Andrey Zelenskiy
LPTMS, Université Paris-Saclay
From kagome antiferromagnets to self-assembly: anisotropic hierarchy in dense and dilute systems
Geometric frustration arises when interactions favour local configurations that are incompatible with the global geometry of the system. To alleviate frustration, many systems adopt locally suboptimal arrangements, often leading to the emergence of complex structures and patterns.
In this talk, I will explore geometric incompatibility in two contrasting systems: magnetic kagome crystals and solutions of patchy particles. In both cases, increasing the anisotropy of interactions generates a hierarchy of competitions, which manifests in the structure of the equilibrium phases.
In kagome magnets with AB-stacked layers, while anisotropic interactions lower the symmetry of the order parameter, they at the same time induce self-duality mappings between distinct regions of parameter space. These mappings reveal extended regimes of high frustration, where even moderate anisotropy drives a cascade of exotic phases, including states that simultaneously exhibit both chiral and nematic order.
By contrast, in solutions of anisotropic particles with short-range interactions, frustration is often relieved through changes in the overall density profile, which defines the shape of the aggregate. Drawing analogies with frustrated magnets, we identify the anisotropic hierarchy for generic patchy particles, and use it as a design principle for encoding structural features and motifs of self-assembled clusters.
