| Summary: | 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 (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size <i>n</i>, and with probability <i>p</i> 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 <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula> frustrated triangles per <i>n</i>-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 <i>n</i>. At the same time, remnant magnetisation occurs when <i>n</i> is even, and in poly-disperse assemblies of cliques in the range <inline-formula> <math display="inline"> <semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mo>[</mo> <mn>2</mn> <mo>,</mo> <mn>10</mn> <mo>]</mo> </mrow> </semantics> </math> </inline-formula>. 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.
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