Fig. 3: Landau model of the electronic order parameter and its ordering wavevector.

a The Landau free-energy, \(F\left(\psi ,{Q}_{m}\right)\), as a function of the transient temperature of the electron gas, T_e, and the order parameter ψ, shown for the wavevector Q_m that minimizes the free-energy (color scale shown at the top). b The free-energy \(F\left({\psi }_{m},Q\right)\) as a function of the electronic temperature, T_e, and wavevector Q, shown for the order parameter \({\psi }_{m}\) that minimizes the energy (color scale shown at the top). In a and b, the equilibrium (gray dashed line) and non-equilibrium (red solid line) paths during order formation are shown. c The wavevector dynamics revealed through measuring the satellite-peak intensity and position: in equilibrium, the spin density wave (SDW) forms with a smaller wavevector Q_H and then transitions to Q_L via an abrupt (first-order) phase transition (consistent with the energy barrier indicated by the gray dashed line in b. Out-of-equilibrium, the order immediately forms with Q_L, bypassing the state at Q_H (see red line in b). d A schematic phonon distribution during the formation of the SDW: in equilibrium the SDW forms at the Néel temperature (T_lattice = T_N, top, gray), and out-of-equilibrium the SDW forms at a lower lattice temperature T_lattice < T_N and in presence of wavevector-matched acoustic phonons at Q_L (red, bottom).