Magnetisation processes in geometrically frustrated spin networks with self-assembled cliques

Abstract

(c) 2020 by the authors. Functional design of nanostructured materials seeks to exploit 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:1912.4331v1], we grow nanonetworks with geometrical constraint self-assembly of simplexes (cliques) of a given size n; 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, entropy, and graph-theoretic measures to characterise the structure of these assemblies. Further, we show how the size 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 multi-scale 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, remanent magnetisation occurs when n is even, as well as in poly-disperse assemblies of cliques in the range n 2 [2, 10]. These results shed light on spin dynamics in complex nano-magnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.