  In this paper, we combine thermal effects with Landau-Zener (LZ) quantum
tunneling effects in a dynamical Monte Carlo (DMC) framework to produce
satisfactory magnetization curves of single-molecule magnet (SMM) systems. We
use the giant spin approximation for SMM spins and consider regular lattices of
SMMs with magnetic dipolar interactions (MDI). We calculate spin reversal
probabilities from thermal-activated barrier hurdling, direct LZ tunneling, and
thermal-assisted LZ tunnelings in the presence of sweeping magnetic fields. We
do systematical DMC simulations for Mn$_{12}$ systems with various temperatures
and sweeping rates. Our simulations produce clear step structures in
low-temperature magnetization curves, and our results show that the thermally
activated barrier hurdling becomes dominating at high temperature near 3K and
the thermal-assisted tunnelings play important roles at intermediate
temperature. These are consistent with corresponding experimental results on
good Mn$_{12}$ samples (with less disorders) in the presence of little
misalignments between the easy axis and applied magnetic fields, and therefore
our magnetization curves are satisfactory. Furthermore, our DMC results show
that the MDI, with the thermal effects, have important effects on the LZ
tunneling processes, but both the MDI and the LZ tunneling give place to the
thermal-activated barrier hurdling effect in determining the magnetization
curves when the temperature is near 3K. This DMC approach can be applicable to
other SMM systems, and could be used to study other properties of SMM systems.

Mesoscale and Nanoscale Physics;Computational Physics