Finite-temperature toroidal moment amenable to direct observation in an Fe$_{10}$Dy$_{10}$ molecular ring

Single-molecule toroics host closed magnetic vortices carrying toroidal moments τ, whose electric-dipole symmetry enables magnetoelectric spin control. Yet opposite toroidal chiralities are degenerate in conventional magnetic fields, making direct detection of τ challenging. Current approaches probe toroidal dynamics only indirectly through weak residual magnetism, while finite-temperature toroidal polarisation and realistic preparation/readout conditions remain unestablished. Here we show that the Fe$_{10}$Dy$_{10}$ molecule hosts a 62-billion-dimensional low-energy manifold pervaded by toroidal character, rendered tractable by an ab initio-informed transfer-matrix framework that reproduces experimental data. The model reveals a large toroidal response robust to thermal fluctuations, quantified by a finite-temperature toroidal susceptibility ξ. We then propose a preparation-and-readout protocol in which a train of temporally asymmetric near-infrared pulses accumulates toroidal polarisation, converted through magnetoelectric response into a measurable electric-field-induced magnetic signal. These results establish Fe10Dy10 as a molecular system where τ can be prepared, accumulated and read out under realistic conditions.