Scaling behavior of the proton spin-lattice relaxation rate in antiferromagnetic molecular rings

We present new and refined data for the magnetic field (H) and temperature (T) dependence of the proton spin-lattice relaxation rate (1/T-1) in antiferromagnetic molecular rings as well as a new explicit scaling formula that accurately reproduces our data. The key ingredients of our formulation are (1) a reduced relaxation rate, R(H,T)=(1/T-1)/(Tchi(T)), given by R(H,T)=Aomega(c)(T)/(omega(c)(2)(T)+omega(N)(2)), where chi=(partial derivativeM/partial derivativeH)(T) is the differential susceptibility, A is a fitting constant, and omega(N) is the proton Larmor frequency, and (2) a temperature-dependent correlation frequency omega(c)(T) which at low T is given by omega(c)(T)proportional toT(alpha), that we identify as a lifetime broadening of the energy levels of the exchange-coupled paramagnetic spins due to spin-acoustic phonon coupling. The main consequences are (1) R(H,T) has a local maximum for fixed H and variable T that is proportional to 1/H; the maximum occurs at the temperature T-0(H) for which omega(c)(T)=omega(N); (2) for low T a scaling formula applies, R(H,T)/R(H,T-0(H))=2t(alpha)/(1+t(2alpha)), where tequivalent toT/T-0(H). Both results are confirmed by our experimental data for the choice alpha=3.5+/-0.5.