Fig. 1.

Equilibrium phases. a Phase diagram as a function of Hubbard U and hopping integral, t_σ, at T = 0.016 eV (186 K). The red dashed line indicates the chosen parameter subspace for our calculations at t_σ = −0.62 eV. For small interactions, U ≤ 1.22 eV, the system exhibits a paramagnetic metallic phase (PMM). In the intermediate regime, 1.22 eV < U ≤ 1.25 eV, TRS is broken by spontaneous magnetic all-in/all-out (AIAO) order. A further increase of U above 1.25 eV leads to a gapped antiferromagnetic insulating phase (AFI) with larger magnetisation. For $∣t_{\sigma }∣\ge 0.62$ eV the WSM–AFI transition is of second order, indicated by black dots. Below that value, the transition is of first order (bicoloured dots). The dots’ increasing size corresponds to the increasing region of hysteresis. The red square indicates the chosen initial state (U_i = 1.28 eV) in parameter space. The red arrow shows the intended quenching direction. b Magnetisation as a function of U for the choice of t_σ = −0.62 eV. The dashed lines indicate the region of hysteresis. The coloured arrows show the final values of U = U_q right after the interaction quench for the nonequilibrium calculations (see Fig. 2)