On the rotation of co-orbital bodies in eccentric orbits

We investigate the resonant rotation of co-orbital bodies in eccentric and planar orbits. We develop a simple analytical model to study the impact of the eccentricity and orbital perturbations on the spin dynamics. This model is relevant in the entire domain of horseshoe and tadpole orbit, for moderate eccentricities. We show that there are three different families of spin-orbit resonances, one depending on the eccentricity, one depending on the orbital libration frequency, and another depending on the pericenter's dynamics. We can estimate the width and the location of the different resonant islands in the phase space, predicting which are the more likely to capture the spin of the rotating body. In some regions of the phase space the resonant islands may overlap, giving rise to chaotic rotation.

Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.

Measurement and modeling of hyperfine properties in ferroic materials

This thesis presents the results of perturbed angular correlation (PAC) experiments , an experimental technique which measures the hyperfine interaction at probes (radioactive ions implanted in the materials to study), from which one infers local information on an atomic scale. Furthermore, abinitio calculations using density functional theory electronic obtain results that directly complement the experiments, and are also used for theoretical research. These methods were applied in two families of materials. The manganites, with the possible existence of magnetic, charge, orbital and ferroelectric orders, are of fundamental and technological interest. The experimental results are obtained in the alkaline-earth manganites (Ca, Ba, Sr), with special interest due to the structural variety of possible polymorphs. With probes of Cd and In the stability of the probe and its location in a wide temperature range is established and a comparison with calculations allows the physical interpretation of the results. Calculations of hyperfine properties in rare-earth manganites are also presented. The second type of materials in which hyperfine properties were studied are the Manganese pnictides: MnAs, MnSb, and MnBi, compounds in which magnetism is fundamental. The experimental results obtained mainly consider the MnAs compound, whose magneto-structural transition is of great interest. The transition is analyzed in detail with the local resolution characteristic of the technique, obtaining information of the character of the transition also with complementary, more conventional techniques. The last work in this thesis uses only the first principles calculations, continuing the theme of the hyperfine interactions, but this time with respect to ferroelectrics. Several transition metal oxides with perovskite or distorted structures are considered. The electric field gradient which exists due to the quadrupole interaction in nuclei is related to the spontaneous electric polarization, the main quantity measured in ferroelectrics. This study provides a fundamental theoretical basis for previous empirical studies, suggesting new directions for research in ferroelectrics and multiferroics using techniques which measure the electric field gradient.