Low-frequency spin dynamics and NMR spin-lattice relaxation in antiferromagnetic rings

Abstract

We develop a general theory of the spin dynamics of Heisenberg antiferromagnetic rings (HAFRs) that explains the mechanism of NMR spin-lattice relaxation at low temperatures. In HAFRs, the imaginary parts of the q-summed dynamic spin susceptibilities parallel and perpendicular to an applied static field, χ ′′ sum‖(ω) and χ ′′ sum⊥(ω), are composed of the sum of many slightly broadened δ-functional modes at many frequencies. The NMR relaxation is caused by the quasielastic mode in χ ′′ sum‖(ω) at around zero frequency. This quasielastic mode is characterized by two physical quantities, intensity P0‖ and frequency width 0‖. Although P0‖ has to date been assumed to be identical to the uniform static susceptibility, we point out that the two quantities are not identical. Without making this unreliable assumption for P0‖, we demonstrate experimentally how P0‖ and 0‖ behave, by analyzing the NMR relaxation rates of two different nuclei, 1H and 13C, in a real HAFR. This analysis is more rigorous and thus can be used to estimate 0‖ and P0‖ more precisely than previously possible. We find that the temperature dependence of P0‖ exhibits activation-type behavior reflecting the first excitation gap. We also find that 0‖ decreases monotonically on cooling but saturates to a nonzero value at zero temperature. This strongly suggests that 0‖ is dominated not only by the electron-phonon interactions but also by internanomagnet dipole interactions, which have been neglected to date.