The present paper is rather negative in character. Its aim is to show that the conventional models of paramagnetic relaxation cannot be used at helium temperatures, because the lattice vibrations cannot possibly serve as a thermostat in the way ordinarily supposed. Namely, if the quanta exchanged between the spin system and the lattice oscillators are of the order 0.2 ${\mathrm{cm}}^{-1\mathrm{}}$ characteristic of the usual Stark splittings in chrome or iron alum, the spins will be in thermal contact only with oscillators at the extreme low frequency end of the lattice spectrum which are too few in number to conduct away the surplus spin energy. It is found that this limited band of oscillators is interrupted much more frequently by interactions with the spins than by (a) collisions with the walls or (b) interplay with other oscillators due to anharmonic terms (calculated in the next paper). Consequently the lattice vibrations in thermal contact with the spin system will be at nearly the spin temperature, and not at that of the helium container as ordinarily supposed. Impurities with abnormally large Stark splittings, of the order 2.0 ${\mathrm{cm}}^{-1\mathrm{}}$, would make a wider band of lattice oscillators available and so would avoid the difficulty of insufficient lattice conductivity, but it is very doubtful whether the impurities could be in thermal equilibrium with the great bulk of the paramagnetic ions. By thus showing that conventional hypotheses will not work, we aim to pave the way for a future paper proposing a rather unusual substitute conduction mechanism which is, however, compatible with the thermodynamic formulae of Casimir and du Pré.

• Received 3 March 1941

DOI:https://doi.org/10.1103/PhysRev.59.724