Fig. 4: MOKE measurement and model calculation of the 3% Rh-doped Sr₂IrO₄.

a Quiver plot of local magnetic responses, where blue arrows indicate the magnetization vectors M. b Comparison between experimental data (circles) and model calculation (lines) under external magnetic fields of 0.3 T (red), 0.5 T (green), and 0.7 T (blue). \({M}_{{{\rm{L}}}}\) (\({M}_{{{\rm{T}}}}\)) represents magnetization component parallel (perpendicular) to the external magnetic field H. \(\phi\) is the angle of the magnetic field vector with respect to the a-axis. In the model calculation, we used parameters of J_1c = −13.0 μeV, J_2c = 3.0 μeV, N_xy = 1.9 μeV, Γ₂ = 1.2 μeV, and an effective parameter E_Th = 0.4 μeV, which was introduced to describe magnetic hysteresis (see methods for details of each parameter). c Magnetization direction image at zero magnetic field, with respect to the x-axis. Magnetizations are aligned along the x-axis (denoted as X) or the y-axis (denoted as Y). The pink (blue) arrow indicates the direction of the remanent magnetization in domain X (Y). The configuration in the dashed red box represents the magnetic configuration of domain X, where the thin red arrow indicates the pseudospin at each Ir site, the thick black arrow indicates the net moment of each layer, and the thick blue arrow indicates the net magnetization M in a unit cell. An optical microscope image of the sample is shown on the right. All measurements were performed at T = 5 K.