Effects of finite lattice capacity on spin lattice relaxation :

Abstract

The transient magnetic behavior of a paramagnetic substance, after an initial disturbance, is considered theoretically for a variety of situations in which the lattice temperature rises as a result of energy flow from the magnetic (electron spin) system. The relaxation mechanisms considered are the direct process, involving interaction between spins and the resonant-phonon modes, and a T 9 Raman process, involving the remaining phonon modes. It is first assumed that the resonant and remaining modes are strongly coupled to each other, and that the helium bath has been removed (helium temperatures are assumed). The resulting transient behavior typically does not differ much from exponential relaxation (the rate increases somewhat during the relaxation), but the difference should be experimentally observable, particularly if the resonance line is inverted initially.Next, the opposite extreme is consideredthat in which the resonant and remaining modes are totally uncoupled; the helium bath is again assumed to have been removed. Two dramatic effects can then occur, depending upon initial conditions. One is the rapid decay to saturation from initial inversion, due to an avalanching creation of resonant phonons by the spins. The second is the pronounced inhibition of the subsequent decay, with the spins remaining near saturation. This decay rate is typically very much slower than the Raman rate, and is due to the flow of the resonant-phonon energy back into the spin system as the spin energy flows into the remaining lattice. Eventually the rate increases to the Raman rate characteristic of the final lattice temperature. Because of inelastic phonon scattering at crystal boundaries, which couples the phonon modes together, this effect of inhibited decay may be difficult to observe.Finally, we consider the case of spins coupled only to the resonant phonons, which in turn are coupled to a constant temperature bath, whether this be the helium or the remaining modes. Recent phonon avalanche experiments are discussed in this context. It is pointed out that such experiments, performed in the absence of a bath, may provide a reliable measurement of inelastic phonon-boundary scattering.