Fig. 4: Magnetic phase diagram for twisted bilayer MoS₂.

a Classical ground state energy per orbital in units of \({{{{{{{\rm{{{\Delta }}}}}}}}}}={t}_{\sigma }^{2}/U\), assuming ferro- (blue) or antiferromagnetic (red) order for the spin degrees of freedom. We take the ab initio parameters, t_π = 0.25t_σ and use an iterative energy minimization. The lower panel determines the phase boundaries for the orbital degrees of freedom given the energetically more favorable spin order shown in the top panel. At J/U = 0.1 we find the spin order to change from AFM to FM, with AFO nematic order for the orbital degrees of freedom remaining stable in agreement with ref. ⁵³. b Configurations of orbital vectors are found at the end of iterative minimization. Note that we display the projection of τ to the plane in \({{\mathbb{R}}}^{3}\) (indicated by the axis shown in the bottom left), such that nematic states with finite contributions only in xz direction ((1) & (2)) can be distinguished from magnetic states (3) which point perpendicular, i.e along the y-axis.