Fig. 4: Isospin texture in the 1/4M phase.

a, Measured \({B}_{z}^{{ac}}(x,y)\) at the 1/2M-to-1/4M transition (yellow star in Fig. 2a) for B_a along θ_B = 0. b, Same data as a, but for θ_B = 83°. In contrast to Fig. 3h, the negative \({B}_{z}^{{ac}}\) occurs at the right graphene edge due to spin tilting in the 1/2M phase. c, Same data as b, but for θ_B = –83°. d, Local differential magnetization m(x, y) reconstructed from a. e, \({B}_{z}^{{ac}}(x,y)\) calculated using a superposition of the orbital m(x, y) in the 1/4M shown in d and of a tilted spin m(x, y) in the 1/2M phase based on Fig. 3j, qualitatively reproducing the measured \({B}_{z}^{{ac}}\left(x,y\right)\) in b. f, Derived spin tilt angle |θ_s| versus the applied field tilt angle |θ_B| for positive (black squares) and negative (blue diamonds) angles across the M-to-1/2M and 1/2M-to-1/4M (solid magenta triangles) transitions. The magenta error bars at 1/2M-to-1/4M transitions are estimated by comparing \({B}_{z}^{{ac}}\) for |θ_B| = 78° and |θ_B| = 83° (Methods). The green open circles represent the average spin tilt angle, \({\bar{\theta }}_{s}={(|\theta }_{s}\left( > 0\right)|+{|\theta }_{s}\left( < 0\right)|)/2\), and the corresponding black error bars are defined as (|θ_s(>0)| – |θ_s(<0)|). The solid lines show the calculated θ_s versus θ_B (Methods) for various indicated values of λ_SOC in 1/4M and α in 1/2M for B_z = 15 mT and variable B_x = B_ztanθ_B. The 1/4M lines set a lower bound on Ising SOC of λ_SOC ≳ 120 µeV, substantially higher than the previously evaluated λ_SOC = 50 µeV (yellow curve) in ABC graphene¹⁸. The magnetism in the 1/2M phase is essentially fully isotropic with the calculated solid lines setting an upper bound on spin anisotropy of |α| < 0.25 µeV, which sets a lower bound on U_Hu ≳ 6.5 meV (Methods). The red dashed line shows the calculated θ_s versus θ_B for α = 0.4 µeV based on previously assumed U_Hu = 4.2 meV (refs. ^41,51), which is inconsistent with the data.