Fig. 4

Identification of the strongly and weakly coupled phonons. a Transient changes in the electronic (T_e), strongly coupled phonon (T_s), and weakly coupled phonon (T_w) temperatures as extracted from a three-temperature thermalization model (TTM) of the relaxation dynamics of LiOsO₃. Color scale represents different initial experiment temperatures before the pump pulse arrives. b Representative fit of an experimental reflectivity transient at an initial temperature of T = 120 K (black circles) produced by the TTM (teal line). Inset: transient temperatures T_e, T_s, and T_w from which the model reflectivity transient is generated. c Comparison of the extracted electron–phonon coupling function g_ep with an average of the square roots of the ¹E_g and ²E_g phonon linewidths Γ_ph as reported by Raman spectroscopy¹², suggesting these modes are strongly coupled phonons. Inset: Real space distortions of these modes with blue and pink spheres representing Os and O atoms respectively. d Temperature dependence of the heat capacity of the weakly coupled phonons represented by 1 − α. The dashed vertical line denotes the reported value of T_c⁸. The solid black line is a fit to a model where this heat capacity is attributed to a displacive A_2u polar mode (lower inset) that softens and hardens across the polar transition. Upper inset: Resonant frequency \(f_{{\mathrm{A}}_{2{\mathrm{u}}}}\)(open circles) and heat capacity \(C_{{\mathrm{A}}_{2{\mathrm{u}}}}\) (closed squares) of the polar mode extracted from the displacive soft mode model. The solid black line is a fit of the resonant frequency in the polar phase to the Cochran relation²⁷ \(hf \propto \sqrt {1 - T/T_{\mathrm{c}}}\) expected of polar soft modes, in which T_c was shifted to coincide with the peak of 1 - α at T_c = 125 K. All error bars derive from the χ² of the three-temperature model fits