Extended Data Fig. 9: Analysis of isospin orientation at the 1/2M-to-1/4M transition.
From: Isospin magnetic texture and intervalley exchange interaction in rhombohedral tetralayer graphene
a, Schematic vector representation of isospin moments at 1/2M-1/4M transition in a tilted magnetic field with angle \({\theta }_{B}\). b, Measured \({B}_{z}^{{ac}}(x,y)\) at 1/2M-1/4M transition for \({B}_{a}\) along θB = 78°. c, Trial \({B}_{z}^{ac}(x,y,{\theta}_{\rm{tr}})\) calculated from the vector analysis in (a) for θtr = 1.4°. d, Plot of the mean square error vs. the trial angle \({\theta }_{\rm{tr}}\). The green dashed line marks θtr = 1.4° with the minimal error, which defines the tilt angle \({\theta }_{s}\) of \({{\mathscr{M}}}_{{\bf{1}}/{\bf{4}}{\bf{M}}}^{{\bf{s}}}\) (green vector in (a)). e, \({B}_{z}^{ac\pm }(x,y)\) in presence of a small \({B}_{z}=\) 15 mT, obtained by subtracting \({B}_{z}^{{ac}-}(x,y)\) measured in presence of in-plane magnetic field \({B}_{x}=-\)70 mT from \({B}_{z}^{ac+}(x,y)\) acquired at \({B}_{x}=\) 70 mT. f, Same as (a) at \({B}_{x}=\) 120 mT. g, The difference \(\Delta {B}_{z}^{{ac}}\left(x,y\right)\) between (a) and (b). h, \({B}_{z}^{{ac}\pm }\left(x\right)\) from (b) averaged over \(y\) axis (red), and \(\Delta {B}_{z}^{{ac}}\left(x\right)\) from (c) averaged over \(y\) (black), allowing estimation of the upper bound of the isospin tilt angle in the 1/4M phase of about 5°.
