state 3$'$) or positive (from state 5$'$ to state 2), depending on the sign of the polarization.

Such possibility of having both negative and positive gyrotropic coefficients in the same system originates from the fact that the polarization can be down or up, and is consistent with Eqs. (\[eq38\]), (\[eq35a\]) and (\[eq33\]). As a result, one can turn the polarization of light either in clockwise or anticlockwise manner in electrotoroidic systems, via the control of the direction of the polarization by an external electric field – which induces the switching between the dextrorotatory and laevorotatory forms of these materials (see states 1 and 1$'$). Such control may be promising for the design of original devices [@footnotedegen; @footnoteconj].

Figure 3 shows how the gyrotropic coefficient $g_{11}$ depends on temperature. One can clearly see that $g_{11}$ significantly increases as the temperature increases up to 240K. As indicated in the figure, the temperature behavior of $g_{11}$ is very well fitted by $A/\sqrt{(T_C-T)(T_G-T)}$, where $A$ is a constant, $T_C=240K$ is the lowest temperature at which the polarization vanishes and $T_G=330K$ is the lowest temperature at which the electric toroidal moment is annihilated [@submitted]. In order to understand such fitting, let us combine Eqs (\[eq33\]), 