. In NMR spectroscopy, J-coupling contains information about relative bond distances and angles. Most importantly, J-coupling provides information on the connectivity of chemical bonds. It is responsible for the often complex splitting of resonance lines in the NMR spectra of fairly simple molecules.
J-coupling is a frequency difference that is not affected by the strength of the magnetic field, so is always stated in Hz.
Vector model and manifestations for chemical structure assignments
The origin of J-coupling can be visualized by a vector model for a simple molecule such as hydrogen fluoride (HF). In HF, the two nuclei have spin 1/2. Four states ar

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Multiple refocusing cycles can be used to extract transverse relaxation rates, R2, while homonuclear scalar couplings do not interfere. In this work, I have demonstrated the usefulness of a hybrid sequence, which is a compromise between single and multiple refocusing sequences, in order to investigate homonuclear scalar coupled spin systems, and to find a regime where the decays used to extract transverse relaxation rates are not modulated by cosine functions due to J-couplings. It was possible to measure the transverse relaxation rates of carbon-13 in doubly-enriched glycine and compare them with those of carbon-13 in singly-enriched glycine samples, which were in good agreement, and confirmed the feasibility of extracting R2 rates in coupled spin systems. I also investigated spin systems with more than one J-coupling interaction, and showed by experiments and numerical simulations that the increased complexity of the system reduces the possibilities of extracting unmodulated decays.

This thesis presents results of studies of novel compounds modeling complex fundamental physics phenomena. Cu2OSO4 is a copper based magnetic Mott Insulator system, where spin half magnetic moments form a new type of lattice. These intrinsically quantum pins are exhibiting atypical magnetic order and spin dynamics. The recent success in the growth of large single crystals of Cu2OSO4 enabled to perform measurements probing its static and fluctuating properties. The peculiarity of this sample is that its atoms are forming layers, with a geometry close to the intensively studied Kagomé lattice, but with a third of its spins replaced by dimers. This quantum magnetism system has been probed in its bulk, by the means of heat capacity and DC-susceptibility measurements, revealing a transition to a magnetically long range ordered state upon cooling, the details of which are revealed by neutron scattering. Single crystal inelastic neutron scattering shed light on the spin-dynamics in the system, with clear spin waves appearing as fluctuations around the peculiar ground state of the system: a 120 degrees spin configuration where the magnetic moment of the spin-dimer causes the sample to be globally ferrimagnetic. The presented results indicate that Cu2OSO4 represents a new type of model lattice with frustrated interactions where interplay between magnetic order, thermal and quantum fluctuations can be explored. The magnetic excitations of the compound can be modeled by a yet-to-be-understood internal effective mean-field that no simple magnetic coupling seems to reproduce. K2Ni2(SO4)3 is another compound that allows for the existence of non-trivial topological phases. This thesis presents results of the study of the unusual magnetic behavior of K2Ni2(SO4)3. No clear sign of well-established magnetic long range order has been observed down to dilution temperatures. Neutron scattering reveals the details of the competition between frustration and fluctuations that prevent order from settling in. Low temperature spin excitations take the form of a continuum at 500 mK, but also of broad, energy independent continua at higher temperatures. Bulk and neutron scattering measurements are put in perspective and linked together with a view to building up a better understanding of how quantum spin liquids can be stabilized in general, and in particular in this model compound. Finally, the last contribution of this thesis to the field of condensed matter physics regards the establishment of a state-of-the-art technique to fit heat capacity and unit cell volume of samples to try and make the extraction of magnetic information from specific heat measurements more robust. This newly-developed technique consists in modeling lattice contributions with better accuracy by using data from multiple experimentally accessible quantities to consolidate the fitting scheme. This method has been cautiously applied to several compounds at the forefront of research in experimental physics.

Magnetic impurities generate a wealth of phenomena on surfaces. On metals, conducting electrons screen the magnetic moment giving rise to the Kondo effect. On superconductors, the Yu-Shiba-Rusinov (YSR) states emerge inside the superconducting gap due to the exchange coupling. In this thesis, we use a scanning tunneling microscope (STM) with a base temperature of 10mK to study magnetic impurities on surfaces. This thesis contains two parts, the interplay between magnetic impurities and superconductivity as well as the tunneling processes between YSR states.Concerning the interplay between magnetic impurities and superconductivity, the single impurity Anderson model (SIAM) offers a consistent picture, in which the impurity substrate coupling is a central parameter of experimental relevance. For YSR phenomena, the mean field (MF) approximation is usually sufficient which gives analytical results for a quantitative interpretation of the experimental data. We tune the coupling by the atomic forces in the junction and quantitatively identify the key role of the coupling in the YSR energy. We further investigate multiple Andreev reflections (MARs) involving a single YSR state, confirming the absence of a spin forbidden family of MARs thereby proving the spin non-degeneracy of the YSR states experimentally.The presence of YSR impurities not only gives rise to peaks in the tunneling spectra, but also influences the superconducting ground state. At a small coupling, the impurity spin is unscreened, which results in a pi phase shift in the Josephson transport. At a large coupling, the impurity spin is screened and the phase is 0. The change of the YSR ground state qualifies as a quantum phase transition (QPT). We observe a significant step in the Josephson current when tuning the coupling across the QPT, which signals the 0-pi transition and the change of the ground state.We then go beyond the MF approximation and include correlation effects in the SIAM to fit the Kondo effect in the magnetic field. We present the scaling between the YSR energy and the Kondo temperature connected by the SIAM. Despite the close relation between the two phenomena, the question remains that to which extent the correlation effects persist in the superconducting state. On this, we show that the correlation effects manifest as an offset current in the YSR measurements.Conventionally, the STM tip only serves as a probe to unravel the sample properties. However, in principle the tip, sample and junction form one quantum system. With the capability to controllably introduce YSR states of desired properties on the tip apex (the YSR-STM), we construct a minimal tunnel junction between two discrete levels, a YSR state on the sample and a YSR state on the tip apex. The tunneling between two YSR states, Shiba-Shiba tunneling, features sharp current peaks, the area of which reveals the relaxation dynamics. We further show that the spin plays an important role in Shiba-Shiba tunneling and we find a behavior consistent with paramagnetic impurities. To conclude, this thesis presents multiple experimental aspects of a single YSR state quantitatively explained by the SIAM, both on the MF level and in the fully correlated situation. The possibility to functionalize the STM tip with a YSR state opens more possibilities, and we show the tunneling between two YSR states as a first application, laying the basis for possible extension of the YSR-STM to more scenarios.