fig1

Figure 1. Overview of the classification and functionalities of complex oxide heterostructures based on different gradient engineering strategies. (A-E) Strain gradient engineering. (A) Flexo-photovoltaic effect. Reproduced with permission^[20]. Copyright 2015, Springer Nature; (B) Flexocatalysis. Reproduced with permission^[62]. Copyright 2023, John Wiley and Sons; (C) Polarization switching and domain tailoring. Reproduced with permission^[25]. Copyright 2012, American Association for the Advancement of Science; (D) Magnetic skyrmions. Reproduced with permission^[34]. Copyright 2021, American Physical Society; (E) Ferromagnetic polar metal. Reproduced with permission^[17]. Copyright 2024, Springer Nature; (F-H) Electric-field gradient engineering. (F) Flexoelectric actuators. Reproduced with permission^[27]. Copyright 2016, Springer Nature; (G) Converse flexoelectric effect through piezoresponse force microscopy. Reproduced with permission^[26]. Copyright 2019, Springer Nature; (H) Converse flexoelectric effect-induced bending. Reproduced with permission^[83]. Copyright 2018, American Chemical Society; (I-K) Chemical gradient engineering. (I) Domain structure engineering. Reproduced with permission^[109]. Copyright 2016, Springer Nature; (J) Polarization gradient. Reproduced with permission^[108]. Copyright 2017, Springer Nature; (K) Improved pyroelectric effect. Reproduced with permission^[106]. Copyright 2013, American Chemical Society. 2D: Two-dimensional.