Evolution of structure and density wave order in La$_{3}$Ni$_{2}$O$_{7-\delta}$</inline-formula> single crystals at ambient pressure

The recent discovery of high-temperature superconductivity in bilayer nickelate La$_{3}$Ni$_{2}$O$_{7-\delta}$ single crystals under high pressure has sparked significant interest in the correlated electronic physics and unconventional pairing mechanisms within Ruddlesden-Popper phase nickelates, where the oxygen content plays a crucial role in both structure and superconductivity. Here we report the evolution of the structure and density wave order in La$_{3}$Ni$_{2}$O$_{7-\delta}$ single crystals at ambient pressure under various oxygen annealing conditions. Structural analysis reveals that with the increase of annealing oxygen pressure, La$_{3}$Ni$_{2}$O$_{7-\delta}$ undergoes a structural phase transition from an orthorhombic to a tetragonal phase. Magnetic torque measurements indicate that the density wave order, present in the orthorhombic phase, vanishes upon transition to the tetragonal structure, accompanied by an abrupt change in carrier concentration. A phase diagram illustrating the dependence of both the crystal structure and density wave order on the annealing oxygen pressure is mapped. Our findings suggest a promising pathway for studying the interplay between structure, density wave order, and superconductivity in bulk nickel-based materials.