fig10

Figure 10. Flexoelectric control of magnetism and spin textures in correlated oxides and ferromagnetic metals. (A-C) Strain-driven Dzyaloshinskii-Moriya interaction in LSMO thin films. (A) Schematic of an epitaxial heterostructure showing tensile strain relaxation across the thickness. (B) Experimentally estimated strain gradient as a function of thickness. (C) Magnetic imaging of a skyrmion lattice at 300 K. (A-C) Reproduced with permission^[34]. Copyright 2021, American Physical Society; (D and E) Flexomagnetism in Cr₂O₃ thin films. (D) Illustration of the strain gradient-induced modulation of the Néel temperature across the film thickness. (E) Phase diagram of the antiferromagnetic (AFM)-paramagnetic (PM) transition as a function of temperature and coordinate z. (D and E) Reproduced with permission^[75]. Copyright 2022, Springer Nature; (F and G) Flexomagnetoelectric effect in Sr₂IrO₄ thin films. (F) Crystal schematic highlighting broken inversion symmetry and orbital hybridization along the out-of-plane axis. (G) Out-of-plane magnetization as a function of temperature. (F and G) Reproduced with permission^[35]. Copyright 2024, American Physical Society; (H-L) Flexoelectric polarization in the ferromagnetic metal SrRuO₃. (H) Schematic illustrating shear strain formation and its gradient in a SrRuO₃/SrTiO₃ (111) heterostructure. (I) Atomic-scale images of SrTiO₃ and SrRuO₃ regions corresponding to the boxed areas in (J), showing B-site cation displacement (δ_B) and the projected octahedral tilting angle (θ). (J) Cross-sectional ABF-STEM image of the SrRuO₃ layer. (K) Spatial map of cation displacement (δ_B) in (J). (L) Spatial map of octahedral tilt (θ) in (J). (H-L) Reproduced with permission^[17]. Copyright 2024, Springer Nature; (M and N) Strain gradient-induced momentum-space spin textures in SrIrO₃ thin films. (M) Thickness-dependent strain relaxation and lattice constant variation. (N) Nonlinear magnetoresistance (NLMR) measured as a function of angle and temperature. (M-N) Reproduced with permission^[77]. Copyright 2024, Oxford University Press. LSMO: La_0.67Sr_0.33MnO₃; AFM: atomic force microscopy; STEM: scanning transmission electron microscopy; PM: paramagnetic; ABF: annular bright field.