PCMW2D and 2D Raman correlation spectroscopy evidence for presence of spin-phonon coupling in hexagonal LuMnO₃

Two-dimensional correlation spectroscopy (2D-COS) and perturbation-correlation moving window two-dimensional correlation spectroscopy (PCMW2D) analysis are performed on the temperature-dependent Raman spectra of hexagonal LuMnO₃ single crystal. Under the resonance with the on-site Mn d-d transitions, the correlation between the phonons which are relate to the vibration of Mn ions' bonds and spin-excitation peaks suggest a strong spin-phonon coupling in LuMnO₃. The PCMW2D results clearly show that the significant change in phonons and spin-excitation peaks occurs around the Néel temperature and the spin reorientation transition. The multiple components in the broad spin-excitation peaks also suggest variations in spin symmetries in the ground state. Furthermore, we propose that the 2D-COS and PCMW2D Raman correlation spectroscopies provide a simple and powerful method for investigating the couplings and the transitions, which would be very important for understanding systematically the magnetoelectric properties of multiferroic materials.