  The quantum nanomagnets show interesting site-dependent magnetic properties
as a function of the temperature and the external magnetic field. In the paper
we present the results of calculations for a finite quantum spin ladder with
two legs, consisting of 12 spins $S=1/2$. We describe our system with isotropic
quantum Heisenberg model and perform exact numerical diagonalization of the
Hamiltonian to use canonical ensemble approach. Our analysis focuses on the
site-dependent magnetization in the system, presenting magnetization
distributions for various interaction parameters. We discuss extensively the
temperature and magnetic field dependences of individual site magnetizations.
The interesting behaviour, with pronounced non-uniformity of magnetization
across the ladder, is found.
