Toroidal ordering of artificial magnetic systems by spontaneous symmetry breaking

A magnetization protocol is proposed for structures with magnetic ferrotoroidal order as the ground state. First the structures should be magnetized by an out-of-plane magnetic field until saturation, then the out-of-plane magnetic field should be slowly turned off. During the demagnetization process from saturation, a series of spontaneous symmetry-breaking events occur. These symmetry-breaking events create new metastable states at lower fields. The ferrotoroidal state is stable after the first spontaneous symmetry breaking and it remains the lowest-energy state during the switching off of the external magnetic field. The out-of-plane field thus not only lowers the barriers among states, but also destabilizes the higher-energy metastable states of the artificial crystal unit cell, qualitatively changing the free-energy map of the system. This protocol is studied analytically within the macrospin model, numerically on a realistic structure, and is realized experimentally. Switching from nontoroidal to toroidal order is demonstrated on isolated magnetic submicrometer structures as well as on arrays of such structures.