Nuclear relaxation and Overhauser effect in a nearly-one-dimensional Heisenberg system

Abstract

The spin dynamics in a nearly-one-dimensional Heisenberg system---the solid free radical Tanol (2,2,6,6-tetramethyl-4-piperidinol-1-oxyl)---is studied through dynamical-nuclear-polarization (DNP) experiments (Overhauser effect) and proton spin-lattice relaxation-time (${T}_{1}$) measurements. As the couplings between the electronic spins and the protons have been determined in Tanol, absolute determinations of the values of the electronic-spin-frequency correlation functions at the electronic Larmor frequency (${\ensuremath{\omega}}_{e}$) and at the nuclear Larmor frequency (${\ensuremath{\omega}}_{N}$) can be achieved by performing both DNP and ${T}_{1}$ measurements. The value obtained at ${\ensuremath{\omega}}_{e}$ is in agreement with theoretical calculations in one-dimensional Heisenberg systems using the method of Tahir-Kheli and McFadden. The value obtained at ${\ensuremath{\omega}}_{N}$ together with the frequency dependence of ${T}_{1}$ are explained by introducing a cutoff effect in the spin-diffusion process in one dimension. A derivation is given which expresses the magnitude of the cutoff effect in terms of the interchain couplings. An evaluation of the interchain couplings, using ${T}_{1}$ measurements, is presented. The values of the interchain couplings, which are consistent with both the ${T}_{1}$ measurements and the N\'eel temperature, are ${J}_{1}\ensuremath{\simeq}{J}_{2}\ensuremath{\simeq}{10}^{\ensuremath{-}2}J$, where $J$ is the intrachain exchange ($\frac{J}{k=4.1}$ K), and ${J}_{1}$ and ${J}_{2}$ are the interchain couplings along two axis perpendicular to the chain. However, it cannot be excluded that, in Tanol, the disturbance of the spin-diffusion process is due to finite-length effects.