Fig. 1: The structure and magnetic torque measurements for orthorhombic and tetragonal La3Ni2O7-δ at ambient pressure.

a and b The crystal structure model of orthorhombic and tetragonal La3Ni2O7-δ at ambient pressure, respectively. There is a tilting angle between the adjacent NiO6 octahedra for orthorhombic La3Ni2O7-δ, while the tilt along the c-axis disappears in the tetragonal La3Ni2O7-δ. c The powder XRD pattern for tetragonal La3Ni2O7-δ at ambient pressure. d The enlarged XRD pattern between 30 and 35°, and the powder XRD pattern of the orthorhombic La3Ni2O7-δ at ambient pressure are also plotted for comparison. e and g Temperature-dependent magnetic torque data of orthorhombic and tetragonal La3Ni2O7-δ, respectively. f Temperature-dependent dτ/dT at the angles of 35°, 45°, and 55°. There is an obvious feature in τ(T) around 150 K for orthorhombic La3Ni2O7-δ, implying the SDW transition, which is consistent with previous μSR and NMR results. Such a feature is not observed in the magnetic torque data for the tetragonal La3Ni2O7-δ, indicating no SDW transition for the tetragonal La3Ni2O7-δ.