Giant Molecular Toroidal Moment Amenable to Direct Observation in a Fe$_{10}$Dy$_{10}$ Ring (2509.05424v1)

Abstract: In single molecule toroics (SMTs) atomic spins and orbital currents generate magnetic vortices known as toroidal moments $\boldsymbol{\tau}$, endowed with both magnetic and electric dipole symmetries, which can enable spin control via magnetoelectric effects as well as the development of robust qubits. In the archetypal Dy$3$ SMT, $\boldsymbol{\tau}$ is challenging to detect and control. Larger molecular rings can offer an enhanced toroidal response amenable to direct observation and manipulation. Here we report SMT properties for the $3d$-$4f$ icosanuclear molecular ring Fe${10}$Dy${10}$, displaying toroidal excitations of unprecedented magnitude and energy dispersion spanning a $\sim$62 billion dimensional toroidal space. We show these properties can be modeled using an ab initio-parameterised transfer matrix approach yielding excellent agreement with experiments. To assess the bulk toroidal polarization attainable in this system, we introduce the molar toroidal susceptibility $\xi$, a thermodynamic linear response function measuring the SMT finite-temperature toroidal polarization induced by a magnetic field with a small non-vanishing curl. Direct calculation of $\xi$ for Fe${10}$Dy$_{10}$ reveals a significant finite-temperature ground state toroidal polarization which should be amenable to experimental detection via spatially-focused magnetic field curls, as attainable e.g. using focused femtosecond laser pulses. Our findings could thus pave the way for direct observation and manipulation of molecular toroidal moments.