  Using the framework of semi-classical Landau-Lifshitz dynamics (LLD), we
conduct a systematic investigation of the temperature-dependent spin dynamics
in the S = 1/2 Heisenberg square-lattice antiferromagnet (SqAF). By performing
inelastic neutron scattering measurements on Zn2VO(PO4)2 (ZVPO) and
corresponding finite-temperature spin dynamics simulations based on LLD, we
present a comprehensive analysis that bridges quantum and classical spin
dynamics over a broad temperature range. First, a remarkable agreement between
experimental data and LLD simulations is found in the paramagnetic phase of
ZVPO, demonstrating the capability of LLD in accurately determining the spin
Hamiltonian of S = 1/2 systems and capturing the quantum-to-classical crossover
of their spin dynamics. Second, by analyzing the discrepancies between the
experimental data and the LLD simulations at lower temperatures, we determine
the experimental temperature dependence of the quantum effects in the
excitation spectrum of the S = 1/2 SqAF: the quantum renormalization factor for
the magnon energies and the quantum continuum above the one-magnon bands.
Notably, the emergence of each quantum effect is found to correlate with the
formation of three-dimensional long-range order. This work demonstrates the
utility of LLD in gaining experimental insights into the temperature-induced
modifications of quantum spin dynamics and their convergence towards classical
expectations at higher temperatures. This motivates further applications to
more challenging quantum antiferromagnets dominated by stronger quantum
fluctuations.
