Inverse symmetry breaking in low dimensional systems

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Competing interactions on various length scales lead to the spontaneous formation of modulated phases in many physical and chemical systems. This thesis investigates the magnetic domain patterns of atomically-thin iron films on the copper (001)-surface, focusing on the two-parameter space of temperature and applied magnetic field. Heating the sample in a constant field reveals a transition from a uniform, saturated state to circular domains, known as the bubble state. This transition breaks the translational symmetry of the domain pattern, followed by a second transition from bubbles to regular stripes of alternating magnetization, which also breaks rotational symmetry. The phase diagram of the system exhibits systematic inverse symmetry breaking, and experiments show scaling and universality in this regime. By utilizing these scaling properties, we can predict the high-temperature phase diagram from ground-state calculations, revealing that inverse symmetry breaking arises from the truly two-dimensional nature of the system. Additionally, dynamic aspects of pattern formation are explored through time-dependent measurements, indicating that the temperature dependence of relaxation times, in response to changes in temperature or magnetic field, suggests a non-Arrhenius-like behavior typical of glassy systems.