Theory of Magnetic Exchange-Lattice Relaxation in Two Organic Free Radicals

Abstract

A calculation of the spin-lattice relaxation rate is made for conditions appropriate to certain organic free radicals with exchange-narrowed paramagnetic resonance lines, at temperatures well above the Néel temperature. The relaxation is supposed to be a two-step process: 1. Energy is transferred from the "Zeeman" system to the "exchange" system by spin-spin relaxation. 2. The energy is then transferred from the "exchange" system to the lattice. It is the rate of energy transfer in the latter process which is here computed, assuming that the exchange-lattice coupling is due to (a) the variation of exchange energy when the distance between two adjacent spins is changed or (b) the corresponding variation of magnetic dipolar energy. The calculation shows that in the case of diphenyl picryl hydrazyl (DPPH) and bisdiphenylene phenyl allyl (BDPA) the exchange-lattice relaxation rate above liquid nitrogen temperatures is rapid enough (under the usual experimental conditions) to make the experimental spin- "lattice" relaxation time equal to the Zeeman-exchange relaxation time and hence temperature independent, as experimentally observed.