Aspects of magnetism: topology, transport, and quantum entanglement

The general theme in this thesis is the exploration of topology, transport, and quantum entanglement in magnetic systems.We first set up the stage in chapter 1 by introducing some notions that we use in later chapters. In chapters 2 and 3, we discuss the (hydro)dynamics of vortices and hedgehogs in two- and three-dimensional insulating magnets, respectively, in both classical and quantum regimes based on the topological conservation laws of vortices and hedgehogs, which follow from their topological nature instead of symmetries of the system Hamiltonian (thus are robust against impurities and anisotropies). To illustrate the applications in spintronics, we formulate an experimentally feasible energy-storage concept based on vorticity (hydro)dynamics within an easy-plane insulating magnet in chapter 2.In chapter 4, we investigate entanglement between two arbitrary spins in a magnetic system in the presence of applied magnetic fields and axial anisotropies. We demonstrate that spins are generally entangled in thermodynamic equilibrium, indicating that the magnetic medium can serve as a resource to store and process quantum information in general. We, furthermore, show that the entanglement can jump discontinuously when varying the magnetic field. This tunable entanglement can be potentially used as an efficient switch in quantum-information processing tasks.Finally, in chapter 5, we present a study on the steady entanglement generation for two distant spin qubits interacting with a common magnetic medium. Our focus is a medium-induced effective coupling (between the two qubits) of dissipative nature. We explore the different dynamical regimes of the entanglement evolution in the presence of this dissipative coupling and demonstrate the advantage of its utilization as a route to generate steady entanglement and even Bell state, insensitive to the initial state. Our work points to a new direction of the application of spintronic schemes in future quantum information technology