Dinâmica de mágnons na presença de defeito topológico - Silva, Daniel Borges (2018)
"The advent of Quantum Mechanics brought a new understanding of the world and new perspectives of technology, such as methods of optimization and alternatives to classical electronics. Recently an alternative has been sought for conventional electronics based on the electric current, this electronics would be based on spin propagations, and therefore we call it spintronics. In view of this perspective, the study of spin waves and magnetic phenomena in solid state physics is of paramount importance. Therefore, we have studied Magnons from the quantum Hall eﬀect and sought the dynamics of these quasi particles subjected to a topological defect. In this work we will review the Aharonov-Bohm and Aharonov-Casher Eﬀect to understand the quantum phases as geometric phases. We will study the Berry phase as the result of an external inﬂuence and Berry’s curvature to then verify the occurrence of the Quantum Hall eﬀect. We sought the quantization of Landau for neutral particles with magnetic and electric dipole moment subjected to external electromagnetic ﬁelds. We sought to conceptualize magnons as collective low energy excitations and look for the occurrence of Hall Eﬀect for them through the quantization of the Transverse Hall conductance. We also look for the Thermal Hall conductance due to a temperature gradient and thus the thermomagnetic ratio, we observe that such a reason follows Wiedemann-Franz’s law. We also review the Landau quantization for a neutral particle with a magnetic dipole moment and subjected to a topological defect of the cosmic string type and verify that the presence of the defect breaks the inﬁnite degeneration of the Landau levels. In this work we consider the Hamiltonian proposed by Bakke, Ribeiro, Furtado and Nascimento (2009) [25] as the eﬀective hamiltonian of the magnons in the presence of topological defect of the type cosmic string and we ﬁnd the levels of Landau for the system. With this, it was possible to ﬁnd preliminary results of Hall and Hall Thermal conductance of magnons in the curved space of the cosmic string at the non-relativistic and low temperature limits. Studying the properties of a network of magnons this work also seeks to instigate research that seeks to understand the behavior of the properties of these quasi-particles subjected to topological defects of various types and thus contribute to a better understanding of the dynamics of magnons and their properties."