Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.
Symmetry Classes of Spin and Orbital Ordered States in a t2g Hubbard Model on a Two-Dimensional Square Lattice