Interaction between an electron and a skyrmion in a Néel antiferromagnet, and combined study of families of classical spin liquids. – (Naïmo Davier / LPT / Thèses). – 11/07/23, 10H30

Thesis defense

Naïmo Davier, LPT, Salle de Conférence FERMI 3R4

Summary
In this thesis, we are interested in two distinct subjects, which nevertheless have in common the fact that they deal with magnetism and topology, and that they are both treated almost exclusively in an analytical manner.

The first subject concerns the behaviour of an electron in a two-dimensional Néel antiferromagnet. We are particularly interested in the presence of a very special defect called a skyrmion, which intrinsically carries a topological charge. The case of a ferromagnetic material has already been studied and revealed that the electron is scattered by the skyrmion, and that this scattering depends on the spin orientation of the electron and the topological charge of the skyrmion. The antiferromagnetic case turns out to be richer here, since there is certainly a potential scattering of the electron by the skyrmion, again involving the spin orientation of the electron and the topological charge of the skyrmion. the electron spin, but also the possibility of the existence of electron-skyrmion bound states. In particular, we show that the spatial structure, energy and existence of such bound states depend on the profile of the skyrmion at hand. We begin by constructing a quantum description of the electron-skyrmion coupling, before applying it to different relevant skyrmion profiles, in order to illustrate the different physical consequences of this cooupling. It appears that the number of existing bound states increases with the spatial extent of the skyrmion, and that the spatial and energy structure of these states depend very strongly on the skyrmion profile. Contrary to what intuition might suggest, the existence of these bound states results in a global energy cost for the skyrmion and not a gain. This energy cost also turns out to be sensitive to the spatial structure of the skyrmion, and will therefore favour certain skyrmion profiles. It also appears that pairing a skyrmion with electrons modifies the optical absorption properties locally around the skyrmion, making it possible to detect an antiferromagnetic skyrmion.

The second subject concerns classical spin liquids, a state of matter with very specific properties that has attracted great attention in recent years. We are particularly interested in a family of Hamiltonians, having the peculiarity of beings defined on groups of spins, and likely to harbor such states. We focus on different methods of analytical and numerical analysis to identify and characterize the different classical spin liquids obtained with this family. These methods are applied to three different Hamiltonians, allowing us to illustrate the effectiveness of these analysis tools on the one hand, and the richness of the spin liquids generated by this family of Hamiltonians on the other hand. Some specific characteristics of observed spin liquids are studied in detail, thus serving as novel case studies.