Dynamics of Interacting Spin Systems

The dynamics of the approach of two spin systems to the same spin temperature is examined. It is found that for two spin systems in a rigid lattice interacting weakly with the lattice and with each other, differential equations governing the time rate of change of the spin temperatures can be derived. The derivation assumes the validity of the concept of spin temperature and the validity of the principle of detailed balance applied to eigenstates of the spin Hamiltonians of the systems. The spin mixing experiments of Abragam and Proctor provide evidence for the correctness of the differential equations thus derived. Additional experiments on spin-lattice relaxation times in NaBr, NaI, and NaCl are reported and interpreted in terms of the differential equations developed here. It is shown that under certain conditions the presence of a second spin system can shorten the relaxation time of a spin system even at rather high values of the external field.