Negative thermal expansion, lattice dynamics, and complex magnetism in TbFeO$_3$
We report a temperature-dependent investigation of orthoferrite TbFeO$_3$ using x-ray diffraction, DC magnetization, and Raman scattering, complemented by room-temperature x-ray photoelectron spectroscopy. X-ray diffraction reveals negative thermal expansion over 5-300 K, with a small but systematic increase in unit-cell volume upon cooling in the absence of any structural phase transition. Raman scattering measurements identify the Raman-active phonon modes and show clear deviations from the conventional Klemens anharmonic decay model, particularly in phonon frequencies, indicating the presence of spin-phonon coupling. Two modes of $A_g$ and $B_{1g}$ symmetry exhibit a crossover from Gaussian-dominated line shapes at low temperatures to mixed Gaussian-Lorentzian profiles at higher temperatures, reflecting a transition from inhomogeneous broadening to lifetime-driven dynamics. High-energy Raman spectra reveal two-magnon excitations associated with the Fe sublattice, consistent with linear spin-wave theory, whose spectral weight shows only weak temperature dependence. In addition, a broad Raman mode emerging below $\sim 175$ K exhibits an order-parameter-like temperature evolution and coincides with the onset of phonon anomalies, while no corresponding strong anomaly is observed in the two-magnon response. Taken together, these results establish TbFeO$_3$ as a system with pronounced interplay among lattice dynamics, spin correlations, and emergent local magnetic-lattice anomalies.