  We consider the adiabatic demagnetization in the rotating reference frame
(ADRF) of a system of dipolar coupled nuclear spins $s=1/2$ in the external
magnetic field. The demagnetization starts with the offset of the external
magnetic field (in frequency units) from the Larmor frequency being several
times greater than the local dipolar field. For different subsystem sizes, we
have found from numerical simulations the temperatures at which subsystems of a
one-dimensional nine-spin chain and a plane nine-spin cluster become entangled.
These temperatures are of the order of microkelvins and are almost independent
of the subsystem size. There is a weak dependence of the temperature on the
space dimension of the system.
