Ferrotoroidic polarons in antiferrodistortive SrTiO3

Ultrasmall ferroelectrics with nontrivial topological field textures such as polar vortices, skyrmions, and merons hold promise in technological paradigms. Such nontrivial ferroic orders and their functionalities, however, inevitably disappear below a critical size of several nanometers. Here, we propose a strategy to overcome this limitation and design atomically small ferroelectrics with topological polarization vortices by engineering excess-electron polarons. Our first-principles calculations demonstrate that excess-electron polarons formed in antiferrodistortive SrTiO3 induce localized ferroelectric polarization with a topological vortex form due to local symmetry breaking and demonstrate the possibility of an atomic-scale "ferrotoroidic" materials. We further show that the electron polaron carries a magnetic moment coupled with ferrotoroidicity, i.e., the magnetoelectric effect. We also discuss possible methods to switch the toroidal moment via the magnetoelectric effect. Our result, thus, provides insight into the ultimate miniaturization of ferrotoroic materials and a class of functional polaron families.