Doctoral Defense in Chemistry - Moritz Sallermann

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Doctoral candidate:
Moritz Sallermann

Title of thesis:
Simulation Study of Hopfions using Atomistic Spin Models

Opponents:
Dr. Viðar Guðmundsson, Professor Emeritus at Faculty of Physical Sciences, University of Iceland
Dr. Vitaliy Lomakin, Professor at the Department of Electrical and Computer Engineering, University of California San Diego, USA

Advisor:
Dr. Hannes Jónsson, Professor at the Faculty of Physical Sciences, University of Iceland

This is a joint defense between the University of Iceland and RWTH Aachen, Germany

Other members of the doctoral committee:
Dr. Pavel Bessarab, Associate Professor at the Department of Mathematics and Physics, Linnaeus University, Sweden
Dr. Nikolai Kiselev, Scientific Staff at Peter Grünberg Institute I, Research Center Jülich, Germany
Dr. Stefan Blügel, Professor at Peter Grünberg Institute I, Research Center Jülich & RWTH Aachen University, Germany

Chair of Ceremony:
Dr. Birgir Hrafnkelsson, Professor and Head of the Faculty of Physical Sciences, University of Iceland

Abstract:
The main protagonists of this thesis, magnetic Hopfions, are three-dimensional topological solitons characterized by the Hopf invariant, a quantity that measures the linking number of pre-images of constant magnetization within magnetic textures. These intriguing solitons appear as local, spatially compact, energy minima in bulk magnetic materials featuring competing exchange interactions, making them ideal candidates for exploring fundamental physical phenomena as well as potential building blocks for advanced spintronic devices. However, determining their practical stability and viability in technological applications necessitates an in-depth analysis of their decay mechanisms, especially in environments subject to thermal fluctuations. In this thesis, we employ an atomistic spin lattice model, concretely a Heisenberg model with competing exchange interactions, to describe the Hopfion, which we investigate by means of atomistic spin dynamics. In particular, we employ harmonic transition state theory (HTST), a powerful and computationally efficient framework, to rigorously assess the lifetime and decay dynamics of Hopfions. We further extend the conventional HTST approach -- as commonly applied to spin systems where only magnetization precession over the transition state is considered -- by explicitly incorporating thermal crossings of the transition state. This extension provides a more complete and physically accurate description of thermally activated decay processes, accounting not only for precessional dynamics but also for thermal fluctuations enabling magnetization states to cross the saddle region, thus improving lifetime predictions. A fundamental example where this contribution is, perhaps, felt the most is the reversal of a single spin under the influence of uniaxial anisotropy (think of a hard ferromagnet) -- where conventional HTST fails to predict any rate at all. To accurately quantify these dynamics, we implement computational techniques such as the geodesic nudged elastic band (GNEB) method combined with an adapted dimer method, enabling precise identification of transition states and corresponding energy barriers associated with Hopfion decay. Following common methodology, we locate first-order saddle points on an energy landscape, representing critical states where decay occurs via the nucleation and subsequent propagation of Bloch points. Our investigations reveal a clear dependence of Hopfion stability on their size, relative to the underlying lattice structure, demonstrating that larger Hopfions generally exhibit increased robustness against decay. Moreover, this research explicitly addresses several critical technical challenges inherent to the computational methods employed. These include (i) the accurate treatment and interpretation of Goldstone modes, which emerge due to inherent symmetry properties of the Hopfion configurations, and (ii) the computational complexity associated with evaluating sparse positive-definite determinants, which is essential for determining entropic pre-factors. By resolving these challenges, our study not only provides quantitative predictions of Hopfion lifetimes but also offers qualitative insights into the interplay between energy and entropy in these topological systems. Through this comprehensive theoretical and numerical analysis, the work presented in this thesis significantly advances the understanding of the fundamental principles governing Hopfion stability.

About the doctoral candidate:
Moritz Sallermann obtained his Bachelor's and Master's degrees in Physics from RWTH Aachen University, Germany. He subsequently joined a joint Ph.D. programme in Physics at RWTH Aachen (conducting research at Forschungszentrum Jülich) and Chemistry at the University of Iceland. His doctoral research focused on the entropy and lifetime of topologically protected magnetic spin structures. At the University of Iceland, he also contributed to the development of a polarizable atomistic water model parametrized against first-principles calculations. He later worked on protein modelling at the Complutense University of Madrid. Beyond physics, his interests include mathematics (particularly numerical methods), scientific programming in C++ and Python, open-source software development, video games, reading, and moderate amounts of exercise.