  Using a recently proposed measure for divisibility of a dynamical map, we
study the non-Markovian character of a quantum evolution of a driven spin-$S$
system weakly coupled to a bosonic bath. The complete tomographic knowledge
about the dynamics of the open system is obtained by the time-convolutionless
master equation in the secular approximation. The derived equation can be
applied to a wide range of spin-boson models with the Hermitian or
non-Hermitian coupling operator in the system-environment interaction
Hamiltonian. Besides the influence of the environmental spectral densities, the
tunneling energy of the system Hamiltonian can affect the measure of quantum
non-Markovianity. It is found that the non-Markovian feature of a dynamical map
of a high-dimension spin system is noticeable in contrast to that of a
low-dimension spin system.
