Ferroic systems under considerable geometrical restrictions at nanoscale have successfully introduced novel phases such as multiferroic and topological phases. However, ferroic orders completely disappear below the critical size limit of several nanometers and the geometry cannot be relied upon to produce a variety of phases. Here, via first-principles calculations, we demonstrate that a rich variety of phases and their transitions can be realized by dislocations in paraelectric ${\mathrm{SrTiO}}_3$. We show that atomic-scale ferroelectricity and (anti)ferromagnetism are induced by the strain concentration and nonstoichiometry intrinsic to dislocations in ${\mathrm{SrTiO}}_3$, resulting in ferroelectric-(anti)ferromagnetic-multiferroic phase transitions depending on the core structure. Furthermore, we also show that electrical polarization configurations strongly depend on the strain distribution around a dislocation and topological phases can be realized without geometrical restrictions. The present result suggests that the utilization of defects in a material is a powerful strategy to design ferroic orders below the critical size, thereby expanding the application of ferroic nanostructures to the atomic scale.

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• Defects
• Electric polarization
• Electronic structure
• Ferroelectricity
• Magnetism
• Phase transitions
• Topological phase transition