Comparing Quantum and Semi-Classical Approaches to Non-Collinear Magnetism in an Electron-Spin Dimer

Abstract: In this bachelor thesis, an explorative theoretical analysis is presented on a model system characterized by various and competing magnetic interactions. The system comprises two localized magnetic moments (spins), and a single itinerant electron that hops between two orbitals located at the spins’ positions. The spins, treated as either fully quantum, hybrid quantum-classical, or fully classical, interact via Heisenberg exchange and Dzyaloshinskii-Moriya interaction (DMI), with the always quantum-mechanically treated itinerant electron coupled to the spins through s-d (Kondo-like) coupling. The core objective of this research was to scrutinize and compare the results obtained from these three distinct approaches for treating the spins. Findings suggest that the agreement between the different methods improves when the DMI term is less influential than the others, and that slow perturbations tend to enhance the agreement between the solutions. It was observed that the hybrid quantum-classical solutions often align more closely with the full quantum solution than the fully classical ones, with discrepancies arising likely due to complex quantum effects and entanglement. Future research could further this study of the simple model studied here (and related ones) via an extensive exploration in the parameter space, and discern the general conditions under which the mixed quantum-classical methods perform optimally. This in turn would give useful indications on the scope of mixed quantum classical treatments of realistic magnetic materials thereby offering deeper insights into the behavior of such systems