Fig. 4: From local charge-transfer polarons to macroscopic photoinduced phase transition driven by lattice expansion.

a Transient polaronic regime at low fluence inside thermal hysteresis, where \(G\left(\eta \right)\) corresponds to equally stable low-temperature (LT, \({\eta }_{{{{{{\rm{LT}}}}}}}\ne 0\)) and high-temperature (HT, \({\eta }_{{{{{{\rm{HT}}}}}}}=0\)) phases (dark blue curve). Excitation of the tetragonal Mn^IIIFe^II ground state results in charge-transfer (CT) polarons (represented as red sites in the crystal) responsible for a weak volume expansion \({{{{{\rm{\delta }}}}}}v\). The additional elastic coupling cost \(\propto {{{{{\rm{\delta }}}}}}v{\eta }^{2}\) (dashed green curve) reduces the amplitude of the ferroelastic distortion, which equilibrates on elastic timescale (100 ps) to \({\eta }_{{{{{{\rm{PT}}}}}}}\) in the photoexcited tetragonal (PT) lattice (light blue curve). As CT polarons, and therefore \({{{{{\rm{\delta }}}}}}v\), decay within 10 µs, the system relaxes towards the initial ground Mn^IIIFe^II state (dark blue curve). b Persistent photoinduced phase transition (PIPT) regime at high fluence, where the larger volume expansion \(\triangle V\) strongly destabilizes the tetragonal lattice within 100 ps (purple curve), converting crystals towards the photoinduced cubic phase (PIC, \({\eta }_{{{{{{\rm{PIC}}}}}}}=0\), red curve). The relaxed photoinduced cubic Mn^IIFe^III phase is then persistent at room temperature, due to the energy barrier with the initial tetragonal Mn^IIIFe^II phase, matching the HT phase (red curve).