  Spin-phonon interaction is an important channel for spin and energy
relaxation in magnetic insulators. Understanding this interaction is critical
for developing magnetic insulator-based spintronic devices. Quantifying this
interaction in yttrium iron garnet (YIG), one of the most extensively
investigated magnetic insulators, remains challenging because of the large
number of atoms in a unit cell. Here, we report temperature-dependent and
polarization-resolved Raman measurements in a YIG bulk crystal. We first
classify the phonon modes based on their symmetry. We then develop a modified
mean-field theory and define a symmetry-adapted parameter to quantify
spin-phonon interaction in a phonon-mode specific way for the first time in
YIG. Based on this improved mean-field theory, we discover a positive
correlation between the spin-phonon interaction strength and the phonon
frequency.
