Fig. 5: Evolution of the orthorhombicity and Jahn–Teller distortion in the LaMnO₃ freestanding film.

a–c Schematic of the photoinduced structural change at (a) t = 0, (b) t = 0.2 ps and (c) t = 10 ps due to the change of MnO₆ octahedral tilt and La displacement. The red arrows in the (a) and (b) represent the spin order. d–f Schematic of evolution of the orthorhombicity (a/b ratio) of a pair of twin variants (a⁺b⁻c⁻₃ and a⁻b⁺c⁻₃) at time delay (d) t = 0, (e) t = 0.2 ps and (f) t = 10 ps in the [001] projection. Note, a⁺b⁻c⁻₃ and a⁻b⁺c⁻₃ have the (110) reflection twinning relationship in which (110)_a3 || (−1−10)_b3 (twin boundary is indicated by the black line). The subscripts a3 and b3 represent twin variant a⁺b⁻c⁻₃ and a⁻b⁺c⁻₃, respectively. When a/b < 1, (−110)_a3 is not parallel to (−110)_b3 (red lines), resulting in the spot splitting of −kk0 (bottom insets). When the a/b ratio moves toward the unity, spot splitting reduces and vanishes when a/b = 1 [(−110)_a3 || (−110)_b3]. Note, the drawing of the lattice is exaggerated for clarity. For the complete description of twelve equivalent twin variants in the system and their corresponding diffraction patterns, please see Supplementary Fig. 7.