accuracy of this method for several properties. For instance, Curie temperatures and phase diagrams, as well as the subtle temperature-gradient-induced polarization, were well reproduced in BST materials. Similarly, the existence of two modes (rather than a single one as previously believed for a long time) contributing to the GHz-THz dielectric response of pure BaTiO$_3$ and disordered BST solid solutions were predicted via this numerical tool and experimentally confirmed.

Figures 2(a) and 2(b) report the evolution of the $z$-component of the electrical toroidal moment, G$_z$, and of the polarization, P$_z$, respectively, as a function of the electric field, for a frequency of 1GHz at a temperature of 15K. In practice, G$_z$ is computed within a lattice model [@submitted], by summing over the electric dipoles located at the lattice sites rather than by continuously integrating the polarization field of Eq. (\[eqn1\]) over the space occupied by the nanowires. The panels in Fig. 1 show snapshots of important states occurring during these hysteresis loops, in order to understand gyrotropy at a microscopic level. A striking piece of information revealed by Fig. 2 (a) is that G$_z$ [*linearly decreases*]{} with a slope of $-1.6$ e/V when the applied $ac$ field varies between 0 (state 