  We examine the general features of the non-commutativity of the magnetization
operator and Hamiltonian for the small quantum spin clusters. The source of
this non-commutativity can be a difference in the Land\'{e} g-factors for
different spins in the cluster, XY-anisotropy in the exchange interaction and
the presence of the Dzyaloshinskii-Moriya term in the direction different for
the direction of the magnetic field. As a result, a zero-temperature
magnetization curve for the small spin clusters mimics that for the macroscopic
systems with the band(s) of magnetic excitations, i.e. for the given eigenstate
of the spin cluster the corresponding magnetic moment can be an explicit
function of the external magnetic field yielding the non-constant (non-plateau)
form of the magnetization curve within the given eigenstate. Also, the
XY-anisotropy makes the saturated magnetization (the eigenstate when all spins
in cluster are aligned along the magnetic field) inaccessible for finite
magnetic field magnitude (asymptotical saturation). We demonstrate all these
features on three examples: spin-1/2 dimer, mixed spin-(1/2,1) dimer, spin-1/2
ring trimer. We consider the simplest Ising-Heisenberg chain, the XYZ-Ising
diamond chain with four different g-factors as well. In the chain model the
magnetization curve has more complicated and non trivial structure with than
that for clusters.
