Understanding finite-temperature dynamics of the spin-orbital-entangled magnet FeI2

The dynamical correlation functions of interacting quantum spin systems can be directly probed by spectroscopic experiments such as inelastic neutron or x-ray scattering. Semi-classical approximations based on spin coherent state offer an efficient and universal approach to compute these correlation functions and produce useful insights for a generic system with low entanglement. To recover quantum-mechanical results, a well-known renormalization scheme based on the quantum-classical correspondence principle for the harmonic normal modes is commonly used in the low-temperature regime. It is not clear how to extend this renormalization scheme to arbitrary high temperatures. In this talk, I will introduce a temperature-dependent normalization of the classical moments, whose magnitude is determined by imposing the quantum sum rule. Using temperature-dependent spin dynamics of a spin-orbital-entangled magnet Fe2 as a benchmark case, I will show that this simple renormalization scheme leads to a substantial improvement in the agreement between the calculated and measured dynamical spin structure factors at all temperatures. Our study establishes a necessary and minimal approach to obtain best agreement with experimental data of a quantum spin system using semi-classical simulations.