Energy Minimization and Thermal Fluctuation in Artificial Magnetic Penrose Ice

This thesis addresses the behaviour of the artificial magnetic Penrose tiling pattern in three different states: the as-fabricated state, the ac demagnetised state and the thermally annealed state. The artificial magnetic Penrose tiling comprises magnetic nano-elements, which are
termed "islands", forming a Penrose tiling patterned from a 2-D film. The main focus is the energy minimisation effect of these three protocols and the effect of frustration on the thermal fluctuation processes. The experimental investigations were conducted via magnetic force microscopy.

A well-defined ground state for the Penrose pattern was theoretically predicted based on consideration of the nearest neighbour dipolar interaction. In this predicted ground state, a twofold degenerate rigid
framework that spans the system is interspersed with islands for which the moment direction is not defined, since both directions are energetically degenerate. The experimental samples were then characterised
in terms of the population of the rhombuses which are the basic units of the Penrose tiling. The predicted long-range order in the system-spanning framework was not found from any states in the experiments.
Further to this, a correlation function was defined for this pattern and evaluated for the three different states. The correlation length extracted from the correlation function indicates that the thermally annealed state has longer range order than other two states, and this conclusion is corroborated by the domain size measurement from colour mapping of domains (the configuration of arrays are mapped by different colours depending on whether the configuration is the as or different to the ground state). The moments of the nano-elements are found to be only locally correlated in the thermally annealed samples,
which was believed to be due to the blocking temperature distribution emerging during the thermal annealing process. However, this hypothesis failed to explain an anomaly in the vertex energy distributions from the thermally annealed samples. One certain type of vertex was found be stuck in a high energy state rather than the lowest energy state after the thermal annealing. Based on the blocking temperature
estimation and magneto-static energy calculation, the energy distribution of each vertex at the blocking temperature was found to follow the Boltzmann distribution multiplied by a degeneracy factor. This result agrees with the vertex energy distribution extracted from the experiments at room temperature. This agreement shows that the energy minimization of the Penrose tiling is restricted by the ratio of vertex energy and the blocking temperature, giving a guide for future investigations.