  Toroidal classification and geometric duality in quantum spin systems is
presented. Through our classification and duality, we reveal that various
bipartite quantum features in magnon-systems can manifest equivalently in both
bipartite ferromagnetic and antiferromagnetic materials, based upon the
availability of relevant Hamiltonian parameters. Additionally, the results
highlight the antiferromagnetic regime as an ultra-fast dual counterpart to the
ferromagnetic regime, both exhibiting identical capabilities for quantum
spintronics and technological applications. Concrete illustrations are
provided, demonstrating how splitting and squeezing types of two-mode magnon
quantum correlations can be realized across ferro- and antiferromagnetic
regimes.
