Figure 1

Schematization of the two setups considered in this study, the resulting inhomogeneous electric fields at the sites of the dot, and the ground-state dipole pattern.Reuse & Permissions

Figure 2

(a) Temperature dependency of the toroidal moment (squares) and polarization (dots) in the setup shown in Fig. 1a; and (b–d) resulting dipole pattern at 625, 300, and 1 K, respectively. The filled symbols of panel (a) correspond to simulations in which the inhomogeneous field is turned on while open symbols show results for an isolated dot (that is a dot under no field, and which does not exhibit any polarization). The long and thick arrows of panels (b–d) are guides for the eyes to show the tendency of some dipoles to align along some specific directions. The temperature has been rescaled, as in Ref. 10, to fit the experimental value of the Curie temperature of $\mathrm{Pb}({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}){\mathrm{O}}_3$ solid solution.Reuse & Permissions

Figure 3

Dependency of the Cartesian components of the ground-state toroidal moment and polarization (in the top inset) on the angle of rotation about the $x$ axis of the dipolar source associated with the setup of Fig. 1a. For each angle, the calculations are first performed at high temperature and then slowly cooled down until 1 K. The bottom inset reports the dependency of the ground-state toroidal moment for the setup of Fig. 1b (for which no polarization exists) with respect to the angle of rotation about the $x$ axis of the two dipolar sources.Reuse & Permissions