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/T1) 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/T1)/(Tχ(T)), given by R(H,T)=Aωc(T)/(ωc2(T) + ωN2), where χ=(∂M/∂H)T is the differential susceptibility, A is a fitting constant, and ωN is the proton Larmor frequency, and (2) a temperature-dependent correlation frequency ωc(T) which at low T is given by ωc(T) ∝Tα, 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 T0(H) for which ωc(T) = ωN; (2) for low T a scaling formula applies, R(H,T)/R(H,T0(H))=2tα/(1+t 2α), where t≡T/T0(H). Both results are confirmed by our experimental data for the choice α=3.5±0.5.