Comparing Quantum and Semi-Classical Approaches to Non-Collinear Magnetism in an Electron-Spin Dimer
(2023) FYSK03 20231Department of Physics
Mathematical Physics
- 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.... (More)
- 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 (Less)
- Popular Abstract
- Welcome aboard on this thrilling journey through the realm of quantum mechanics with this bachelor's thesis! We're setting sail into a model system, a microcosm brimming with various and competing magnetic interactions. Think of this system as a magnetic playhouse where two localized magnetic moments, or "spins", and a single itinerant electron—that hops between two orbitals—put on a captivating show.
These magnetic actors aren't merely two-dimensional characters; they're full of complexities, and it's these complexities that we aim to explore. Picture our spins as actors donning different costumes, sometimes fully quantum, sometimes hybrid quantum-classical, and other times fully classical. Their performances change with each role, and... (More) - Welcome aboard on this thrilling journey through the realm of quantum mechanics with this bachelor's thesis! We're setting sail into a model system, a microcosm brimming with various and competing magnetic interactions. Think of this system as a magnetic playhouse where two localized magnetic moments, or "spins", and a single itinerant electron—that hops between two orbitals—put on a captivating show.
These magnetic actors aren't merely two-dimensional characters; they're full of complexities, and it's these complexities that we aim to explore. Picture our spins as actors donning different costumes, sometimes fully quantum, sometimes hybrid quantum-classical, and other times fully classical. Their performances change with each role, and this system is their stage. The spins engage in a dramatic interplay via Heisenberg exchange and Dzyaloshinskii-Moriya interaction (DMI), while the itinerant electron, always quantum-mechanically treated, binds to the spins through s-d (Kondo-like) coupling.
But what's a play without a twist? Our plot revolves around comparing the results from these three distinct approaches to treating the spins. The burning question is: which approach best captures the magnetic dance taking place on our stage? As the curtain rises, our initial findings suggest that coherence between the different methods improves when the DMI term plays a smaller role than the others. Moreover, slow perturbations in the plot seem to enhance the agreement between the solutions.
There's no cut-and-dry ending to this quantum tale. The hybrid quantum-classical solutions often align more closely with the full quantum solution than the fully classical ones. However, discrepancies arising may be due to quantum plot twists and entanglement. What's next in this magnetic drama? Further research might continue this saga by thoroughly exploring the parameter space to pinpoint under what conditions mixed quantum-classical methods perform best.
So fasten your seatbelts, folks! Join us on this exhilarating journey as we delve deeper into the magnetic universe, pushing the boundaries of our understanding of quantum mechanics and magnetic systems. There's plenty to learn and lots to ponder, so let's set the stage and watch the magnetic dance unfold! (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9133488
- author
- Jamo Abdi, Sherwan LU
- supervisor
- organization
- course
- FYSK03 20231
- year
- 2023
- type
- M2 - Bachelor Degree
- subject
- keywords
- Skyrmion Electron Spin Dzyaloshinskii-Moriya Interaction (DMI) Ehrenfest Semiclassical
- language
- English
- id
- 9133488
- date added to LUP
- 2023-08-15 08:55:03
- date last changed
- 2023-08-15 08:55:03
@misc{9133488,
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}},
author = {{Jamo Abdi, Sherwan}},
language = {{eng}},
note = {{Student Paper}},
title = {{Comparing Quantum and Semi-Classical Approaches to Non-Collinear Magnetism in an Electron-Spin Dimer}},
year = {{2023}},
}