fig5

Figure 5. Representative methods for generating strain gradients in oxide materials. (A and B) Misfit strain relaxation in epitaxial thin films. (A) Schematic illustration of strain relaxation in HoMnO₃ thin films. Reproduced with permission^[6]. Copyright 2011, American Physical Society. (B) Relaxation behavior of BiFeO₃ epitaxial films. Reproduced with permission^[54]. Copyright 2013, John Wiley and Sons; (C and D) SPM-tip-induced flexoelectric effects. (C) Schematic illustration of AFM-tip loading on a BaTiO₃/La_0.67Sr_0.33MnO₃ heterostructure. Reproduced with permission^[25]. Copyright 2012, American Association for the Advancement of Science. (D) Schematic and phase-field simulation of ultrathin SrTiO₃ under AFM-tip loading. Reproduced with permission^[33]. Copyright 2020, Springer Nature; (E-G) Interfacial strain gradients in oxide heterostructures and multilayers. (E) Strain and polarization mapping of a-c domain films with corresponding schematic. Reproduced with permission^[21]. Copyright 2011, Springer Nature. (F) Photocurrent mapping and surface morphology of mixed-phase regions. Reproduced with permission^[20]. Copyright 2015, Springer Nature. (G) In-plane piezoresponse vector mapping of strain-graded ferroelectric nanoplates. Reproduced with permission^[59]. Copyright 2018, Springer Nature; (H and I) Bending of freestanding membranes. (H) Schematic and optical images of bent BiFeO₃ membranes. Reproduced with permission^[29]. Copyright 2020, Springer Nature. (I) Cross-sectional STEM image of a wrinkled freestanding BiFeO₃ membrane. Reproduced with permission^[43]. Copyright 2022, Springer Nature. SPM: Scanning probe microscopy; AFM: atomic force microscopy; STEM: scanning transmission electron microscopy; BFO: BiFeO₃; SRO: SrRuO₃; STO: SrTiO₃.