Abstract
The magnetic behavior of two-dimensional (2D) periodic ensembles of dipole-coupled nanoparticles (NPs) is investigated theoretically by considering all possible structural organizations in 2D Bravais lattices, namely, square, triangular, rectangular, rhombic, and oblique lattices. The different interaction-energy landscapes (ELs) are characterized by determining the local minima that define the stable and metastable magnetic configurations as well as the transition states connecting them. The topology of the resulting ergodic ensemble of stationary states is analyzed from both local and energy perspectives by calculating the corresponding kinetic networks and disconnectivity graphs. For all lattices, the magnetic orders of the ground-state and low-lying metastable configurations are identified, including the elementary relaxation processes between them. A remarkable profound dependence of the collective magnetic behavior on the structural arrangement of the NPs is revealed. Square and triangular nanostructures are extremely good structure seekers, showing starlike kinetic networks and disconnectivity graphs with palm-tree form. Their continuously degenerate ground states are throughout-reaching hubs connected to nearly all excited magnetic configurations over a single first-order saddle point. Rhombic ensembles have double-funnel ELs in which the time-inversion-related ground states play the role of hubs with exceedingly high connectivity densities. These systems need to undergo very few elementary transitions with small downward energy barriers to relax from any configuration towards one of the ground states. However, the energy barriers between the two funnels are quite large and, furthermore, they increase as the number of particles in the unit cell is increased. Therefore, ergodicity breaking is expected in the thermodynamic limit. Finally, the rectangular and oblique lattices show contrasting ground-state orders, the former consists of an antiferromagnetic alternation of head-to-tail chains of spins while the latter is ferromagnetic. Nevertheless, the ELs of these nanostructures are qualitatively very similar. In both cases, all excited magnetic configurations consist of independent flipping of the chains of spins that are formed along the direction of the shorter Bravais vector. The whole energy spectrum of metastable magnetic configurations can thus be mapped to a one-dimensional Ising model. As a result, the kinetic network of stationary points is latticelike and the disconnectivity graphs have a willow-tree form. In conclusion, the collective magnetic behaviors of nanostructures having different point-group symmetries are contrasted and related by varying the parameters of the lattices that interpolate between them.
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