We present the first measurements of spin-lattice relaxation times wit
h the energy being transferred from the lattice to the spins. On a sem
i-adiabatically suspended bolometer, consisting of a paramagnetic samp
le and an absorber, the lattice is heated up by absorbing single alpha
-particles, and the relaxation of the magnetisation is measured with a
SQUID of special design. With decreasing temperatures the relaxation
time first increases as tau1 approximately 1/T, but then it decreases
strongly and at 30 mK it is reduced by orders of magnitude compared wi
th tau1. This result is in agreement with a theoretical model which ta
kes into account the heat capacities of the lattice, the resonant phon
ons and the spins and thermal resistances between these capacities. Un
der the condition of the bottleneck effect the relaxation time is foun
d to be proportional to T3 at low temperatures.