Transverse Square Toroidal Vortices with Giant Ferrotoroidic Coupling in Dy-Bridged Single-Molecule Toroics

Toroidal moments in single-molecular toroics (SMTs) are promising degrees of freedom for next-generation qubits that are protected from weak, short-range magnetic interactions, with immediate application to quantum computation, molecular spintronics and information storage. While the intramolecular entanglement of toroidal moments has been achieved by bridging triangular Dy SMT moieties with ions, an analogous coupling via ions has been only partially explored. Here, we utilise a joint computational and theoretical approach to study two previously synthesised heterometallic complexes, Cu2Dy7 and Cu4Dy12, comprised of two and four triangular Dy magnetic subunits, respectively, bridged by trivalent dysprosium ions. Using multiconfigurational ab initio calculations in conjunction with a microscopic model, we reproduce the experimentally observed magnetic responses and determine the ground and excited state spin textures of each molecule. Unlike the MLn6 systems studied previously in the literature, the maximal toroidal moments in Cu2Dy7 are hosted by high-lying excited states and are delocalised across both SMT moieties, forming a planar, quadrilateral magnetic vortex configuration perpendicular to the triangles' pseudo-C symmetry axis. These unconventional excited states also exist in the larger complex, Cu4Dy12 and strongly couple in ferrotoroidic and antiferrotoroidic configurations with coupling constants of unprecedented magnitude.