Tunable ferromagnetism via in situ strain engineering in single-crystal freestanding SrTiO3-δ membrane

Engineering stoichiometry and lattice field in transition metal oxides (TMOs) is recognized as a promising approach for achieving emergent functional properties and exploring fundamental scientific questions. To overcome the constraints of rigid epitaxial TMOs, this study releases and transfers freestanding SrTiO_3-δ (STO_3-δ) membranes, derived using a water-dissolution method from STO_3-δ/Sr₃Al₂O₆/SrTiO₃, onto flexible polyimide. In-plane mechanical strains were then applied to investigate the strain evolution-induced ferromagnetism. Continuous strain modulates interplane and intraplane exchange interactions between neighboring atoms in the ferromagnetic STO_3-δ membranes, thereby influencing their ferromagnetic properties. STO_3-δ initially undergoes in-plane octahedral distortion when strain is less than 1.5%, followed by a decrease in the out-plane lattice constant. This structural variation leads to complex strain-dependent behaviors in the saturation magnetic moment (M_s) and coercive field (H_c) of STO_3-δ, with M_s and H_c exhibiting a nonlinear, volcano-shaped, and step-wise correlation, respectively. Our research demonstrates that freestanding STO_3-δ serves as a platform for studying local defects and their impacts on tunable magnetic properties, greatly enhancing our understanding of t_2g electron engineering through modulable inter/intra plane exchange coupling with lattice field.