toroidal moment can independently be parallel or antiparallel to the z-axis. These four states have the same probability (of 25%) to occur when cooling the system from high to low temperature. In our simulations, when the system statistically chooses one of these states below the critical temperature, it stays in it when further decreasing the temperature, likely because the potential barrier to go from one of these states to the other three states is too high. Moreover, one can also force the system to be in one of these four states by applying, and then removing, the conjugate fields of the polarization and electrical toroidal moment. For instance, the selection of the states for which the polarization is parallel to the z-axis requires the application of an homogeneous electric field along \[001\]. Similarly, obtaining states with electrical toroidal moment being aligned along \[001\] can be done by applying specific curled electric fields [@Weicurled] (see also Refs. [@Dubovik; @Sergeyinho1; @Sergeyinho2] for more details about how to control toroidal moments). Notice that creating a curled electric field along \[001\] can be practically realized by applying a magnetic field having a time derivative being oriented along \[00$\bar{1}$\], since Maxwell equations directly relate the 