Figure 2

Results of the m = 4.5 SL with n-n type interfaces.

(a) Schematic crystal structure. The initial FE polarization points from left to right; (b) The local displacements between anions and cations. Both the PE and FE conditions with (+M)/without magnetism are shown by different symbols. The corresponding symbols with magnetism almost overlap with those without magnetism. The vertical olive dash lines and cyan dot lines denote the interfaces and domain walls, respectively. For reference, the red and blue dot lines denote the Ti-O and Pb-O relative displacements of PTO bulk on LAO substrate, respectively. (c) Local magnetic moments. Here only Ti atoms show finite magnetic moments. (d,e) Sketch of the mechanisms for the (d) PE and (e) FE conditions. The internal built electric fields from the two interfaces to the center of doped electron tune the FE domains.