Fig. 2: Local magnetic behavior of undoped Sr₂IrO₄.

a Optical microscope image of the sample. b Magnetization M at position P5 in (a) as a function of the magnetic field applied along the a-axis. \({M}_{{{\rm{L}}}}\) (\({M}_{{{\rm{T}}}}\)) represents magnetization component parallel (perpendicular) to the external magnetic field H. The magnetization is normalized by the value of M_S, which is the saturation magnetization when all layer moments are fully aligned. The raw data can be found in Supplementary Fig. 4a. The shaded region represents H < H_C, and the unshaded region represents H > H_C, where H_C is the critical field. c Magnetization magnitude |M| (color map) as a function of an in-plane magnetic field in a polar plot, at three different positions as indicated. Critical fields H_C are indicated by black circles. Detailed magnetic responses at (d) P1, (e) P4, and (f) P5. The blue arrows display net magnetizations M at various in-plane magnetic fields whose values are in the polar maps. For illustration, the arrows for H < H_C are magnified four times, while for H > H_C, a single arrow is plotted per field direction. Insets in (d–f) depict the schematics of the uniaxial anisotropic energy terms extracted from the model calculation. Increasing external magnetic field induces the spin-flip, accompanied by a change in the energetically favorable axes. All measurements were performed at T = 5 K.