Fig. 4. Possible origin of phonon-driven enhancement of ferromagnetism.

a, Temperature dependence of non-equilibrium magnetization for each pump excitation frequency (coloured circles). Error bars represent propagated uncertainty in M, as detailed in the Methods. b, The energy gap Δ between the orbital ground state $\mid \mathrm{GS}⟩$ and first excited orbital state $\mid \mathrm{ES}⟩$ for each of the three excited phonons. The experimental mode displacements are on the order of $1\sqrt{u}\mathrm{Å}$ in magnitude (u, atomic mass units). c, Illustration of the equilibrium orbital ground state and the changes $\left({\mid \mathrm{GS}⟩}_{\mathrm{pumped}}-{\mid \mathrm{GS}⟩}_{\mathrm{equil.}}\right)$ induced by driving the 4 THz and 9 THz phonons. We propose that the structural and orbital changes push the system farther or closer to the phase boundary, respectively, thereby suppressing or enhancing detrimental spin fluctuations.

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