  Atomistic spin dynamics (ASD) is a standard tool to model the magnetization
dynamics of a variety of materials. The fundamental dynamical model underlying
ASD is entirely classical. In this paper, we present two approaches to
effectively incorporate quantum effects into ASD simulations, thus enhancing
their low temperature predictions. The first allows to simulate the magnetic
behavior of a quantum spin system by solving the equations of motion of a
classical spin system at an effective temperature relative to the critical
temperature. This effective temperature is determined a priori from the
microscopic properties of the system. The second approach is based on a \semi
model where classical spins interact with an environment with a quantum-like
power spectrum. The parameters that characterize this model can be calculated
ab initio or extracted from experiments. This semi-classical model
quantitatively reproduces the absolute temperature behavior of a magnetic
system, thus accounting for the quantum mechanical aspects of its dynamics,
even at low temperature. The methods presented here can be readily implemented
in current ASD simulations with no additional complexity cost.
