Fig. 4: Whole magnetization process of In-kapellasite.

Magnetization curves normalized by the saturation value (Ms) in high magnetic fields (upper panel) and its differential dM/dH (lower panel). The magnetization curve at 4.2 K is offset by 0.3. The absolute value of pulsed magnetization data was corrected by the magnetization data obtained with a SQUID magnetometer at 4.2 K. The horizontal axis H/J₁ is normalized by the nearest-neighbor antiferromagnetic interaction J₁ = 11.5 K determined by the HTSE fitting of magnetic susceptibility. The dashed red line shows the calculated finite temperature magnetization curve assuming uniform nearest-neighbor interaction at T/J₁ = 0.1 by the OFTLM method with N = 36. The dashed-dotted line shows the theoretical curve assuming three nearest-neighbor interactions with the ratio J₁′ (thick, solid, red) : J₁ (thin, solid, blue) : J₁″ (dotted, green) = 2 : 1 : 0.5 of which the spatial distribution is depicted in the inset of the upper panel. The black vertical arrows in the lower panel indicate the starting and terminating magnetic fields of the 1/3 plateau calculated with a DMRG method¹⁰. Blue and purple vertical arrows show the experimental magnetic fields of the 1/3 plateau corresponding to the calculated one. Since the 4.2 K data is blunted, the lower end of the plateau field is determined by the intersection of extrapolated lines as shown in the upper panel. The saturation fields H/J₁ = 3 for both 1.3 K and 4.2 K are determined by the peak top of dM/dH. The weak oscillation of theoretical dM/dH between H/J = 1.5 – 2 in the lower panel is due to the finite size effect.