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Concept# Spin (physics)

Summary

Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin should not be understood as in the "rotating internal mass" sense: spin is a quantized wave property.
The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The existence of the electron spin can also be inferred theoretically from the spin–statistics theorem and from the Pauli exclusion principle—and vice versa, given the particular spin of the electron, one may derive the Pauli exclusion principle.
Spin is described mathematically as a vector for some particles such as photons, and as spinors and bispinors for other particles such as electrons. Spinors and bispinors behave similarly to vectors: they have definite magnitudes and change unde

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High Cr (9-14% Cr) ferritic/martensitic steels are considered as one of the most promising candidates for structural materials for advanced nuclear power plants. Therefore, the understanding of the evolution of properties under operation conditions is of primary importance. This work focuses on the effect of Cr composition on the local atomic and magnetic structure of pristine and ion-irradiated FeCr alloys. The materials considered for this study are commercial purity FeCr binary alloys with varying Cr content up to 16% at.Cr, which were also implanted with heavy ions (Fe+) under different conditions. Using a combination of spatially resolved and element specific techniques the following results were obtained: - The dependence of the total (bulk) magnetic moments is linearly decreasing as the Cr-content is increasing - The Fe magnetic moments at the surface reduced by the presence of impurities and defects. The dependence on Cr-content is non-linear, with a tendency of increasing the spin moments above 10% Cr. - The Cr spin moments exhibit a reorientation transition around 9% Cr from ferromagnetically to anti-ferromagnetically aligned with respect to the Fe spin moments. - The effects of ion irradiation are fairly complex, with an overall higher spin magnetic moment after exposure to the heavy ions. The ion dose has a reduced effect on the spin moments while the target temperature shows a more significant, but scattered influence on the Fe spin moments. - All specimens show a decrease of the Cr nearest neighbor distance for Cr contents between 6 – 10% Cr. Also, the atomic disorder around the Cr atoms is enhanced compared to the Fe atoms. - For the Fe9% Cr irradiated alloy the effect of elevated temperatures and dose is clearly seen as a reduction of atomic coordination numbers around the Cr atoms, which can be associated with formation of vacancies. - For the Fe5% Cr and Fe12% Cr alloys, the number of nearest neighbors around the Cr atoms is not sensitive to irradiation.

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This thesis investigates the magnetic properties of single atoms and dimers adsorbed on graphene and oxide decoupling layers supported by single crystal metal substrates, using scanning tunneling microscopy (STM) and spin-polarized scanning tunneling microscopy (SP-STM). The goal is twofold: to use SP-STM to further advance the understanding of the interactions that determine the magnetic stability of Dy adatoms on graphene/Ir(111) and Ho adatoms on MgO/Ag(100), and to use insights from these systems to motivate the study of new systems-- mainly, IrCo heterodimers on graphene/Ir(111).For Dy adatoms on graphene/Ir(111), the characteristic lifetime of the spin system is measured as a function of temperature and tunnel bias, probing the available magnetization reversal pathways in the energy level diagram. The necessity of including the intra-atomic exchange to correctly describe spin lifetimes is demonstrated. In addition, naturally abundant Dy isotopes possess two possible nuclear spin values. Models of both nuclear spin cases of Dy are compared, and shown to produce similar behavior in the temperature and bias ranges probed by SP-STM. Furthermore, accounting for both nuclear spin cases allows for modeling of X-ray magnetic circular dichroism (XMCD) magnetization sweeps. For Ho adatoms on MgO/Ag(100), novel measurement protocols are used to determine the zero-field stability, and the correct ground state model. These protocols are also used to induce magnetic state reversal via Landau-Zener tunneling at avoided level crossings due to the hyperfine interaction. Finally, the study of the IrCo heterodimer adsorbed on graphene is motivated with stability considerations derived from the studies of Dy adatoms on graphene/Ir(111) and Ho adatoms on MgO/Ag(100), in addition to calculations based on density function theory (DFT). Strategies of engineering these heterodimers using statistical growth and atomic manipulation are successfully implemented. The heterodimer is highly mobile on graphene/Ir(111) and displays geometric instability, consistent with its predicted upstanding geometry. Despite this, measurement via STM and SP-STM is demonstrated. Observations are consistent with the robust magnetic stability expected from DFT studies, but additional investigation is needed to disentangle the measurements made thus far.

Conformal field theories (CFTs) play a very significant role in modern physics, appearing in such diverse fields as particle physics, condensed matter and statistical physics and in quantum gravity both as the string worldsheet theory and through the AdS/CFT correspondence. In recent years major breakthroughs have been made in solving these CFTs through a method called numerical conformal bootstrap. This method uses consistency conditions on the CFT data in order to find and constrain conformal field theories and obtain precise measurements of physical observables. In this thesis we apply the conformal bootstrap to study among others the O(2)- and the ARP^3- models in 3D.
In the first chapter we extend the conventional scalar numerical conformal bootstrap to a mixed system of correlators involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current J. The inclusion of a conserved spinning operator is an important advance in the numerical bootstrap program. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. Concentrating on the O(2) model we extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.
In the second chapter we investigate the existence of a second-order phase transition in the ARP^3 model. This model has a global O(4) symmetry and a discrete Z_2 gauge symmetry. It was shown by a perturbative renormalization group analysis that its Landau-Ginzburg-Wilson effective description does not have any stable fixed point, thus disallowing a second-order phase transition. However, it was also shown that lattice simulations contradict this, finding strong evidence for the existence of a second-order phase transition. In this chapter we apply conformal bootstrap methods to the correlator of four scalars t transforming in the traceless symmetric representation of O(4) in order to investigate the existence of this second order phase transition. We find various features that stand out in the region predicted by the lattice data. Moreover, under reasonable assumptions a candidate island can be isolated. We also apply a mixed t-s bootstrap setup in which this island persists. In addition we study the kink-landscape for all representations appearing in the t times t OPE for general N. Among others, we find a new family of kinks in the upper-bound on the dimension of the first scalar operator in the "Box" and "Hook" representations.