Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques.

Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadic et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n - 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.

Large-scale influence of defect bonds in geometrically constrained self-assembly.

Recently, the importance of higher-order interactions in the physics of quantum systems and nanoparticle assemblies has prompted the exploration of new classes of networks that grow through geometrically constrained simplex aggregation. Based on the model of chemically tunable self-assembly of simplexes [Suvakov et al., Sci. Rep. 8, 1987 (2018)2045-232210.1038/s41598-018-20398-x], here we extend the model to allow the presence of a defect edge per simplex. Using a wide distribution of simplex sizes (from edges, triangles, tetrahedrons, etc., up to 10-cliques) and various chemical affinity parameters, we investigate the magnitude of the impact of defects on the self-assembly process and the emerging higher-order networks. Their essential characteristics are treelike patterns of defect bonds, hyperbolic geometry, and simplicial complexes, which are described using the algebraic topology method. Furthermore, we demonstrate how the presence of patterned defects can be used to alter the structure of the assembly after the growth process is complete. In the assemblies grown under different chemical affinities, we consider the removal of defect bonds and analyze the progressive changes in the hierarchical architecture of simplicial complexes and the hyperbolicity parameters of the underlying graphs. Within the framework of cooperative self-assembly of nanonetworks, these results shed light on the use of defects in the design of complex materials. They also provide a different perspective on the understanding of extended connectivity beyond pairwise interactions in many complex systems.

The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary.

The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the time-scale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the two-dimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.