  In low concentration Tm$^{3+}$:YAG, we observe efficient adiabatic rapid
passage (ARP) of thulium nuclear spin over flipping times much longer than
$T_2$. Efficient ARP with long flipping time has been observed in monoatomic
solids for decades and has been analyzed in terms of spin temperature and of
the thermodynamic equilibrium of a coupled spin ensemble. In low-concentration
impurity-doped crystals the spin temperature concept may be questioned. A
single spin model should be preferred since the impurity ions are weakly
coupled together but interact with the numerous off-resonant matrix ions that
originate the spin-spin relaxation. The experiment takes place in the context
of quantum information investigation, involving impurity-doped crystals, spin
hyperpolarization by optical pumping, and optical detection of the spin
evolution.
